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+tt.descname, tt.descclassname, code.descname, code.descclassname { + font-size: 0.95em; +} + +tt.descname, code.descname { + padding-right: 0.08em; +} + +img.screenshot { + -moz-box-shadow: 2px 2px 4px #EEE; + -webkit-box-shadow: 2px 2px 4px #EEE; + box-shadow: 2px 2px 4px #EEE; +} + +table.docutils { + border: 1px solid #888; + -moz-box-shadow: 2px 2px 4px #EEE; + -webkit-box-shadow: 2px 2px 4px #EEE; + box-shadow: 2px 2px 4px #EEE; +} + +table.docutils td, table.docutils th { + border: 1px solid #888; + padding: 0.25em 0.7em; +} + +table.field-list, table.footnote { + border: none; + -moz-box-shadow: none; + -webkit-box-shadow: none; + box-shadow: none; +} + +table.footnote { + margin: 15px 0; + width: 100%; + border: 1px solid #EEE; + background: #FDFDFD; + font-size: 0.9em; +} + +table.footnote + table.footnote { + margin-top: -15px; + border-top: none; +} + +table.field-list th { + padding: 0 0.8em 0 0; +} + +table.field-list td { + padding: 0; +} + +table.field-list p { + margin-bottom: 0.8em; +} + +/* Cloned from + * https://github.com/sphinx-doc/sphinx/commit/ef60dbfce09286b20b7385333d63a60321784e68 + */ +.field-name { + -moz-hyphens: manual; + -ms-hyphens: manual; + -webkit-hyphens: manual; + hyphens: manual; +} + +table.footnote td.label { + width: .1px; + padding: 0.3em 0 0.3em 0.5em; +} + +table.footnote td { + padding: 0.3em 0.5em; +} + +dl { + margin: 0; + padding: 0; +} + +dl dd { + margin-left: 30px; +} + +blockquote { + margin: 0 0 0 30px; + padding: 0; +} + +ul, ol { + /* Matches the 30px from the narrow-screen "li > ul" selector below */ + margin: 10px 0 10px 30px; + padding: 0; +} + +pre { + background: #EEE; + padding: 7px 30px; + margin: 15px 0px; + line-height: 1.3em; +} + +div.viewcode-block:target { + background: #ffd; +} + +dl pre, blockquote pre, li pre { + margin-left: 0; + padding-left: 30px; +} + +tt, code { + background-color: #ecf0f3; + color: #222; + /* padding: 1px 2px; */ +} + +tt.xref, code.xref, a tt { + background-color: #FBFBFB; + border-bottom: 1px solid #fff; +} + +a.reference { + text-decoration: none; + border-bottom: 1px dotted #004B6B; +} + +/* Don't put an underline on images */ +a.image-reference, a.image-reference:hover { + border-bottom: none; +} + +a.reference:hover { + border-bottom: 1px solid #6D4100; +} + +a.footnote-reference { + text-decoration: none; + font-size: 0.7em; + vertical-align: top; + border-bottom: 1px dotted #004B6B; +} + +a.footnote-reference:hover { + border-bottom: 1px solid #6D4100; +} + +a:hover tt, a:hover code { + background: #EEE; +} + + +@media screen and (max-width: 870px) { + + div.sphinxsidebar { + display: none; + } + + div.document { + width: 100%; + + } + + div.documentwrapper { + margin-left: 0; + margin-top: 0; + margin-right: 0; + margin-bottom: 0; + } + + div.bodywrapper { + margin-top: 0; + margin-right: 0; + margin-bottom: 0; + margin-left: 0; + } + + ul { + margin-left: 0; + } + + li > ul { + /* Matches the 30px from the "ul, ol" selector above */ + margin-left: 30px; + } + + .document { + width: auto; + } + + .footer { + width: auto; + } + + .bodywrapper { + margin: 0; + } + + .footer { + width: auto; + } + + .github { + display: none; + } + + + +} + + + +@media screen and (max-width: 875px) { + + body { + margin: 0; + padding: 20px 30px; + } + + div.documentwrapper { + float: none; + background: #fff; + } + + div.sphinxsidebar { + display: block; + float: none; + width: 102.5%; + margin: -20px -30px 20px -30px; + padding: 10px 20px; + background: #333; + color: #FFF; + } + + div.sphinxsidebar h3, div.sphinxsidebar h4, div.sphinxsidebar p, + div.sphinxsidebar h3 a { + color: #fff; + } + + div.sphinxsidebar a { + color: #AAA; + } + + div.sphinxsidebar p.logo { + display: none; + } + + div.document { + width: 100%; + margin: 0; + } + + div.footer { + display: none; + } + + div.bodywrapper { + margin: 0; + } + + div.body { + min-height: 0; + padding: 0; + } + + .rtd_doc_footer { + display: none; + } + + .document { + width: auto; + } + + .footer { + width: auto; + } + + .footer { + width: auto; + } + + .github { + display: none; + } +} +@media screen and (min-width: 876px) { + div.sphinxsidebar { + position: fixed; + margin-left: 0; + } +} + + +/* misc. */ + +.revsys-inline { + display: none!important; +} + +/* Make nested-list/multi-paragraph items look better in Releases changelog + * pages. Without this, docutils' magical list fuckery causes inconsistent + * formatting between different release sub-lists. + */ +div#changelog > div.section > ul > li > p:only-child { + margin-bottom: 0; +} + +/* Hide fugly table cell borders in ..bibliography:: directive output */ +table.docutils.citation, table.docutils.citation td, table.docutils.citation th { + border: none; + /* Below needed in some edge cases; if not applied, bottom shadows appear */ + -moz-box-shadow: none; + -webkit-box-shadow: none; + box-shadow: none; +} + + +/* relbar */ + +.related { + line-height: 30px; + width: 100%; + font-size: 0.9rem; +} + +.related.top { + border-bottom: 1px solid #EEE; + margin-bottom: 20px; +} + +.related.bottom { + border-top: 1px solid #EEE; +} + +.related ul { + padding: 0; + margin: 0; + list-style: none; +} + +.related li { + display: inline; +} + +nav#rellinks { + float: right; +} + +nav#rellinks li+li:before { + content: "|"; +} + +nav#breadcrumbs li+li:before { + content: "\00BB"; +} + +/* Hide certain items when printing */ +@media print { + div.related { + display: none; + } +} \ No newline at end of file diff --git a/core/_static/basic.css b/core/_static/basic.css new file mode 100644 index 00000000..aa9df316 --- /dev/null +++ b/core/_static/basic.css @@ -0,0 +1,904 @@ +/* + * basic.css + * ~~~~~~~~~ + * + * Sphinx stylesheet -- basic theme. + * + * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/* -- main layout ----------------------------------------------------------- */ + +div.clearer { + clear: both; +} + +div.section::after { + display: block; + content: ''; + clear: left; +} + +/* -- relbar ---------------------------------------------------------------- */ + +div.related { + width: 100%; + font-size: 90%; +} + +div.related h3 { + display: none; +} + +div.related ul { + margin: 0; + padding: 0 0 0 10px; + list-style: none; +} + +div.related li { + display: inline; +} + +div.related li.right { + float: right; + margin-right: 5px; +} + +/* -- sidebar --------------------------------------------------------------- */ + +div.sphinxsidebarwrapper { + padding: 10px 5px 0 10px; +} + +div.sphinxsidebar { + float: left; + width: 230px; + margin-left: -100%; + font-size: 90%; + word-wrap: break-word; + overflow-wrap : break-word; +} + +div.sphinxsidebar ul { + list-style: none; +} + +div.sphinxsidebar ul ul, +div.sphinxsidebar ul.want-points { + margin-left: 20px; + list-style: square; +} + +div.sphinxsidebar ul ul { + margin-top: 0; + margin-bottom: 0; +} + +div.sphinxsidebar form { + margin-top: 10px; +} + +div.sphinxsidebar input { + border: 1px solid #98dbcc; + font-family: sans-serif; + font-size: 1em; +} + +div.sphinxsidebar #searchbox form.search { + overflow: hidden; +} + +div.sphinxsidebar #searchbox input[type="text"] { + float: left; + width: 80%; + padding: 0.25em; + box-sizing: border-box; +} + +div.sphinxsidebar #searchbox input[type="submit"] { + float: left; + width: 20%; + border-left: none; + padding: 0.25em; + box-sizing: border-box; +} + + +img { + border: 0; + max-width: 100%; +} + +/* -- search page ----------------------------------------------------------- */ + +ul.search { + margin: 10px 0 0 20px; + padding: 0; +} + +ul.search li { + padding: 5px 0 5px 20px; + background-image: url(file.png); + background-repeat: no-repeat; + background-position: 0 7px; +} + +ul.search li a { + font-weight: bold; +} + +ul.search li p.context { + color: #888; + margin: 2px 0 0 30px; + text-align: left; +} + +ul.keywordmatches li.goodmatch a { + font-weight: bold; +} + +/* -- index page ------------------------------------------------------------ */ + +table.contentstable { + width: 90%; + margin-left: auto; + margin-right: auto; +} + +table.contentstable p.biglink { + line-height: 150%; +} + +a.biglink { + font-size: 1.3em; +} + +span.linkdescr { + font-style: italic; + padding-top: 5px; + font-size: 90%; +} + +/* -- general index --------------------------------------------------------- */ + +table.indextable { + width: 100%; +} + +table.indextable td { + text-align: left; + vertical-align: top; +} + +table.indextable ul { + margin-top: 0; + margin-bottom: 0; + list-style-type: none; +} + +table.indextable > tbody > tr > td > ul { + padding-left: 0em; +} + +table.indextable tr.pcap { + height: 10px; +} + +table.indextable tr.cap { + margin-top: 10px; + background-color: #f2f2f2; +} + +img.toggler { + margin-right: 3px; + margin-top: 3px; + cursor: pointer; +} + +div.modindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +div.genindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +/* -- domain module index --------------------------------------------------- */ + +table.modindextable td { + padding: 2px; + border-collapse: collapse; +} + +/* -- general body styles --------------------------------------------------- */ + +div.body { + min-width: 450px; + max-width: 800px; +} + +div.body p, div.body dd, div.body li, div.body blockquote { + -moz-hyphens: auto; + -ms-hyphens: auto; + -webkit-hyphens: auto; + hyphens: auto; +} + +a.headerlink { + visibility: hidden; +} + +a.brackets:before, +span.brackets > a:before{ + content: "["; +} + +a.brackets:after, +span.brackets > a:after { + content: "]"; +} + +h1:hover > a.headerlink, +h2:hover > a.headerlink, +h3:hover > a.headerlink, +h4:hover > a.headerlink, +h5:hover > a.headerlink, +h6:hover > a.headerlink, +dt:hover > a.headerlink, +caption:hover > a.headerlink, +p.caption:hover > a.headerlink, +div.code-block-caption:hover > a.headerlink { + visibility: visible; +} + +div.body p.caption { + text-align: inherit; +} + +div.body td { + text-align: left; +} + +.first { + margin-top: 0 !important; +} + +p.rubric { + margin-top: 30px; + font-weight: bold; +} + +img.align-left, figure.align-left, .figure.align-left, object.align-left { + clear: left; + float: left; + margin-right: 1em; +} + +img.align-right, figure.align-right, .figure.align-right, object.align-right { + clear: right; + float: right; + margin-left: 1em; +} + +img.align-center, figure.align-center, .figure.align-center, object.align-center { + display: block; + margin-left: auto; + margin-right: auto; +} + +img.align-default, figure.align-default, .figure.align-default { + display: block; + margin-left: auto; + margin-right: auto; +} + +.align-left { + text-align: left; +} + +.align-center { + text-align: center; +} + +.align-default { + text-align: center; +} + +.align-right { + text-align: right; +} + +/* -- sidebars -------------------------------------------------------------- */ + +div.sidebar, +aside.sidebar { + margin: 0 0 0.5em 1em; + border: 1px solid #ddb; + padding: 7px; + background-color: #ffe; + width: 40%; + float: right; + clear: right; + overflow-x: auto; +} + +p.sidebar-title { + font-weight: bold; +} + +div.admonition, div.topic, blockquote { + clear: left; +} + +/* -- topics ---------------------------------------------------------------- */ + +div.topic { + border: 1px solid #ccc; + padding: 7px; + margin: 10px 0 10px 0; +} + +p.topic-title { + font-size: 1.1em; + font-weight: bold; + margin-top: 10px; +} + +/* -- admonitions ----------------------------------------------------------- */ + +div.admonition { + margin-top: 10px; + margin-bottom: 10px; + padding: 7px; +} + +div.admonition dt { + font-weight: bold; +} + +p.admonition-title { + margin: 0px 10px 5px 0px; + font-weight: bold; +} + +div.body p.centered { + text-align: center; + margin-top: 25px; +} + +/* -- content of sidebars/topics/admonitions -------------------------------- */ + +div.sidebar > :last-child, +aside.sidebar > :last-child, +div.topic > :last-child, +div.admonition > :last-child { + margin-bottom: 0; +} + +div.sidebar::after, +aside.sidebar::after, +div.topic::after, +div.admonition::after, +blockquote::after { + display: block; + content: ''; + clear: both; +} + +/* -- tables ---------------------------------------------------------------- */ + +table.docutils { + margin-top: 10px; + margin-bottom: 10px; + border: 0; + border-collapse: collapse; +} + +table.align-center { + margin-left: auto; + margin-right: auto; +} + +table.align-default { + margin-left: auto; + margin-right: auto; +} + +table caption span.caption-number { + font-style: italic; +} + +table caption span.caption-text { +} + +table.docutils td, table.docutils th { + padding: 1px 8px 1px 5px; + border-top: 0; + border-left: 0; + border-right: 0; + border-bottom: 1px solid #aaa; +} + +table.footnote td, table.footnote th { + border: 0 !important; +} + +th { + text-align: left; + padding-right: 5px; +} + +table.citation { + border-left: solid 1px gray; + margin-left: 1px; +} + +table.citation td { + border-bottom: none; +} + +th > :first-child, +td > :first-child { + margin-top: 0px; +} + +th > :last-child, +td > :last-child { + margin-bottom: 0px; +} + +/* -- figures --------------------------------------------------------------- */ + +div.figure, figure { + margin: 0.5em; + padding: 0.5em; +} + +div.figure p.caption, figcaption { + padding: 0.3em; +} + +div.figure p.caption span.caption-number, +figcaption span.caption-number { + font-style: italic; +} + +div.figure p.caption span.caption-text, +figcaption span.caption-text { +} + +/* -- field list styles ----------------------------------------------------- */ + +table.field-list td, table.field-list th { + border: 0 !important; +} + +.field-list ul { + margin: 0; + padding-left: 1em; +} + +.field-list p { + margin: 0; +} + +.field-name { + -moz-hyphens: manual; + -ms-hyphens: manual; + -webkit-hyphens: manual; + hyphens: manual; +} + +/* -- hlist styles ---------------------------------------------------------- */ + +table.hlist { + margin: 1em 0; +} + +table.hlist td { + vertical-align: top; +} + +/* -- object description styles --------------------------------------------- */ + +.sig { + font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace; +} + +.sig-name, code.descname { + background-color: transparent; + font-weight: bold; +} + +.sig-name { + font-size: 1.1em; +} + +code.descname { + font-size: 1.2em; +} + +.sig-prename, code.descclassname { + background-color: transparent; +} + +.optional { + font-size: 1.3em; +} + +.sig-paren { + font-size: larger; +} + +.sig-param.n { + font-style: italic; +} + +/* C++ specific styling */ + +.sig-inline.c-texpr, +.sig-inline.cpp-texpr { + font-family: unset; +} + +.sig.c .k, .sig.c .kt, +.sig.cpp .k, .sig.cpp .kt { + color: #0033B3; +} + +.sig.c .m, +.sig.cpp .m { + color: #1750EB; +} + +.sig.c .s, .sig.c .sc, +.sig.cpp .s, .sig.cpp .sc { + color: #067D17; +} + + +/* -- other body styles ----------------------------------------------------- */ + +ol.arabic { + list-style: decimal; +} + +ol.loweralpha { + list-style: lower-alpha; +} + +ol.upperalpha { + list-style: upper-alpha; +} + +ol.lowerroman { + list-style: lower-roman; +} + +ol.upperroman { + list-style: upper-roman; +} + +:not(li) > ol > li:first-child > :first-child, +:not(li) > ul > li:first-child > :first-child { + margin-top: 0px; +} + +:not(li) > ol > li:last-child > :last-child, +:not(li) > ul > li:last-child > :last-child { + margin-bottom: 0px; +} + +ol.simple ol p, +ol.simple ul p, +ul.simple ol p, +ul.simple ul p { + margin-top: 0; +} + +ol.simple > li:not(:first-child) > p, +ul.simple > li:not(:first-child) > p { + margin-top: 0; +} + +ol.simple p, +ul.simple p { + margin-bottom: 0; +} + +dl.footnote > dt, +dl.citation > dt { + float: left; + margin-right: 0.5em; +} + +dl.footnote > dd, +dl.citation > dd { + margin-bottom: 0em; +} + +dl.footnote > dd:after, +dl.citation > dd:after { + content: ""; + clear: both; +} + +dl.field-list { + display: grid; + grid-template-columns: fit-content(30%) auto; +} + +dl.field-list > dt { + font-weight: bold; + word-break: break-word; + padding-left: 0.5em; + padding-right: 5px; +} + +dl.field-list > dt:after { + content: ":"; +} + +dl.field-list > dd { + padding-left: 0.5em; + margin-top: 0em; + margin-left: 0em; + margin-bottom: 0em; +} + +dl { + margin-bottom: 15px; +} + +dd > :first-child { + margin-top: 0px; +} + +dd ul, dd table { + margin-bottom: 10px; +} + +dd { + margin-top: 3px; + margin-bottom: 10px; + margin-left: 30px; +} + +dl > dd:last-child, +dl > dd:last-child > :last-child { + margin-bottom: 0; +} + +dt:target, span.highlighted { + background-color: #fbe54e; +} + +rect.highlighted { + fill: #fbe54e; +} + +dl.glossary dt { + font-weight: bold; + font-size: 1.1em; +} + +.versionmodified { + font-style: italic; +} + +.system-message { + background-color: #fda; + padding: 5px; + border: 3px solid red; +} + +.footnote:target { + background-color: #ffa; +} + +.line-block { + display: block; + margin-top: 1em; + margin-bottom: 1em; +} + +.line-block .line-block { + margin-top: 0; + margin-bottom: 0; + margin-left: 1.5em; +} + +.guilabel, .menuselection { + font-family: sans-serif; +} + +.accelerator { + text-decoration: underline; +} + +.classifier { + font-style: oblique; +} + +.classifier:before { + font-style: normal; + margin: 0.5em; + content: ":"; +} + +abbr, acronym { + border-bottom: dotted 1px; + cursor: help; +} + +/* -- code displays --------------------------------------------------------- */ + +pre { + overflow: auto; + overflow-y: hidden; /* fixes display issues on Chrome browsers */ +} + +pre, div[class*="highlight-"] { + clear: both; +} + +span.pre { + -moz-hyphens: none; + -ms-hyphens: none; + -webkit-hyphens: none; + hyphens: none; +} + +div[class*="highlight-"] { + margin: 1em 0; +} + +td.linenos pre { + border: 0; + background-color: transparent; + color: #aaa; +} + +table.highlighttable { + display: block; +} + +table.highlighttable tbody { + display: block; +} + +table.highlighttable tr { + display: flex; +} + +table.highlighttable td { + margin: 0; + padding: 0; +} + +table.highlighttable td.linenos { + padding-right: 0.5em; +} + +table.highlighttable td.code { + flex: 1; + overflow: hidden; +} + +.highlight .hll { + display: block; +} + +div.highlight pre, +table.highlighttable pre { + margin: 0; +} + +div.code-block-caption + div { + margin-top: 0; +} + +div.code-block-caption { + margin-top: 1em; + padding: 2px 5px; + font-size: small; +} + +div.code-block-caption code { + background-color: transparent; +} + +table.highlighttable td.linenos, +span.linenos, +div.doctest > div.highlight span.gp { /* gp: Generic.Prompt */ + user-select: none; + -webkit-user-select: text; /* Safari fallback only */ + -webkit-user-select: none; /* Chrome/Safari */ + -moz-user-select: none; /* Firefox */ + -ms-user-select: none; /* IE10+ */ +} + +div.code-block-caption span.caption-number { + padding: 0.1em 0.3em; + font-style: italic; +} + +div.code-block-caption span.caption-text { +} + +div.literal-block-wrapper { + margin: 1em 0; +} + +code.xref, a code { + background-color: transparent; + font-weight: bold; +} + +h1 code, h2 code, h3 code, h4 code, h5 code, h6 code { + background-color: transparent; +} + +.viewcode-link { + float: right; +} + +.viewcode-back { + float: right; + font-family: sans-serif; +} + +div.viewcode-block:target { + margin: -1px -10px; + padding: 0 10px; +} + +/* -- math display ---------------------------------------------------------- */ + +img.math { + vertical-align: middle; +} + +div.body div.math p { + text-align: center; +} + +span.eqno { + float: right; +} + +span.eqno a.headerlink { + position: absolute; + z-index: 1; +} + +div.math:hover a.headerlink { + visibility: visible; +} + +/* -- printout stylesheet --------------------------------------------------- */ + +@media print { + div.document, + div.documentwrapper, + div.bodywrapper { + margin: 0 !important; + width: 100%; + } + + div.sphinxsidebar, + div.related, + div.footer, + #top-link { + display: none; + } +} \ No newline at end of file diff --git a/core/_static/custom.css b/core/_static/custom.css new file mode 100644 index 00000000..45838c1e --- /dev/null +++ b/core/_static/custom.css @@ -0,0 +1,76 @@ +a { + color: #004BAB; + text-decoration: none; +} + +a.reference { + border-bottom: none; +} + +a.reference:hover { + border-bottom: 1px dotted #004BAB; +} + +body { + font-size: 15px; +} + +div.document { width: 1000px; } +div.bodywrapper { margin: 0 0 0 200px; } +div.body { padding: 0 10px 0 10px; } +div.footer { width: 1000px; } + +div.body h1 { font-size: 200%; } +div.body h2 { font-size: 150%; } +div.body h3 { font-size: 120%; } +div.body h4 { font-size: 110%; } + +div.note { + border: 0px; + font-size: 90%; + background-color: #F6F8FF; +} + +div.admonition { + padding: 10px; +} + +div.admonition p.admonition-title { + margin: 0px 0px 0px 0px; + font-size: 100%; + font-weight: bold; +} + +div.math { + background-color: #F0F0F0; + padding: 3px 0 3px 0; +} + +div.relations { + display: block; +} + +div.sphinxsidebar { + z-index: 1; + background: #FFF; + margin-top: -30px; + font-size: 13px; + width: 200px; + height: 100%; +} + +div.sphinxsidebarwrapper p.logo { + padding: 30px 40px 10px 0px; +} + +div.sphinxsidebar h3 { + font-size: 0px; +} + +div.sphinxsidebar a { + border-bottom: 0px; +} + +div.sphinxsidebar a:hover { + border-bottom: 1px dotted; +} diff --git a/core/_static/doctools.js b/core/_static/doctools.js new file mode 100644 index 00000000..61ac9d26 --- /dev/null +++ b/core/_static/doctools.js @@ -0,0 +1,321 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Sphinx JavaScript utilities for all documentation. + * + * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/** + * select a different prefix for underscore + */ +$u = _.noConflict(); + +/** + * make the code below compatible with browsers without + * an installed firebug like debugger +if (!window.console || !console.firebug) { + var names = ["log", "debug", "info", "warn", "error", "assert", "dir", + "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace", + "profile", "profileEnd"]; + window.console = {}; + for (var i = 0; i < names.length; ++i) + window.console[names[i]] = function() {}; +} + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} + +/** + * Small JavaScript module for the documentation. + */ +var Documentation = { + + init : function() { + this.fixFirefoxAnchorBug(); + this.highlightSearchWords(); + this.initIndexTable(); + if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) { + this.initOnKeyListeners(); + } + }, + + /** + * i18n support + */ + TRANSLATIONS : {}, + PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; }, + LOCALE : 'unknown', + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext : function(string) { + var translated = Documentation.TRANSLATIONS[string]; + if (typeof translated === 'undefined') + return string; + return (typeof translated === 'string') ? translated : translated[0]; + }, + + ngettext : function(singular, plural, n) { + var translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated === 'undefined') + return (n == 1) ? singular : plural; + return translated[Documentation.PLURALEXPR(n)]; + }, + + addTranslations : function(catalog) { + for (var key in catalog.messages) + this.TRANSLATIONS[key] = catalog.messages[key]; + this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')'); + this.LOCALE = catalog.locale; + }, + + /** + * add context elements like header anchor links + */ + addContextElements : function() { + $('div[id] > :header:first').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this headline')). + appendTo(this); + }); + $('dt[id]').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this definition')). + appendTo(this); + }); + }, + + /** + * workaround a firefox stupidity + * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075 + */ + fixFirefoxAnchorBug : function() { + if (document.location.hash && $.browser.mozilla) + window.setTimeout(function() { + document.location.href += ''; + }, 10); + }, + + /** + * highlight the search words provided in the url in the text + */ + highlightSearchWords : function() { + var params = $.getQueryParameters(); + var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : []; + if (terms.length) { + var body = $('div.body'); + if (!body.length) { + body = $('body'); + } + window.setTimeout(function() { + $.each(terms, function() { + body.highlightText(this.toLowerCase(), 'highlighted'); + }); + }, 10); + $('

    ' + _('Hide Search Matches') + '

    ') + .appendTo($('#searchbox')); + } + }, + + /** + * init the domain index toggle buttons + */ + initIndexTable : function() { + var togglers = $('img.toggler').click(function() { + var src = $(this).attr('src'); + var idnum = $(this).attr('id').substr(7); + $('tr.cg-' + idnum).toggle(); + if (src.substr(-9) === 'minus.png') + $(this).attr('src', src.substr(0, src.length-9) + 'plus.png'); + else + $(this).attr('src', src.substr(0, src.length-8) + 'minus.png'); + }).css('display', ''); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) { + togglers.click(); + } + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords : function() { + $('#searchbox .highlight-link').fadeOut(300); + $('span.highlighted').removeClass('highlighted'); + }, + + /** + * make the url absolute + */ + makeURL : function(relativeURL) { + return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL; + }, + + /** + * get the current relative url + */ + getCurrentURL : function() { + var path = document.location.pathname; + var parts = path.split(/\//); + $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() { + if (this === '..') + parts.pop(); + }); + var url = parts.join('/'); + return path.substring(url.lastIndexOf('/') + 1, path.length - 1); + }, + + initOnKeyListeners: function() { + $(document).keydown(function(event) { + var activeElementType = document.activeElement.tagName; + // don't navigate when in search box, textarea, dropdown or button + if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT' + && activeElementType !== 'BUTTON' && !event.altKey && !event.ctrlKey && !event.metaKey + && !event.shiftKey) { + switch (event.keyCode) { + case 37: // left + var prevHref = $('link[rel="prev"]').prop('href'); + if (prevHref) { + window.location.href = prevHref; + return false; + } + case 39: // right + var nextHref = $('link[rel="next"]').prop('href'); + if (nextHref) { + window.location.href = nextHref; + return false; + } + } + } + }); + } +}; + +// quick alias for translations +_ = Documentation.gettext; + +$(document).ready(function() { + Documentation.init(); +}); diff --git a/core/_static/documentation_options.js b/core/_static/documentation_options.js new file mode 100644 index 00000000..5dae6739 --- /dev/null +++ b/core/_static/documentation_options.js @@ -0,0 +1,12 @@ +var DOCUMENTATION_OPTIONS = { + URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), + VERSION: '2.0 + stringref (Draft 2022-04-27)', + LANGUAGE: 'None', + COLLAPSE_INDEX: false, + BUILDER: 'html', + FILE_SUFFIX: '.html', + LINK_SUFFIX: '.html', + HAS_SOURCE: false, + SOURCELINK_SUFFIX: '.txt', + NAVIGATION_WITH_KEYS: false +}; \ No newline at end of file diff --git a/core/_static/file.png b/core/_static/file.png new file mode 100644 index 0000000000000000000000000000000000000000..a858a410e4faa62ce324d814e4b816fff83a6fb3 GIT binary patch literal 286 zcmV+(0pb3MP)s`hMrGg#P~ix$^RISR_I47Y|r1 z_CyJOe}D1){SET-^Amu_i71Lt6eYfZjRyw@I6OQAIXXHDfiX^GbOlHe=Ae4>0m)d(f|Me07*qoM6N<$f}vM^LjV8( literal 0 HcmV?d00001 diff --git a/core/_static/jquery-3.5.1.js b/core/_static/jquery-3.5.1.js new file mode 100644 index 00000000..50937333 --- /dev/null +++ b/core/_static/jquery-3.5.1.js @@ -0,0 +1,10872 @@ +/*! + * jQuery JavaScript Library v3.5.1 + * https://jquery.com/ + * + * Includes Sizzle.js + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://jquery.org/license + * + * Date: 2020-05-04T22:49Z + */ +( function( global, factory ) { + + "use strict"; + + if ( typeof module === "object" && typeof module.exports === "object" ) { + + // For CommonJS and CommonJS-like environments where a proper `window` + // is present, execute the factory and get jQuery. + // For environments that do not have a `window` with a `document` + // (such as Node.js), expose a factory as module.exports. + // This accentuates the need for the creation of a real `window`. + // e.g. var jQuery = require("jquery")(window); + // See ticket #14549 for more info. + module.exports = global.document ? + factory( global, true ) : + function( w ) { + if ( !w.document ) { + throw new Error( "jQuery requires a window with a document" ); + } + return factory( w ); + }; + } else { + factory( global ); + } + +// Pass this if window is not defined yet +} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { + +// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 +// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode +// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common +// enough that all such attempts are guarded in a try block. +"use strict"; + +var arr = []; + +var getProto = Object.getPrototypeOf; + +var slice = arr.slice; + +var flat = arr.flat ? function( array ) { + return arr.flat.call( array ); +} : function( array ) { + return arr.concat.apply( [], array ); +}; + + +var push = arr.push; + +var indexOf = arr.indexOf; + +var class2type = {}; + +var toString = class2type.toString; + +var hasOwn = class2type.hasOwnProperty; + +var fnToString = hasOwn.toString; + +var ObjectFunctionString = fnToString.call( Object ); + +var support = {}; + +var isFunction = function isFunction( obj ) { + + // Support: Chrome <=57, Firefox <=52 + // In some browsers, typeof returns "function" for HTML elements + // (i.e., `typeof document.createElement( "object" ) === "function"`). + // We don't want to classify *any* DOM node as a function. + return typeof obj === "function" && typeof obj.nodeType !== "number"; + }; + + +var isWindow = function isWindow( obj ) { + return obj != null && obj === obj.window; + }; + + +var document = window.document; + + + + var preservedScriptAttributes = { + type: true, + src: true, + nonce: true, + noModule: true + }; + + function DOMEval( code, node, doc ) { + doc = doc || document; + + var i, val, + script = doc.createElement( "script" ); + + script.text = code; + if ( node ) { + for ( i in preservedScriptAttributes ) { + + // Support: Firefox 64+, Edge 18+ + // Some browsers don't support the "nonce" property on scripts. + // On the other hand, just using `getAttribute` is not enough as + // the `nonce` attribute is reset to an empty string whenever it + // becomes browsing-context connected. + // See https://github.com/whatwg/html/issues/2369 + // See https://html.spec.whatwg.org/#nonce-attributes + // The `node.getAttribute` check was added for the sake of + // `jQuery.globalEval` so that it can fake a nonce-containing node + // via an object. + val = node[ i ] || node.getAttribute && node.getAttribute( i ); + if ( val ) { + script.setAttribute( i, val ); + } + } + } + doc.head.appendChild( script ).parentNode.removeChild( script ); + } + + +function toType( obj ) { + if ( obj == null ) { + return obj + ""; + } + + // Support: Android <=2.3 only (functionish RegExp) + return typeof obj === "object" || typeof obj === "function" ? + class2type[ toString.call( obj ) ] || "object" : + typeof obj; +} +/* global Symbol */ +// Defining this global in .eslintrc.json would create a danger of using the global +// unguarded in another place, it seems safer to define global only for this module + + + +var + version = "3.5.1", + + // Define a local copy of jQuery + jQuery = function( selector, context ) { + + // The jQuery object is actually just the init constructor 'enhanced' + // Need init if jQuery is called (just allow error to be thrown if not included) + return new jQuery.fn.init( selector, context ); + }; + +jQuery.fn = jQuery.prototype = { + + // The current version of jQuery being used + jquery: version, + + constructor: jQuery, + + // The default length of a jQuery object is 0 + length: 0, + + toArray: function() { + return slice.call( this ); + }, + + // Get the Nth element in the matched element set OR + // Get the whole matched element set as a clean array + get: function( num ) { + + // Return all the elements in a clean array + if ( num == null ) { + return slice.call( this ); + } + + // Return just the one element from the set + return num < 0 ? this[ num + this.length ] : this[ num ]; + }, + + // Take an array of elements and push it onto the stack + // (returning the new matched element set) + pushStack: function( elems ) { + + // Build a new jQuery matched element set + var ret = jQuery.merge( this.constructor(), elems ); + + // Add the old object onto the stack (as a reference) + ret.prevObject = this; + + // Return the newly-formed element set + return ret; + }, + + // Execute a callback for every element in the matched set. + each: function( callback ) { + return jQuery.each( this, callback ); + }, + + map: function( callback ) { + return this.pushStack( jQuery.map( this, function( elem, i ) { + return callback.call( elem, i, elem ); + } ) ); + }, + + slice: function() { + return this.pushStack( slice.apply( this, arguments ) ); + }, + + first: function() { + return this.eq( 0 ); + }, + + last: function() { + return this.eq( -1 ); + }, + + even: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return ( i + 1 ) % 2; + } ) ); + }, + + odd: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return i % 2; + } ) ); + }, + + eq: function( i ) { + var len = this.length, + j = +i + ( i < 0 ? len : 0 ); + return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); + }, + + end: function() { + return this.prevObject || this.constructor(); + }, + + // For internal use only. + // Behaves like an Array's method, not like a jQuery method. + push: push, + sort: arr.sort, + splice: arr.splice +}; + +jQuery.extend = jQuery.fn.extend = function() { + var options, name, src, copy, copyIsArray, clone, + target = arguments[ 0 ] || {}, + i = 1, + length = arguments.length, + deep = false; + + // Handle a deep copy situation + if ( typeof target === "boolean" ) { + deep = target; + + // Skip the boolean and the target + target = arguments[ i ] || {}; + i++; + } + + // Handle case when target is a string or something (possible in deep copy) + if ( typeof target !== "object" && !isFunction( target ) ) { + target = {}; + } + + // Extend jQuery itself if only one argument is passed + if ( i === length ) { + target = this; + i--; + } + + for ( ; i < length; i++ ) { + + // Only deal with non-null/undefined values + if ( ( options = arguments[ i ] ) != null ) { + + // Extend the base object + for ( name in options ) { + copy = options[ name ]; + + // Prevent Object.prototype pollution + // Prevent never-ending loop + if ( name === "__proto__" || target === copy ) { + continue; + } + + // Recurse if we're merging plain objects or arrays + if ( deep && copy && ( jQuery.isPlainObject( copy ) || + ( copyIsArray = Array.isArray( copy ) ) ) ) { + src = target[ name ]; + + // Ensure proper type for the source value + if ( copyIsArray && !Array.isArray( src ) ) { + clone = []; + } else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) { + clone = {}; + } else { + clone = src; + } + copyIsArray = false; + + // Never move original objects, clone them + target[ name ] = jQuery.extend( deep, clone, copy ); + + // Don't bring in undefined values + } else if ( copy !== undefined ) { + target[ name ] = copy; + } + } + } + } + + // Return the modified object + return target; +}; + +jQuery.extend( { + + // Unique for each copy of jQuery on the page + expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), + + // Assume jQuery is ready without the ready module + isReady: true, + + error: function( msg ) { + throw new Error( msg ); + }, + + noop: function() {}, + + isPlainObject: function( obj ) { + var proto, Ctor; + + // Detect obvious negatives + // Use toString instead of jQuery.type to catch host objects + if ( !obj || toString.call( obj ) !== "[object Object]" ) { + return false; + } + + proto = getProto( obj ); + + // Objects with no prototype (e.g., `Object.create( null )`) are plain + if ( !proto ) { + return true; + } + + // Objects with prototype are plain iff they were constructed by a global Object function + Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; + return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; + }, + + isEmptyObject: function( obj ) { + var name; + + for ( name in obj ) { + return false; + } + return true; + }, + + // Evaluates a script in a provided context; falls back to the global one + // if not specified. + globalEval: function( code, options, doc ) { + DOMEval( code, { nonce: options && options.nonce }, doc ); + }, + + each: function( obj, callback ) { + var length, i = 0; + + if ( isArrayLike( obj ) ) { + length = obj.length; + for ( ; i < length; i++ ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } else { + for ( i in obj ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } + + return obj; + }, + + // results is for internal usage only + makeArray: function( arr, results ) { + var ret = results || []; + + if ( arr != null ) { + if ( isArrayLike( Object( arr ) ) ) { + jQuery.merge( ret, + typeof arr === "string" ? + [ arr ] : arr + ); + } else { + push.call( ret, arr ); + } + } + + return ret; + }, + + inArray: function( elem, arr, i ) { + return arr == null ? -1 : indexOf.call( arr, elem, i ); + }, + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + merge: function( first, second ) { + var len = +second.length, + j = 0, + i = first.length; + + for ( ; j < len; j++ ) { + first[ i++ ] = second[ j ]; + } + + first.length = i; + + return first; + }, + + grep: function( elems, callback, invert ) { + var callbackInverse, + matches = [], + i = 0, + length = elems.length, + callbackExpect = !invert; + + // Go through the array, only saving the items + // that pass the validator function + for ( ; i < length; i++ ) { + callbackInverse = !callback( elems[ i ], i ); + if ( callbackInverse !== callbackExpect ) { + matches.push( elems[ i ] ); + } + } + + return matches; + }, + + // arg is for internal usage only + map: function( elems, callback, arg ) { + var length, value, + i = 0, + ret = []; + + // Go through the array, translating each of the items to their new values + if ( isArrayLike( elems ) ) { + length = elems.length; + for ( ; i < length; i++ ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + + // Go through every key on the object, + } else { + for ( i in elems ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + } + + // Flatten any nested arrays + return flat( ret ); + }, + + // A global GUID counter for objects + guid: 1, + + // jQuery.support is not used in Core but other projects attach their + // properties to it so it needs to exist. + support: support +} ); + +if ( typeof Symbol === "function" ) { + jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; +} + +// Populate the class2type map +jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), +function( _i, name ) { + class2type[ "[object " + name + "]" ] = name.toLowerCase(); +} ); + +function isArrayLike( obj ) { + + // Support: real iOS 8.2 only (not reproducible in simulator) + // `in` check used to prevent JIT error (gh-2145) + // hasOwn isn't used here due to false negatives + // regarding Nodelist length in IE + var length = !!obj && "length" in obj && obj.length, + type = toType( obj ); + + if ( isFunction( obj ) || isWindow( obj ) ) { + return false; + } + + return type === "array" || length === 0 || + typeof length === "number" && length > 0 && ( length - 1 ) in obj; +} +var Sizzle = +/*! + * Sizzle CSS Selector Engine v2.3.5 + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://js.foundation/ + * + * Date: 2020-03-14 + */ +( function( window ) { +var i, + support, + Expr, + getText, + isXML, + tokenize, + compile, + select, + outermostContext, + sortInput, + hasDuplicate, + + // Local document vars + setDocument, + document, + docElem, + documentIsHTML, + rbuggyQSA, + rbuggyMatches, + matches, + contains, + + // Instance-specific data + expando = "sizzle" + 1 * new Date(), + preferredDoc = window.document, + dirruns = 0, + done = 0, + classCache = createCache(), + tokenCache = createCache(), + compilerCache = createCache(), + nonnativeSelectorCache = createCache(), + sortOrder = function( a, b ) { + if ( a === b ) { + hasDuplicate = true; + } + return 0; + }, + + // Instance methods + hasOwn = ( {} ).hasOwnProperty, + arr = [], + pop = arr.pop, + pushNative = arr.push, + push = arr.push, + slice = arr.slice, + + // Use a stripped-down indexOf as it's faster than native + // https://jsperf.com/thor-indexof-vs-for/5 + indexOf = function( list, elem ) { + var i = 0, + len = list.length; + for ( ; i < len; i++ ) { + if ( list[ i ] === elem ) { + return i; + } + } + return -1; + }, + + booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" + + "ismap|loop|multiple|open|readonly|required|scoped", + + // Regular expressions + + // http://www.w3.org/TR/css3-selectors/#whitespace + whitespace = "[\\x20\\t\\r\\n\\f]", + + // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram + identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace + + "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+", + + // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors + attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + + + // Operator (capture 2) + "*([*^$|!~]?=)" + whitespace + + + // "Attribute values must be CSS identifiers [capture 5] + // or strings [capture 3 or capture 4]" + "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + + whitespace + "*\\]", + + pseudos = ":(" + identifier + ")(?:\\((" + + + // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: + // 1. quoted (capture 3; capture 4 or capture 5) + "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + + + // 2. simple (capture 6) + "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + + + // 3. anything else (capture 2) + ".*" + + ")\\)|)", + + // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter + rwhitespace = new RegExp( whitespace + "+", "g" ), + rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + + whitespace + "+$", "g" ), + + rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), + rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + + "*" ), + rdescend = new RegExp( whitespace + "|>" ), + + rpseudo = new RegExp( pseudos ), + ridentifier = new RegExp( "^" + identifier + "$" ), + + matchExpr = { + "ID": new RegExp( "^#(" + identifier + ")" ), + "CLASS": new RegExp( "^\\.(" + identifier + ")" ), + "TAG": new RegExp( "^(" + identifier + "|[*])" ), + "ATTR": new RegExp( "^" + attributes ), + "PSEUDO": new RegExp( "^" + pseudos ), + "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + + whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + + whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), + "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), + + // For use in libraries implementing .is() + // We use this for POS matching in `select` + "needsContext": new RegExp( "^" + whitespace + + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace + + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) + }, + + rhtml = /HTML$/i, + rinputs = /^(?:input|select|textarea|button)$/i, + rheader = /^h\d$/i, + + rnative = /^[^{]+\{\s*\[native \w/, + + // Easily-parseable/retrievable ID or TAG or CLASS selectors + rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, + + rsibling = /[+~]/, + + // CSS escapes + // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters + runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ), + funescape = function( escape, nonHex ) { + var high = "0x" + escape.slice( 1 ) - 0x10000; + + return nonHex ? + + // Strip the backslash prefix from a non-hex escape sequence + nonHex : + + // Replace a hexadecimal escape sequence with the encoded Unicode code point + // Support: IE <=11+ + // For values outside the Basic Multilingual Plane (BMP), manually construct a + // surrogate pair + high < 0 ? + String.fromCharCode( high + 0x10000 ) : + String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); + }, + + // CSS string/identifier serialization + // https://drafts.csswg.org/cssom/#common-serializing-idioms + rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, + fcssescape = function( ch, asCodePoint ) { + if ( asCodePoint ) { + + // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER + if ( ch === "\0" ) { + return "\uFFFD"; + } + + // Control characters and (dependent upon position) numbers get escaped as code points + return ch.slice( 0, -1 ) + "\\" + + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; + } + + // Other potentially-special ASCII characters get backslash-escaped + return "\\" + ch; + }, + + // Used for iframes + // See setDocument() + // Removing the function wrapper causes a "Permission Denied" + // error in IE + unloadHandler = function() { + setDocument(); + }, + + inDisabledFieldset = addCombinator( + function( elem ) { + return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset"; + }, + { dir: "parentNode", next: "legend" } + ); + +// Optimize for push.apply( _, NodeList ) +try { + push.apply( + ( arr = slice.call( preferredDoc.childNodes ) ), + preferredDoc.childNodes + ); + + // Support: Android<4.0 + // Detect silently failing push.apply + // eslint-disable-next-line no-unused-expressions + arr[ preferredDoc.childNodes.length ].nodeType; +} catch ( e ) { + push = { apply: arr.length ? + + // Leverage slice if possible + function( target, els ) { + pushNative.apply( target, slice.call( els ) ); + } : + + // Support: IE<9 + // Otherwise append directly + function( target, els ) { + var j = target.length, + i = 0; + + // Can't trust NodeList.length + while ( ( target[ j++ ] = els[ i++ ] ) ) {} + target.length = j - 1; + } + }; +} + +function Sizzle( selector, context, results, seed ) { + var m, i, elem, nid, match, groups, newSelector, + newContext = context && context.ownerDocument, + + // nodeType defaults to 9, since context defaults to document + nodeType = context ? context.nodeType : 9; + + results = results || []; + + // Return early from calls with invalid selector or context + if ( typeof selector !== "string" || !selector || + nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { + + return results; + } + + // Try to shortcut find operations (as opposed to filters) in HTML documents + if ( !seed ) { + setDocument( context ); + context = context || document; + + if ( documentIsHTML ) { + + // If the selector is sufficiently simple, try using a "get*By*" DOM method + // (excepting DocumentFragment context, where the methods don't exist) + if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) { + + // ID selector + if ( ( m = match[ 1 ] ) ) { + + // Document context + if ( nodeType === 9 ) { + if ( ( elem = context.getElementById( m ) ) ) { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( elem.id === m ) { + results.push( elem ); + return results; + } + } else { + return results; + } + + // Element context + } else { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( newContext && ( elem = newContext.getElementById( m ) ) && + contains( context, elem ) && + elem.id === m ) { + + results.push( elem ); + return results; + } + } + + // Type selector + } else if ( match[ 2 ] ) { + push.apply( results, context.getElementsByTagName( selector ) ); + return results; + + // Class selector + } else if ( ( m = match[ 3 ] ) && support.getElementsByClassName && + context.getElementsByClassName ) { + + push.apply( results, context.getElementsByClassName( m ) ); + return results; + } + } + + // Take advantage of querySelectorAll + if ( support.qsa && + !nonnativeSelectorCache[ selector + " " ] && + ( !rbuggyQSA || !rbuggyQSA.test( selector ) ) && + + // Support: IE 8 only + // Exclude object elements + ( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) { + + newSelector = selector; + newContext = context; + + // qSA considers elements outside a scoping root when evaluating child or + // descendant combinators, which is not what we want. + // In such cases, we work around the behavior by prefixing every selector in the + // list with an ID selector referencing the scope context. + // The technique has to be used as well when a leading combinator is used + // as such selectors are not recognized by querySelectorAll. + // Thanks to Andrew Dupont for this technique. + if ( nodeType === 1 && + ( rdescend.test( selector ) || rcombinators.test( selector ) ) ) { + + // Expand context for sibling selectors + newContext = rsibling.test( selector ) && testContext( context.parentNode ) || + context; + + // We can use :scope instead of the ID hack if the browser + // supports it & if we're not changing the context. + if ( newContext !== context || !support.scope ) { + + // Capture the context ID, setting it first if necessary + if ( ( nid = context.getAttribute( "id" ) ) ) { + nid = nid.replace( rcssescape, fcssescape ); + } else { + context.setAttribute( "id", ( nid = expando ) ); + } + } + + // Prefix every selector in the list + groups = tokenize( selector ); + i = groups.length; + while ( i-- ) { + groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " + + toSelector( groups[ i ] ); + } + newSelector = groups.join( "," ); + } + + try { + push.apply( results, + newContext.querySelectorAll( newSelector ) + ); + return results; + } catch ( qsaError ) { + nonnativeSelectorCache( selector, true ); + } finally { + if ( nid === expando ) { + context.removeAttribute( "id" ); + } + } + } + } + } + + // All others + return select( selector.replace( rtrim, "$1" ), context, results, seed ); +} + +/** + * Create key-value caches of limited size + * @returns {function(string, object)} Returns the Object data after storing it on itself with + * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) + * deleting the oldest entry + */ +function createCache() { + var keys = []; + + function cache( key, value ) { + + // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) + if ( keys.push( key + " " ) > Expr.cacheLength ) { + + // Only keep the most recent entries + delete cache[ keys.shift() ]; + } + return ( cache[ key + " " ] = value ); + } + return cache; +} + +/** + * Mark a function for special use by Sizzle + * @param {Function} fn The function to mark + */ +function markFunction( fn ) { + fn[ expando ] = true; + return fn; +} + +/** + * Support testing using an element + * @param {Function} fn Passed the created element and returns a boolean result + */ +function assert( fn ) { + var el = document.createElement( "fieldset" ); + + try { + return !!fn( el ); + } catch ( e ) { + return false; + } finally { + + // Remove from its parent by default + if ( el.parentNode ) { + el.parentNode.removeChild( el ); + } + + // release memory in IE + el = null; + } +} + +/** + * Adds the same handler for all of the specified attrs + * @param {String} attrs Pipe-separated list of attributes + * @param {Function} handler The method that will be applied + */ +function addHandle( attrs, handler ) { + var arr = attrs.split( "|" ), + i = arr.length; + + while ( i-- ) { + Expr.attrHandle[ arr[ i ] ] = handler; + } +} + +/** + * Checks document order of two siblings + * @param {Element} a + * @param {Element} b + * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b + */ +function siblingCheck( a, b ) { + var cur = b && a, + diff = cur && a.nodeType === 1 && b.nodeType === 1 && + a.sourceIndex - b.sourceIndex; + + // Use IE sourceIndex if available on both nodes + if ( diff ) { + return diff; + } + + // Check if b follows a + if ( cur ) { + while ( ( cur = cur.nextSibling ) ) { + if ( cur === b ) { + return -1; + } + } + } + + return a ? 1 : -1; +} + +/** + * Returns a function to use in pseudos for input types + * @param {String} type + */ +function createInputPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for buttons + * @param {String} type + */ +function createButtonPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return ( name === "input" || name === "button" ) && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for :enabled/:disabled + * @param {Boolean} disabled true for :disabled; false for :enabled + */ +function createDisabledPseudo( disabled ) { + + // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable + return function( elem ) { + + // Only certain elements can match :enabled or :disabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled + if ( "form" in elem ) { + + // Check for inherited disabledness on relevant non-disabled elements: + // * listed form-associated elements in a disabled fieldset + // https://html.spec.whatwg.org/multipage/forms.html#category-listed + // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled + // * option elements in a disabled optgroup + // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled + // All such elements have a "form" property. + if ( elem.parentNode && elem.disabled === false ) { + + // Option elements defer to a parent optgroup if present + if ( "label" in elem ) { + if ( "label" in elem.parentNode ) { + return elem.parentNode.disabled === disabled; + } else { + return elem.disabled === disabled; + } + } + + // Support: IE 6 - 11 + // Use the isDisabled shortcut property to check for disabled fieldset ancestors + return elem.isDisabled === disabled || + + // Where there is no isDisabled, check manually + /* jshint -W018 */ + elem.isDisabled !== !disabled && + inDisabledFieldset( elem ) === disabled; + } + + return elem.disabled === disabled; + + // Try to winnow out elements that can't be disabled before trusting the disabled property. + // Some victims get caught in our net (label, legend, menu, track), but it shouldn't + // even exist on them, let alone have a boolean value. + } else if ( "label" in elem ) { + return elem.disabled === disabled; + } + + // Remaining elements are neither :enabled nor :disabled + return false; + }; +} + +/** + * Returns a function to use in pseudos for positionals + * @param {Function} fn + */ +function createPositionalPseudo( fn ) { + return markFunction( function( argument ) { + argument = +argument; + return markFunction( function( seed, matches ) { + var j, + matchIndexes = fn( [], seed.length, argument ), + i = matchIndexes.length; + + // Match elements found at the specified indexes + while ( i-- ) { + if ( seed[ ( j = matchIndexes[ i ] ) ] ) { + seed[ j ] = !( matches[ j ] = seed[ j ] ); + } + } + } ); + } ); +} + +/** + * Checks a node for validity as a Sizzle context + * @param {Element|Object=} context + * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value + */ +function testContext( context ) { + return context && typeof context.getElementsByTagName !== "undefined" && context; +} + +// Expose support vars for convenience +support = Sizzle.support = {}; + +/** + * Detects XML nodes + * @param {Element|Object} elem An element or a document + * @returns {Boolean} True iff elem is a non-HTML XML node + */ +isXML = Sizzle.isXML = function( elem ) { + var namespace = elem.namespaceURI, + docElem = ( elem.ownerDocument || elem ).documentElement; + + // Support: IE <=8 + // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes + // https://bugs.jquery.com/ticket/4833 + return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" ); +}; + +/** + * Sets document-related variables once based on the current document + * @param {Element|Object} [doc] An element or document object to use to set the document + * @returns {Object} Returns the current document + */ +setDocument = Sizzle.setDocument = function( node ) { + var hasCompare, subWindow, + doc = node ? node.ownerDocument || node : preferredDoc; + + // Return early if doc is invalid or already selected + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) { + return document; + } + + // Update global variables + document = doc; + docElem = document.documentElement; + documentIsHTML = !isXML( document ); + + // Support: IE 9 - 11+, Edge 12 - 18+ + // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( preferredDoc != document && + ( subWindow = document.defaultView ) && subWindow.top !== subWindow ) { + + // Support: IE 11, Edge + if ( subWindow.addEventListener ) { + subWindow.addEventListener( "unload", unloadHandler, false ); + + // Support: IE 9 - 10 only + } else if ( subWindow.attachEvent ) { + subWindow.attachEvent( "onunload", unloadHandler ); + } + } + + // Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only, + // Safari 4 - 5 only, Opera <=11.6 - 12.x only + // IE/Edge & older browsers don't support the :scope pseudo-class. + // Support: Safari 6.0 only + // Safari 6.0 supports :scope but it's an alias of :root there. + support.scope = assert( function( el ) { + docElem.appendChild( el ).appendChild( document.createElement( "div" ) ); + return typeof el.querySelectorAll !== "undefined" && + !el.querySelectorAll( ":scope fieldset div" ).length; + } ); + + /* Attributes + ---------------------------------------------------------------------- */ + + // Support: IE<8 + // Verify that getAttribute really returns attributes and not properties + // (excepting IE8 booleans) + support.attributes = assert( function( el ) { + el.className = "i"; + return !el.getAttribute( "className" ); + } ); + + /* getElement(s)By* + ---------------------------------------------------------------------- */ + + // Check if getElementsByTagName("*") returns only elements + support.getElementsByTagName = assert( function( el ) { + el.appendChild( document.createComment( "" ) ); + return !el.getElementsByTagName( "*" ).length; + } ); + + // Support: IE<9 + support.getElementsByClassName = rnative.test( document.getElementsByClassName ); + + // Support: IE<10 + // Check if getElementById returns elements by name + // The broken getElementById methods don't pick up programmatically-set names, + // so use a roundabout getElementsByName test + support.getById = assert( function( el ) { + docElem.appendChild( el ).id = expando; + return !document.getElementsByName || !document.getElementsByName( expando ).length; + } ); + + // ID filter and find + if ( support.getById ) { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + return elem.getAttribute( "id" ) === attrId; + }; + }; + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var elem = context.getElementById( id ); + return elem ? [ elem ] : []; + } + }; + } else { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + var node = typeof elem.getAttributeNode !== "undefined" && + elem.getAttributeNode( "id" ); + return node && node.value === attrId; + }; + }; + + // Support: IE 6 - 7 only + // getElementById is not reliable as a find shortcut + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var node, i, elems, + elem = context.getElementById( id ); + + if ( elem ) { + + // Verify the id attribute + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + + // Fall back on getElementsByName + elems = context.getElementsByName( id ); + i = 0; + while ( ( elem = elems[ i++ ] ) ) { + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + } + } + + return []; + } + }; + } + + // Tag + Expr.find[ "TAG" ] = support.getElementsByTagName ? + function( tag, context ) { + if ( typeof context.getElementsByTagName !== "undefined" ) { + return context.getElementsByTagName( tag ); + + // DocumentFragment nodes don't have gEBTN + } else if ( support.qsa ) { + return context.querySelectorAll( tag ); + } + } : + + function( tag, context ) { + var elem, + tmp = [], + i = 0, + + // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too + results = context.getElementsByTagName( tag ); + + // Filter out possible comments + if ( tag === "*" ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem.nodeType === 1 ) { + tmp.push( elem ); + } + } + + return tmp; + } + return results; + }; + + // Class + Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) { + if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { + return context.getElementsByClassName( className ); + } + }; + + /* QSA/matchesSelector + ---------------------------------------------------------------------- */ + + // QSA and matchesSelector support + + // matchesSelector(:active) reports false when true (IE9/Opera 11.5) + rbuggyMatches = []; + + // qSa(:focus) reports false when true (Chrome 21) + // We allow this because of a bug in IE8/9 that throws an error + // whenever `document.activeElement` is accessed on an iframe + // So, we allow :focus to pass through QSA all the time to avoid the IE error + // See https://bugs.jquery.com/ticket/13378 + rbuggyQSA = []; + + if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) { + + // Build QSA regex + // Regex strategy adopted from Diego Perini + assert( function( el ) { + + var input; + + // Select is set to empty string on purpose + // This is to test IE's treatment of not explicitly + // setting a boolean content attribute, + // since its presence should be enough + // https://bugs.jquery.com/ticket/12359 + docElem.appendChild( el ).innerHTML = "" + + ""; + + // Support: IE8, Opera 11-12.16 + // Nothing should be selected when empty strings follow ^= or $= or *= + // The test attribute must be unknown in Opera but "safe" for WinRT + // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section + if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) { + rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); + } + + // Support: IE8 + // Boolean attributes and "value" are not treated correctly + if ( !el.querySelectorAll( "[selected]" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); + } + + // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ + if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { + rbuggyQSA.push( "~=" ); + } + + // Support: IE 11+, Edge 15 - 18+ + // IE 11/Edge don't find elements on a `[name='']` query in some cases. + // Adding a temporary attribute to the document before the selection works + // around the issue. + // Interestingly, IE 10 & older don't seem to have the issue. + input = document.createElement( "input" ); + input.setAttribute( "name", "" ); + el.appendChild( input ); + if ( !el.querySelectorAll( "[name='']" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" + + whitespace + "*(?:''|\"\")" ); + } + + // Webkit/Opera - :checked should return selected option elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + // IE8 throws error here and will not see later tests + if ( !el.querySelectorAll( ":checked" ).length ) { + rbuggyQSA.push( ":checked" ); + } + + // Support: Safari 8+, iOS 8+ + // https://bugs.webkit.org/show_bug.cgi?id=136851 + // In-page `selector#id sibling-combinator selector` fails + if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { + rbuggyQSA.push( ".#.+[+~]" ); + } + + // Support: Firefox <=3.6 - 5 only + // Old Firefox doesn't throw on a badly-escaped identifier. + el.querySelectorAll( "\\\f" ); + rbuggyQSA.push( "[\\r\\n\\f]" ); + } ); + + assert( function( el ) { + el.innerHTML = "" + + ""; + + // Support: Windows 8 Native Apps + // The type and name attributes are restricted during .innerHTML assignment + var input = document.createElement( "input" ); + input.setAttribute( "type", "hidden" ); + el.appendChild( input ).setAttribute( "name", "D" ); + + // Support: IE8 + // Enforce case-sensitivity of name attribute + if ( el.querySelectorAll( "[name=d]" ).length ) { + rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); + } + + // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) + // IE8 throws error here and will not see later tests + if ( el.querySelectorAll( ":enabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: IE9-11+ + // IE's :disabled selector does not pick up the children of disabled fieldsets + docElem.appendChild( el ).disabled = true; + if ( el.querySelectorAll( ":disabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: Opera 10 - 11 only + // Opera 10-11 does not throw on post-comma invalid pseudos + el.querySelectorAll( "*,:x" ); + rbuggyQSA.push( ",.*:" ); + } ); + } + + if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches || + docElem.webkitMatchesSelector || + docElem.mozMatchesSelector || + docElem.oMatchesSelector || + docElem.msMatchesSelector ) ) ) ) { + + assert( function( el ) { + + // Check to see if it's possible to do matchesSelector + // on a disconnected node (IE 9) + support.disconnectedMatch = matches.call( el, "*" ); + + // This should fail with an exception + // Gecko does not error, returns false instead + matches.call( el, "[s!='']:x" ); + rbuggyMatches.push( "!=", pseudos ); + } ); + } + + rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) ); + rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) ); + + /* Contains + ---------------------------------------------------------------------- */ + hasCompare = rnative.test( docElem.compareDocumentPosition ); + + // Element contains another + // Purposefully self-exclusive + // As in, an element does not contain itself + contains = hasCompare || rnative.test( docElem.contains ) ? + function( a, b ) { + var adown = a.nodeType === 9 ? a.documentElement : a, + bup = b && b.parentNode; + return a === bup || !!( bup && bup.nodeType === 1 && ( + adown.contains ? + adown.contains( bup ) : + a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 + ) ); + } : + function( a, b ) { + if ( b ) { + while ( ( b = b.parentNode ) ) { + if ( b === a ) { + return true; + } + } + } + return false; + }; + + /* Sorting + ---------------------------------------------------------------------- */ + + // Document order sorting + sortOrder = hasCompare ? + function( a, b ) { + + // Flag for duplicate removal + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + // Sort on method existence if only one input has compareDocumentPosition + var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; + if ( compare ) { + return compare; + } + + // Calculate position if both inputs belong to the same document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ? + a.compareDocumentPosition( b ) : + + // Otherwise we know they are disconnected + 1; + + // Disconnected nodes + if ( compare & 1 || + ( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) { + + // Choose the first element that is related to our preferred document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( a == document || a.ownerDocument == preferredDoc && + contains( preferredDoc, a ) ) { + return -1; + } + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( b == document || b.ownerDocument == preferredDoc && + contains( preferredDoc, b ) ) { + return 1; + } + + // Maintain original order + return sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + } + + return compare & 4 ? -1 : 1; + } : + function( a, b ) { + + // Exit early if the nodes are identical + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + var cur, + i = 0, + aup = a.parentNode, + bup = b.parentNode, + ap = [ a ], + bp = [ b ]; + + // Parentless nodes are either documents or disconnected + if ( !aup || !bup ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + return a == document ? -1 : + b == document ? 1 : + /* eslint-enable eqeqeq */ + aup ? -1 : + bup ? 1 : + sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + + // If the nodes are siblings, we can do a quick check + } else if ( aup === bup ) { + return siblingCheck( a, b ); + } + + // Otherwise we need full lists of their ancestors for comparison + cur = a; + while ( ( cur = cur.parentNode ) ) { + ap.unshift( cur ); + } + cur = b; + while ( ( cur = cur.parentNode ) ) { + bp.unshift( cur ); + } + + // Walk down the tree looking for a discrepancy + while ( ap[ i ] === bp[ i ] ) { + i++; + } + + return i ? + + // Do a sibling check if the nodes have a common ancestor + siblingCheck( ap[ i ], bp[ i ] ) : + + // Otherwise nodes in our document sort first + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + ap[ i ] == preferredDoc ? -1 : + bp[ i ] == preferredDoc ? 1 : + /* eslint-enable eqeqeq */ + 0; + }; + + return document; +}; + +Sizzle.matches = function( expr, elements ) { + return Sizzle( expr, null, null, elements ); +}; + +Sizzle.matchesSelector = function( elem, expr ) { + setDocument( elem ); + + if ( support.matchesSelector && documentIsHTML && + !nonnativeSelectorCache[ expr + " " ] && + ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && + ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { + + try { + var ret = matches.call( elem, expr ); + + // IE 9's matchesSelector returns false on disconnected nodes + if ( ret || support.disconnectedMatch || + + // As well, disconnected nodes are said to be in a document + // fragment in IE 9 + elem.document && elem.document.nodeType !== 11 ) { + return ret; + } + } catch ( e ) { + nonnativeSelectorCache( expr, true ); + } + } + + return Sizzle( expr, document, null, [ elem ] ).length > 0; +}; + +Sizzle.contains = function( context, elem ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( context.ownerDocument || context ) != document ) { + setDocument( context ); + } + return contains( context, elem ); +}; + +Sizzle.attr = function( elem, name ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( elem.ownerDocument || elem ) != document ) { + setDocument( elem ); + } + + var fn = Expr.attrHandle[ name.toLowerCase() ], + + // Don't get fooled by Object.prototype properties (jQuery #13807) + val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? + fn( elem, name, !documentIsHTML ) : + undefined; + + return val !== undefined ? + val : + support.attributes || !documentIsHTML ? + elem.getAttribute( name ) : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; +}; + +Sizzle.escape = function( sel ) { + return ( sel + "" ).replace( rcssescape, fcssescape ); +}; + +Sizzle.error = function( msg ) { + throw new Error( "Syntax error, unrecognized expression: " + msg ); +}; + +/** + * Document sorting and removing duplicates + * @param {ArrayLike} results + */ +Sizzle.uniqueSort = function( results ) { + var elem, + duplicates = [], + j = 0, + i = 0; + + // Unless we *know* we can detect duplicates, assume their presence + hasDuplicate = !support.detectDuplicates; + sortInput = !support.sortStable && results.slice( 0 ); + results.sort( sortOrder ); + + if ( hasDuplicate ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem === results[ i ] ) { + j = duplicates.push( i ); + } + } + while ( j-- ) { + results.splice( duplicates[ j ], 1 ); + } + } + + // Clear input after sorting to release objects + // See https://github.com/jquery/sizzle/pull/225 + sortInput = null; + + return results; +}; + +/** + * Utility function for retrieving the text value of an array of DOM nodes + * @param {Array|Element} elem + */ +getText = Sizzle.getText = function( elem ) { + var node, + ret = "", + i = 0, + nodeType = elem.nodeType; + + if ( !nodeType ) { + + // If no nodeType, this is expected to be an array + while ( ( node = elem[ i++ ] ) ) { + + // Do not traverse comment nodes + ret += getText( node ); + } + } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { + + // Use textContent for elements + // innerText usage removed for consistency of new lines (jQuery #11153) + if ( typeof elem.textContent === "string" ) { + return elem.textContent; + } else { + + // Traverse its children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + ret += getText( elem ); + } + } + } else if ( nodeType === 3 || nodeType === 4 ) { + return elem.nodeValue; + } + + // Do not include comment or processing instruction nodes + + return ret; +}; + +Expr = Sizzle.selectors = { + + // Can be adjusted by the user + cacheLength: 50, + + createPseudo: markFunction, + + match: matchExpr, + + attrHandle: {}, + + find: {}, + + relative: { + ">": { dir: "parentNode", first: true }, + " ": { dir: "parentNode" }, + "+": { dir: "previousSibling", first: true }, + "~": { dir: "previousSibling" } + }, + + preFilter: { + "ATTR": function( match ) { + match[ 1 ] = match[ 1 ].replace( runescape, funescape ); + + // Move the given value to match[3] whether quoted or unquoted + match[ 3 ] = ( match[ 3 ] || match[ 4 ] || + match[ 5 ] || "" ).replace( runescape, funescape ); + + if ( match[ 2 ] === "~=" ) { + match[ 3 ] = " " + match[ 3 ] + " "; + } + + return match.slice( 0, 4 ); + }, + + "CHILD": function( match ) { + + /* matches from matchExpr["CHILD"] + 1 type (only|nth|...) + 2 what (child|of-type) + 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) + 4 xn-component of xn+y argument ([+-]?\d*n|) + 5 sign of xn-component + 6 x of xn-component + 7 sign of y-component + 8 y of y-component + */ + match[ 1 ] = match[ 1 ].toLowerCase(); + + if ( match[ 1 ].slice( 0, 3 ) === "nth" ) { + + // nth-* requires argument + if ( !match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + // numeric x and y parameters for Expr.filter.CHILD + // remember that false/true cast respectively to 0/1 + match[ 4 ] = +( match[ 4 ] ? + match[ 5 ] + ( match[ 6 ] || 1 ) : + 2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) ); + match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" ); + + // other types prohibit arguments + } else if ( match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + return match; + }, + + "PSEUDO": function( match ) { + var excess, + unquoted = !match[ 6 ] && match[ 2 ]; + + if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) { + return null; + } + + // Accept quoted arguments as-is + if ( match[ 3 ] ) { + match[ 2 ] = match[ 4 ] || match[ 5 ] || ""; + + // Strip excess characters from unquoted arguments + } else if ( unquoted && rpseudo.test( unquoted ) && + + // Get excess from tokenize (recursively) + ( excess = tokenize( unquoted, true ) ) && + + // advance to the next closing parenthesis + ( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) { + + // excess is a negative index + match[ 0 ] = match[ 0 ].slice( 0, excess ); + match[ 2 ] = unquoted.slice( 0, excess ); + } + + // Return only captures needed by the pseudo filter method (type and argument) + return match.slice( 0, 3 ); + } + }, + + filter: { + + "TAG": function( nodeNameSelector ) { + var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); + return nodeNameSelector === "*" ? + function() { + return true; + } : + function( elem ) { + return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; + }; + }, + + "CLASS": function( className ) { + var pattern = classCache[ className + " " ]; + + return pattern || + ( pattern = new RegExp( "(^|" + whitespace + + ")" + className + "(" + whitespace + "|$)" ) ) && classCache( + className, function( elem ) { + return pattern.test( + typeof elem.className === "string" && elem.className || + typeof elem.getAttribute !== "undefined" && + elem.getAttribute( "class" ) || + "" + ); + } ); + }, + + "ATTR": function( name, operator, check ) { + return function( elem ) { + var result = Sizzle.attr( elem, name ); + + if ( result == null ) { + return operator === "!="; + } + if ( !operator ) { + return true; + } + + result += ""; + + /* eslint-disable max-len */ + + return operator === "=" ? result === check : + operator === "!=" ? result !== check : + operator === "^=" ? check && result.indexOf( check ) === 0 : + operator === "*=" ? check && result.indexOf( check ) > -1 : + operator === "$=" ? check && result.slice( -check.length ) === check : + operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : + operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : + false; + /* eslint-enable max-len */ + + }; + }, + + "CHILD": function( type, what, _argument, first, last ) { + var simple = type.slice( 0, 3 ) !== "nth", + forward = type.slice( -4 ) !== "last", + ofType = what === "of-type"; + + return first === 1 && last === 0 ? + + // Shortcut for :nth-*(n) + function( elem ) { + return !!elem.parentNode; + } : + + function( elem, _context, xml ) { + var cache, uniqueCache, outerCache, node, nodeIndex, start, + dir = simple !== forward ? "nextSibling" : "previousSibling", + parent = elem.parentNode, + name = ofType && elem.nodeName.toLowerCase(), + useCache = !xml && !ofType, + diff = false; + + if ( parent ) { + + // :(first|last|only)-(child|of-type) + if ( simple ) { + while ( dir ) { + node = elem; + while ( ( node = node[ dir ] ) ) { + if ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) { + + return false; + } + } + + // Reverse direction for :only-* (if we haven't yet done so) + start = dir = type === "only" && !start && "nextSibling"; + } + return true; + } + + start = [ forward ? parent.firstChild : parent.lastChild ]; + + // non-xml :nth-child(...) stores cache data on `parent` + if ( forward && useCache ) { + + // Seek `elem` from a previously-cached index + + // ...in a gzip-friendly way + node = parent; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex && cache[ 2 ]; + node = nodeIndex && parent.childNodes[ nodeIndex ]; + + while ( ( node = ++nodeIndex && node && node[ dir ] || + + // Fallback to seeking `elem` from the start + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + // When found, cache indexes on `parent` and break + if ( node.nodeType === 1 && ++diff && node === elem ) { + uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; + break; + } + } + + } else { + + // Use previously-cached element index if available + if ( useCache ) { + + // ...in a gzip-friendly way + node = elem; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex; + } + + // xml :nth-child(...) + // or :nth-last-child(...) or :nth(-last)?-of-type(...) + if ( diff === false ) { + + // Use the same loop as above to seek `elem` from the start + while ( ( node = ++nodeIndex && node && node[ dir ] || + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + if ( ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) && + ++diff ) { + + // Cache the index of each encountered element + if ( useCache ) { + outerCache = node[ expando ] || + ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + uniqueCache[ type ] = [ dirruns, diff ]; + } + + if ( node === elem ) { + break; + } + } + } + } + } + + // Incorporate the offset, then check against cycle size + diff -= last; + return diff === first || ( diff % first === 0 && diff / first >= 0 ); + } + }; + }, + + "PSEUDO": function( pseudo, argument ) { + + // pseudo-class names are case-insensitive + // http://www.w3.org/TR/selectors/#pseudo-classes + // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters + // Remember that setFilters inherits from pseudos + var args, + fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || + Sizzle.error( "unsupported pseudo: " + pseudo ); + + // The user may use createPseudo to indicate that + // arguments are needed to create the filter function + // just as Sizzle does + if ( fn[ expando ] ) { + return fn( argument ); + } + + // But maintain support for old signatures + if ( fn.length > 1 ) { + args = [ pseudo, pseudo, "", argument ]; + return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? + markFunction( function( seed, matches ) { + var idx, + matched = fn( seed, argument ), + i = matched.length; + while ( i-- ) { + idx = indexOf( seed, matched[ i ] ); + seed[ idx ] = !( matches[ idx ] = matched[ i ] ); + } + } ) : + function( elem ) { + return fn( elem, 0, args ); + }; + } + + return fn; + } + }, + + pseudos: { + + // Potentially complex pseudos + "not": markFunction( function( selector ) { + + // Trim the selector passed to compile + // to avoid treating leading and trailing + // spaces as combinators + var input = [], + results = [], + matcher = compile( selector.replace( rtrim, "$1" ) ); + + return matcher[ expando ] ? + markFunction( function( seed, matches, _context, xml ) { + var elem, + unmatched = matcher( seed, null, xml, [] ), + i = seed.length; + + // Match elements unmatched by `matcher` + while ( i-- ) { + if ( ( elem = unmatched[ i ] ) ) { + seed[ i ] = !( matches[ i ] = elem ); + } + } + } ) : + function( elem, _context, xml ) { + input[ 0 ] = elem; + matcher( input, null, xml, results ); + + // Don't keep the element (issue #299) + input[ 0 ] = null; + return !results.pop(); + }; + } ), + + "has": markFunction( function( selector ) { + return function( elem ) { + return Sizzle( selector, elem ).length > 0; + }; + } ), + + "contains": markFunction( function( text ) { + text = text.replace( runescape, funescape ); + return function( elem ) { + return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1; + }; + } ), + + // "Whether an element is represented by a :lang() selector + // is based solely on the element's language value + // being equal to the identifier C, + // or beginning with the identifier C immediately followed by "-". + // The matching of C against the element's language value is performed case-insensitively. + // The identifier C does not have to be a valid language name." + // http://www.w3.org/TR/selectors/#lang-pseudo + "lang": markFunction( function( lang ) { + + // lang value must be a valid identifier + if ( !ridentifier.test( lang || "" ) ) { + Sizzle.error( "unsupported lang: " + lang ); + } + lang = lang.replace( runescape, funescape ).toLowerCase(); + return function( elem ) { + var elemLang; + do { + if ( ( elemLang = documentIsHTML ? + elem.lang : + elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) { + + elemLang = elemLang.toLowerCase(); + return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; + } + } while ( ( elem = elem.parentNode ) && elem.nodeType === 1 ); + return false; + }; + } ), + + // Miscellaneous + "target": function( elem ) { + var hash = window.location && window.location.hash; + return hash && hash.slice( 1 ) === elem.id; + }, + + "root": function( elem ) { + return elem === docElem; + }, + + "focus": function( elem ) { + return elem === document.activeElement && + ( !document.hasFocus || document.hasFocus() ) && + !!( elem.type || elem.href || ~elem.tabIndex ); + }, + + // Boolean properties + "enabled": createDisabledPseudo( false ), + "disabled": createDisabledPseudo( true ), + + "checked": function( elem ) { + + // In CSS3, :checked should return both checked and selected elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + var nodeName = elem.nodeName.toLowerCase(); + return ( nodeName === "input" && !!elem.checked ) || + ( nodeName === "option" && !!elem.selected ); + }, + + "selected": function( elem ) { + + // Accessing this property makes selected-by-default + // options in Safari work properly + if ( elem.parentNode ) { + // eslint-disable-next-line no-unused-expressions + elem.parentNode.selectedIndex; + } + + return elem.selected === true; + }, + + // Contents + "empty": function( elem ) { + + // http://www.w3.org/TR/selectors/#empty-pseudo + // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), + // but not by others (comment: 8; processing instruction: 7; etc.) + // nodeType < 6 works because attributes (2) do not appear as children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + if ( elem.nodeType < 6 ) { + return false; + } + } + return true; + }, + + "parent": function( elem ) { + return !Expr.pseudos[ "empty" ]( elem ); + }, + + // Element/input types + "header": function( elem ) { + return rheader.test( elem.nodeName ); + }, + + "input": function( elem ) { + return rinputs.test( elem.nodeName ); + }, + + "button": function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === "button" || name === "button"; + }, + + "text": function( elem ) { + var attr; + return elem.nodeName.toLowerCase() === "input" && + elem.type === "text" && + + // Support: IE<8 + // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" + ( ( attr = elem.getAttribute( "type" ) ) == null || + attr.toLowerCase() === "text" ); + }, + + // Position-in-collection + "first": createPositionalPseudo( function() { + return [ 0 ]; + } ), + + "last": createPositionalPseudo( function( _matchIndexes, length ) { + return [ length - 1 ]; + } ), + + "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) { + return [ argument < 0 ? argument + length : argument ]; + } ), + + "even": createPositionalPseudo( function( matchIndexes, length ) { + var i = 0; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "odd": createPositionalPseudo( function( matchIndexes, length ) { + var i = 1; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "lt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? + argument + length : + argument > length ? + length : + argument; + for ( ; --i >= 0; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "gt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? argument + length : argument; + for ( ; ++i < length; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ) + } +}; + +Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ]; + +// Add button/input type pseudos +for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { + Expr.pseudos[ i ] = createInputPseudo( i ); +} +for ( i in { submit: true, reset: true } ) { + Expr.pseudos[ i ] = createButtonPseudo( i ); +} + +// Easy API for creating new setFilters +function setFilters() {} +setFilters.prototype = Expr.filters = Expr.pseudos; +Expr.setFilters = new setFilters(); + +tokenize = Sizzle.tokenize = function( selector, parseOnly ) { + var matched, match, tokens, type, + soFar, groups, preFilters, + cached = tokenCache[ selector + " " ]; + + if ( cached ) { + return parseOnly ? 0 : cached.slice( 0 ); + } + + soFar = selector; + groups = []; + preFilters = Expr.preFilter; + + while ( soFar ) { + + // Comma and first run + if ( !matched || ( match = rcomma.exec( soFar ) ) ) { + if ( match ) { + + // Don't consume trailing commas as valid + soFar = soFar.slice( match[ 0 ].length ) || soFar; + } + groups.push( ( tokens = [] ) ); + } + + matched = false; + + // Combinators + if ( ( match = rcombinators.exec( soFar ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + + // Cast descendant combinators to space + type: match[ 0 ].replace( rtrim, " " ) + } ); + soFar = soFar.slice( matched.length ); + } + + // Filters + for ( type in Expr.filter ) { + if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] || + ( match = preFilters[ type ]( match ) ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + type: type, + matches: match + } ); + soFar = soFar.slice( matched.length ); + } + } + + if ( !matched ) { + break; + } + } + + // Return the length of the invalid excess + // if we're just parsing + // Otherwise, throw an error or return tokens + return parseOnly ? + soFar.length : + soFar ? + Sizzle.error( selector ) : + + // Cache the tokens + tokenCache( selector, groups ).slice( 0 ); +}; + +function toSelector( tokens ) { + var i = 0, + len = tokens.length, + selector = ""; + for ( ; i < len; i++ ) { + selector += tokens[ i ].value; + } + return selector; +} + +function addCombinator( matcher, combinator, base ) { + var dir = combinator.dir, + skip = combinator.next, + key = skip || dir, + checkNonElements = base && key === "parentNode", + doneName = done++; + + return combinator.first ? + + // Check against closest ancestor/preceding element + function( elem, context, xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + return matcher( elem, context, xml ); + } + } + return false; + } : + + // Check against all ancestor/preceding elements + function( elem, context, xml ) { + var oldCache, uniqueCache, outerCache, + newCache = [ dirruns, doneName ]; + + // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching + if ( xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + if ( matcher( elem, context, xml ) ) { + return true; + } + } + } + } else { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + outerCache = elem[ expando ] || ( elem[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ elem.uniqueID ] || + ( outerCache[ elem.uniqueID ] = {} ); + + if ( skip && skip === elem.nodeName.toLowerCase() ) { + elem = elem[ dir ] || elem; + } else if ( ( oldCache = uniqueCache[ key ] ) && + oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { + + // Assign to newCache so results back-propagate to previous elements + return ( newCache[ 2 ] = oldCache[ 2 ] ); + } else { + + // Reuse newcache so results back-propagate to previous elements + uniqueCache[ key ] = newCache; + + // A match means we're done; a fail means we have to keep checking + if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) { + return true; + } + } + } + } + } + return false; + }; +} + +function elementMatcher( matchers ) { + return matchers.length > 1 ? + function( elem, context, xml ) { + var i = matchers.length; + while ( i-- ) { + if ( !matchers[ i ]( elem, context, xml ) ) { + return false; + } + } + return true; + } : + matchers[ 0 ]; +} + +function multipleContexts( selector, contexts, results ) { + var i = 0, + len = contexts.length; + for ( ; i < len; i++ ) { + Sizzle( selector, contexts[ i ], results ); + } + return results; +} + +function condense( unmatched, map, filter, context, xml ) { + var elem, + newUnmatched = [], + i = 0, + len = unmatched.length, + mapped = map != null; + + for ( ; i < len; i++ ) { + if ( ( elem = unmatched[ i ] ) ) { + if ( !filter || filter( elem, context, xml ) ) { + newUnmatched.push( elem ); + if ( mapped ) { + map.push( i ); + } + } + } + } + + return newUnmatched; +} + +function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { + if ( postFilter && !postFilter[ expando ] ) { + postFilter = setMatcher( postFilter ); + } + if ( postFinder && !postFinder[ expando ] ) { + postFinder = setMatcher( postFinder, postSelector ); + } + return markFunction( function( seed, results, context, xml ) { + var temp, i, elem, + preMap = [], + postMap = [], + preexisting = results.length, + + // Get initial elements from seed or context + elems = seed || multipleContexts( + selector || "*", + context.nodeType ? [ context ] : context, + [] + ), + + // Prefilter to get matcher input, preserving a map for seed-results synchronization + matcherIn = preFilter && ( seed || !selector ) ? + condense( elems, preMap, preFilter, context, xml ) : + elems, + + matcherOut = matcher ? + + // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, + postFinder || ( seed ? preFilter : preexisting || postFilter ) ? + + // ...intermediate processing is necessary + [] : + + // ...otherwise use results directly + results : + matcherIn; + + // Find primary matches + if ( matcher ) { + matcher( matcherIn, matcherOut, context, xml ); + } + + // Apply postFilter + if ( postFilter ) { + temp = condense( matcherOut, postMap ); + postFilter( temp, [], context, xml ); + + // Un-match failing elements by moving them back to matcherIn + i = temp.length; + while ( i-- ) { + if ( ( elem = temp[ i ] ) ) { + matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem ); + } + } + } + + if ( seed ) { + if ( postFinder || preFilter ) { + if ( postFinder ) { + + // Get the final matcherOut by condensing this intermediate into postFinder contexts + temp = []; + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) ) { + + // Restore matcherIn since elem is not yet a final match + temp.push( ( matcherIn[ i ] = elem ) ); + } + } + postFinder( null, ( matcherOut = [] ), temp, xml ); + } + + // Move matched elements from seed to results to keep them synchronized + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) && + ( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) { + + seed[ temp ] = !( results[ temp ] = elem ); + } + } + } + + // Add elements to results, through postFinder if defined + } else { + matcherOut = condense( + matcherOut === results ? + matcherOut.splice( preexisting, matcherOut.length ) : + matcherOut + ); + if ( postFinder ) { + postFinder( null, results, matcherOut, xml ); + } else { + push.apply( results, matcherOut ); + } + } + } ); +} + +function matcherFromTokens( tokens ) { + var checkContext, matcher, j, + len = tokens.length, + leadingRelative = Expr.relative[ tokens[ 0 ].type ], + implicitRelative = leadingRelative || Expr.relative[ " " ], + i = leadingRelative ? 1 : 0, + + // The foundational matcher ensures that elements are reachable from top-level context(s) + matchContext = addCombinator( function( elem ) { + return elem === checkContext; + }, implicitRelative, true ), + matchAnyContext = addCombinator( function( elem ) { + return indexOf( checkContext, elem ) > -1; + }, implicitRelative, true ), + matchers = [ function( elem, context, xml ) { + var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( + ( checkContext = context ).nodeType ? + matchContext( elem, context, xml ) : + matchAnyContext( elem, context, xml ) ); + + // Avoid hanging onto element (issue #299) + checkContext = null; + return ret; + } ]; + + for ( ; i < len; i++ ) { + if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) { + matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ]; + } else { + matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches ); + + // Return special upon seeing a positional matcher + if ( matcher[ expando ] ) { + + // Find the next relative operator (if any) for proper handling + j = ++i; + for ( ; j < len; j++ ) { + if ( Expr.relative[ tokens[ j ].type ] ) { + break; + } + } + return setMatcher( + i > 1 && elementMatcher( matchers ), + i > 1 && toSelector( + + // If the preceding token was a descendant combinator, insert an implicit any-element `*` + tokens + .slice( 0, i - 1 ) + .concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } ) + ).replace( rtrim, "$1" ), + matcher, + i < j && matcherFromTokens( tokens.slice( i, j ) ), + j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ), + j < len && toSelector( tokens ) + ); + } + matchers.push( matcher ); + } + } + + return elementMatcher( matchers ); +} + +function matcherFromGroupMatchers( elementMatchers, setMatchers ) { + var bySet = setMatchers.length > 0, + byElement = elementMatchers.length > 0, + superMatcher = function( seed, context, xml, results, outermost ) { + var elem, j, matcher, + matchedCount = 0, + i = "0", + unmatched = seed && [], + setMatched = [], + contextBackup = outermostContext, + + // We must always have either seed elements or outermost context + elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ), + + // Use integer dirruns iff this is the outermost matcher + dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ), + len = elems.length; + + if ( outermost ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + outermostContext = context == document || context || outermost; + } + + // Add elements passing elementMatchers directly to results + // Support: IE<9, Safari + // Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id + for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) { + if ( byElement && elem ) { + j = 0; + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( !context && elem.ownerDocument != document ) { + setDocument( elem ); + xml = !documentIsHTML; + } + while ( ( matcher = elementMatchers[ j++ ] ) ) { + if ( matcher( elem, context || document, xml ) ) { + results.push( elem ); + break; + } + } + if ( outermost ) { + dirruns = dirrunsUnique; + } + } + + // Track unmatched elements for set filters + if ( bySet ) { + + // They will have gone through all possible matchers + if ( ( elem = !matcher && elem ) ) { + matchedCount--; + } + + // Lengthen the array for every element, matched or not + if ( seed ) { + unmatched.push( elem ); + } + } + } + + // `i` is now the count of elements visited above, and adding it to `matchedCount` + // makes the latter nonnegative. + matchedCount += i; + + // Apply set filters to unmatched elements + // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` + // equals `i`), unless we didn't visit _any_ elements in the above loop because we have + // no element matchers and no seed. + // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that + // case, which will result in a "00" `matchedCount` that differs from `i` but is also + // numerically zero. + if ( bySet && i !== matchedCount ) { + j = 0; + while ( ( matcher = setMatchers[ j++ ] ) ) { + matcher( unmatched, setMatched, context, xml ); + } + + if ( seed ) { + + // Reintegrate element matches to eliminate the need for sorting + if ( matchedCount > 0 ) { + while ( i-- ) { + if ( !( unmatched[ i ] || setMatched[ i ] ) ) { + setMatched[ i ] = pop.call( results ); + } + } + } + + // Discard index placeholder values to get only actual matches + setMatched = condense( setMatched ); + } + + // Add matches to results + push.apply( results, setMatched ); + + // Seedless set matches succeeding multiple successful matchers stipulate sorting + if ( outermost && !seed && setMatched.length > 0 && + ( matchedCount + setMatchers.length ) > 1 ) { + + Sizzle.uniqueSort( results ); + } + } + + // Override manipulation of globals by nested matchers + if ( outermost ) { + dirruns = dirrunsUnique; + outermostContext = contextBackup; + } + + return unmatched; + }; + + return bySet ? + markFunction( superMatcher ) : + superMatcher; +} + +compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { + var i, + setMatchers = [], + elementMatchers = [], + cached = compilerCache[ selector + " " ]; + + if ( !cached ) { + + // Generate a function of recursive functions that can be used to check each element + if ( !match ) { + match = tokenize( selector ); + } + i = match.length; + while ( i-- ) { + cached = matcherFromTokens( match[ i ] ); + if ( cached[ expando ] ) { + setMatchers.push( cached ); + } else { + elementMatchers.push( cached ); + } + } + + // Cache the compiled function + cached = compilerCache( + selector, + matcherFromGroupMatchers( elementMatchers, setMatchers ) + ); + + // Save selector and tokenization + cached.selector = selector; + } + return cached; +}; + +/** + * A low-level selection function that works with Sizzle's compiled + * selector functions + * @param {String|Function} selector A selector or a pre-compiled + * selector function built with Sizzle.compile + * @param {Element} context + * @param {Array} [results] + * @param {Array} [seed] A set of elements to match against + */ +select = Sizzle.select = function( selector, context, results, seed ) { + var i, tokens, token, type, find, + compiled = typeof selector === "function" && selector, + match = !seed && tokenize( ( selector = compiled.selector || selector ) ); + + results = results || []; + + // Try to minimize operations if there is only one selector in the list and no seed + // (the latter of which guarantees us context) + if ( match.length === 1 ) { + + // Reduce context if the leading compound selector is an ID + tokens = match[ 0 ] = match[ 0 ].slice( 0 ); + if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" && + context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) { + + context = ( Expr.find[ "ID" ]( token.matches[ 0 ] + .replace( runescape, funescape ), context ) || [] )[ 0 ]; + if ( !context ) { + return results; + + // Precompiled matchers will still verify ancestry, so step up a level + } else if ( compiled ) { + context = context.parentNode; + } + + selector = selector.slice( tokens.shift().value.length ); + } + + // Fetch a seed set for right-to-left matching + i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length; + while ( i-- ) { + token = tokens[ i ]; + + // Abort if we hit a combinator + if ( Expr.relative[ ( type = token.type ) ] ) { + break; + } + if ( ( find = Expr.find[ type ] ) ) { + + // Search, expanding context for leading sibling combinators + if ( ( seed = find( + token.matches[ 0 ].replace( runescape, funescape ), + rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) || + context + ) ) ) { + + // If seed is empty or no tokens remain, we can return early + tokens.splice( i, 1 ); + selector = seed.length && toSelector( tokens ); + if ( !selector ) { + push.apply( results, seed ); + return results; + } + + break; + } + } + } + } + + // Compile and execute a filtering function if one is not provided + // Provide `match` to avoid retokenization if we modified the selector above + ( compiled || compile( selector, match ) )( + seed, + context, + !documentIsHTML, + results, + !context || rsibling.test( selector ) && testContext( context.parentNode ) || context + ); + return results; +}; + +// One-time assignments + +// Sort stability +support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando; + +// Support: Chrome 14-35+ +// Always assume duplicates if they aren't passed to the comparison function +support.detectDuplicates = !!hasDuplicate; + +// Initialize against the default document +setDocument(); + +// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) +// Detached nodes confoundingly follow *each other* +support.sortDetached = assert( function( el ) { + + // Should return 1, but returns 4 (following) + return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1; +} ); + +// Support: IE<8 +// Prevent attribute/property "interpolation" +// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx +if ( !assert( function( el ) { + el.innerHTML = ""; + return el.firstChild.getAttribute( "href" ) === "#"; +} ) ) { + addHandle( "type|href|height|width", function( elem, name, isXML ) { + if ( !isXML ) { + return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); + } + } ); +} + +// Support: IE<9 +// Use defaultValue in place of getAttribute("value") +if ( !support.attributes || !assert( function( el ) { + el.innerHTML = ""; + el.firstChild.setAttribute( "value", "" ); + return el.firstChild.getAttribute( "value" ) === ""; +} ) ) { + addHandle( "value", function( elem, _name, isXML ) { + if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { + return elem.defaultValue; + } + } ); +} + +// Support: IE<9 +// Use getAttributeNode to fetch booleans when getAttribute lies +if ( !assert( function( el ) { + return el.getAttribute( "disabled" ) == null; +} ) ) { + addHandle( booleans, function( elem, name, isXML ) { + var val; + if ( !isXML ) { + return elem[ name ] === true ? name.toLowerCase() : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; + } + } ); +} + +return Sizzle; + +} )( window ); + + + +jQuery.find = Sizzle; +jQuery.expr = Sizzle.selectors; + +// Deprecated +jQuery.expr[ ":" ] = jQuery.expr.pseudos; +jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; +jQuery.text = Sizzle.getText; +jQuery.isXMLDoc = Sizzle.isXML; +jQuery.contains = Sizzle.contains; +jQuery.escapeSelector = Sizzle.escape; + + + + +var dir = function( elem, dir, until ) { + var matched = [], + truncate = until !== undefined; + + while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { + if ( elem.nodeType === 1 ) { + if ( truncate && jQuery( elem ).is( until ) ) { + break; + } + matched.push( elem ); + } + } + return matched; +}; + + +var siblings = function( n, elem ) { + var matched = []; + + for ( ; n; n = n.nextSibling ) { + if ( n.nodeType === 1 && n !== elem ) { + matched.push( n ); + } + } + + return matched; +}; + + +var rneedsContext = jQuery.expr.match.needsContext; + + + +function nodeName( elem, name ) { + + return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); + +}; +var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); + + + +// Implement the identical functionality for filter and not +function winnow( elements, qualifier, not ) { + if ( isFunction( qualifier ) ) { + return jQuery.grep( elements, function( elem, i ) { + return !!qualifier.call( elem, i, elem ) !== not; + } ); + } + + // Single element + if ( qualifier.nodeType ) { + return jQuery.grep( elements, function( elem ) { + return ( elem === qualifier ) !== not; + } ); + } + + // Arraylike of elements (jQuery, arguments, Array) + if ( typeof qualifier !== "string" ) { + return jQuery.grep( elements, function( elem ) { + return ( indexOf.call( qualifier, elem ) > -1 ) !== not; + } ); + } + + // Filtered directly for both simple and complex selectors + return jQuery.filter( qualifier, elements, not ); +} + +jQuery.filter = function( expr, elems, not ) { + var elem = elems[ 0 ]; + + if ( not ) { + expr = ":not(" + expr + ")"; + } + + if ( elems.length === 1 && elem.nodeType === 1 ) { + return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; + } + + return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { + return elem.nodeType === 1; + } ) ); +}; + +jQuery.fn.extend( { + find: function( selector ) { + var i, ret, + len = this.length, + self = this; + + if ( typeof selector !== "string" ) { + return this.pushStack( jQuery( selector ).filter( function() { + for ( i = 0; i < len; i++ ) { + if ( jQuery.contains( self[ i ], this ) ) { + return true; + } + } + } ) ); + } + + ret = this.pushStack( [] ); + + for ( i = 0; i < len; i++ ) { + jQuery.find( selector, self[ i ], ret ); + } + + return len > 1 ? jQuery.uniqueSort( ret ) : ret; + }, + filter: function( selector ) { + return this.pushStack( winnow( this, selector || [], false ) ); + }, + not: function( selector ) { + return this.pushStack( winnow( this, selector || [], true ) ); + }, + is: function( selector ) { + return !!winnow( + this, + + // If this is a positional/relative selector, check membership in the returned set + // so $("p:first").is("p:last") won't return true for a doc with two "p". + typeof selector === "string" && rneedsContext.test( selector ) ? + jQuery( selector ) : + selector || [], + false + ).length; + } +} ); + + +// Initialize a jQuery object + + +// A central reference to the root jQuery(document) +var rootjQuery, + + // A simple way to check for HTML strings + // Prioritize #id over to avoid XSS via location.hash (#9521) + // Strict HTML recognition (#11290: must start with <) + // Shortcut simple #id case for speed + rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, + + init = jQuery.fn.init = function( selector, context, root ) { + var match, elem; + + // HANDLE: $(""), $(null), $(undefined), $(false) + if ( !selector ) { + return this; + } + + // Method init() accepts an alternate rootjQuery + // so migrate can support jQuery.sub (gh-2101) + root = root || rootjQuery; + + // Handle HTML strings + if ( typeof selector === "string" ) { + if ( selector[ 0 ] === "<" && + selector[ selector.length - 1 ] === ">" && + selector.length >= 3 ) { + + // Assume that strings that start and end with <> are HTML and skip the regex check + match = [ null, selector, null ]; + + } else { + match = rquickExpr.exec( selector ); + } + + // Match html or make sure no context is specified for #id + if ( match && ( match[ 1 ] || !context ) ) { + + // HANDLE: $(html) -> $(array) + if ( match[ 1 ] ) { + context = context instanceof jQuery ? context[ 0 ] : context; + + // Option to run scripts is true for back-compat + // Intentionally let the error be thrown if parseHTML is not present + jQuery.merge( this, jQuery.parseHTML( + match[ 1 ], + context && context.nodeType ? context.ownerDocument || context : document, + true + ) ); + + // HANDLE: $(html, props) + if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { + for ( match in context ) { + + // Properties of context are called as methods if possible + if ( isFunction( this[ match ] ) ) { + this[ match ]( context[ match ] ); + + // ...and otherwise set as attributes + } else { + this.attr( match, context[ match ] ); + } + } + } + + return this; + + // HANDLE: $(#id) + } else { + elem = document.getElementById( match[ 2 ] ); + + if ( elem ) { + + // Inject the element directly into the jQuery object + this[ 0 ] = elem; + this.length = 1; + } + return this; + } + + // HANDLE: $(expr, $(...)) + } else if ( !context || context.jquery ) { + return ( context || root ).find( selector ); + + // HANDLE: $(expr, context) + // (which is just equivalent to: $(context).find(expr) + } else { + return this.constructor( context ).find( selector ); + } + + // HANDLE: $(DOMElement) + } else if ( selector.nodeType ) { + this[ 0 ] = selector; + this.length = 1; + return this; + + // HANDLE: $(function) + // Shortcut for document ready + } else if ( isFunction( selector ) ) { + return root.ready !== undefined ? + root.ready( selector ) : + + // Execute immediately if ready is not present + selector( jQuery ); + } + + return jQuery.makeArray( selector, this ); + }; + +// Give the init function the jQuery prototype for later instantiation +init.prototype = jQuery.fn; + +// Initialize central reference +rootjQuery = jQuery( document ); + + +var rparentsprev = /^(?:parents|prev(?:Until|All))/, + + // Methods guaranteed to produce a unique set when starting from a unique set + guaranteedUnique = { + children: true, + contents: true, + next: true, + prev: true + }; + +jQuery.fn.extend( { + has: function( target ) { + var targets = jQuery( target, this ), + l = targets.length; + + return this.filter( function() { + var i = 0; + for ( ; i < l; i++ ) { + if ( jQuery.contains( this, targets[ i ] ) ) { + return true; + } + } + } ); + }, + + closest: function( selectors, context ) { + var cur, + i = 0, + l = this.length, + matched = [], + targets = typeof selectors !== "string" && jQuery( selectors ); + + // Positional selectors never match, since there's no _selection_ context + if ( !rneedsContext.test( selectors ) ) { + for ( ; i < l; i++ ) { + for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { + + // Always skip document fragments + if ( cur.nodeType < 11 && ( targets ? + targets.index( cur ) > -1 : + + // Don't pass non-elements to Sizzle + cur.nodeType === 1 && + jQuery.find.matchesSelector( cur, selectors ) ) ) { + + matched.push( cur ); + break; + } + } + } + } + + return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); + }, + + // Determine the position of an element within the set + index: function( elem ) { + + // No argument, return index in parent + if ( !elem ) { + return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; + } + + // Index in selector + if ( typeof elem === "string" ) { + return indexOf.call( jQuery( elem ), this[ 0 ] ); + } + + // Locate the position of the desired element + return indexOf.call( this, + + // If it receives a jQuery object, the first element is used + elem.jquery ? elem[ 0 ] : elem + ); + }, + + add: function( selector, context ) { + return this.pushStack( + jQuery.uniqueSort( + jQuery.merge( this.get(), jQuery( selector, context ) ) + ) + ); + }, + + addBack: function( selector ) { + return this.add( selector == null ? + this.prevObject : this.prevObject.filter( selector ) + ); + } +} ); + +function sibling( cur, dir ) { + while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} + return cur; +} + +jQuery.each( { + parent: function( elem ) { + var parent = elem.parentNode; + return parent && parent.nodeType !== 11 ? parent : null; + }, + parents: function( elem ) { + return dir( elem, "parentNode" ); + }, + parentsUntil: function( elem, _i, until ) { + return dir( elem, "parentNode", until ); + }, + next: function( elem ) { + return sibling( elem, "nextSibling" ); + }, + prev: function( elem ) { + return sibling( elem, "previousSibling" ); + }, + nextAll: function( elem ) { + return dir( elem, "nextSibling" ); + }, + prevAll: function( elem ) { + return dir( elem, "previousSibling" ); + }, + nextUntil: function( elem, _i, until ) { + return dir( elem, "nextSibling", until ); + }, + prevUntil: function( elem, _i, until ) { + return dir( elem, "previousSibling", until ); + }, + siblings: function( elem ) { + return siblings( ( elem.parentNode || {} ).firstChild, elem ); + }, + children: function( elem ) { + return siblings( elem.firstChild ); + }, + contents: function( elem ) { + if ( elem.contentDocument != null && + + // Support: IE 11+ + // elements with no `data` attribute has an object + // `contentDocument` with a `null` prototype. + getProto( elem.contentDocument ) ) { + + return elem.contentDocument; + } + + // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only + // Treat the template element as a regular one in browsers that + // don't support it. + if ( nodeName( elem, "template" ) ) { + elem = elem.content || elem; + } + + return jQuery.merge( [], elem.childNodes ); + } +}, function( name, fn ) { + jQuery.fn[ name ] = function( until, selector ) { + var matched = jQuery.map( this, fn, until ); + + if ( name.slice( -5 ) !== "Until" ) { + selector = until; + } + + if ( selector && typeof selector === "string" ) { + matched = jQuery.filter( selector, matched ); + } + + if ( this.length > 1 ) { + + // Remove duplicates + if ( !guaranteedUnique[ name ] ) { + jQuery.uniqueSort( matched ); + } + + // Reverse order for parents* and prev-derivatives + if ( rparentsprev.test( name ) ) { + matched.reverse(); + } + } + + return this.pushStack( matched ); + }; +} ); +var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); + + + +// Convert String-formatted options into Object-formatted ones +function createOptions( options ) { + var object = {}; + jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { + object[ flag ] = true; + } ); + return object; +} + +/* + * Create a callback list using the following parameters: + * + * options: an optional list of space-separated options that will change how + * the callback list behaves or a more traditional option object + * + * By default a callback list will act like an event callback list and can be + * "fired" multiple times. + * + * Possible options: + * + * once: will ensure the callback list can only be fired once (like a Deferred) + * + * memory: will keep track of previous values and will call any callback added + * after the list has been fired right away with the latest "memorized" + * values (like a Deferred) + * + * unique: will ensure a callback can only be added once (no duplicate in the list) + * + * stopOnFalse: interrupt callings when a callback returns false + * + */ +jQuery.Callbacks = function( options ) { + + // Convert options from String-formatted to Object-formatted if needed + // (we check in cache first) + options = typeof options === "string" ? + createOptions( options ) : + jQuery.extend( {}, options ); + + var // Flag to know if list is currently firing + firing, + + // Last fire value for non-forgettable lists + memory, + + // Flag to know if list was already fired + fired, + + // Flag to prevent firing + locked, + + // Actual callback list + list = [], + + // Queue of execution data for repeatable lists + queue = [], + + // Index of currently firing callback (modified by add/remove as needed) + firingIndex = -1, + + // Fire callbacks + fire = function() { + + // Enforce single-firing + locked = locked || options.once; + + // Execute callbacks for all pending executions, + // respecting firingIndex overrides and runtime changes + fired = firing = true; + for ( ; queue.length; firingIndex = -1 ) { + memory = queue.shift(); + while ( ++firingIndex < list.length ) { + + // Run callback and check for early termination + if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && + options.stopOnFalse ) { + + // Jump to end and forget the data so .add doesn't re-fire + firingIndex = list.length; + memory = false; + } + } + } + + // Forget the data if we're done with it + if ( !options.memory ) { + memory = false; + } + + firing = false; + + // Clean up if we're done firing for good + if ( locked ) { + + // Keep an empty list if we have data for future add calls + if ( memory ) { + list = []; + + // Otherwise, this object is spent + } else { + list = ""; + } + } + }, + + // Actual Callbacks object + self = { + + // Add a callback or a collection of callbacks to the list + add: function() { + if ( list ) { + + // If we have memory from a past run, we should fire after adding + if ( memory && !firing ) { + firingIndex = list.length - 1; + queue.push( memory ); + } + + ( function add( args ) { + jQuery.each( args, function( _, arg ) { + if ( isFunction( arg ) ) { + if ( !options.unique || !self.has( arg ) ) { + list.push( arg ); + } + } else if ( arg && arg.length && toType( arg ) !== "string" ) { + + // Inspect recursively + add( arg ); + } + } ); + } )( arguments ); + + if ( memory && !firing ) { + fire(); + } + } + return this; + }, + + // Remove a callback from the list + remove: function() { + jQuery.each( arguments, function( _, arg ) { + var index; + while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { + list.splice( index, 1 ); + + // Handle firing indexes + if ( index <= firingIndex ) { + firingIndex--; + } + } + } ); + return this; + }, + + // Check if a given callback is in the list. + // If no argument is given, return whether or not list has callbacks attached. + has: function( fn ) { + return fn ? + jQuery.inArray( fn, list ) > -1 : + list.length > 0; + }, + + // Remove all callbacks from the list + empty: function() { + if ( list ) { + list = []; + } + return this; + }, + + // Disable .fire and .add + // Abort any current/pending executions + // Clear all callbacks and values + disable: function() { + locked = queue = []; + list = memory = ""; + return this; + }, + disabled: function() { + return !list; + }, + + // Disable .fire + // Also disable .add unless we have memory (since it would have no effect) + // Abort any pending executions + lock: function() { + locked = queue = []; + if ( !memory && !firing ) { + list = memory = ""; + } + return this; + }, + locked: function() { + return !!locked; + }, + + // Call all callbacks with the given context and arguments + fireWith: function( context, args ) { + if ( !locked ) { + args = args || []; + args = [ context, args.slice ? args.slice() : args ]; + queue.push( args ); + if ( !firing ) { + fire(); + } + } + return this; + }, + + // Call all the callbacks with the given arguments + fire: function() { + self.fireWith( this, arguments ); + return this; + }, + + // To know if the callbacks have already been called at least once + fired: function() { + return !!fired; + } + }; + + return self; +}; + + +function Identity( v ) { + return v; +} +function Thrower( ex ) { + throw ex; +} + +function adoptValue( value, resolve, reject, noValue ) { + var method; + + try { + + // Check for promise aspect first to privilege synchronous behavior + if ( value && isFunction( ( method = value.promise ) ) ) { + method.call( value ).done( resolve ).fail( reject ); + + // Other thenables + } else if ( value && isFunction( ( method = value.then ) ) ) { + method.call( value, resolve, reject ); + + // Other non-thenables + } else { + + // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: + // * false: [ value ].slice( 0 ) => resolve( value ) + // * true: [ value ].slice( 1 ) => resolve() + resolve.apply( undefined, [ value ].slice( noValue ) ); + } + + // For Promises/A+, convert exceptions into rejections + // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in + // Deferred#then to conditionally suppress rejection. + } catch ( value ) { + + // Support: Android 4.0 only + // Strict mode functions invoked without .call/.apply get global-object context + reject.apply( undefined, [ value ] ); + } +} + +jQuery.extend( { + + Deferred: function( func ) { + var tuples = [ + + // action, add listener, callbacks, + // ... .then handlers, argument index, [final state] + [ "notify", "progress", jQuery.Callbacks( "memory" ), + jQuery.Callbacks( "memory" ), 2 ], + [ "resolve", "done", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 0, "resolved" ], + [ "reject", "fail", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 1, "rejected" ] + ], + state = "pending", + promise = { + state: function() { + return state; + }, + always: function() { + deferred.done( arguments ).fail( arguments ); + return this; + }, + "catch": function( fn ) { + return promise.then( null, fn ); + }, + + // Keep pipe for back-compat + pipe: function( /* fnDone, fnFail, fnProgress */ ) { + var fns = arguments; + + return jQuery.Deferred( function( newDefer ) { + jQuery.each( tuples, function( _i, tuple ) { + + // Map tuples (progress, done, fail) to arguments (done, fail, progress) + var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; + + // deferred.progress(function() { bind to newDefer or newDefer.notify }) + // deferred.done(function() { bind to newDefer or newDefer.resolve }) + // deferred.fail(function() { bind to newDefer or newDefer.reject }) + deferred[ tuple[ 1 ] ]( function() { + var returned = fn && fn.apply( this, arguments ); + if ( returned && isFunction( returned.promise ) ) { + returned.promise() + .progress( newDefer.notify ) + .done( newDefer.resolve ) + .fail( newDefer.reject ); + } else { + newDefer[ tuple[ 0 ] + "With" ]( + this, + fn ? [ returned ] : arguments + ); + } + } ); + } ); + fns = null; + } ).promise(); + }, + then: function( onFulfilled, onRejected, onProgress ) { + var maxDepth = 0; + function resolve( depth, deferred, handler, special ) { + return function() { + var that = this, + args = arguments, + mightThrow = function() { + var returned, then; + + // Support: Promises/A+ section 2.3.3.3.3 + // https://promisesaplus.com/#point-59 + // Ignore double-resolution attempts + if ( depth < maxDepth ) { + return; + } + + returned = handler.apply( that, args ); + + // Support: Promises/A+ section 2.3.1 + // https://promisesaplus.com/#point-48 + if ( returned === deferred.promise() ) { + throw new TypeError( "Thenable self-resolution" ); + } + + // Support: Promises/A+ sections 2.3.3.1, 3.5 + // https://promisesaplus.com/#point-54 + // https://promisesaplus.com/#point-75 + // Retrieve `then` only once + then = returned && + + // Support: Promises/A+ section 2.3.4 + // https://promisesaplus.com/#point-64 + // Only check objects and functions for thenability + ( typeof returned === "object" || + typeof returned === "function" ) && + returned.then; + + // Handle a returned thenable + if ( isFunction( then ) ) { + + // Special processors (notify) just wait for resolution + if ( special ) { + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ) + ); + + // Normal processors (resolve) also hook into progress + } else { + + // ...and disregard older resolution values + maxDepth++; + + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ), + resolve( maxDepth, deferred, Identity, + deferred.notifyWith ) + ); + } + + // Handle all other returned values + } else { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Identity ) { + that = undefined; + args = [ returned ]; + } + + // Process the value(s) + // Default process is resolve + ( special || deferred.resolveWith )( that, args ); + } + }, + + // Only normal processors (resolve) catch and reject exceptions + process = special ? + mightThrow : + function() { + try { + mightThrow(); + } catch ( e ) { + + if ( jQuery.Deferred.exceptionHook ) { + jQuery.Deferred.exceptionHook( e, + process.stackTrace ); + } + + // Support: Promises/A+ section 2.3.3.3.4.1 + // https://promisesaplus.com/#point-61 + // Ignore post-resolution exceptions + if ( depth + 1 >= maxDepth ) { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Thrower ) { + that = undefined; + args = [ e ]; + } + + deferred.rejectWith( that, args ); + } + } + }; + + // Support: Promises/A+ section 2.3.3.3.1 + // https://promisesaplus.com/#point-57 + // Re-resolve promises immediately to dodge false rejection from + // subsequent errors + if ( depth ) { + process(); + } else { + + // Call an optional hook to record the stack, in case of exception + // since it's otherwise lost when execution goes async + if ( jQuery.Deferred.getStackHook ) { + process.stackTrace = jQuery.Deferred.getStackHook(); + } + window.setTimeout( process ); + } + }; + } + + return jQuery.Deferred( function( newDefer ) { + + // progress_handlers.add( ... ) + tuples[ 0 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onProgress ) ? + onProgress : + Identity, + newDefer.notifyWith + ) + ); + + // fulfilled_handlers.add( ... ) + tuples[ 1 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onFulfilled ) ? + onFulfilled : + Identity + ) + ); + + // rejected_handlers.add( ... ) + tuples[ 2 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onRejected ) ? + onRejected : + Thrower + ) + ); + } ).promise(); + }, + + // Get a promise for this deferred + // If obj is provided, the promise aspect is added to the object + promise: function( obj ) { + return obj != null ? jQuery.extend( obj, promise ) : promise; + } + }, + deferred = {}; + + // Add list-specific methods + jQuery.each( tuples, function( i, tuple ) { + var list = tuple[ 2 ], + stateString = tuple[ 5 ]; + + // promise.progress = list.add + // promise.done = list.add + // promise.fail = list.add + promise[ tuple[ 1 ] ] = list.add; + + // Handle state + if ( stateString ) { + list.add( + function() { + + // state = "resolved" (i.e., fulfilled) + // state = "rejected" + state = stateString; + }, + + // rejected_callbacks.disable + // fulfilled_callbacks.disable + tuples[ 3 - i ][ 2 ].disable, + + // rejected_handlers.disable + // fulfilled_handlers.disable + tuples[ 3 - i ][ 3 ].disable, + + // progress_callbacks.lock + tuples[ 0 ][ 2 ].lock, + + // progress_handlers.lock + tuples[ 0 ][ 3 ].lock + ); + } + + // progress_handlers.fire + // fulfilled_handlers.fire + // rejected_handlers.fire + list.add( tuple[ 3 ].fire ); + + // deferred.notify = function() { deferred.notifyWith(...) } + // deferred.resolve = function() { deferred.resolveWith(...) } + // deferred.reject = function() { deferred.rejectWith(...) } + deferred[ tuple[ 0 ] ] = function() { + deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); + return this; + }; + + // deferred.notifyWith = list.fireWith + // deferred.resolveWith = list.fireWith + // deferred.rejectWith = list.fireWith + deferred[ tuple[ 0 ] + "With" ] = list.fireWith; + } ); + + // Make the deferred a promise + promise.promise( deferred ); + + // Call given func if any + if ( func ) { + func.call( deferred, deferred ); + } + + // All done! + return deferred; + }, + + // Deferred helper + when: function( singleValue ) { + var + + // count of uncompleted subordinates + remaining = arguments.length, + + // count of unprocessed arguments + i = remaining, + + // subordinate fulfillment data + resolveContexts = Array( i ), + resolveValues = slice.call( arguments ), + + // the master Deferred + master = jQuery.Deferred(), + + // subordinate callback factory + updateFunc = function( i ) { + return function( value ) { + resolveContexts[ i ] = this; + resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; + if ( !( --remaining ) ) { + master.resolveWith( resolveContexts, resolveValues ); + } + }; + }; + + // Single- and empty arguments are adopted like Promise.resolve + if ( remaining <= 1 ) { + adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject, + !remaining ); + + // Use .then() to unwrap secondary thenables (cf. gh-3000) + if ( master.state() === "pending" || + isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { + + return master.then(); + } + } + + // Multiple arguments are aggregated like Promise.all array elements + while ( i-- ) { + adoptValue( resolveValues[ i ], updateFunc( i ), master.reject ); + } + + return master.promise(); + } +} ); + + +// These usually indicate a programmer mistake during development, +// warn about them ASAP rather than swallowing them by default. +var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; + +jQuery.Deferred.exceptionHook = function( error, stack ) { + + // Support: IE 8 - 9 only + // Console exists when dev tools are open, which can happen at any time + if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { + window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); + } +}; + + + + +jQuery.readyException = function( error ) { + window.setTimeout( function() { + throw error; + } ); +}; + + + + +// The deferred used on DOM ready +var readyList = jQuery.Deferred(); + +jQuery.fn.ready = function( fn ) { + + readyList + .then( fn ) + + // Wrap jQuery.readyException in a function so that the lookup + // happens at the time of error handling instead of callback + // registration. + .catch( function( error ) { + jQuery.readyException( error ); + } ); + + return this; +}; + +jQuery.extend( { + + // Is the DOM ready to be used? Set to true once it occurs. + isReady: false, + + // A counter to track how many items to wait for before + // the ready event fires. See #6781 + readyWait: 1, + + // Handle when the DOM is ready + ready: function( wait ) { + + // Abort if there are pending holds or we're already ready + if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { + return; + } + + // Remember that the DOM is ready + jQuery.isReady = true; + + // If a normal DOM Ready event fired, decrement, and wait if need be + if ( wait !== true && --jQuery.readyWait > 0 ) { + return; + } + + // If there are functions bound, to execute + readyList.resolveWith( document, [ jQuery ] ); + } +} ); + +jQuery.ready.then = readyList.then; + +// The ready event handler and self cleanup method +function completed() { + document.removeEventListener( "DOMContentLoaded", completed ); + window.removeEventListener( "load", completed ); + jQuery.ready(); +} + +// Catch cases where $(document).ready() is called +// after the browser event has already occurred. +// Support: IE <=9 - 10 only +// Older IE sometimes signals "interactive" too soon +if ( document.readyState === "complete" || + ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { + + // Handle it asynchronously to allow scripts the opportunity to delay ready + window.setTimeout( jQuery.ready ); + +} else { + + // Use the handy event callback + document.addEventListener( "DOMContentLoaded", completed ); + + // A fallback to window.onload, that will always work + window.addEventListener( "load", completed ); +} + + + + +// Multifunctional method to get and set values of a collection +// The value/s can optionally be executed if it's a function +var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { + var i = 0, + len = elems.length, + bulk = key == null; + + // Sets many values + if ( toType( key ) === "object" ) { + chainable = true; + for ( i in key ) { + access( elems, fn, i, key[ i ], true, emptyGet, raw ); + } + + // Sets one value + } else if ( value !== undefined ) { + chainable = true; + + if ( !isFunction( value ) ) { + raw = true; + } + + if ( bulk ) { + + // Bulk operations run against the entire set + if ( raw ) { + fn.call( elems, value ); + fn = null; + + // ...except when executing function values + } else { + bulk = fn; + fn = function( elem, _key, value ) { + return bulk.call( jQuery( elem ), value ); + }; + } + } + + if ( fn ) { + for ( ; i < len; i++ ) { + fn( + elems[ i ], key, raw ? + value : + value.call( elems[ i ], i, fn( elems[ i ], key ) ) + ); + } + } + } + + if ( chainable ) { + return elems; + } + + // Gets + if ( bulk ) { + return fn.call( elems ); + } + + return len ? fn( elems[ 0 ], key ) : emptyGet; +}; + + +// Matches dashed string for camelizing +var rmsPrefix = /^-ms-/, + rdashAlpha = /-([a-z])/g; + +// Used by camelCase as callback to replace() +function fcamelCase( _all, letter ) { + return letter.toUpperCase(); +} + +// Convert dashed to camelCase; used by the css and data modules +// Support: IE <=9 - 11, Edge 12 - 15 +// Microsoft forgot to hump their vendor prefix (#9572) +function camelCase( string ) { + return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); +} +var acceptData = function( owner ) { + + // Accepts only: + // - Node + // - Node.ELEMENT_NODE + // - Node.DOCUMENT_NODE + // - Object + // - Any + return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); +}; + + + + +function Data() { + this.expando = jQuery.expando + Data.uid++; +} + +Data.uid = 1; + +Data.prototype = { + + cache: function( owner ) { + + // Check if the owner object already has a cache + var value = owner[ this.expando ]; + + // If not, create one + if ( !value ) { + value = {}; + + // We can accept data for non-element nodes in modern browsers, + // but we should not, see #8335. + // Always return an empty object. + if ( acceptData( owner ) ) { + + // If it is a node unlikely to be stringify-ed or looped over + // use plain assignment + if ( owner.nodeType ) { + owner[ this.expando ] = value; + + // Otherwise secure it in a non-enumerable property + // configurable must be true to allow the property to be + // deleted when data is removed + } else { + Object.defineProperty( owner, this.expando, { + value: value, + configurable: true + } ); + } + } + } + + return value; + }, + set: function( owner, data, value ) { + var prop, + cache = this.cache( owner ); + + // Handle: [ owner, key, value ] args + // Always use camelCase key (gh-2257) + if ( typeof data === "string" ) { + cache[ camelCase( data ) ] = value; + + // Handle: [ owner, { properties } ] args + } else { + + // Copy the properties one-by-one to the cache object + for ( prop in data ) { + cache[ camelCase( prop ) ] = data[ prop ]; + } + } + return cache; + }, + get: function( owner, key ) { + return key === undefined ? + this.cache( owner ) : + + // Always use camelCase key (gh-2257) + owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ]; + }, + access: function( owner, key, value ) { + + // In cases where either: + // + // 1. No key was specified + // 2. A string key was specified, but no value provided + // + // Take the "read" path and allow the get method to determine + // which value to return, respectively either: + // + // 1. The entire cache object + // 2. The data stored at the key + // + if ( key === undefined || + ( ( key && typeof key === "string" ) && value === undefined ) ) { + + return this.get( owner, key ); + } + + // When the key is not a string, or both a key and value + // are specified, set or extend (existing objects) with either: + // + // 1. An object of properties + // 2. A key and value + // + this.set( owner, key, value ); + + // Since the "set" path can have two possible entry points + // return the expected data based on which path was taken[*] + return value !== undefined ? value : key; + }, + remove: function( owner, key ) { + var i, + cache = owner[ this.expando ]; + + if ( cache === undefined ) { + return; + } + + if ( key !== undefined ) { + + // Support array or space separated string of keys + if ( Array.isArray( key ) ) { + + // If key is an array of keys... + // We always set camelCase keys, so remove that. + key = key.map( camelCase ); + } else { + key = camelCase( key ); + + // If a key with the spaces exists, use it. + // Otherwise, create an array by matching non-whitespace + key = key in cache ? + [ key ] : + ( key.match( rnothtmlwhite ) || [] ); + } + + i = key.length; + + while ( i-- ) { + delete cache[ key[ i ] ]; + } + } + + // Remove the expando if there's no more data + if ( key === undefined || jQuery.isEmptyObject( cache ) ) { + + // Support: Chrome <=35 - 45 + // Webkit & Blink performance suffers when deleting properties + // from DOM nodes, so set to undefined instead + // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) + if ( owner.nodeType ) { + owner[ this.expando ] = undefined; + } else { + delete owner[ this.expando ]; + } + } + }, + hasData: function( owner ) { + var cache = owner[ this.expando ]; + return cache !== undefined && !jQuery.isEmptyObject( cache ); + } +}; +var dataPriv = new Data(); + +var dataUser = new Data(); + + + +// Implementation Summary +// +// 1. Enforce API surface and semantic compatibility with 1.9.x branch +// 2. Improve the module's maintainability by reducing the storage +// paths to a single mechanism. +// 3. Use the same single mechanism to support "private" and "user" data. +// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) +// 5. Avoid exposing implementation details on user objects (eg. expando properties) +// 6. Provide a clear path for implementation upgrade to WeakMap in 2014 + +var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, + rmultiDash = /[A-Z]/g; + +function getData( data ) { + if ( data === "true" ) { + return true; + } + + if ( data === "false" ) { + return false; + } + + if ( data === "null" ) { + return null; + } + + // Only convert to a number if it doesn't change the string + if ( data === +data + "" ) { + return +data; + } + + if ( rbrace.test( data ) ) { + return JSON.parse( data ); + } + + return data; +} + +function dataAttr( elem, key, data ) { + var name; + + // If nothing was found internally, try to fetch any + // data from the HTML5 data-* attribute + if ( data === undefined && elem.nodeType === 1 ) { + name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); + data = elem.getAttribute( name ); + + if ( typeof data === "string" ) { + try { + data = getData( data ); + } catch ( e ) {} + + // Make sure we set the data so it isn't changed later + dataUser.set( elem, key, data ); + } else { + data = undefined; + } + } + return data; +} + +jQuery.extend( { + hasData: function( elem ) { + return dataUser.hasData( elem ) || dataPriv.hasData( elem ); + }, + + data: function( elem, name, data ) { + return dataUser.access( elem, name, data ); + }, + + removeData: function( elem, name ) { + dataUser.remove( elem, name ); + }, + + // TODO: Now that all calls to _data and _removeData have been replaced + // with direct calls to dataPriv methods, these can be deprecated. + _data: function( elem, name, data ) { + return dataPriv.access( elem, name, data ); + }, + + _removeData: function( elem, name ) { + dataPriv.remove( elem, name ); + } +} ); + +jQuery.fn.extend( { + data: function( key, value ) { + var i, name, data, + elem = this[ 0 ], + attrs = elem && elem.attributes; + + // Gets all values + if ( key === undefined ) { + if ( this.length ) { + data = dataUser.get( elem ); + + if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { + i = attrs.length; + while ( i-- ) { + + // Support: IE 11 only + // The attrs elements can be null (#14894) + if ( attrs[ i ] ) { + name = attrs[ i ].name; + if ( name.indexOf( "data-" ) === 0 ) { + name = camelCase( name.slice( 5 ) ); + dataAttr( elem, name, data[ name ] ); + } + } + } + dataPriv.set( elem, "hasDataAttrs", true ); + } + } + + return data; + } + + // Sets multiple values + if ( typeof key === "object" ) { + return this.each( function() { + dataUser.set( this, key ); + } ); + } + + return access( this, function( value ) { + var data; + + // The calling jQuery object (element matches) is not empty + // (and therefore has an element appears at this[ 0 ]) and the + // `value` parameter was not undefined. An empty jQuery object + // will result in `undefined` for elem = this[ 0 ] which will + // throw an exception if an attempt to read a data cache is made. + if ( elem && value === undefined ) { + + // Attempt to get data from the cache + // The key will always be camelCased in Data + data = dataUser.get( elem, key ); + if ( data !== undefined ) { + return data; + } + + // Attempt to "discover" the data in + // HTML5 custom data-* attrs + data = dataAttr( elem, key ); + if ( data !== undefined ) { + return data; + } + + // We tried really hard, but the data doesn't exist. + return; + } + + // Set the data... + this.each( function() { + + // We always store the camelCased key + dataUser.set( this, key, value ); + } ); + }, null, value, arguments.length > 1, null, true ); + }, + + removeData: function( key ) { + return this.each( function() { + dataUser.remove( this, key ); + } ); + } +} ); + + +jQuery.extend( { + queue: function( elem, type, data ) { + var queue; + + if ( elem ) { + type = ( type || "fx" ) + "queue"; + queue = dataPriv.get( elem, type ); + + // Speed up dequeue by getting out quickly if this is just a lookup + if ( data ) { + if ( !queue || Array.isArray( data ) ) { + queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); + } else { + queue.push( data ); + } + } + return queue || []; + } + }, + + dequeue: function( elem, type ) { + type = type || "fx"; + + var queue = jQuery.queue( elem, type ), + startLength = queue.length, + fn = queue.shift(), + hooks = jQuery._queueHooks( elem, type ), + next = function() { + jQuery.dequeue( elem, type ); + }; + + // If the fx queue is dequeued, always remove the progress sentinel + if ( fn === "inprogress" ) { + fn = queue.shift(); + startLength--; + } + + if ( fn ) { + + // Add a progress sentinel to prevent the fx queue from being + // automatically dequeued + if ( type === "fx" ) { + queue.unshift( "inprogress" ); + } + + // Clear up the last queue stop function + delete hooks.stop; + fn.call( elem, next, hooks ); + } + + if ( !startLength && hooks ) { + hooks.empty.fire(); + } + }, + + // Not public - generate a queueHooks object, or return the current one + _queueHooks: function( elem, type ) { + var key = type + "queueHooks"; + return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { + empty: jQuery.Callbacks( "once memory" ).add( function() { + dataPriv.remove( elem, [ type + "queue", key ] ); + } ) + } ); + } +} ); + +jQuery.fn.extend( { + queue: function( type, data ) { + var setter = 2; + + if ( typeof type !== "string" ) { + data = type; + type = "fx"; + setter--; + } + + if ( arguments.length < setter ) { + return jQuery.queue( this[ 0 ], type ); + } + + return data === undefined ? + this : + this.each( function() { + var queue = jQuery.queue( this, type, data ); + + // Ensure a hooks for this queue + jQuery._queueHooks( this, type ); + + if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { + jQuery.dequeue( this, type ); + } + } ); + }, + dequeue: function( type ) { + return this.each( function() { + jQuery.dequeue( this, type ); + } ); + }, + clearQueue: function( type ) { + return this.queue( type || "fx", [] ); + }, + + // Get a promise resolved when queues of a certain type + // are emptied (fx is the type by default) + promise: function( type, obj ) { + var tmp, + count = 1, + defer = jQuery.Deferred(), + elements = this, + i = this.length, + resolve = function() { + if ( !( --count ) ) { + defer.resolveWith( elements, [ elements ] ); + } + }; + + if ( typeof type !== "string" ) { + obj = type; + type = undefined; + } + type = type || "fx"; + + while ( i-- ) { + tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); + if ( tmp && tmp.empty ) { + count++; + tmp.empty.add( resolve ); + } + } + resolve(); + return defer.promise( obj ); + } +} ); +var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; + +var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); + + +var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; + +var documentElement = document.documentElement; + + + + var isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ); + }, + composed = { composed: true }; + + // Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only + // Check attachment across shadow DOM boundaries when possible (gh-3504) + // Support: iOS 10.0-10.2 only + // Early iOS 10 versions support `attachShadow` but not `getRootNode`, + // leading to errors. We need to check for `getRootNode`. + if ( documentElement.getRootNode ) { + isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ) || + elem.getRootNode( composed ) === elem.ownerDocument; + }; + } +var isHiddenWithinTree = function( elem, el ) { + + // isHiddenWithinTree might be called from jQuery#filter function; + // in that case, element will be second argument + elem = el || elem; + + // Inline style trumps all + return elem.style.display === "none" || + elem.style.display === "" && + + // Otherwise, check computed style + // Support: Firefox <=43 - 45 + // Disconnected elements can have computed display: none, so first confirm that elem is + // in the document. + isAttached( elem ) && + + jQuery.css( elem, "display" ) === "none"; + }; + + + +function adjustCSS( elem, prop, valueParts, tween ) { + var adjusted, scale, + maxIterations = 20, + currentValue = tween ? + function() { + return tween.cur(); + } : + function() { + return jQuery.css( elem, prop, "" ); + }, + initial = currentValue(), + unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), + + // Starting value computation is required for potential unit mismatches + initialInUnit = elem.nodeType && + ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && + rcssNum.exec( jQuery.css( elem, prop ) ); + + if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { + + // Support: Firefox <=54 + // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144) + initial = initial / 2; + + // Trust units reported by jQuery.css + unit = unit || initialInUnit[ 3 ]; + + // Iteratively approximate from a nonzero starting point + initialInUnit = +initial || 1; + + while ( maxIterations-- ) { + + // Evaluate and update our best guess (doubling guesses that zero out). + // Finish if the scale equals or crosses 1 (making the old*new product non-positive). + jQuery.style( elem, prop, initialInUnit + unit ); + if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) { + maxIterations = 0; + } + initialInUnit = initialInUnit / scale; + + } + + initialInUnit = initialInUnit * 2; + jQuery.style( elem, prop, initialInUnit + unit ); + + // Make sure we update the tween properties later on + valueParts = valueParts || []; + } + + if ( valueParts ) { + initialInUnit = +initialInUnit || +initial || 0; + + // Apply relative offset (+=/-=) if specified + adjusted = valueParts[ 1 ] ? + initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : + +valueParts[ 2 ]; + if ( tween ) { + tween.unit = unit; + tween.start = initialInUnit; + tween.end = adjusted; + } + } + return adjusted; +} + + +var defaultDisplayMap = {}; + +function getDefaultDisplay( elem ) { + var temp, + doc = elem.ownerDocument, + nodeName = elem.nodeName, + display = defaultDisplayMap[ nodeName ]; + + if ( display ) { + return display; + } + + temp = doc.body.appendChild( doc.createElement( nodeName ) ); + display = jQuery.css( temp, "display" ); + + temp.parentNode.removeChild( temp ); + + if ( display === "none" ) { + display = "block"; + } + defaultDisplayMap[ nodeName ] = display; + + return display; +} + +function showHide( elements, show ) { + var display, elem, + values = [], + index = 0, + length = elements.length; + + // Determine new display value for elements that need to change + for ( ; index < length; index++ ) { + elem = elements[ index ]; + if ( !elem.style ) { + continue; + } + + display = elem.style.display; + if ( show ) { + + // Since we force visibility upon cascade-hidden elements, an immediate (and slow) + // check is required in this first loop unless we have a nonempty display value (either + // inline or about-to-be-restored) + if ( display === "none" ) { + values[ index ] = dataPriv.get( elem, "display" ) || null; + if ( !values[ index ] ) { + elem.style.display = ""; + } + } + if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { + values[ index ] = getDefaultDisplay( elem ); + } + } else { + if ( display !== "none" ) { + values[ index ] = "none"; + + // Remember what we're overwriting + dataPriv.set( elem, "display", display ); + } + } + } + + // Set the display of the elements in a second loop to avoid constant reflow + for ( index = 0; index < length; index++ ) { + if ( values[ index ] != null ) { + elements[ index ].style.display = values[ index ]; + } + } + + return elements; +} + +jQuery.fn.extend( { + show: function() { + return showHide( this, true ); + }, + hide: function() { + return showHide( this ); + }, + toggle: function( state ) { + if ( typeof state === "boolean" ) { + return state ? this.show() : this.hide(); + } + + return this.each( function() { + if ( isHiddenWithinTree( this ) ) { + jQuery( this ).show(); + } else { + jQuery( this ).hide(); + } + } ); + } +} ); +var rcheckableType = ( /^(?:checkbox|radio)$/i ); + +var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i ); + +var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i ); + + + +( function() { + var fragment = document.createDocumentFragment(), + div = fragment.appendChild( document.createElement( "div" ) ), + input = document.createElement( "input" ); + + // Support: Android 4.0 - 4.3 only + // Check state lost if the name is set (#11217) + // Support: Windows Web Apps (WWA) + // `name` and `type` must use .setAttribute for WWA (#14901) + input.setAttribute( "type", "radio" ); + input.setAttribute( "checked", "checked" ); + input.setAttribute( "name", "t" ); + + div.appendChild( input ); + + // Support: Android <=4.1 only + // Older WebKit doesn't clone checked state correctly in fragments + support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; + + // Support: IE <=11 only + // Make sure textarea (and checkbox) defaultValue is properly cloned + div.innerHTML = ""; + support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; + + // Support: IE <=9 only + // IE <=9 replaces "; + support.option = !!div.lastChild; +} )(); + + +// We have to close these tags to support XHTML (#13200) +var wrapMap = { + + // XHTML parsers do not magically insert elements in the + // same way that tag soup parsers do. So we cannot shorten + // this by omitting or other required elements. + thead: [ 1, "", "
    " ], + col: [ 2, "", "
    " ], + tr: [ 2, "", "
    " ], + td: [ 3, "", "
    " ], + + _default: [ 0, "", "" ] +}; + +wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; +wrapMap.th = wrapMap.td; + +// Support: IE <=9 only +if ( !support.option ) { + wrapMap.optgroup = wrapMap.option = [ 1, "" ]; +} + + +function getAll( context, tag ) { + + // Support: IE <=9 - 11 only + // Use typeof to avoid zero-argument method invocation on host objects (#15151) + var ret; + + if ( typeof context.getElementsByTagName !== "undefined" ) { + ret = context.getElementsByTagName( tag || "*" ); + + } else if ( typeof context.querySelectorAll !== "undefined" ) { + ret = context.querySelectorAll( tag || "*" ); + + } else { + ret = []; + } + + if ( tag === undefined || tag && nodeName( context, tag ) ) { + return jQuery.merge( [ context ], ret ); + } + + return ret; +} + + +// Mark scripts as having already been evaluated +function setGlobalEval( elems, refElements ) { + var i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + dataPriv.set( + elems[ i ], + "globalEval", + !refElements || dataPriv.get( refElements[ i ], "globalEval" ) + ); + } +} + + +var rhtml = /<|&#?\w+;/; + +function buildFragment( elems, context, scripts, selection, ignored ) { + var elem, tmp, tag, wrap, attached, j, + fragment = context.createDocumentFragment(), + nodes = [], + i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + elem = elems[ i ]; + + if ( elem || elem === 0 ) { + + // Add nodes directly + if ( toType( elem ) === "object" ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); + + // Convert non-html into a text node + } else if ( !rhtml.test( elem ) ) { + nodes.push( context.createTextNode( elem ) ); + + // Convert html into DOM nodes + } else { + tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); + + // Deserialize a standard representation + tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); + wrap = wrapMap[ tag ] || wrapMap._default; + tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; + + // Descend through wrappers to the right content + j = wrap[ 0 ]; + while ( j-- ) { + tmp = tmp.lastChild; + } + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, tmp.childNodes ); + + // Remember the top-level container + tmp = fragment.firstChild; + + // Ensure the created nodes are orphaned (#12392) + tmp.textContent = ""; + } + } + } + + // Remove wrapper from fragment + fragment.textContent = ""; + + i = 0; + while ( ( elem = nodes[ i++ ] ) ) { + + // Skip elements already in the context collection (trac-4087) + if ( selection && jQuery.inArray( elem, selection ) > -1 ) { + if ( ignored ) { + ignored.push( elem ); + } + continue; + } + + attached = isAttached( elem ); + + // Append to fragment + tmp = getAll( fragment.appendChild( elem ), "script" ); + + // Preserve script evaluation history + if ( attached ) { + setGlobalEval( tmp ); + } + + // Capture executables + if ( scripts ) { + j = 0; + while ( ( elem = tmp[ j++ ] ) ) { + if ( rscriptType.test( elem.type || "" ) ) { + scripts.push( elem ); + } + } + } + } + + return fragment; +} + + +var + rkeyEvent = /^key/, + rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/, + rtypenamespace = /^([^.]*)(?:\.(.+)|)/; + +function returnTrue() { + return true; +} + +function returnFalse() { + return false; +} + +// Support: IE <=9 - 11+ +// focus() and blur() are asynchronous, except when they are no-op. +// So expect focus to be synchronous when the element is already active, +// and blur to be synchronous when the element is not already active. +// (focus and blur are always synchronous in other supported browsers, +// this just defines when we can count on it). +function expectSync( elem, type ) { + return ( elem === safeActiveElement() ) === ( type === "focus" ); +} + +// Support: IE <=9 only +// Accessing document.activeElement can throw unexpectedly +// https://bugs.jquery.com/ticket/13393 +function safeActiveElement() { + try { + return document.activeElement; + } catch ( err ) { } +} + +function on( elem, types, selector, data, fn, one ) { + var origFn, type; + + // Types can be a map of types/handlers + if ( typeof types === "object" ) { + + // ( types-Object, selector, data ) + if ( typeof selector !== "string" ) { + + // ( types-Object, data ) + data = data || selector; + selector = undefined; + } + for ( type in types ) { + on( elem, type, selector, data, types[ type ], one ); + } + return elem; + } + + if ( data == null && fn == null ) { + + // ( types, fn ) + fn = selector; + data = selector = undefined; + } else if ( fn == null ) { + if ( typeof selector === "string" ) { + + // ( types, selector, fn ) + fn = data; + data = undefined; + } else { + + // ( types, data, fn ) + fn = data; + data = selector; + selector = undefined; + } + } + if ( fn === false ) { + fn = returnFalse; + } else if ( !fn ) { + return elem; + } + + if ( one === 1 ) { + origFn = fn; + fn = function( event ) { + + // Can use an empty set, since event contains the info + jQuery().off( event ); + return origFn.apply( this, arguments ); + }; + + // Use same guid so caller can remove using origFn + fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); + } + return elem.each( function() { + jQuery.event.add( this, types, fn, data, selector ); + } ); +} + +/* + * Helper functions for managing events -- not part of the public interface. + * Props to Dean Edwards' addEvent library for many of the ideas. + */ +jQuery.event = { + + global: {}, + + add: function( elem, types, handler, data, selector ) { + + var handleObjIn, eventHandle, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.get( elem ); + + // Only attach events to objects that accept data + if ( !acceptData( elem ) ) { + return; + } + + // Caller can pass in an object of custom data in lieu of the handler + if ( handler.handler ) { + handleObjIn = handler; + handler = handleObjIn.handler; + selector = handleObjIn.selector; + } + + // Ensure that invalid selectors throw exceptions at attach time + // Evaluate against documentElement in case elem is a non-element node (e.g., document) + if ( selector ) { + jQuery.find.matchesSelector( documentElement, selector ); + } + + // Make sure that the handler has a unique ID, used to find/remove it later + if ( !handler.guid ) { + handler.guid = jQuery.guid++; + } + + // Init the element's event structure and main handler, if this is the first + if ( !( events = elemData.events ) ) { + events = elemData.events = Object.create( null ); + } + if ( !( eventHandle = elemData.handle ) ) { + eventHandle = elemData.handle = function( e ) { + + // Discard the second event of a jQuery.event.trigger() and + // when an event is called after a page has unloaded + return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? + jQuery.event.dispatch.apply( elem, arguments ) : undefined; + }; + } + + // Handle multiple events separated by a space + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // There *must* be a type, no attaching namespace-only handlers + if ( !type ) { + continue; + } + + // If event changes its type, use the special event handlers for the changed type + special = jQuery.event.special[ type ] || {}; + + // If selector defined, determine special event api type, otherwise given type + type = ( selector ? special.delegateType : special.bindType ) || type; + + // Update special based on newly reset type + special = jQuery.event.special[ type ] || {}; + + // handleObj is passed to all event handlers + handleObj = jQuery.extend( { + type: type, + origType: origType, + data: data, + handler: handler, + guid: handler.guid, + selector: selector, + needsContext: selector && jQuery.expr.match.needsContext.test( selector ), + namespace: namespaces.join( "." ) + }, handleObjIn ); + + // Init the event handler queue if we're the first + if ( !( handlers = events[ type ] ) ) { + handlers = events[ type ] = []; + handlers.delegateCount = 0; + + // Only use addEventListener if the special events handler returns false + if ( !special.setup || + special.setup.call( elem, data, namespaces, eventHandle ) === false ) { + + if ( elem.addEventListener ) { + elem.addEventListener( type, eventHandle ); + } + } + } + + if ( special.add ) { + special.add.call( elem, handleObj ); + + if ( !handleObj.handler.guid ) { + handleObj.handler.guid = handler.guid; + } + } + + // Add to the element's handler list, delegates in front + if ( selector ) { + handlers.splice( handlers.delegateCount++, 0, handleObj ); + } else { + handlers.push( handleObj ); + } + + // Keep track of which events have ever been used, for event optimization + jQuery.event.global[ type ] = true; + } + + }, + + // Detach an event or set of events from an element + remove: function( elem, types, handler, selector, mappedTypes ) { + + var j, origCount, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); + + if ( !elemData || !( events = elemData.events ) ) { + return; + } + + // Once for each type.namespace in types; type may be omitted + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // Unbind all events (on this namespace, if provided) for the element + if ( !type ) { + for ( type in events ) { + jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); + } + continue; + } + + special = jQuery.event.special[ type ] || {}; + type = ( selector ? special.delegateType : special.bindType ) || type; + handlers = events[ type ] || []; + tmp = tmp[ 2 ] && + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); + + // Remove matching events + origCount = j = handlers.length; + while ( j-- ) { + handleObj = handlers[ j ]; + + if ( ( mappedTypes || origType === handleObj.origType ) && + ( !handler || handler.guid === handleObj.guid ) && + ( !tmp || tmp.test( handleObj.namespace ) ) && + ( !selector || selector === handleObj.selector || + selector === "**" && handleObj.selector ) ) { + handlers.splice( j, 1 ); + + if ( handleObj.selector ) { + handlers.delegateCount--; + } + if ( special.remove ) { + special.remove.call( elem, handleObj ); + } + } + } + + // Remove generic event handler if we removed something and no more handlers exist + // (avoids potential for endless recursion during removal of special event handlers) + if ( origCount && !handlers.length ) { + if ( !special.teardown || + special.teardown.call( elem, namespaces, elemData.handle ) === false ) { + + jQuery.removeEvent( elem, type, elemData.handle ); + } + + delete events[ type ]; + } + } + + // Remove data and the expando if it's no longer used + if ( jQuery.isEmptyObject( events ) ) { + dataPriv.remove( elem, "handle events" ); + } + }, + + dispatch: function( nativeEvent ) { + + var i, j, ret, matched, handleObj, handlerQueue, + args = new Array( arguments.length ), + + // Make a writable jQuery.Event from the native event object + event = jQuery.event.fix( nativeEvent ), + + handlers = ( + dataPriv.get( this, "events" ) || Object.create( null ) + )[ event.type ] || [], + special = jQuery.event.special[ event.type ] || {}; + + // Use the fix-ed jQuery.Event rather than the (read-only) native event + args[ 0 ] = event; + + for ( i = 1; i < arguments.length; i++ ) { + args[ i ] = arguments[ i ]; + } + + event.delegateTarget = this; + + // Call the preDispatch hook for the mapped type, and let it bail if desired + if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { + return; + } + + // Determine handlers + handlerQueue = jQuery.event.handlers.call( this, event, handlers ); + + // Run delegates first; they may want to stop propagation beneath us + i = 0; + while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { + event.currentTarget = matched.elem; + + j = 0; + while ( ( handleObj = matched.handlers[ j++ ] ) && + !event.isImmediatePropagationStopped() ) { + + // If the event is namespaced, then each handler is only invoked if it is + // specially universal or its namespaces are a superset of the event's. + if ( !event.rnamespace || handleObj.namespace === false || + event.rnamespace.test( handleObj.namespace ) ) { + + event.handleObj = handleObj; + event.data = handleObj.data; + + ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || + handleObj.handler ).apply( matched.elem, args ); + + if ( ret !== undefined ) { + if ( ( event.result = ret ) === false ) { + event.preventDefault(); + event.stopPropagation(); + } + } + } + } + } + + // Call the postDispatch hook for the mapped type + if ( special.postDispatch ) { + special.postDispatch.call( this, event ); + } + + return event.result; + }, + + handlers: function( event, handlers ) { + var i, handleObj, sel, matchedHandlers, matchedSelectors, + handlerQueue = [], + delegateCount = handlers.delegateCount, + cur = event.target; + + // Find delegate handlers + if ( delegateCount && + + // Support: IE <=9 + // Black-hole SVG instance trees (trac-13180) + cur.nodeType && + + // Support: Firefox <=42 + // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) + // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click + // Support: IE 11 only + // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) + !( event.type === "click" && event.button >= 1 ) ) { + + for ( ; cur !== this; cur = cur.parentNode || this ) { + + // Don't check non-elements (#13208) + // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) + if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { + matchedHandlers = []; + matchedSelectors = {}; + for ( i = 0; i < delegateCount; i++ ) { + handleObj = handlers[ i ]; + + // Don't conflict with Object.prototype properties (#13203) + sel = handleObj.selector + " "; + + if ( matchedSelectors[ sel ] === undefined ) { + matchedSelectors[ sel ] = handleObj.needsContext ? + jQuery( sel, this ).index( cur ) > -1 : + jQuery.find( sel, this, null, [ cur ] ).length; + } + if ( matchedSelectors[ sel ] ) { + matchedHandlers.push( handleObj ); + } + } + if ( matchedHandlers.length ) { + handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); + } + } + } + } + + // Add the remaining (directly-bound) handlers + cur = this; + if ( delegateCount < handlers.length ) { + handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); + } + + return handlerQueue; + }, + + addProp: function( name, hook ) { + Object.defineProperty( jQuery.Event.prototype, name, { + enumerable: true, + configurable: true, + + get: isFunction( hook ) ? + function() { + if ( this.originalEvent ) { + return hook( this.originalEvent ); + } + } : + function() { + if ( this.originalEvent ) { + return this.originalEvent[ name ]; + } + }, + + set: function( value ) { + Object.defineProperty( this, name, { + enumerable: true, + configurable: true, + writable: true, + value: value + } ); + } + } ); + }, + + fix: function( originalEvent ) { + return originalEvent[ jQuery.expando ] ? + originalEvent : + new jQuery.Event( originalEvent ); + }, + + special: { + load: { + + // Prevent triggered image.load events from bubbling to window.load + noBubble: true + }, + click: { + + // Utilize native event to ensure correct state for checkable inputs + setup: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Claim the first handler + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + // dataPriv.set( el, "click", ... ) + leverageNative( el, "click", returnTrue ); + } + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Force setup before triggering a click + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + leverageNative( el, "click" ); + } + + // Return non-false to allow normal event-path propagation + return true; + }, + + // For cross-browser consistency, suppress native .click() on links + // Also prevent it if we're currently inside a leveraged native-event stack + _default: function( event ) { + var target = event.target; + return rcheckableType.test( target.type ) && + target.click && nodeName( target, "input" ) && + dataPriv.get( target, "click" ) || + nodeName( target, "a" ); + } + }, + + beforeunload: { + postDispatch: function( event ) { + + // Support: Firefox 20+ + // Firefox doesn't alert if the returnValue field is not set. + if ( event.result !== undefined && event.originalEvent ) { + event.originalEvent.returnValue = event.result; + } + } + } + } +}; + +// Ensure the presence of an event listener that handles manually-triggered +// synthetic events by interrupting progress until reinvoked in response to +// *native* events that it fires directly, ensuring that state changes have +// already occurred before other listeners are invoked. +function leverageNative( el, type, expectSync ) { + + // Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add + if ( !expectSync ) { + if ( dataPriv.get( el, type ) === undefined ) { + jQuery.event.add( el, type, returnTrue ); + } + return; + } + + // Register the controller as a special universal handler for all event namespaces + dataPriv.set( el, type, false ); + jQuery.event.add( el, type, { + namespace: false, + handler: function( event ) { + var notAsync, result, + saved = dataPriv.get( this, type ); + + if ( ( event.isTrigger & 1 ) && this[ type ] ) { + + // Interrupt processing of the outer synthetic .trigger()ed event + // Saved data should be false in such cases, but might be a leftover capture object + // from an async native handler (gh-4350) + if ( !saved.length ) { + + // Store arguments for use when handling the inner native event + // There will always be at least one argument (an event object), so this array + // will not be confused with a leftover capture object. + saved = slice.call( arguments ); + dataPriv.set( this, type, saved ); + + // Trigger the native event and capture its result + // Support: IE <=9 - 11+ + // focus() and blur() are asynchronous + notAsync = expectSync( this, type ); + this[ type ](); + result = dataPriv.get( this, type ); + if ( saved !== result || notAsync ) { + dataPriv.set( this, type, false ); + } else { + result = {}; + } + if ( saved !== result ) { + + // Cancel the outer synthetic event + event.stopImmediatePropagation(); + event.preventDefault(); + return result.value; + } + + // If this is an inner synthetic event for an event with a bubbling surrogate + // (focus or blur), assume that the surrogate already propagated from triggering the + // native event and prevent that from happening again here. + // This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the + // bubbling surrogate propagates *after* the non-bubbling base), but that seems + // less bad than duplication. + } else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) { + event.stopPropagation(); + } + + // If this is a native event triggered above, everything is now in order + // Fire an inner synthetic event with the original arguments + } else if ( saved.length ) { + + // ...and capture the result + dataPriv.set( this, type, { + value: jQuery.event.trigger( + + // Support: IE <=9 - 11+ + // Extend with the prototype to reset the above stopImmediatePropagation() + jQuery.extend( saved[ 0 ], jQuery.Event.prototype ), + saved.slice( 1 ), + this + ) + } ); + + // Abort handling of the native event + event.stopImmediatePropagation(); + } + } + } ); +} + +jQuery.removeEvent = function( elem, type, handle ) { + + // This "if" is needed for plain objects + if ( elem.removeEventListener ) { + elem.removeEventListener( type, handle ); + } +}; + +jQuery.Event = function( src, props ) { + + // Allow instantiation without the 'new' keyword + if ( !( this instanceof jQuery.Event ) ) { + return new jQuery.Event( src, props ); + } + + // Event object + if ( src && src.type ) { + this.originalEvent = src; + this.type = src.type; + + // Events bubbling up the document may have been marked as prevented + // by a handler lower down the tree; reflect the correct value. + this.isDefaultPrevented = src.defaultPrevented || + src.defaultPrevented === undefined && + + // Support: Android <=2.3 only + src.returnValue === false ? + returnTrue : + returnFalse; + + // Create target properties + // Support: Safari <=6 - 7 only + // Target should not be a text node (#504, #13143) + this.target = ( src.target && src.target.nodeType === 3 ) ? + src.target.parentNode : + src.target; + + this.currentTarget = src.currentTarget; + this.relatedTarget = src.relatedTarget; + + // Event type + } else { + this.type = src; + } + + // Put explicitly provided properties onto the event object + if ( props ) { + jQuery.extend( this, props ); + } + + // Create a timestamp if incoming event doesn't have one + this.timeStamp = src && src.timeStamp || Date.now(); + + // Mark it as fixed + this[ jQuery.expando ] = true; +}; + +// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding +// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html +jQuery.Event.prototype = { + constructor: jQuery.Event, + isDefaultPrevented: returnFalse, + isPropagationStopped: returnFalse, + isImmediatePropagationStopped: returnFalse, + isSimulated: false, + + preventDefault: function() { + var e = this.originalEvent; + + this.isDefaultPrevented = returnTrue; + + if ( e && !this.isSimulated ) { + e.preventDefault(); + } + }, + stopPropagation: function() { + var e = this.originalEvent; + + this.isPropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopPropagation(); + } + }, + stopImmediatePropagation: function() { + var e = this.originalEvent; + + this.isImmediatePropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopImmediatePropagation(); + } + + this.stopPropagation(); + } +}; + +// Includes all common event props including KeyEvent and MouseEvent specific props +jQuery.each( { + altKey: true, + bubbles: true, + cancelable: true, + changedTouches: true, + ctrlKey: true, + detail: true, + eventPhase: true, + metaKey: true, + pageX: true, + pageY: true, + shiftKey: true, + view: true, + "char": true, + code: true, + charCode: true, + key: true, + keyCode: true, + button: true, + buttons: true, + clientX: true, + clientY: true, + offsetX: true, + offsetY: true, + pointerId: true, + pointerType: true, + screenX: true, + screenY: true, + targetTouches: true, + toElement: true, + touches: true, + + which: function( event ) { + var button = event.button; + + // Add which for key events + if ( event.which == null && rkeyEvent.test( event.type ) ) { + return event.charCode != null ? event.charCode : event.keyCode; + } + + // Add which for click: 1 === left; 2 === middle; 3 === right + if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) { + if ( button & 1 ) { + return 1; + } + + if ( button & 2 ) { + return 3; + } + + if ( button & 4 ) { + return 2; + } + + return 0; + } + + return event.which; + } +}, jQuery.event.addProp ); + +jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) { + jQuery.event.special[ type ] = { + + // Utilize native event if possible so blur/focus sequence is correct + setup: function() { + + // Claim the first handler + // dataPriv.set( this, "focus", ... ) + // dataPriv.set( this, "blur", ... ) + leverageNative( this, type, expectSync ); + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function() { + + // Force setup before trigger + leverageNative( this, type ); + + // Return non-false to allow normal event-path propagation + return true; + }, + + delegateType: delegateType + }; +} ); + +// Create mouseenter/leave events using mouseover/out and event-time checks +// so that event delegation works in jQuery. +// Do the same for pointerenter/pointerleave and pointerover/pointerout +// +// Support: Safari 7 only +// Safari sends mouseenter too often; see: +// https://bugs.chromium.org/p/chromium/issues/detail?id=470258 +// for the description of the bug (it existed in older Chrome versions as well). +jQuery.each( { + mouseenter: "mouseover", + mouseleave: "mouseout", + pointerenter: "pointerover", + pointerleave: "pointerout" +}, function( orig, fix ) { + jQuery.event.special[ orig ] = { + delegateType: fix, + bindType: fix, + + handle: function( event ) { + var ret, + target = this, + related = event.relatedTarget, + handleObj = event.handleObj; + + // For mouseenter/leave call the handler if related is outside the target. + // NB: No relatedTarget if the mouse left/entered the browser window + if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { + event.type = handleObj.origType; + ret = handleObj.handler.apply( this, arguments ); + event.type = fix; + } + return ret; + } + }; +} ); + +jQuery.fn.extend( { + + on: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn ); + }, + one: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn, 1 ); + }, + off: function( types, selector, fn ) { + var handleObj, type; + if ( types && types.preventDefault && types.handleObj ) { + + // ( event ) dispatched jQuery.Event + handleObj = types.handleObj; + jQuery( types.delegateTarget ).off( + handleObj.namespace ? + handleObj.origType + "." + handleObj.namespace : + handleObj.origType, + handleObj.selector, + handleObj.handler + ); + return this; + } + if ( typeof types === "object" ) { + + // ( types-object [, selector] ) + for ( type in types ) { + this.off( type, selector, types[ type ] ); + } + return this; + } + if ( selector === false || typeof selector === "function" ) { + + // ( types [, fn] ) + fn = selector; + selector = undefined; + } + if ( fn === false ) { + fn = returnFalse; + } + return this.each( function() { + jQuery.event.remove( this, types, fn, selector ); + } ); + } +} ); + + +var + + // Support: IE <=10 - 11, Edge 12 - 13 only + // In IE/Edge using regex groups here causes severe slowdowns. + // See https://connect.microsoft.com/IE/feedback/details/1736512/ + rnoInnerhtml = /\s*$/g; + +// Prefer a tbody over its parent table for containing new rows +function manipulationTarget( elem, content ) { + if ( nodeName( elem, "table" ) && + nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { + + return jQuery( elem ).children( "tbody" )[ 0 ] || elem; + } + + return elem; +} + +// Replace/restore the type attribute of script elements for safe DOM manipulation +function disableScript( elem ) { + elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; + return elem; +} +function restoreScript( elem ) { + if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) { + elem.type = elem.type.slice( 5 ); + } else { + elem.removeAttribute( "type" ); + } + + return elem; +} + +function cloneCopyEvent( src, dest ) { + var i, l, type, pdataOld, udataOld, udataCur, events; + + if ( dest.nodeType !== 1 ) { + return; + } + + // 1. Copy private data: events, handlers, etc. + if ( dataPriv.hasData( src ) ) { + pdataOld = dataPriv.get( src ); + events = pdataOld.events; + + if ( events ) { + dataPriv.remove( dest, "handle events" ); + + for ( type in events ) { + for ( i = 0, l = events[ type ].length; i < l; i++ ) { + jQuery.event.add( dest, type, events[ type ][ i ] ); + } + } + } + } + + // 2. Copy user data + if ( dataUser.hasData( src ) ) { + udataOld = dataUser.access( src ); + udataCur = jQuery.extend( {}, udataOld ); + + dataUser.set( dest, udataCur ); + } +} + +// Fix IE bugs, see support tests +function fixInput( src, dest ) { + var nodeName = dest.nodeName.toLowerCase(); + + // Fails to persist the checked state of a cloned checkbox or radio button. + if ( nodeName === "input" && rcheckableType.test( src.type ) ) { + dest.checked = src.checked; + + // Fails to return the selected option to the default selected state when cloning options + } else if ( nodeName === "input" || nodeName === "textarea" ) { + dest.defaultValue = src.defaultValue; + } +} + +function domManip( collection, args, callback, ignored ) { + + // Flatten any nested arrays + args = flat( args ); + + var fragment, first, scripts, hasScripts, node, doc, + i = 0, + l = collection.length, + iNoClone = l - 1, + value = args[ 0 ], + valueIsFunction = isFunction( value ); + + // We can't cloneNode fragments that contain checked, in WebKit + if ( valueIsFunction || + ( l > 1 && typeof value === "string" && + !support.checkClone && rchecked.test( value ) ) ) { + return collection.each( function( index ) { + var self = collection.eq( index ); + if ( valueIsFunction ) { + args[ 0 ] = value.call( this, index, self.html() ); + } + domManip( self, args, callback, ignored ); + } ); + } + + if ( l ) { + fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); + first = fragment.firstChild; + + if ( fragment.childNodes.length === 1 ) { + fragment = first; + } + + // Require either new content or an interest in ignored elements to invoke the callback + if ( first || ignored ) { + scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); + hasScripts = scripts.length; + + // Use the original fragment for the last item + // instead of the first because it can end up + // being emptied incorrectly in certain situations (#8070). + for ( ; i < l; i++ ) { + node = fragment; + + if ( i !== iNoClone ) { + node = jQuery.clone( node, true, true ); + + // Keep references to cloned scripts for later restoration + if ( hasScripts ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( scripts, getAll( node, "script" ) ); + } + } + + callback.call( collection[ i ], node, i ); + } + + if ( hasScripts ) { + doc = scripts[ scripts.length - 1 ].ownerDocument; + + // Reenable scripts + jQuery.map( scripts, restoreScript ); + + // Evaluate executable scripts on first document insertion + for ( i = 0; i < hasScripts; i++ ) { + node = scripts[ i ]; + if ( rscriptType.test( node.type || "" ) && + !dataPriv.access( node, "globalEval" ) && + jQuery.contains( doc, node ) ) { + + if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) { + + // Optional AJAX dependency, but won't run scripts if not present + if ( jQuery._evalUrl && !node.noModule ) { + jQuery._evalUrl( node.src, { + nonce: node.nonce || node.getAttribute( "nonce" ) + }, doc ); + } + } else { + DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc ); + } + } + } + } + } + } + + return collection; +} + +function remove( elem, selector, keepData ) { + var node, + nodes = selector ? jQuery.filter( selector, elem ) : elem, + i = 0; + + for ( ; ( node = nodes[ i ] ) != null; i++ ) { + if ( !keepData && node.nodeType === 1 ) { + jQuery.cleanData( getAll( node ) ); + } + + if ( node.parentNode ) { + if ( keepData && isAttached( node ) ) { + setGlobalEval( getAll( node, "script" ) ); + } + node.parentNode.removeChild( node ); + } + } + + return elem; +} + +jQuery.extend( { + htmlPrefilter: function( html ) { + return html; + }, + + clone: function( elem, dataAndEvents, deepDataAndEvents ) { + var i, l, srcElements, destElements, + clone = elem.cloneNode( true ), + inPage = isAttached( elem ); + + // Fix IE cloning issues + if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && + !jQuery.isXMLDoc( elem ) ) { + + // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 + destElements = getAll( clone ); + srcElements = getAll( elem ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + fixInput( srcElements[ i ], destElements[ i ] ); + } + } + + // Copy the events from the original to the clone + if ( dataAndEvents ) { + if ( deepDataAndEvents ) { + srcElements = srcElements || getAll( elem ); + destElements = destElements || getAll( clone ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + cloneCopyEvent( srcElements[ i ], destElements[ i ] ); + } + } else { + cloneCopyEvent( elem, clone ); + } + } + + // Preserve script evaluation history + destElements = getAll( clone, "script" ); + if ( destElements.length > 0 ) { + setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); + } + + // Return the cloned set + return clone; + }, + + cleanData: function( elems ) { + var data, elem, type, + special = jQuery.event.special, + i = 0; + + for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { + if ( acceptData( elem ) ) { + if ( ( data = elem[ dataPriv.expando ] ) ) { + if ( data.events ) { + for ( type in data.events ) { + if ( special[ type ] ) { + jQuery.event.remove( elem, type ); + + // This is a shortcut to avoid jQuery.event.remove's overhead + } else { + jQuery.removeEvent( elem, type, data.handle ); + } + } + } + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataPriv.expando ] = undefined; + } + if ( elem[ dataUser.expando ] ) { + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataUser.expando ] = undefined; + } + } + } + } +} ); + +jQuery.fn.extend( { + detach: function( selector ) { + return remove( this, selector, true ); + }, + + remove: function( selector ) { + return remove( this, selector ); + }, + + text: function( value ) { + return access( this, function( value ) { + return value === undefined ? + jQuery.text( this ) : + this.empty().each( function() { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + this.textContent = value; + } + } ); + }, null, value, arguments.length ); + }, + + append: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.appendChild( elem ); + } + } ); + }, + + prepend: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.insertBefore( elem, target.firstChild ); + } + } ); + }, + + before: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this ); + } + } ); + }, + + after: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this.nextSibling ); + } + } ); + }, + + empty: function() { + var elem, + i = 0; + + for ( ; ( elem = this[ i ] ) != null; i++ ) { + if ( elem.nodeType === 1 ) { + + // Prevent memory leaks + jQuery.cleanData( getAll( elem, false ) ); + + // Remove any remaining nodes + elem.textContent = ""; + } + } + + return this; + }, + + clone: function( dataAndEvents, deepDataAndEvents ) { + dataAndEvents = dataAndEvents == null ? false : dataAndEvents; + deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; + + return this.map( function() { + return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); + } ); + }, + + html: function( value ) { + return access( this, function( value ) { + var elem = this[ 0 ] || {}, + i = 0, + l = this.length; + + if ( value === undefined && elem.nodeType === 1 ) { + return elem.innerHTML; + } + + // See if we can take a shortcut and just use innerHTML + if ( typeof value === "string" && !rnoInnerhtml.test( value ) && + !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { + + value = jQuery.htmlPrefilter( value ); + + try { + for ( ; i < l; i++ ) { + elem = this[ i ] || {}; + + // Remove element nodes and prevent memory leaks + if ( elem.nodeType === 1 ) { + jQuery.cleanData( getAll( elem, false ) ); + elem.innerHTML = value; + } + } + + elem = 0; + + // If using innerHTML throws an exception, use the fallback method + } catch ( e ) {} + } + + if ( elem ) { + this.empty().append( value ); + } + }, null, value, arguments.length ); + }, + + replaceWith: function() { + var ignored = []; + + // Make the changes, replacing each non-ignored context element with the new content + return domManip( this, arguments, function( elem ) { + var parent = this.parentNode; + + if ( jQuery.inArray( this, ignored ) < 0 ) { + jQuery.cleanData( getAll( this ) ); + if ( parent ) { + parent.replaceChild( elem, this ); + } + } + + // Force callback invocation + }, ignored ); + } +} ); + +jQuery.each( { + appendTo: "append", + prependTo: "prepend", + insertBefore: "before", + insertAfter: "after", + replaceAll: "replaceWith" +}, function( name, original ) { + jQuery.fn[ name ] = function( selector ) { + var elems, + ret = [], + insert = jQuery( selector ), + last = insert.length - 1, + i = 0; + + for ( ; i <= last; i++ ) { + elems = i === last ? this : this.clone( true ); + jQuery( insert[ i ] )[ original ]( elems ); + + // Support: Android <=4.0 only, PhantomJS 1 only + // .get() because push.apply(_, arraylike) throws on ancient WebKit + push.apply( ret, elems.get() ); + } + + return this.pushStack( ret ); + }; +} ); +var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); + +var getStyles = function( elem ) { + + // Support: IE <=11 only, Firefox <=30 (#15098, #14150) + // IE throws on elements created in popups + // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" + var view = elem.ownerDocument.defaultView; + + if ( !view || !view.opener ) { + view = window; + } + + return view.getComputedStyle( elem ); + }; + +var swap = function( elem, options, callback ) { + var ret, name, + old = {}; + + // Remember the old values, and insert the new ones + for ( name in options ) { + old[ name ] = elem.style[ name ]; + elem.style[ name ] = options[ name ]; + } + + ret = callback.call( elem ); + + // Revert the old values + for ( name in options ) { + elem.style[ name ] = old[ name ]; + } + + return ret; +}; + + +var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" ); + + + +( function() { + + // Executing both pixelPosition & boxSizingReliable tests require only one layout + // so they're executed at the same time to save the second computation. + function computeStyleTests() { + + // This is a singleton, we need to execute it only once + if ( !div ) { + return; + } + + container.style.cssText = "position:absolute;left:-11111px;width:60px;" + + "margin-top:1px;padding:0;border:0"; + div.style.cssText = + "position:relative;display:block;box-sizing:border-box;overflow:scroll;" + + "margin:auto;border:1px;padding:1px;" + + "width:60%;top:1%"; + documentElement.appendChild( container ).appendChild( div ); + + var divStyle = window.getComputedStyle( div ); + pixelPositionVal = divStyle.top !== "1%"; + + // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 + reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12; + + // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3 + // Some styles come back with percentage values, even though they shouldn't + div.style.right = "60%"; + pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36; + + // Support: IE 9 - 11 only + // Detect misreporting of content dimensions for box-sizing:border-box elements + boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36; + + // Support: IE 9 only + // Detect overflow:scroll screwiness (gh-3699) + // Support: Chrome <=64 + // Don't get tricked when zoom affects offsetWidth (gh-4029) + div.style.position = "absolute"; + scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12; + + documentElement.removeChild( container ); + + // Nullify the div so it wouldn't be stored in the memory and + // it will also be a sign that checks already performed + div = null; + } + + function roundPixelMeasures( measure ) { + return Math.round( parseFloat( measure ) ); + } + + var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal, + reliableTrDimensionsVal, reliableMarginLeftVal, + container = document.createElement( "div" ), + div = document.createElement( "div" ); + + // Finish early in limited (non-browser) environments + if ( !div.style ) { + return; + } + + // Support: IE <=9 - 11 only + // Style of cloned element affects source element cloned (#8908) + div.style.backgroundClip = "content-box"; + div.cloneNode( true ).style.backgroundClip = ""; + support.clearCloneStyle = div.style.backgroundClip === "content-box"; + + jQuery.extend( support, { + boxSizingReliable: function() { + computeStyleTests(); + return boxSizingReliableVal; + }, + pixelBoxStyles: function() { + computeStyleTests(); + return pixelBoxStylesVal; + }, + pixelPosition: function() { + computeStyleTests(); + return pixelPositionVal; + }, + reliableMarginLeft: function() { + computeStyleTests(); + return reliableMarginLeftVal; + }, + scrollboxSize: function() { + computeStyleTests(); + return scrollboxSizeVal; + }, + + // Support: IE 9 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Behavior in IE 9 is more subtle than in newer versions & it passes + // some versions of this test; make sure not to make it pass there! + reliableTrDimensions: function() { + var table, tr, trChild, trStyle; + if ( reliableTrDimensionsVal == null ) { + table = document.createElement( "table" ); + tr = document.createElement( "tr" ); + trChild = document.createElement( "div" ); + + table.style.cssText = "position:absolute;left:-11111px"; + tr.style.height = "1px"; + trChild.style.height = "9px"; + + documentElement + .appendChild( table ) + .appendChild( tr ) + .appendChild( trChild ); + + trStyle = window.getComputedStyle( tr ); + reliableTrDimensionsVal = parseInt( trStyle.height ) > 3; + + documentElement.removeChild( table ); + } + return reliableTrDimensionsVal; + } + } ); +} )(); + + +function curCSS( elem, name, computed ) { + var width, minWidth, maxWidth, ret, + + // Support: Firefox 51+ + // Retrieving style before computed somehow + // fixes an issue with getting wrong values + // on detached elements + style = elem.style; + + computed = computed || getStyles( elem ); + + // getPropertyValue is needed for: + // .css('filter') (IE 9 only, #12537) + // .css('--customProperty) (#3144) + if ( computed ) { + ret = computed.getPropertyValue( name ) || computed[ name ]; + + if ( ret === "" && !isAttached( elem ) ) { + ret = jQuery.style( elem, name ); + } + + // A tribute to the "awesome hack by Dean Edwards" + // Android Browser returns percentage for some values, + // but width seems to be reliably pixels. + // This is against the CSSOM draft spec: + // https://drafts.csswg.org/cssom/#resolved-values + if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) { + + // Remember the original values + width = style.width; + minWidth = style.minWidth; + maxWidth = style.maxWidth; + + // Put in the new values to get a computed value out + style.minWidth = style.maxWidth = style.width = ret; + ret = computed.width; + + // Revert the changed values + style.width = width; + style.minWidth = minWidth; + style.maxWidth = maxWidth; + } + } + + return ret !== undefined ? + + // Support: IE <=9 - 11 only + // IE returns zIndex value as an integer. + ret + "" : + ret; +} + + +function addGetHookIf( conditionFn, hookFn ) { + + // Define the hook, we'll check on the first run if it's really needed. + return { + get: function() { + if ( conditionFn() ) { + + // Hook not needed (or it's not possible to use it due + // to missing dependency), remove it. + delete this.get; + return; + } + + // Hook needed; redefine it so that the support test is not executed again. + return ( this.get = hookFn ).apply( this, arguments ); + } + }; +} + + +var cssPrefixes = [ "Webkit", "Moz", "ms" ], + emptyStyle = document.createElement( "div" ).style, + vendorProps = {}; + +// Return a vendor-prefixed property or undefined +function vendorPropName( name ) { + + // Check for vendor prefixed names + var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), + i = cssPrefixes.length; + + while ( i-- ) { + name = cssPrefixes[ i ] + capName; + if ( name in emptyStyle ) { + return name; + } + } +} + +// Return a potentially-mapped jQuery.cssProps or vendor prefixed property +function finalPropName( name ) { + var final = jQuery.cssProps[ name ] || vendorProps[ name ]; + + if ( final ) { + return final; + } + if ( name in emptyStyle ) { + return name; + } + return vendorProps[ name ] = vendorPropName( name ) || name; +} + + +var + + // Swappable if display is none or starts with table + // except "table", "table-cell", or "table-caption" + // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display + rdisplayswap = /^(none|table(?!-c[ea]).+)/, + rcustomProp = /^--/, + cssShow = { position: "absolute", visibility: "hidden", display: "block" }, + cssNormalTransform = { + letterSpacing: "0", + fontWeight: "400" + }; + +function setPositiveNumber( _elem, value, subtract ) { + + // Any relative (+/-) values have already been + // normalized at this point + var matches = rcssNum.exec( value ); + return matches ? + + // Guard against undefined "subtract", e.g., when used as in cssHooks + Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : + value; +} + +function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) { + var i = dimension === "width" ? 1 : 0, + extra = 0, + delta = 0; + + // Adjustment may not be necessary + if ( box === ( isBorderBox ? "border" : "content" ) ) { + return 0; + } + + for ( ; i < 4; i += 2 ) { + + // Both box models exclude margin + if ( box === "margin" ) { + delta += jQuery.css( elem, box + cssExpand[ i ], true, styles ); + } + + // If we get here with a content-box, we're seeking "padding" or "border" or "margin" + if ( !isBorderBox ) { + + // Add padding + delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + + // For "border" or "margin", add border + if ( box !== "padding" ) { + delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + + // But still keep track of it otherwise + } else { + extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + + // If we get here with a border-box (content + padding + border), we're seeking "content" or + // "padding" or "margin" + } else { + + // For "content", subtract padding + if ( box === "content" ) { + delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + } + + // For "content" or "padding", subtract border + if ( box !== "margin" ) { + delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + } + } + + // Account for positive content-box scroll gutter when requested by providing computedVal + if ( !isBorderBox && computedVal >= 0 ) { + + // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border + // Assuming integer scroll gutter, subtract the rest and round down + delta += Math.max( 0, Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + computedVal - + delta - + extra - + 0.5 + + // If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter + // Use an explicit zero to avoid NaN (gh-3964) + ) ) || 0; + } + + return delta; +} + +function getWidthOrHeight( elem, dimension, extra ) { + + // Start with computed style + var styles = getStyles( elem ), + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322). + // Fake content-box until we know it's needed to know the true value. + boxSizingNeeded = !support.boxSizingReliable() || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + valueIsBorderBox = isBorderBox, + + val = curCSS( elem, dimension, styles ), + offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ); + + // Support: Firefox <=54 + // Return a confounding non-pixel value or feign ignorance, as appropriate. + if ( rnumnonpx.test( val ) ) { + if ( !extra ) { + return val; + } + val = "auto"; + } + + + // Support: IE 9 - 11 only + // Use offsetWidth/offsetHeight for when box sizing is unreliable. + // In those cases, the computed value can be trusted to be border-box. + if ( ( !support.boxSizingReliable() && isBorderBox || + + // Support: IE 10 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Interestingly, in some cases IE 9 doesn't suffer from this issue. + !support.reliableTrDimensions() && nodeName( elem, "tr" ) || + + // Fall back to offsetWidth/offsetHeight when value is "auto" + // This happens for inline elements with no explicit setting (gh-3571) + val === "auto" || + + // Support: Android <=4.1 - 4.3 only + // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602) + !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) && + + // Make sure the element is visible & connected + elem.getClientRects().length ) { + + isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box"; + + // Where available, offsetWidth/offsetHeight approximate border box dimensions. + // Where not available (e.g., SVG), assume unreliable box-sizing and interpret the + // retrieved value as a content box dimension. + valueIsBorderBox = offsetProp in elem; + if ( valueIsBorderBox ) { + val = elem[ offsetProp ]; + } + } + + // Normalize "" and auto + val = parseFloat( val ) || 0; + + // Adjust for the element's box model + return ( val + + boxModelAdjustment( + elem, + dimension, + extra || ( isBorderBox ? "border" : "content" ), + valueIsBorderBox, + styles, + + // Provide the current computed size to request scroll gutter calculation (gh-3589) + val + ) + ) + "px"; +} + +jQuery.extend( { + + // Add in style property hooks for overriding the default + // behavior of getting and setting a style property + cssHooks: { + opacity: { + get: function( elem, computed ) { + if ( computed ) { + + // We should always get a number back from opacity + var ret = curCSS( elem, "opacity" ); + return ret === "" ? "1" : ret; + } + } + } + }, + + // Don't automatically add "px" to these possibly-unitless properties + cssNumber: { + "animationIterationCount": true, + "columnCount": true, + "fillOpacity": true, + "flexGrow": true, + "flexShrink": true, + "fontWeight": true, + "gridArea": true, + "gridColumn": true, + "gridColumnEnd": true, + "gridColumnStart": true, + "gridRow": true, + "gridRowEnd": true, + "gridRowStart": true, + "lineHeight": true, + "opacity": true, + "order": true, + "orphans": true, + "widows": true, + "zIndex": true, + "zoom": true + }, + + // Add in properties whose names you wish to fix before + // setting or getting the value + cssProps: {}, + + // Get and set the style property on a DOM Node + style: function( elem, name, value, extra ) { + + // Don't set styles on text and comment nodes + if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { + return; + } + + // Make sure that we're working with the right name + var ret, type, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ), + style = elem.style; + + // Make sure that we're working with the right name. We don't + // want to query the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Gets hook for the prefixed version, then unprefixed version + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // Check if we're setting a value + if ( value !== undefined ) { + type = typeof value; + + // Convert "+=" or "-=" to relative numbers (#7345) + if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { + value = adjustCSS( elem, name, ret ); + + // Fixes bug #9237 + type = "number"; + } + + // Make sure that null and NaN values aren't set (#7116) + if ( value == null || value !== value ) { + return; + } + + // If a number was passed in, add the unit (except for certain CSS properties) + // The isCustomProp check can be removed in jQuery 4.0 when we only auto-append + // "px" to a few hardcoded values. + if ( type === "number" && !isCustomProp ) { + value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); + } + + // background-* props affect original clone's values + if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { + style[ name ] = "inherit"; + } + + // If a hook was provided, use that value, otherwise just set the specified value + if ( !hooks || !( "set" in hooks ) || + ( value = hooks.set( elem, value, extra ) ) !== undefined ) { + + if ( isCustomProp ) { + style.setProperty( name, value ); + } else { + style[ name ] = value; + } + } + + } else { + + // If a hook was provided get the non-computed value from there + if ( hooks && "get" in hooks && + ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { + + return ret; + } + + // Otherwise just get the value from the style object + return style[ name ]; + } + }, + + css: function( elem, name, extra, styles ) { + var val, num, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ); + + // Make sure that we're working with the right name. We don't + // want to modify the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Try prefixed name followed by the unprefixed name + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // If a hook was provided get the computed value from there + if ( hooks && "get" in hooks ) { + val = hooks.get( elem, true, extra ); + } + + // Otherwise, if a way to get the computed value exists, use that + if ( val === undefined ) { + val = curCSS( elem, name, styles ); + } + + // Convert "normal" to computed value + if ( val === "normal" && name in cssNormalTransform ) { + val = cssNormalTransform[ name ]; + } + + // Make numeric if forced or a qualifier was provided and val looks numeric + if ( extra === "" || extra ) { + num = parseFloat( val ); + return extra === true || isFinite( num ) ? num || 0 : val; + } + + return val; + } +} ); + +jQuery.each( [ "height", "width" ], function( _i, dimension ) { + jQuery.cssHooks[ dimension ] = { + get: function( elem, computed, extra ) { + if ( computed ) { + + // Certain elements can have dimension info if we invisibly show them + // but it must have a current display style that would benefit + return rdisplayswap.test( jQuery.css( elem, "display" ) ) && + + // Support: Safari 8+ + // Table columns in Safari have non-zero offsetWidth & zero + // getBoundingClientRect().width unless display is changed. + // Support: IE <=11 only + // Running getBoundingClientRect on a disconnected node + // in IE throws an error. + ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? + swap( elem, cssShow, function() { + return getWidthOrHeight( elem, dimension, extra ); + } ) : + getWidthOrHeight( elem, dimension, extra ); + } + }, + + set: function( elem, value, extra ) { + var matches, + styles = getStyles( elem ), + + // Only read styles.position if the test has a chance to fail + // to avoid forcing a reflow. + scrollboxSizeBuggy = !support.scrollboxSize() && + styles.position === "absolute", + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991) + boxSizingNeeded = scrollboxSizeBuggy || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + subtract = extra ? + boxModelAdjustment( + elem, + dimension, + extra, + isBorderBox, + styles + ) : + 0; + + // Account for unreliable border-box dimensions by comparing offset* to computed and + // faking a content-box to get border and padding (gh-3699) + if ( isBorderBox && scrollboxSizeBuggy ) { + subtract -= Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + parseFloat( styles[ dimension ] ) - + boxModelAdjustment( elem, dimension, "border", false, styles ) - + 0.5 + ); + } + + // Convert to pixels if value adjustment is needed + if ( subtract && ( matches = rcssNum.exec( value ) ) && + ( matches[ 3 ] || "px" ) !== "px" ) { + + elem.style[ dimension ] = value; + value = jQuery.css( elem, dimension ); + } + + return setPositiveNumber( elem, value, subtract ); + } + }; +} ); + +jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, + function( elem, computed ) { + if ( computed ) { + return ( parseFloat( curCSS( elem, "marginLeft" ) ) || + elem.getBoundingClientRect().left - + swap( elem, { marginLeft: 0 }, function() { + return elem.getBoundingClientRect().left; + } ) + ) + "px"; + } + } +); + +// These hooks are used by animate to expand properties +jQuery.each( { + margin: "", + padding: "", + border: "Width" +}, function( prefix, suffix ) { + jQuery.cssHooks[ prefix + suffix ] = { + expand: function( value ) { + var i = 0, + expanded = {}, + + // Assumes a single number if not a string + parts = typeof value === "string" ? value.split( " " ) : [ value ]; + + for ( ; i < 4; i++ ) { + expanded[ prefix + cssExpand[ i ] + suffix ] = + parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; + } + + return expanded; + } + }; + + if ( prefix !== "margin" ) { + jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; + } +} ); + +jQuery.fn.extend( { + css: function( name, value ) { + return access( this, function( elem, name, value ) { + var styles, len, + map = {}, + i = 0; + + if ( Array.isArray( name ) ) { + styles = getStyles( elem ); + len = name.length; + + for ( ; i < len; i++ ) { + map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); + } + + return map; + } + + return value !== undefined ? + jQuery.style( elem, name, value ) : + jQuery.css( elem, name ); + }, name, value, arguments.length > 1 ); + } +} ); + + +function Tween( elem, options, prop, end, easing ) { + return new Tween.prototype.init( elem, options, prop, end, easing ); +} +jQuery.Tween = Tween; + +Tween.prototype = { + constructor: Tween, + init: function( elem, options, prop, end, easing, unit ) { + this.elem = elem; + this.prop = prop; + this.easing = easing || jQuery.easing._default; + this.options = options; + this.start = this.now = this.cur(); + this.end = end; + this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); + }, + cur: function() { + var hooks = Tween.propHooks[ this.prop ]; + + return hooks && hooks.get ? + hooks.get( this ) : + Tween.propHooks._default.get( this ); + }, + run: function( percent ) { + var eased, + hooks = Tween.propHooks[ this.prop ]; + + if ( this.options.duration ) { + this.pos = eased = jQuery.easing[ this.easing ]( + percent, this.options.duration * percent, 0, 1, this.options.duration + ); + } else { + this.pos = eased = percent; + } + this.now = ( this.end - this.start ) * eased + this.start; + + if ( this.options.step ) { + this.options.step.call( this.elem, this.now, this ); + } + + if ( hooks && hooks.set ) { + hooks.set( this ); + } else { + Tween.propHooks._default.set( this ); + } + return this; + } +}; + +Tween.prototype.init.prototype = Tween.prototype; + +Tween.propHooks = { + _default: { + get: function( tween ) { + var result; + + // Use a property on the element directly when it is not a DOM element, + // or when there is no matching style property that exists. + if ( tween.elem.nodeType !== 1 || + tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { + return tween.elem[ tween.prop ]; + } + + // Passing an empty string as a 3rd parameter to .css will automatically + // attempt a parseFloat and fallback to a string if the parse fails. + // Simple values such as "10px" are parsed to Float; + // complex values such as "rotate(1rad)" are returned as-is. + result = jQuery.css( tween.elem, tween.prop, "" ); + + // Empty strings, null, undefined and "auto" are converted to 0. + return !result || result === "auto" ? 0 : result; + }, + set: function( tween ) { + + // Use step hook for back compat. + // Use cssHook if its there. + // Use .style if available and use plain properties where available. + if ( jQuery.fx.step[ tween.prop ] ) { + jQuery.fx.step[ tween.prop ]( tween ); + } else if ( tween.elem.nodeType === 1 && ( + jQuery.cssHooks[ tween.prop ] || + tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) { + jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); + } else { + tween.elem[ tween.prop ] = tween.now; + } + } + } +}; + +// Support: IE <=9 only +// Panic based approach to setting things on disconnected nodes +Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { + set: function( tween ) { + if ( tween.elem.nodeType && tween.elem.parentNode ) { + tween.elem[ tween.prop ] = tween.now; + } + } +}; + +jQuery.easing = { + linear: function( p ) { + return p; + }, + swing: function( p ) { + return 0.5 - Math.cos( p * Math.PI ) / 2; + }, + _default: "swing" +}; + +jQuery.fx = Tween.prototype.init; + +// Back compat <1.8 extension point +jQuery.fx.step = {}; + + + + +var + fxNow, inProgress, + rfxtypes = /^(?:toggle|show|hide)$/, + rrun = /queueHooks$/; + +function schedule() { + if ( inProgress ) { + if ( document.hidden === false && window.requestAnimationFrame ) { + window.requestAnimationFrame( schedule ); + } else { + window.setTimeout( schedule, jQuery.fx.interval ); + } + + jQuery.fx.tick(); + } +} + +// Animations created synchronously will run synchronously +function createFxNow() { + window.setTimeout( function() { + fxNow = undefined; + } ); + return ( fxNow = Date.now() ); +} + +// Generate parameters to create a standard animation +function genFx( type, includeWidth ) { + var which, + i = 0, + attrs = { height: type }; + + // If we include width, step value is 1 to do all cssExpand values, + // otherwise step value is 2 to skip over Left and Right + includeWidth = includeWidth ? 1 : 0; + for ( ; i < 4; i += 2 - includeWidth ) { + which = cssExpand[ i ]; + attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; + } + + if ( includeWidth ) { + attrs.opacity = attrs.width = type; + } + + return attrs; +} + +function createTween( value, prop, animation ) { + var tween, + collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), + index = 0, + length = collection.length; + for ( ; index < length; index++ ) { + if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { + + // We're done with this property + return tween; + } + } +} + +function defaultPrefilter( elem, props, opts ) { + var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, + isBox = "width" in props || "height" in props, + anim = this, + orig = {}, + style = elem.style, + hidden = elem.nodeType && isHiddenWithinTree( elem ), + dataShow = dataPriv.get( elem, "fxshow" ); + + // Queue-skipping animations hijack the fx hooks + if ( !opts.queue ) { + hooks = jQuery._queueHooks( elem, "fx" ); + if ( hooks.unqueued == null ) { + hooks.unqueued = 0; + oldfire = hooks.empty.fire; + hooks.empty.fire = function() { + if ( !hooks.unqueued ) { + oldfire(); + } + }; + } + hooks.unqueued++; + + anim.always( function() { + + // Ensure the complete handler is called before this completes + anim.always( function() { + hooks.unqueued--; + if ( !jQuery.queue( elem, "fx" ).length ) { + hooks.empty.fire(); + } + } ); + } ); + } + + // Detect show/hide animations + for ( prop in props ) { + value = props[ prop ]; + if ( rfxtypes.test( value ) ) { + delete props[ prop ]; + toggle = toggle || value === "toggle"; + if ( value === ( hidden ? "hide" : "show" ) ) { + + // Pretend to be hidden if this is a "show" and + // there is still data from a stopped show/hide + if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { + hidden = true; + + // Ignore all other no-op show/hide data + } else { + continue; + } + } + orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); + } + } + + // Bail out if this is a no-op like .hide().hide() + propTween = !jQuery.isEmptyObject( props ); + if ( !propTween && jQuery.isEmptyObject( orig ) ) { + return; + } + + // Restrict "overflow" and "display" styles during box animations + if ( isBox && elem.nodeType === 1 ) { + + // Support: IE <=9 - 11, Edge 12 - 15 + // Record all 3 overflow attributes because IE does not infer the shorthand + // from identically-valued overflowX and overflowY and Edge just mirrors + // the overflowX value there. + opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; + + // Identify a display type, preferring old show/hide data over the CSS cascade + restoreDisplay = dataShow && dataShow.display; + if ( restoreDisplay == null ) { + restoreDisplay = dataPriv.get( elem, "display" ); + } + display = jQuery.css( elem, "display" ); + if ( display === "none" ) { + if ( restoreDisplay ) { + display = restoreDisplay; + } else { + + // Get nonempty value(s) by temporarily forcing visibility + showHide( [ elem ], true ); + restoreDisplay = elem.style.display || restoreDisplay; + display = jQuery.css( elem, "display" ); + showHide( [ elem ] ); + } + } + + // Animate inline elements as inline-block + if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { + if ( jQuery.css( elem, "float" ) === "none" ) { + + // Restore the original display value at the end of pure show/hide animations + if ( !propTween ) { + anim.done( function() { + style.display = restoreDisplay; + } ); + if ( restoreDisplay == null ) { + display = style.display; + restoreDisplay = display === "none" ? "" : display; + } + } + style.display = "inline-block"; + } + } + } + + if ( opts.overflow ) { + style.overflow = "hidden"; + anim.always( function() { + style.overflow = opts.overflow[ 0 ]; + style.overflowX = opts.overflow[ 1 ]; + style.overflowY = opts.overflow[ 2 ]; + } ); + } + + // Implement show/hide animations + propTween = false; + for ( prop in orig ) { + + // General show/hide setup for this element animation + if ( !propTween ) { + if ( dataShow ) { + if ( "hidden" in dataShow ) { + hidden = dataShow.hidden; + } + } else { + dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); + } + + // Store hidden/visible for toggle so `.stop().toggle()` "reverses" + if ( toggle ) { + dataShow.hidden = !hidden; + } + + // Show elements before animating them + if ( hidden ) { + showHide( [ elem ], true ); + } + + /* eslint-disable no-loop-func */ + + anim.done( function() { + + /* eslint-enable no-loop-func */ + + // The final step of a "hide" animation is actually hiding the element + if ( !hidden ) { + showHide( [ elem ] ); + } + dataPriv.remove( elem, "fxshow" ); + for ( prop in orig ) { + jQuery.style( elem, prop, orig[ prop ] ); + } + } ); + } + + // Per-property setup + propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); + if ( !( prop in dataShow ) ) { + dataShow[ prop ] = propTween.start; + if ( hidden ) { + propTween.end = propTween.start; + propTween.start = 0; + } + } + } +} + +function propFilter( props, specialEasing ) { + var index, name, easing, value, hooks; + + // camelCase, specialEasing and expand cssHook pass + for ( index in props ) { + name = camelCase( index ); + easing = specialEasing[ name ]; + value = props[ index ]; + if ( Array.isArray( value ) ) { + easing = value[ 1 ]; + value = props[ index ] = value[ 0 ]; + } + + if ( index !== name ) { + props[ name ] = value; + delete props[ index ]; + } + + hooks = jQuery.cssHooks[ name ]; + if ( hooks && "expand" in hooks ) { + value = hooks.expand( value ); + delete props[ name ]; + + // Not quite $.extend, this won't overwrite existing keys. + // Reusing 'index' because we have the correct "name" + for ( index in value ) { + if ( !( index in props ) ) { + props[ index ] = value[ index ]; + specialEasing[ index ] = easing; + } + } + } else { + specialEasing[ name ] = easing; + } + } +} + +function Animation( elem, properties, options ) { + var result, + stopped, + index = 0, + length = Animation.prefilters.length, + deferred = jQuery.Deferred().always( function() { + + // Don't match elem in the :animated selector + delete tick.elem; + } ), + tick = function() { + if ( stopped ) { + return false; + } + var currentTime = fxNow || createFxNow(), + remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), + + // Support: Android 2.3 only + // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) + temp = remaining / animation.duration || 0, + percent = 1 - temp, + index = 0, + length = animation.tweens.length; + + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( percent ); + } + + deferred.notifyWith( elem, [ animation, percent, remaining ] ); + + // If there's more to do, yield + if ( percent < 1 && length ) { + return remaining; + } + + // If this was an empty animation, synthesize a final progress notification + if ( !length ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + } + + // Resolve the animation and report its conclusion + deferred.resolveWith( elem, [ animation ] ); + return false; + }, + animation = deferred.promise( { + elem: elem, + props: jQuery.extend( {}, properties ), + opts: jQuery.extend( true, { + specialEasing: {}, + easing: jQuery.easing._default + }, options ), + originalProperties: properties, + originalOptions: options, + startTime: fxNow || createFxNow(), + duration: options.duration, + tweens: [], + createTween: function( prop, end ) { + var tween = jQuery.Tween( elem, animation.opts, prop, end, + animation.opts.specialEasing[ prop ] || animation.opts.easing ); + animation.tweens.push( tween ); + return tween; + }, + stop: function( gotoEnd ) { + var index = 0, + + // If we are going to the end, we want to run all the tweens + // otherwise we skip this part + length = gotoEnd ? animation.tweens.length : 0; + if ( stopped ) { + return this; + } + stopped = true; + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( 1 ); + } + + // Resolve when we played the last frame; otherwise, reject + if ( gotoEnd ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + deferred.resolveWith( elem, [ animation, gotoEnd ] ); + } else { + deferred.rejectWith( elem, [ animation, gotoEnd ] ); + } + return this; + } + } ), + props = animation.props; + + propFilter( props, animation.opts.specialEasing ); + + for ( ; index < length; index++ ) { + result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); + if ( result ) { + if ( isFunction( result.stop ) ) { + jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = + result.stop.bind( result ); + } + return result; + } + } + + jQuery.map( props, createTween, animation ); + + if ( isFunction( animation.opts.start ) ) { + animation.opts.start.call( elem, animation ); + } + + // Attach callbacks from options + animation + .progress( animation.opts.progress ) + .done( animation.opts.done, animation.opts.complete ) + .fail( animation.opts.fail ) + .always( animation.opts.always ); + + jQuery.fx.timer( + jQuery.extend( tick, { + elem: elem, + anim: animation, + queue: animation.opts.queue + } ) + ); + + return animation; +} + +jQuery.Animation = jQuery.extend( Animation, { + + tweeners: { + "*": [ function( prop, value ) { + var tween = this.createTween( prop, value ); + adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); + return tween; + } ] + }, + + tweener: function( props, callback ) { + if ( isFunction( props ) ) { + callback = props; + props = [ "*" ]; + } else { + props = props.match( rnothtmlwhite ); + } + + var prop, + index = 0, + length = props.length; + + for ( ; index < length; index++ ) { + prop = props[ index ]; + Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; + Animation.tweeners[ prop ].unshift( callback ); + } + }, + + prefilters: [ defaultPrefilter ], + + prefilter: function( callback, prepend ) { + if ( prepend ) { + Animation.prefilters.unshift( callback ); + } else { + Animation.prefilters.push( callback ); + } + } +} ); + +jQuery.speed = function( speed, easing, fn ) { + var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { + complete: fn || !fn && easing || + isFunction( speed ) && speed, + duration: speed, + easing: fn && easing || easing && !isFunction( easing ) && easing + }; + + // Go to the end state if fx are off + if ( jQuery.fx.off ) { + opt.duration = 0; + + } else { + if ( typeof opt.duration !== "number" ) { + if ( opt.duration in jQuery.fx.speeds ) { + opt.duration = jQuery.fx.speeds[ opt.duration ]; + + } else { + opt.duration = jQuery.fx.speeds._default; + } + } + } + + // Normalize opt.queue - true/undefined/null -> "fx" + if ( opt.queue == null || opt.queue === true ) { + opt.queue = "fx"; + } + + // Queueing + opt.old = opt.complete; + + opt.complete = function() { + if ( isFunction( opt.old ) ) { + opt.old.call( this ); + } + + if ( opt.queue ) { + jQuery.dequeue( this, opt.queue ); + } + }; + + return opt; +}; + +jQuery.fn.extend( { + fadeTo: function( speed, to, easing, callback ) { + + // Show any hidden elements after setting opacity to 0 + return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() + + // Animate to the value specified + .end().animate( { opacity: to }, speed, easing, callback ); + }, + animate: function( prop, speed, easing, callback ) { + var empty = jQuery.isEmptyObject( prop ), + optall = jQuery.speed( speed, easing, callback ), + doAnimation = function() { + + // Operate on a copy of prop so per-property easing won't be lost + var anim = Animation( this, jQuery.extend( {}, prop ), optall ); + + // Empty animations, or finishing resolves immediately + if ( empty || dataPriv.get( this, "finish" ) ) { + anim.stop( true ); + } + }; + doAnimation.finish = doAnimation; + + return empty || optall.queue === false ? + this.each( doAnimation ) : + this.queue( optall.queue, doAnimation ); + }, + stop: function( type, clearQueue, gotoEnd ) { + var stopQueue = function( hooks ) { + var stop = hooks.stop; + delete hooks.stop; + stop( gotoEnd ); + }; + + if ( typeof type !== "string" ) { + gotoEnd = clearQueue; + clearQueue = type; + type = undefined; + } + if ( clearQueue ) { + this.queue( type || "fx", [] ); + } + + return this.each( function() { + var dequeue = true, + index = type != null && type + "queueHooks", + timers = jQuery.timers, + data = dataPriv.get( this ); + + if ( index ) { + if ( data[ index ] && data[ index ].stop ) { + stopQueue( data[ index ] ); + } + } else { + for ( index in data ) { + if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { + stopQueue( data[ index ] ); + } + } + } + + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && + ( type == null || timers[ index ].queue === type ) ) { + + timers[ index ].anim.stop( gotoEnd ); + dequeue = false; + timers.splice( index, 1 ); + } + } + + // Start the next in the queue if the last step wasn't forced. + // Timers currently will call their complete callbacks, which + // will dequeue but only if they were gotoEnd. + if ( dequeue || !gotoEnd ) { + jQuery.dequeue( this, type ); + } + } ); + }, + finish: function( type ) { + if ( type !== false ) { + type = type || "fx"; + } + return this.each( function() { + var index, + data = dataPriv.get( this ), + queue = data[ type + "queue" ], + hooks = data[ type + "queueHooks" ], + timers = jQuery.timers, + length = queue ? queue.length : 0; + + // Enable finishing flag on private data + data.finish = true; + + // Empty the queue first + jQuery.queue( this, type, [] ); + + if ( hooks && hooks.stop ) { + hooks.stop.call( this, true ); + } + + // Look for any active animations, and finish them + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && timers[ index ].queue === type ) { + timers[ index ].anim.stop( true ); + timers.splice( index, 1 ); + } + } + + // Look for any animations in the old queue and finish them + for ( index = 0; index < length; index++ ) { + if ( queue[ index ] && queue[ index ].finish ) { + queue[ index ].finish.call( this ); + } + } + + // Turn off finishing flag + delete data.finish; + } ); + } +} ); + +jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) { + var cssFn = jQuery.fn[ name ]; + jQuery.fn[ name ] = function( speed, easing, callback ) { + return speed == null || typeof speed === "boolean" ? + cssFn.apply( this, arguments ) : + this.animate( genFx( name, true ), speed, easing, callback ); + }; +} ); + +// Generate shortcuts for custom animations +jQuery.each( { + slideDown: genFx( "show" ), + slideUp: genFx( "hide" ), + slideToggle: genFx( "toggle" ), + fadeIn: { opacity: "show" }, + fadeOut: { opacity: "hide" }, + fadeToggle: { opacity: "toggle" } +}, function( name, props ) { + jQuery.fn[ name ] = function( speed, easing, callback ) { + return this.animate( props, speed, easing, callback ); + }; +} ); + +jQuery.timers = []; +jQuery.fx.tick = function() { + var timer, + i = 0, + timers = jQuery.timers; + + fxNow = Date.now(); + + for ( ; i < timers.length; i++ ) { + timer = timers[ i ]; + + // Run the timer and safely remove it when done (allowing for external removal) + if ( !timer() && timers[ i ] === timer ) { + timers.splice( i--, 1 ); + } + } + + if ( !timers.length ) { + jQuery.fx.stop(); + } + fxNow = undefined; +}; + +jQuery.fx.timer = function( timer ) { + jQuery.timers.push( timer ); + jQuery.fx.start(); +}; + +jQuery.fx.interval = 13; +jQuery.fx.start = function() { + if ( inProgress ) { + return; + } + + inProgress = true; + schedule(); +}; + +jQuery.fx.stop = function() { + inProgress = null; +}; + +jQuery.fx.speeds = { + slow: 600, + fast: 200, + + // Default speed + _default: 400 +}; + + +// Based off of the plugin by Clint Helfers, with permission. +// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ +jQuery.fn.delay = function( time, type ) { + time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; + type = type || "fx"; + + return this.queue( type, function( next, hooks ) { + var timeout = window.setTimeout( next, time ); + hooks.stop = function() { + window.clearTimeout( timeout ); + }; + } ); +}; + + +( function() { + var input = document.createElement( "input" ), + select = document.createElement( "select" ), + opt = select.appendChild( document.createElement( "option" ) ); + + input.type = "checkbox"; + + // Support: Android <=4.3 only + // Default value for a checkbox should be "on" + support.checkOn = input.value !== ""; + + // Support: IE <=11 only + // Must access selectedIndex to make default options select + support.optSelected = opt.selected; + + // Support: IE <=11 only + // An input loses its value after becoming a radio + input = document.createElement( "input" ); + input.value = "t"; + input.type = "radio"; + support.radioValue = input.value === "t"; +} )(); + + +var boolHook, + attrHandle = jQuery.expr.attrHandle; + +jQuery.fn.extend( { + attr: function( name, value ) { + return access( this, jQuery.attr, name, value, arguments.length > 1 ); + }, + + removeAttr: function( name ) { + return this.each( function() { + jQuery.removeAttr( this, name ); + } ); + } +} ); + +jQuery.extend( { + attr: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set attributes on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + // Fallback to prop when attributes are not supported + if ( typeof elem.getAttribute === "undefined" ) { + return jQuery.prop( elem, name, value ); + } + + // Attribute hooks are determined by the lowercase version + // Grab necessary hook if one is defined + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + hooks = jQuery.attrHooks[ name.toLowerCase() ] || + ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); + } + + if ( value !== undefined ) { + if ( value === null ) { + jQuery.removeAttr( elem, name ); + return; + } + + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + elem.setAttribute( name, value + "" ); + return value; + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + ret = jQuery.find.attr( elem, name ); + + // Non-existent attributes return null, we normalize to undefined + return ret == null ? undefined : ret; + }, + + attrHooks: { + type: { + set: function( elem, value ) { + if ( !support.radioValue && value === "radio" && + nodeName( elem, "input" ) ) { + var val = elem.value; + elem.setAttribute( "type", value ); + if ( val ) { + elem.value = val; + } + return value; + } + } + } + }, + + removeAttr: function( elem, value ) { + var name, + i = 0, + + // Attribute names can contain non-HTML whitespace characters + // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 + attrNames = value && value.match( rnothtmlwhite ); + + if ( attrNames && elem.nodeType === 1 ) { + while ( ( name = attrNames[ i++ ] ) ) { + elem.removeAttribute( name ); + } + } + } +} ); + +// Hooks for boolean attributes +boolHook = { + set: function( elem, value, name ) { + if ( value === false ) { + + // Remove boolean attributes when set to false + jQuery.removeAttr( elem, name ); + } else { + elem.setAttribute( name, name ); + } + return name; + } +}; + +jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) { + var getter = attrHandle[ name ] || jQuery.find.attr; + + attrHandle[ name ] = function( elem, name, isXML ) { + var ret, handle, + lowercaseName = name.toLowerCase(); + + if ( !isXML ) { + + // Avoid an infinite loop by temporarily removing this function from the getter + handle = attrHandle[ lowercaseName ]; + attrHandle[ lowercaseName ] = ret; + ret = getter( elem, name, isXML ) != null ? + lowercaseName : + null; + attrHandle[ lowercaseName ] = handle; + } + return ret; + }; +} ); + + + + +var rfocusable = /^(?:input|select|textarea|button)$/i, + rclickable = /^(?:a|area)$/i; + +jQuery.fn.extend( { + prop: function( name, value ) { + return access( this, jQuery.prop, name, value, arguments.length > 1 ); + }, + + removeProp: function( name ) { + return this.each( function() { + delete this[ jQuery.propFix[ name ] || name ]; + } ); + } +} ); + +jQuery.extend( { + prop: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set properties on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + + // Fix name and attach hooks + name = jQuery.propFix[ name ] || name; + hooks = jQuery.propHooks[ name ]; + } + + if ( value !== undefined ) { + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + return ( elem[ name ] = value ); + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + return elem[ name ]; + }, + + propHooks: { + tabIndex: { + get: function( elem ) { + + // Support: IE <=9 - 11 only + // elem.tabIndex doesn't always return the + // correct value when it hasn't been explicitly set + // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ + // Use proper attribute retrieval(#12072) + var tabindex = jQuery.find.attr( elem, "tabindex" ); + + if ( tabindex ) { + return parseInt( tabindex, 10 ); + } + + if ( + rfocusable.test( elem.nodeName ) || + rclickable.test( elem.nodeName ) && + elem.href + ) { + return 0; + } + + return -1; + } + } + }, + + propFix: { + "for": "htmlFor", + "class": "className" + } +} ); + +// Support: IE <=11 only +// Accessing the selectedIndex property +// forces the browser to respect setting selected +// on the option +// The getter ensures a default option is selected +// when in an optgroup +// eslint rule "no-unused-expressions" is disabled for this code +// since it considers such accessions noop +if ( !support.optSelected ) { + jQuery.propHooks.selected = { + get: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent && parent.parentNode ) { + parent.parentNode.selectedIndex; + } + return null; + }, + set: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent ) { + parent.selectedIndex; + + if ( parent.parentNode ) { + parent.parentNode.selectedIndex; + } + } + } + }; +} + +jQuery.each( [ + "tabIndex", + "readOnly", + "maxLength", + "cellSpacing", + "cellPadding", + "rowSpan", + "colSpan", + "useMap", + "frameBorder", + "contentEditable" +], function() { + jQuery.propFix[ this.toLowerCase() ] = this; +} ); + + + + + // Strip and collapse whitespace according to HTML spec + // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace + function stripAndCollapse( value ) { + var tokens = value.match( rnothtmlwhite ) || []; + return tokens.join( " " ); + } + + +function getClass( elem ) { + return elem.getAttribute && elem.getAttribute( "class" ) || ""; +} + +function classesToArray( value ) { + if ( Array.isArray( value ) ) { + return value; + } + if ( typeof value === "string" ) { + return value.match( rnothtmlwhite ) || []; + } + return []; +} + +jQuery.fn.extend( { + addClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + if ( cur.indexOf( " " + clazz + " " ) < 0 ) { + cur += clazz + " "; + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + removeClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + if ( !arguments.length ) { + return this.attr( "class", "" ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + + // This expression is here for better compressibility (see addClass) + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + + // Remove *all* instances + while ( cur.indexOf( " " + clazz + " " ) > -1 ) { + cur = cur.replace( " " + clazz + " ", " " ); + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + toggleClass: function( value, stateVal ) { + var type = typeof value, + isValidValue = type === "string" || Array.isArray( value ); + + if ( typeof stateVal === "boolean" && isValidValue ) { + return stateVal ? this.addClass( value ) : this.removeClass( value ); + } + + if ( isFunction( value ) ) { + return this.each( function( i ) { + jQuery( this ).toggleClass( + value.call( this, i, getClass( this ), stateVal ), + stateVal + ); + } ); + } + + return this.each( function() { + var className, i, self, classNames; + + if ( isValidValue ) { + + // Toggle individual class names + i = 0; + self = jQuery( this ); + classNames = classesToArray( value ); + + while ( ( className = classNames[ i++ ] ) ) { + + // Check each className given, space separated list + if ( self.hasClass( className ) ) { + self.removeClass( className ); + } else { + self.addClass( className ); + } + } + + // Toggle whole class name + } else if ( value === undefined || type === "boolean" ) { + className = getClass( this ); + if ( className ) { + + // Store className if set + dataPriv.set( this, "__className__", className ); + } + + // If the element has a class name or if we're passed `false`, + // then remove the whole classname (if there was one, the above saved it). + // Otherwise bring back whatever was previously saved (if anything), + // falling back to the empty string if nothing was stored. + if ( this.setAttribute ) { + this.setAttribute( "class", + className || value === false ? + "" : + dataPriv.get( this, "__className__" ) || "" + ); + } + } + } ); + }, + + hasClass: function( selector ) { + var className, elem, + i = 0; + + className = " " + selector + " "; + while ( ( elem = this[ i++ ] ) ) { + if ( elem.nodeType === 1 && + ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { + return true; + } + } + + return false; + } +} ); + + + + +var rreturn = /\r/g; + +jQuery.fn.extend( { + val: function( value ) { + var hooks, ret, valueIsFunction, + elem = this[ 0 ]; + + if ( !arguments.length ) { + if ( elem ) { + hooks = jQuery.valHooks[ elem.type ] || + jQuery.valHooks[ elem.nodeName.toLowerCase() ]; + + if ( hooks && + "get" in hooks && + ( ret = hooks.get( elem, "value" ) ) !== undefined + ) { + return ret; + } + + ret = elem.value; + + // Handle most common string cases + if ( typeof ret === "string" ) { + return ret.replace( rreturn, "" ); + } + + // Handle cases where value is null/undef or number + return ret == null ? "" : ret; + } + + return; + } + + valueIsFunction = isFunction( value ); + + return this.each( function( i ) { + var val; + + if ( this.nodeType !== 1 ) { + return; + } + + if ( valueIsFunction ) { + val = value.call( this, i, jQuery( this ).val() ); + } else { + val = value; + } + + // Treat null/undefined as ""; convert numbers to string + if ( val == null ) { + val = ""; + + } else if ( typeof val === "number" ) { + val += ""; + + } else if ( Array.isArray( val ) ) { + val = jQuery.map( val, function( value ) { + return value == null ? "" : value + ""; + } ); + } + + hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; + + // If set returns undefined, fall back to normal setting + if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { + this.value = val; + } + } ); + } +} ); + +jQuery.extend( { + valHooks: { + option: { + get: function( elem ) { + + var val = jQuery.find.attr( elem, "value" ); + return val != null ? + val : + + // Support: IE <=10 - 11 only + // option.text throws exceptions (#14686, #14858) + // Strip and collapse whitespace + // https://html.spec.whatwg.org/#strip-and-collapse-whitespace + stripAndCollapse( jQuery.text( elem ) ); + } + }, + select: { + get: function( elem ) { + var value, option, i, + options = elem.options, + index = elem.selectedIndex, + one = elem.type === "select-one", + values = one ? null : [], + max = one ? index + 1 : options.length; + + if ( index < 0 ) { + i = max; + + } else { + i = one ? index : 0; + } + + // Loop through all the selected options + for ( ; i < max; i++ ) { + option = options[ i ]; + + // Support: IE <=9 only + // IE8-9 doesn't update selected after form reset (#2551) + if ( ( option.selected || i === index ) && + + // Don't return options that are disabled or in a disabled optgroup + !option.disabled && + ( !option.parentNode.disabled || + !nodeName( option.parentNode, "optgroup" ) ) ) { + + // Get the specific value for the option + value = jQuery( option ).val(); + + // We don't need an array for one selects + if ( one ) { + return value; + } + + // Multi-Selects return an array + values.push( value ); + } + } + + return values; + }, + + set: function( elem, value ) { + var optionSet, option, + options = elem.options, + values = jQuery.makeArray( value ), + i = options.length; + + while ( i-- ) { + option = options[ i ]; + + /* eslint-disable no-cond-assign */ + + if ( option.selected = + jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 + ) { + optionSet = true; + } + + /* eslint-enable no-cond-assign */ + } + + // Force browsers to behave consistently when non-matching value is set + if ( !optionSet ) { + elem.selectedIndex = -1; + } + return values; + } + } + } +} ); + +// Radios and checkboxes getter/setter +jQuery.each( [ "radio", "checkbox" ], function() { + jQuery.valHooks[ this ] = { + set: function( elem, value ) { + if ( Array.isArray( value ) ) { + return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); + } + } + }; + if ( !support.checkOn ) { + jQuery.valHooks[ this ].get = function( elem ) { + return elem.getAttribute( "value" ) === null ? "on" : elem.value; + }; + } +} ); + + + + +// Return jQuery for attributes-only inclusion + + +support.focusin = "onfocusin" in window; + + +var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/, + stopPropagationCallback = function( e ) { + e.stopPropagation(); + }; + +jQuery.extend( jQuery.event, { + + trigger: function( event, data, elem, onlyHandlers ) { + + var i, cur, tmp, bubbleType, ontype, handle, special, lastElement, + eventPath = [ elem || document ], + type = hasOwn.call( event, "type" ) ? event.type : event, + namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; + + cur = lastElement = tmp = elem = elem || document; + + // Don't do events on text and comment nodes + if ( elem.nodeType === 3 || elem.nodeType === 8 ) { + return; + } + + // focus/blur morphs to focusin/out; ensure we're not firing them right now + if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { + return; + } + + if ( type.indexOf( "." ) > -1 ) { + + // Namespaced trigger; create a regexp to match event type in handle() + namespaces = type.split( "." ); + type = namespaces.shift(); + namespaces.sort(); + } + ontype = type.indexOf( ":" ) < 0 && "on" + type; + + // Caller can pass in a jQuery.Event object, Object, or just an event type string + event = event[ jQuery.expando ] ? + event : + new jQuery.Event( type, typeof event === "object" && event ); + + // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) + event.isTrigger = onlyHandlers ? 2 : 3; + event.namespace = namespaces.join( "." ); + event.rnamespace = event.namespace ? + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : + null; + + // Clean up the event in case it is being reused + event.result = undefined; + if ( !event.target ) { + event.target = elem; + } + + // Clone any incoming data and prepend the event, creating the handler arg list + data = data == null ? + [ event ] : + jQuery.makeArray( data, [ event ] ); + + // Allow special events to draw outside the lines + special = jQuery.event.special[ type ] || {}; + if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { + return; + } + + // Determine event propagation path in advance, per W3C events spec (#9951) + // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) + if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) { + + bubbleType = special.delegateType || type; + if ( !rfocusMorph.test( bubbleType + type ) ) { + cur = cur.parentNode; + } + for ( ; cur; cur = cur.parentNode ) { + eventPath.push( cur ); + tmp = cur; + } + + // Only add window if we got to document (e.g., not plain obj or detached DOM) + if ( tmp === ( elem.ownerDocument || document ) ) { + eventPath.push( tmp.defaultView || tmp.parentWindow || window ); + } + } + + // Fire handlers on the event path + i = 0; + while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { + lastElement = cur; + event.type = i > 1 ? + bubbleType : + special.bindType || type; + + // jQuery handler + handle = ( + dataPriv.get( cur, "events" ) || Object.create( null ) + )[ event.type ] && + dataPriv.get( cur, "handle" ); + if ( handle ) { + handle.apply( cur, data ); + } + + // Native handler + handle = ontype && cur[ ontype ]; + if ( handle && handle.apply && acceptData( cur ) ) { + event.result = handle.apply( cur, data ); + if ( event.result === false ) { + event.preventDefault(); + } + } + } + event.type = type; + + // If nobody prevented the default action, do it now + if ( !onlyHandlers && !event.isDefaultPrevented() ) { + + if ( ( !special._default || + special._default.apply( eventPath.pop(), data ) === false ) && + acceptData( elem ) ) { + + // Call a native DOM method on the target with the same name as the event. + // Don't do default actions on window, that's where global variables be (#6170) + if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) { + + // Don't re-trigger an onFOO event when we call its FOO() method + tmp = elem[ ontype ]; + + if ( tmp ) { + elem[ ontype ] = null; + } + + // Prevent re-triggering of the same event, since we already bubbled it above + jQuery.event.triggered = type; + + if ( event.isPropagationStopped() ) { + lastElement.addEventListener( type, stopPropagationCallback ); + } + + elem[ type ](); + + if ( event.isPropagationStopped() ) { + lastElement.removeEventListener( type, stopPropagationCallback ); + } + + jQuery.event.triggered = undefined; + + if ( tmp ) { + elem[ ontype ] = tmp; + } + } + } + } + + return event.result; + }, + + // Piggyback on a donor event to simulate a different one + // Used only for `focus(in | out)` events + simulate: function( type, elem, event ) { + var e = jQuery.extend( + new jQuery.Event(), + event, + { + type: type, + isSimulated: true + } + ); + + jQuery.event.trigger( e, null, elem ); + } + +} ); + +jQuery.fn.extend( { + + trigger: function( type, data ) { + return this.each( function() { + jQuery.event.trigger( type, data, this ); + } ); + }, + triggerHandler: function( type, data ) { + var elem = this[ 0 ]; + if ( elem ) { + return jQuery.event.trigger( type, data, elem, true ); + } + } +} ); + + +// Support: Firefox <=44 +// Firefox doesn't have focus(in | out) events +// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 +// +// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 +// focus(in | out) events fire after focus & blur events, +// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order +// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 +if ( !support.focusin ) { + jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { + + // Attach a single capturing handler on the document while someone wants focusin/focusout + var handler = function( event ) { + jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); + }; + + jQuery.event.special[ fix ] = { + setup: function() { + + // Handle: regular nodes (via `this.ownerDocument`), window + // (via `this.document`) & document (via `this`). + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ); + + if ( !attaches ) { + doc.addEventListener( orig, handler, true ); + } + dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); + }, + teardown: function() { + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ) - 1; + + if ( !attaches ) { + doc.removeEventListener( orig, handler, true ); + dataPriv.remove( doc, fix ); + + } else { + dataPriv.access( doc, fix, attaches ); + } + } + }; + } ); +} +var location = window.location; + +var nonce = { guid: Date.now() }; + +var rquery = ( /\?/ ); + + + +// Cross-browser xml parsing +jQuery.parseXML = function( data ) { + var xml; + if ( !data || typeof data !== "string" ) { + return null; + } + + // Support: IE 9 - 11 only + // IE throws on parseFromString with invalid input. + try { + xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); + } catch ( e ) { + xml = undefined; + } + + if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) { + jQuery.error( "Invalid XML: " + data ); + } + return xml; +}; + + +var + rbracket = /\[\]$/, + rCRLF = /\r?\n/g, + rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, + rsubmittable = /^(?:input|select|textarea|keygen)/i; + +function buildParams( prefix, obj, traditional, add ) { + var name; + + if ( Array.isArray( obj ) ) { + + // Serialize array item. + jQuery.each( obj, function( i, v ) { + if ( traditional || rbracket.test( prefix ) ) { + + // Treat each array item as a scalar. + add( prefix, v ); + + } else { + + // Item is non-scalar (array or object), encode its numeric index. + buildParams( + prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", + v, + traditional, + add + ); + } + } ); + + } else if ( !traditional && toType( obj ) === "object" ) { + + // Serialize object item. + for ( name in obj ) { + buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); + } + + } else { + + // Serialize scalar item. + add( prefix, obj ); + } +} + +// Serialize an array of form elements or a set of +// key/values into a query string +jQuery.param = function( a, traditional ) { + var prefix, + s = [], + add = function( key, valueOrFunction ) { + + // If value is a function, invoke it and use its return value + var value = isFunction( valueOrFunction ) ? + valueOrFunction() : + valueOrFunction; + + s[ s.length ] = encodeURIComponent( key ) + "=" + + encodeURIComponent( value == null ? "" : value ); + }; + + if ( a == null ) { + return ""; + } + + // If an array was passed in, assume that it is an array of form elements. + if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { + + // Serialize the form elements + jQuery.each( a, function() { + add( this.name, this.value ); + } ); + + } else { + + // If traditional, encode the "old" way (the way 1.3.2 or older + // did it), otherwise encode params recursively. + for ( prefix in a ) { + buildParams( prefix, a[ prefix ], traditional, add ); + } + } + + // Return the resulting serialization + return s.join( "&" ); +}; + +jQuery.fn.extend( { + serialize: function() { + return jQuery.param( this.serializeArray() ); + }, + serializeArray: function() { + return this.map( function() { + + // Can add propHook for "elements" to filter or add form elements + var elements = jQuery.prop( this, "elements" ); + return elements ? jQuery.makeArray( elements ) : this; + } ) + .filter( function() { + var type = this.type; + + // Use .is( ":disabled" ) so that fieldset[disabled] works + return this.name && !jQuery( this ).is( ":disabled" ) && + rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && + ( this.checked || !rcheckableType.test( type ) ); + } ) + .map( function( _i, elem ) { + var val = jQuery( this ).val(); + + if ( val == null ) { + return null; + } + + if ( Array.isArray( val ) ) { + return jQuery.map( val, function( val ) { + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ); + } + + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ).get(); + } +} ); + + +var + r20 = /%20/g, + rhash = /#.*$/, + rantiCache = /([?&])_=[^&]*/, + rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, + + // #7653, #8125, #8152: local protocol detection + rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, + rnoContent = /^(?:GET|HEAD)$/, + rprotocol = /^\/\//, + + /* Prefilters + * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) + * 2) These are called: + * - BEFORE asking for a transport + * - AFTER param serialization (s.data is a string if s.processData is true) + * 3) key is the dataType + * 4) the catchall symbol "*" can be used + * 5) execution will start with transport dataType and THEN continue down to "*" if needed + */ + prefilters = {}, + + /* Transports bindings + * 1) key is the dataType + * 2) the catchall symbol "*" can be used + * 3) selection will start with transport dataType and THEN go to "*" if needed + */ + transports = {}, + + // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression + allTypes = "*/".concat( "*" ), + + // Anchor tag for parsing the document origin + originAnchor = document.createElement( "a" ); + originAnchor.href = location.href; + +// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport +function addToPrefiltersOrTransports( structure ) { + + // dataTypeExpression is optional and defaults to "*" + return function( dataTypeExpression, func ) { + + if ( typeof dataTypeExpression !== "string" ) { + func = dataTypeExpression; + dataTypeExpression = "*"; + } + + var dataType, + i = 0, + dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; + + if ( isFunction( func ) ) { + + // For each dataType in the dataTypeExpression + while ( ( dataType = dataTypes[ i++ ] ) ) { + + // Prepend if requested + if ( dataType[ 0 ] === "+" ) { + dataType = dataType.slice( 1 ) || "*"; + ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); + + // Otherwise append + } else { + ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); + } + } + } + }; +} + +// Base inspection function for prefilters and transports +function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { + + var inspected = {}, + seekingTransport = ( structure === transports ); + + function inspect( dataType ) { + var selected; + inspected[ dataType ] = true; + jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { + var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); + if ( typeof dataTypeOrTransport === "string" && + !seekingTransport && !inspected[ dataTypeOrTransport ] ) { + + options.dataTypes.unshift( dataTypeOrTransport ); + inspect( dataTypeOrTransport ); + return false; + } else if ( seekingTransport ) { + return !( selected = dataTypeOrTransport ); + } + } ); + return selected; + } + + return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); +} + +// A special extend for ajax options +// that takes "flat" options (not to be deep extended) +// Fixes #9887 +function ajaxExtend( target, src ) { + var key, deep, + flatOptions = jQuery.ajaxSettings.flatOptions || {}; + + for ( key in src ) { + if ( src[ key ] !== undefined ) { + ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; + } + } + if ( deep ) { + jQuery.extend( true, target, deep ); + } + + return target; +} + +/* Handles responses to an ajax request: + * - finds the right dataType (mediates between content-type and expected dataType) + * - returns the corresponding response + */ +function ajaxHandleResponses( s, jqXHR, responses ) { + + var ct, type, finalDataType, firstDataType, + contents = s.contents, + dataTypes = s.dataTypes; + + // Remove auto dataType and get content-type in the process + while ( dataTypes[ 0 ] === "*" ) { + dataTypes.shift(); + if ( ct === undefined ) { + ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); + } + } + + // Check if we're dealing with a known content-type + if ( ct ) { + for ( type in contents ) { + if ( contents[ type ] && contents[ type ].test( ct ) ) { + dataTypes.unshift( type ); + break; + } + } + } + + // Check to see if we have a response for the expected dataType + if ( dataTypes[ 0 ] in responses ) { + finalDataType = dataTypes[ 0 ]; + } else { + + // Try convertible dataTypes + for ( type in responses ) { + if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { + finalDataType = type; + break; + } + if ( !firstDataType ) { + firstDataType = type; + } + } + + // Or just use first one + finalDataType = finalDataType || firstDataType; + } + + // If we found a dataType + // We add the dataType to the list if needed + // and return the corresponding response + if ( finalDataType ) { + if ( finalDataType !== dataTypes[ 0 ] ) { + dataTypes.unshift( finalDataType ); + } + return responses[ finalDataType ]; + } +} + +/* Chain conversions given the request and the original response + * Also sets the responseXXX fields on the jqXHR instance + */ +function ajaxConvert( s, response, jqXHR, isSuccess ) { + var conv2, current, conv, tmp, prev, + converters = {}, + + // Work with a copy of dataTypes in case we need to modify it for conversion + dataTypes = s.dataTypes.slice(); + + // Create converters map with lowercased keys + if ( dataTypes[ 1 ] ) { + for ( conv in s.converters ) { + converters[ conv.toLowerCase() ] = s.converters[ conv ]; + } + } + + current = dataTypes.shift(); + + // Convert to each sequential dataType + while ( current ) { + + if ( s.responseFields[ current ] ) { + jqXHR[ s.responseFields[ current ] ] = response; + } + + // Apply the dataFilter if provided + if ( !prev && isSuccess && s.dataFilter ) { + response = s.dataFilter( response, s.dataType ); + } + + prev = current; + current = dataTypes.shift(); + + if ( current ) { + + // There's only work to do if current dataType is non-auto + if ( current === "*" ) { + + current = prev; + + // Convert response if prev dataType is non-auto and differs from current + } else if ( prev !== "*" && prev !== current ) { + + // Seek a direct converter + conv = converters[ prev + " " + current ] || converters[ "* " + current ]; + + // If none found, seek a pair + if ( !conv ) { + for ( conv2 in converters ) { + + // If conv2 outputs current + tmp = conv2.split( " " ); + if ( tmp[ 1 ] === current ) { + + // If prev can be converted to accepted input + conv = converters[ prev + " " + tmp[ 0 ] ] || + converters[ "* " + tmp[ 0 ] ]; + if ( conv ) { + + // Condense equivalence converters + if ( conv === true ) { + conv = converters[ conv2 ]; + + // Otherwise, insert the intermediate dataType + } else if ( converters[ conv2 ] !== true ) { + current = tmp[ 0 ]; + dataTypes.unshift( tmp[ 1 ] ); + } + break; + } + } + } + } + + // Apply converter (if not an equivalence) + if ( conv !== true ) { + + // Unless errors are allowed to bubble, catch and return them + if ( conv && s.throws ) { + response = conv( response ); + } else { + try { + response = conv( response ); + } catch ( e ) { + return { + state: "parsererror", + error: conv ? e : "No conversion from " + prev + " to " + current + }; + } + } + } + } + } + } + + return { state: "success", data: response }; +} + +jQuery.extend( { + + // Counter for holding the number of active queries + active: 0, + + // Last-Modified header cache for next request + lastModified: {}, + etag: {}, + + ajaxSettings: { + url: location.href, + type: "GET", + isLocal: rlocalProtocol.test( location.protocol ), + global: true, + processData: true, + async: true, + contentType: "application/x-www-form-urlencoded; charset=UTF-8", + + /* + timeout: 0, + data: null, + dataType: null, + username: null, + password: null, + cache: null, + throws: false, + traditional: false, + headers: {}, + */ + + accepts: { + "*": allTypes, + text: "text/plain", + html: "text/html", + xml: "application/xml, text/xml", + json: "application/json, text/javascript" + }, + + contents: { + xml: /\bxml\b/, + html: /\bhtml/, + json: /\bjson\b/ + }, + + responseFields: { + xml: "responseXML", + text: "responseText", + json: "responseJSON" + }, + + // Data converters + // Keys separate source (or catchall "*") and destination types with a single space + converters: { + + // Convert anything to text + "* text": String, + + // Text to html (true = no transformation) + "text html": true, + + // Evaluate text as a json expression + "text json": JSON.parse, + + // Parse text as xml + "text xml": jQuery.parseXML + }, + + // For options that shouldn't be deep extended: + // you can add your own custom options here if + // and when you create one that shouldn't be + // deep extended (see ajaxExtend) + flatOptions: { + url: true, + context: true + } + }, + + // Creates a full fledged settings object into target + // with both ajaxSettings and settings fields. + // If target is omitted, writes into ajaxSettings. + ajaxSetup: function( target, settings ) { + return settings ? + + // Building a settings object + ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : + + // Extending ajaxSettings + ajaxExtend( jQuery.ajaxSettings, target ); + }, + + ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), + ajaxTransport: addToPrefiltersOrTransports( transports ), + + // Main method + ajax: function( url, options ) { + + // If url is an object, simulate pre-1.5 signature + if ( typeof url === "object" ) { + options = url; + url = undefined; + } + + // Force options to be an object + options = options || {}; + + var transport, + + // URL without anti-cache param + cacheURL, + + // Response headers + responseHeadersString, + responseHeaders, + + // timeout handle + timeoutTimer, + + // Url cleanup var + urlAnchor, + + // Request state (becomes false upon send and true upon completion) + completed, + + // To know if global events are to be dispatched + fireGlobals, + + // Loop variable + i, + + // uncached part of the url + uncached, + + // Create the final options object + s = jQuery.ajaxSetup( {}, options ), + + // Callbacks context + callbackContext = s.context || s, + + // Context for global events is callbackContext if it is a DOM node or jQuery collection + globalEventContext = s.context && + ( callbackContext.nodeType || callbackContext.jquery ) ? + jQuery( callbackContext ) : + jQuery.event, + + // Deferreds + deferred = jQuery.Deferred(), + completeDeferred = jQuery.Callbacks( "once memory" ), + + // Status-dependent callbacks + statusCode = s.statusCode || {}, + + // Headers (they are sent all at once) + requestHeaders = {}, + requestHeadersNames = {}, + + // Default abort message + strAbort = "canceled", + + // Fake xhr + jqXHR = { + readyState: 0, + + // Builds headers hashtable if needed + getResponseHeader: function( key ) { + var match; + if ( completed ) { + if ( !responseHeaders ) { + responseHeaders = {}; + while ( ( match = rheaders.exec( responseHeadersString ) ) ) { + responseHeaders[ match[ 1 ].toLowerCase() + " " ] = + ( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] ) + .concat( match[ 2 ] ); + } + } + match = responseHeaders[ key.toLowerCase() + " " ]; + } + return match == null ? null : match.join( ", " ); + }, + + // Raw string + getAllResponseHeaders: function() { + return completed ? responseHeadersString : null; + }, + + // Caches the header + setRequestHeader: function( name, value ) { + if ( completed == null ) { + name = requestHeadersNames[ name.toLowerCase() ] = + requestHeadersNames[ name.toLowerCase() ] || name; + requestHeaders[ name ] = value; + } + return this; + }, + + // Overrides response content-type header + overrideMimeType: function( type ) { + if ( completed == null ) { + s.mimeType = type; + } + return this; + }, + + // Status-dependent callbacks + statusCode: function( map ) { + var code; + if ( map ) { + if ( completed ) { + + // Execute the appropriate callbacks + jqXHR.always( map[ jqXHR.status ] ); + } else { + + // Lazy-add the new callbacks in a way that preserves old ones + for ( code in map ) { + statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; + } + } + } + return this; + }, + + // Cancel the request + abort: function( statusText ) { + var finalText = statusText || strAbort; + if ( transport ) { + transport.abort( finalText ); + } + done( 0, finalText ); + return this; + } + }; + + // Attach deferreds + deferred.promise( jqXHR ); + + // Add protocol if not provided (prefilters might expect it) + // Handle falsy url in the settings object (#10093: consistency with old signature) + // We also use the url parameter if available + s.url = ( ( url || s.url || location.href ) + "" ) + .replace( rprotocol, location.protocol + "//" ); + + // Alias method option to type as per ticket #12004 + s.type = options.method || options.type || s.method || s.type; + + // Extract dataTypes list + s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; + + // A cross-domain request is in order when the origin doesn't match the current origin. + if ( s.crossDomain == null ) { + urlAnchor = document.createElement( "a" ); + + // Support: IE <=8 - 11, Edge 12 - 15 + // IE throws exception on accessing the href property if url is malformed, + // e.g. http://example.com:80x/ + try { + urlAnchor.href = s.url; + + // Support: IE <=8 - 11 only + // Anchor's host property isn't correctly set when s.url is relative + urlAnchor.href = urlAnchor.href; + s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== + urlAnchor.protocol + "//" + urlAnchor.host; + } catch ( e ) { + + // If there is an error parsing the URL, assume it is crossDomain, + // it can be rejected by the transport if it is invalid + s.crossDomain = true; + } + } + + // Convert data if not already a string + if ( s.data && s.processData && typeof s.data !== "string" ) { + s.data = jQuery.param( s.data, s.traditional ); + } + + // Apply prefilters + inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); + + // If request was aborted inside a prefilter, stop there + if ( completed ) { + return jqXHR; + } + + // We can fire global events as of now if asked to + // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) + fireGlobals = jQuery.event && s.global; + + // Watch for a new set of requests + if ( fireGlobals && jQuery.active++ === 0 ) { + jQuery.event.trigger( "ajaxStart" ); + } + + // Uppercase the type + s.type = s.type.toUpperCase(); + + // Determine if request has content + s.hasContent = !rnoContent.test( s.type ); + + // Save the URL in case we're toying with the If-Modified-Since + // and/or If-None-Match header later on + // Remove hash to simplify url manipulation + cacheURL = s.url.replace( rhash, "" ); + + // More options handling for requests with no content + if ( !s.hasContent ) { + + // Remember the hash so we can put it back + uncached = s.url.slice( cacheURL.length ); + + // If data is available and should be processed, append data to url + if ( s.data && ( s.processData || typeof s.data === "string" ) ) { + cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; + + // #9682: remove data so that it's not used in an eventual retry + delete s.data; + } + + // Add or update anti-cache param if needed + if ( s.cache === false ) { + cacheURL = cacheURL.replace( rantiCache, "$1" ); + uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) + + uncached; + } + + // Put hash and anti-cache on the URL that will be requested (gh-1732) + s.url = cacheURL + uncached; + + // Change '%20' to '+' if this is encoded form body content (gh-2658) + } else if ( s.data && s.processData && + ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { + s.data = s.data.replace( r20, "+" ); + } + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + if ( jQuery.lastModified[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); + } + if ( jQuery.etag[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); + } + } + + // Set the correct header, if data is being sent + if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { + jqXHR.setRequestHeader( "Content-Type", s.contentType ); + } + + // Set the Accepts header for the server, depending on the dataType + jqXHR.setRequestHeader( + "Accept", + s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? + s.accepts[ s.dataTypes[ 0 ] ] + + ( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) : + s.accepts[ "*" ] + ); + + // Check for headers option + for ( i in s.headers ) { + jqXHR.setRequestHeader( i, s.headers[ i ] ); + } + + // Allow custom headers/mimetypes and early abort + if ( s.beforeSend && + ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) { + + // Abort if not done already and return + return jqXHR.abort(); + } + + // Aborting is no longer a cancellation + strAbort = "abort"; + + // Install callbacks on deferreds + completeDeferred.add( s.complete ); + jqXHR.done( s.success ); + jqXHR.fail( s.error ); + + // Get transport + transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR ); + + // If no transport, we auto-abort + if ( !transport ) { + done( -1, "No Transport" ); + } else { + jqXHR.readyState = 1; + + // Send global event + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] ); + } + + // If request was aborted inside ajaxSend, stop there + if ( completed ) { + return jqXHR; + } + + // Timeout + if ( s.async && s.timeout > 0 ) { + timeoutTimer = window.setTimeout( function() { + jqXHR.abort( "timeout" ); + }, s.timeout ); + } + + try { + completed = false; + transport.send( requestHeaders, done ); + } catch ( e ) { + + // Rethrow post-completion exceptions + if ( completed ) { + throw e; + } + + // Propagate others as results + done( -1, e ); + } + } + + // Callback for when everything is done + function done( status, nativeStatusText, responses, headers ) { + var isSuccess, success, error, response, modified, + statusText = nativeStatusText; + + // Ignore repeat invocations + if ( completed ) { + return; + } + + completed = true; + + // Clear timeout if it exists + if ( timeoutTimer ) { + window.clearTimeout( timeoutTimer ); + } + + // Dereference transport for early garbage collection + // (no matter how long the jqXHR object will be used) + transport = undefined; + + // Cache response headers + responseHeadersString = headers || ""; + + // Set readyState + jqXHR.readyState = status > 0 ? 4 : 0; + + // Determine if successful + isSuccess = status >= 200 && status < 300 || status === 304; + + // Get response data + if ( responses ) { + response = ajaxHandleResponses( s, jqXHR, responses ); + } + + // Use a noop converter for missing script + if ( !isSuccess && jQuery.inArray( "script", s.dataTypes ) > -1 ) { + s.converters[ "text script" ] = function() {}; + } + + // Convert no matter what (that way responseXXX fields are always set) + response = ajaxConvert( s, response, jqXHR, isSuccess ); + + // If successful, handle type chaining + if ( isSuccess ) { + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + modified = jqXHR.getResponseHeader( "Last-Modified" ); + if ( modified ) { + jQuery.lastModified[ cacheURL ] = modified; + } + modified = jqXHR.getResponseHeader( "etag" ); + if ( modified ) { + jQuery.etag[ cacheURL ] = modified; + } + } + + // if no content + if ( status === 204 || s.type === "HEAD" ) { + statusText = "nocontent"; + + // if not modified + } else if ( status === 304 ) { + statusText = "notmodified"; + + // If we have data, let's convert it + } else { + statusText = response.state; + success = response.data; + error = response.error; + isSuccess = !error; + } + } else { + + // Extract error from statusText and normalize for non-aborts + error = statusText; + if ( status || !statusText ) { + statusText = "error"; + if ( status < 0 ) { + status = 0; + } + } + } + + // Set data for the fake xhr object + jqXHR.status = status; + jqXHR.statusText = ( nativeStatusText || statusText ) + ""; + + // Success/Error + if ( isSuccess ) { + deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] ); + } else { + deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] ); + } + + // Status-dependent callbacks + jqXHR.statusCode( statusCode ); + statusCode = undefined; + + if ( fireGlobals ) { + globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError", + [ jqXHR, s, isSuccess ? success : error ] ); + } + + // Complete + completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] ); + + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] ); + + // Handle the global AJAX counter + if ( !( --jQuery.active ) ) { + jQuery.event.trigger( "ajaxStop" ); + } + } + } + + return jqXHR; + }, + + getJSON: function( url, data, callback ) { + return jQuery.get( url, data, callback, "json" ); + }, + + getScript: function( url, callback ) { + return jQuery.get( url, undefined, callback, "script" ); + } +} ); + +jQuery.each( [ "get", "post" ], function( _i, method ) { + jQuery[ method ] = function( url, data, callback, type ) { + + // Shift arguments if data argument was omitted + if ( isFunction( data ) ) { + type = type || callback; + callback = data; + data = undefined; + } + + // The url can be an options object (which then must have .url) + return jQuery.ajax( jQuery.extend( { + url: url, + type: method, + dataType: type, + data: data, + success: callback + }, jQuery.isPlainObject( url ) && url ) ); + }; +} ); + +jQuery.ajaxPrefilter( function( s ) { + var i; + for ( i in s.headers ) { + if ( i.toLowerCase() === "content-type" ) { + s.contentType = s.headers[ i ] || ""; + } + } +} ); + + +jQuery._evalUrl = function( url, options, doc ) { + return jQuery.ajax( { + url: url, + + // Make this explicit, since user can override this through ajaxSetup (#11264) + type: "GET", + dataType: "script", + cache: true, + async: false, + global: false, + + // Only evaluate the response if it is successful (gh-4126) + // dataFilter is not invoked for failure responses, so using it instead + // of the default converter is kludgy but it works. + converters: { + "text script": function() {} + }, + dataFilter: function( response ) { + jQuery.globalEval( response, options, doc ); + } + } ); +}; + + +jQuery.fn.extend( { + wrapAll: function( html ) { + var wrap; + + if ( this[ 0 ] ) { + if ( isFunction( html ) ) { + html = html.call( this[ 0 ] ); + } + + // The elements to wrap the target around + wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true ); + + if ( this[ 0 ].parentNode ) { + wrap.insertBefore( this[ 0 ] ); + } + + wrap.map( function() { + var elem = this; + + while ( elem.firstElementChild ) { + elem = elem.firstElementChild; + } + + return elem; + } ).append( this ); + } + + return this; + }, + + wrapInner: function( html ) { + if ( isFunction( html ) ) { + return this.each( function( i ) { + jQuery( this ).wrapInner( html.call( this, i ) ); + } ); + } + + return this.each( function() { + var self = jQuery( this ), + contents = self.contents(); + + if ( contents.length ) { + contents.wrapAll( html ); + + } else { + self.append( html ); + } + } ); + }, + + wrap: function( html ) { + var htmlIsFunction = isFunction( html ); + + return this.each( function( i ) { + jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html ); + } ); + }, + + unwrap: function( selector ) { + this.parent( selector ).not( "body" ).each( function() { + jQuery( this ).replaceWith( this.childNodes ); + } ); + return this; + } +} ); + + +jQuery.expr.pseudos.hidden = function( elem ) { + return !jQuery.expr.pseudos.visible( elem ); +}; +jQuery.expr.pseudos.visible = function( elem ) { + return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length ); +}; + + + + +jQuery.ajaxSettings.xhr = function() { + try { + return new window.XMLHttpRequest(); + } catch ( e ) {} +}; + +var xhrSuccessStatus = { + + // File protocol always yields status code 0, assume 200 + 0: 200, + + // Support: IE <=9 only + // #1450: sometimes IE returns 1223 when it should be 204 + 1223: 204 + }, + xhrSupported = jQuery.ajaxSettings.xhr(); + +support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported ); +support.ajax = xhrSupported = !!xhrSupported; + +jQuery.ajaxTransport( function( options ) { + var callback, errorCallback; + + // Cross domain only allowed if supported through XMLHttpRequest + if ( support.cors || xhrSupported && !options.crossDomain ) { + return { + send: function( headers, complete ) { + var i, + xhr = options.xhr(); + + xhr.open( + options.type, + options.url, + options.async, + options.username, + options.password + ); + + // Apply custom fields if provided + if ( options.xhrFields ) { + for ( i in options.xhrFields ) { + xhr[ i ] = options.xhrFields[ i ]; + } + } + + // Override mime type if needed + if ( options.mimeType && xhr.overrideMimeType ) { + xhr.overrideMimeType( options.mimeType ); + } + + // X-Requested-With header + // For cross-domain requests, seeing as conditions for a preflight are + // akin to a jigsaw puzzle, we simply never set it to be sure. + // (it can always be set on a per-request basis or even using ajaxSetup) + // For same-domain requests, won't change header if already provided. + if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) { + headers[ "X-Requested-With" ] = "XMLHttpRequest"; + } + + // Set headers + for ( i in headers ) { + xhr.setRequestHeader( i, headers[ i ] ); + } + + // Callback + callback = function( type ) { + return function() { + if ( callback ) { + callback = errorCallback = xhr.onload = + xhr.onerror = xhr.onabort = xhr.ontimeout = + xhr.onreadystatechange = null; + + if ( type === "abort" ) { + xhr.abort(); + } else if ( type === "error" ) { + + // Support: IE <=9 only + // On a manual native abort, IE9 throws + // errors on any property access that is not readyState + if ( typeof xhr.status !== "number" ) { + complete( 0, "error" ); + } else { + complete( + + // File: protocol always yields status 0; see #8605, #14207 + xhr.status, + xhr.statusText + ); + } + } else { + complete( + xhrSuccessStatus[ xhr.status ] || xhr.status, + xhr.statusText, + + // Support: IE <=9 only + // IE9 has no XHR2 but throws on binary (trac-11426) + // For XHR2 non-text, let the caller handle it (gh-2498) + ( xhr.responseType || "text" ) !== "text" || + typeof xhr.responseText !== "string" ? + { binary: xhr.response } : + { text: xhr.responseText }, + xhr.getAllResponseHeaders() + ); + } + } + }; + }; + + // Listen to events + xhr.onload = callback(); + errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" ); + + // Support: IE 9 only + // Use onreadystatechange to replace onabort + // to handle uncaught aborts + if ( xhr.onabort !== undefined ) { + xhr.onabort = errorCallback; + } else { + xhr.onreadystatechange = function() { + + // Check readyState before timeout as it changes + if ( xhr.readyState === 4 ) { + + // Allow onerror to be called first, + // but that will not handle a native abort + // Also, save errorCallback to a variable + // as xhr.onerror cannot be accessed + window.setTimeout( function() { + if ( callback ) { + errorCallback(); + } + } ); + } + }; + } + + // Create the abort callback + callback = callback( "abort" ); + + try { + + // Do send the request (this may raise an exception) + xhr.send( options.hasContent && options.data || null ); + } catch ( e ) { + + // #14683: Only rethrow if this hasn't been notified as an error yet + if ( callback ) { + throw e; + } + } + }, + + abort: function() { + if ( callback ) { + callback(); + } + } + }; + } +} ); + + + + +// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432) +jQuery.ajaxPrefilter( function( s ) { + if ( s.crossDomain ) { + s.contents.script = false; + } +} ); + +// Install script dataType +jQuery.ajaxSetup( { + accepts: { + script: "text/javascript, application/javascript, " + + "application/ecmascript, application/x-ecmascript" + }, + contents: { + script: /\b(?:java|ecma)script\b/ + }, + converters: { + "text script": function( text ) { + jQuery.globalEval( text ); + return text; + } + } +} ); + +// Handle cache's special case and crossDomain +jQuery.ajaxPrefilter( "script", function( s ) { + if ( s.cache === undefined ) { + s.cache = false; + } + if ( s.crossDomain ) { + s.type = "GET"; + } +} ); + +// Bind script tag hack transport +jQuery.ajaxTransport( "script", function( s ) { + + // This transport only deals with cross domain or forced-by-attrs requests + if ( s.crossDomain || s.scriptAttrs ) { + var script, callback; + return { + send: function( _, complete ) { + script = jQuery( " + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Validation Algorithm

    +

    The specification of WebAssembly validation is purely declarative. +It describes the constraints that must be met by a module or instruction sequence to be valid.

    +

    This section sketches the skeleton of a sound and complete algorithm for effectively validating code, i.e., sequences of instructions. +(Other aspects of validation are straightforward to implement.)

    +

    In fact, the algorithm is expressed over the flat sequence of opcodes as occurring in the binary format, and performs only a single pass over it. +Consequently, it can be integrated directly into a decoder.

    +

    The algorithm is expressed in typed pseudo code whose semantics is intended to be self-explanatory.

    +
    +

    Data Structures

    +

    Types are representable as an enumeration.

    +
    type val_type = I32 | I64 | F32 | F64 | V128 | Funcref | Externref
+
+func is_num(t : val_type | Unknown) : bool =
+  return t = I32 || t = I64 || t = F32 || t = F64 || t = Unknown
+
+func is_vec(t : val_type | Unknown) : bool =
+  return t = V128 || t = Unknown
+
+func is_ref(t : val_type | Unknown) : bool =
+  return t = Funcref || t = Externref || t = Unknown
+
    +
    +

    The algorithm uses two separate stacks: the value stack and the control stack. +The former tracks the types of operand values on the stack, +the latter surrounding structured control instructions and their associated blocks.

    +
    type val_stack = stack(val_type | Unknown)
+
+type ctrl_stack = stack(ctrl_frame)
+type ctrl_frame = {
+  opcode : opcode
+  start_types : list(val_type)
+  end_types : list(val_type)
+  height : nat
+  unreachable : bool
+}
+
    +
    +

    For each value, the value stack records its value type, or Unknown when the type is not known.

    +

    For each entered block, the control stack records a control frame with the originating opcode, the types on the top of the operand stack at the start and end of the block (used to check its result as well as branches), the height of the operand stack at the start of the block (used to check that operands do not underflow the current block), and a flag recording whether the remainder of the block is unreachable (used to handle stack-polymorphic typing after branches).

    +

    For the purpose of presenting the algorithm, the operand and control stacks are simply maintained as global variables:

    +
    var vals : val_stack
+var ctrls : ctrl_stack
+
    +
    +

    However, these variables are not manipulated directly by the main checking function, but through a set of auxiliary functions:

    +
    func push_val(type : val_type | Unknown) =
+  vals.push(type)
+
+func pop_val() : val_type | Unknown =
+  if (vals.size() = ctrls[0].height && ctrls[0].unreachable) return Unknown
+  error_if(vals.size() = ctrls[0].height)
+  return vals.pop()
+
+func pop_val(expect : val_type | Unknown) : val_type | Unknown =
+  let actual = pop_val()
+  error_if(actual =/= expect && actual =/= Unknown && expect =/= Unknown)
+  return actual
+
+func push_vals(types : list(val_type)) = foreach (t in types) push_val(t)
+func pop_vals(types : list(val_type)) : list(val_type) =
+  var popped := []
+  foreach (t in reverse(types)) popped.prepend(pop_val(t))
+  return popped
+
    +
    +

    Pushing an operand value simply pushes the respective type to the value stack.

    +

    Popping an operand value checks that the value stack does not underflow the current block and then removes one type. +But first, a special case is handled where the block contains no known values, but has been marked as unreachable. +That can occur after an unconditional branch, when the stack is typed polymorphically. +In that case, an unknown type is returned.

    +

    A second function for popping an operand value takes an expected type, which the actual operand type is checked against. +The types may differ in case one of them is Unknown. +The function returns the actual type popped from the stack.

    +

    Finally, there are accumulative functions for pushing or popping multiple operand types.

    +
    +

    Note

    +

    The notation stack[i] is meant to index the stack from the top, +so that, e.g., ctrls[0] accesses the element pushed last.

    +
    +

    The control stack is likewise manipulated through auxiliary functions:

    +
    func push_ctrl(opcode : opcode, in : list(val_type), out : list(val_type)) =
+  let frame = ctrl_frame(opcode, in, out, vals.size(), false)
+  ctrls.push(frame)
+  push_vals(in)
+
+func pop_ctrl() : ctrl_frame =
+  error_if(ctrls.is_empty())
+  let frame = ctrls[0]
+  pop_vals(frame.end_types)
+  error_if(vals.size() =/= frame.height)
+  ctrls.pop()
+  return frame
+
+func label_types(frame : ctrl_frame) : list(val_types) =
+  return (if frame.opcode == loop then frame.start_types else frame.end_types)
+
+func unreachable() =
+  vals.resize(ctrls[0].height)
+  ctrls[0].unreachable := true
+
    +
    +

    Pushing a control frame takes the types of the label and result values. +It allocates a new frame record recording them along with the current height of the operand stack and marks the block as reachable.

    +

    Popping a frame first checks that the control stack is not empty. +It then verifies that the operand stack contains the right types of values expected at the end of the exited block and pops them off the operand stack. +Afterwards, it checks that the stack has shrunk back to its initial height.

    +

    The type of the label associated with a control frame is either that of the stack at the start or the end of the frame, determined by the opcode that it originates from.

    +

    Finally, the current frame can be marked as unreachable. +In that case, all existing operand types are purged from the value stack, in order to allow for the stack-polymorphism logic in pop_val to take effect.

    +
    +

    Note

    +

    Even with the unreachable flag set, consecutive operands are still pushed to and popped from the operand stack. +That is necessary to detect invalid examples like \((\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}})~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}})\). +However, a polymorphic stack cannot underflow, but instead generates Unknown types as needed.

    +
    +
    +
    +

    Validation of Opcode Sequences

    +

    The following function shows the validation of a number of representative instructions that manipulate the stack. +Other instructions are checked in a similar manner.

    +
    +

    Note

    +

    Various instructions not shown here will additionally require the presence of a validation context for checking uses of indices. +That is an easy addition and therefore omitted from this presentation.

    +
    +
    func validate(opcode) =
+  switch (opcode)
+    case (i32.add)
+      pop_val(I32)
+      pop_val(I32)
+      push_val(I32)
+
+    case (drop)
+      pop_val()
+
+    case (select)
+      pop_val(I32)
+      let t1 = pop_val()
+      let t2 = pop_val()
+      error_if(not ((is_num(t1) && is_num(t2)) || (is_vec(t1) && is_vec(t2))))
+      error_if(t1 =/= t2 && t1 =/= Unknown && t2 =/= Unknown)
+      push_val(if (t1 = Unknown) t2 else t1)
+
+    case (select t)
+      pop_val(I32)
+      pop_val(t)
+      pop_val(t)
+      push_val(t)
+
+    case (unreachable)
+      unreachable()
+
+    case (block t1*->t2*)
+      pop_vals([t1*])
+      push_ctrl(block, [t1*], [t2*])
+
+    case (loop t1*->t2*)
+      pop_vals([t1*])
+      push_ctrl(loop, [t1*], [t2*])
+
+    case (if t1*->t2*)
+      pop_val(I32)
+      pop_vals([t1*])
+      push_ctrl(if, [t1*], [t2*])
+
+    case (end)
+      let frame = pop_ctrl()
+      push_vals(frame.end_types)
+
+    case (else)
+      let frame = pop_ctrl()
+      error_if(frame.opcode =/= if)
+      push_ctrl(else, frame.start_types, frame.end_types)
+
+    case (br n)
+      error_if(ctrls.size() < n)
+      pop_vals(label_types(ctrls[n]))
+      unreachable()
+
+    case (br_if n)
+      error_if(ctrls.size() < n)
+      pop_val(I32)
+      pop_vals(label_types(ctrls[n]))
+      push_vals(label_types(ctrls[n]))
+
+    case (br_table n* m)
+      pop_val(I32)
+      error_if(ctrls.size() < m)
+      let arity = label_types(ctrls[m]).size()
+      foreach (n in n*)
+        error_if(ctrls.size() < n)
+        error_if(label_types(ctrls[n]).size() =/= arity)
+        push_vals(pop_vals(label_types(ctrls[n])))
+      pop_vals(label_types(ctrls[m]))
+      unreachable()
+
    +
    +
    +

    Note

    +

    It is an invariant under the current WebAssembly instruction set that an operand of Unknown type is never duplicated on the stack. +This would change if the language were extended with stack instructions like dup. +Under such an extension, the above algorithm would need to be refined by replacing the Unknown type with proper type variables to ensure that all uses are consistent.

    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/appendix/changes.html b/core/appendix/changes.html new file mode 100644 index 00000000..325dbe16 --- /dev/null +++ b/core/appendix/changes.html @@ -0,0 +1,212 @@ + + + + + + + + + Change History — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Change History

    +

    Since the original release 1.0 of the WebAssembly specification, a number of proposals for extensions have been integrated. +The following sections provide an overview of what has changed.

    +
    +

    Release 2.0

    +
    +

    Sign extension instructions

    +

    Added new numeric instructions for performing sign extension within integer representations 1.

    +
      +

    • New numeric instructions: \(\mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathit{N}\mathsf{\_s}\)

      • +
    +
    +
    +

    Non-trapping float-to-int conversions

    +

    Added new conversion instructions that avoid trapping when converting a floating-point number to an integer 2.

    +
      +

    • New numeric instructions: \(\mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_f}\mathit{mm}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\)

      • +
    +
    +
    +

    Multiple values

    +

    Generalized the result type of blocks and functions to allow for multiple values; in addition, introduced the ability to have block parameters 3.

    + +
    +
    +

    Reference types

    +

    Added \(\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}\) and \(\href{../syntax/types.html#syntax-reftype}{\mathsf{externref}}\) as new value types and respective instructions 4.

    +
      +

    • New value types: reference types \(\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}\) and \(\href{../syntax/types.html#syntax-reftype}{\mathsf{externref}}\)

      • +

    • New reference instructions: \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}\), \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}\), \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}is\_null}}\)

      • +

    • Enrich parametric instruction: \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}\) with optional type immediate

      • +

    • New declarative form of element segment

      • +
    +
    +
    +

    Table instructions

    +

    Added instructions to directly access and modify tables 4.

    +
      +

    • Table types allow any reference type as element type

      • +

    • New table instructions: \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}\), \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}\), \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.size}}\), \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.grow}}\)

      • +
    +
    +
    +

    Multiple tables

    +

    Added the ability to use multiple tables per module 4.

    +
      +

    • Modules may define, import, and export multiple tables

      • +

    • Table instructions take a table index immediate: \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}\), \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}\), \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.size}}\), \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.grow}}\), \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}\)

      • +

    • Element segments take a table index

      • +
    +
    +
    +

    Bulk memory and table instructions

    +

    Added instructions that modify ranges of memory or table entries 4 5

    +
      +

    • New memory instructions: \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}}\), \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}\), \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}}\), \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data.drop}}\)

      • +

    • New table instructions: \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.fill}}\), \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}\), \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}\), \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem.drop}}\)

      • +

    • New passive form of data segment

      • +

    • New passive form of element segment

      • +

    • New data count section in binary format

      • +

    • Active data and element segments boundaries are no longer checked at compile time but may trap instead

      • +
    +
    +
    +

    Vector instructions

    +

    Added vector type and instructions that manipulate multiple numeric values in parallel (also known as SIMD, single instruction multiple data) 6

    +
      +

    • New value type: \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\)

      • +

    • New memory instructions: \(\mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\), \(\mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{}\!N\!\mathsf{x}\!M\!\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{}N\mathsf{\_zero}\), \(\mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{}N\mathsf{\_splat}\), \(\mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{}N\mathsf{\_lane}\), \(\mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\), \(\mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}{}N\mathsf{\_lane}\)

      • +

    • New constant vector instruction: \(\mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}\)

      • +

    • New unary vector instructions: \(\mathsf{v128.not}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.abs}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.neg}\), \(\mathsf{i8x16.popcnt}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.abs}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.neg}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.sqrt}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.ceil}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.floor}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.trunc}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.nearest}\)

      • +

    • New binary vector instructions: \(\mathsf{v128.and}\), \(\mathsf{v128.andnot}\), \(\mathsf{v128.or}\), \(\mathsf{v128.xor}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.add}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.sub}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.mul}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.add\_sat\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.sub\_sat\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.min\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.max\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.shl}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.shr\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.add}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.extmul\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_i}\!N'\!\mathsf{x}\!M'\!\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{i16x8.q15mulr\_sat\_s}\), \(\mathsf{i32x4.dot\_i16x8\_s}\), \(\mathsf{i16x8.extadd\_pairwise\_i8x16\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{i32x4.extadd\_pairwise\_i16x8\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{i8x16.avgr\_u}\), \(\mathsf{i16x8.avgr\_u}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.sub}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.mul}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.div}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.min}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.max}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.pmin}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.pmax}\)

      • +

    • New ternary vector instruction: \(\mathsf{v128.bitselect}\)

      • +

    • New test vector instructions: \(\mathsf{v128.any\_true}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.all\_true}\)

      • +

    • New relational vector instructions: \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.eq}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.ne}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.lt\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.gt\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.le\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.ge\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.eq}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.ne}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.lt}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.gt}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.le}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.ge}\)

      • +

    • New conversion vector instructions:\(\mathsf{i32x4.trunc\_sat\_f32x4\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{i32x4.trunc\_sat\_f64x2\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\mathsf{\_zero}\), \(\mathsf{f32x4.convert\_i32x4\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{f32x4.demote\_f64x2\_zero}\), \(\mathsf{f64x2.convert\_low\_i32x4\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{f64x2.promote\_low\_f32x4}\)

      • +

    • New lane access vector instructions: \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.extract\_lane\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.replace\_lane}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.extract\_lane}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.replace\_lane}\)

      • +

    • New lane splitting/combining vector instructions: \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.extend\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_i}\!N'\!\mathsf{x}\!M'\!\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{i8x16.narrow\_i16x8\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\), \(\mathsf{i16x8.narrow\_i32x4\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\)

      • +

    • New byte reordering vector instructions: \(\mathsf{i8x16.shuffle}\), \(\mathsf{i8x16.swizzle}\)

      • +

    • New injection/projection vector instructions: \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.splat}\), \(\mathsf{f}\!N\!\mathsf{x}\!M\!\mathsf{.splat}\), \(\mathsf{i}\!N\!\mathsf{x}\!M\!\mathsf{.bitmask}\)

      • +
    +
    +
    1
    +

    https://github.com/WebAssembly/spec/tree/main/proposals/sign-extension-ops/

    +
    +
    2
    +

    https://github.com/WebAssembly/spec/tree/main/proposals/nontrapping-float-to-int-conversion/

    +
    +
    3
    +

    https://github.com/WebAssembly/spec/tree/main/proposals/multi-value/

    +
    +
    4(1,2,3,4)
    +

    https://github.com/WebAssembly/spec/tree/main/proposals/reference-types/

    +
    +
    5
    +

    https://github.com/WebAssembly/spec/tree/main/proposals/bulk-memory-operations/

    +
    +
    6
    +

    https://github.com/WebAssembly/spec/tree/main/proposals/simd/

    +
    +
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/appendix/custom.html b/core/appendix/custom.html new file mode 100644 index 00000000..4b9855d6 --- /dev/null +++ b/core/appendix/custom.html @@ -0,0 +1,222 @@ + + + + + + + + + Custom Sections — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Custom Sections

    +

    This appendix defines dedicated custom sections for WebAssembly’s binary format. +Such sections do not contribute to, or otherwise affect, the WebAssembly semantics, and like any custom section they may be ignored by an implementation. +However, they provide useful meta data that implementations can make use of to improve user experience or take compilation hints.

    +

    Currently, only one dedicated custom section is defined, the name section.

    +
    +

    Name Section

    +

    The name section is a custom section whose name string is itself \(\def\mathdef118#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef118{name}\). +The name section should appear only once in a module, and only after the data section.

    +

    The purpose of this section is to attach printable names to definitions in a module, which e.g. can be used by a debugger or when parts of the module are to be rendered in text form.

    +
    +

    Note

    +

    All names are represented in Unicode encoded in UTF-8. +Names need not be unique.

    +
    +
    +

    Subsections

    +

    The data of a name section consists of a sequence of subsections. +Each subsection consists of a

    +
      +

    • a one-byte subsection id,

      • +

    • the \(\href{../syntax/values.html#syntax-int}{\mathit{u32}}\) size of the contents, in bytes,

      • +

    • the actual contents, whose structure is dependent on the subsection id.

      • +
    +
    +\[\begin{split}\begin{array}{llcll} +\def\mathdef79#1{{}}\mathdef79{name section} & \href{../appendix/custom.html#binary-namesubsection}{\mathtt{namesec}} &::=& + \href{../binary/modules.html#binary-section}{\mathtt{section}}_0(\href{../appendix/custom.html#binary-namesubsection}{\mathtt{namedata}}) \\ +\def\mathdef79#1{{}}\mathdef79{name data} & \href{../appendix/custom.html#binary-namesubsection}{\mathtt{namedata}} &::=& + n{:}\href{../binary/values.html#binary-name}{\mathtt{name}} & (\mathrel{\mbox{if}} n = \def\mathdef119#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef119{name}) \\ &&& + \href{../appendix/custom.html#binary-modulenamesec}{\mathtt{modulenamesubsec}}^? \\ &&& + \href{../appendix/custom.html#binary-funcnamesec}{\mathtt{funcnamesubsec}}^? \\ &&& + \href{../appendix/custom.html#binary-localnamesec}{\mathtt{localnamesubsec}}^? \\ +\def\mathdef79#1{{}}\mathdef79{name subsection} & \href{../appendix/custom.html#binary-namesubsection}{\mathtt{namesubsection}}_N(\mathtt{B}) &::=& + N{:}\href{../binary/values.html#binary-byte}{\mathtt{byte}}~~\mathit{size}{:}\href{../binary/values.html#binary-int}{\def\mathdef84#1{{\mathtt{u}#1}}\mathdef84{\mathtt{32}}}~~\mathtt{B} + & (\mathrel{\mbox{if}} \mathit{size} = ||\mathtt{B}||) \\ +\end{array}\end{split}\]
    +

    The following subsection ids are used:

    + ++++ + + + + + + + + + + + + + + + + +

    Id

    Subsection

    0

    module name

    1

    function names

    2

    local names

    +

    Each subsection may occur at most once, and in order of increasing id.

    +
    +
    +

    Name Maps

    +

    A name map assigns names to indices in a given index space. +It consists of a vector of index/name pairs in order of increasing index value. +Each index must be unique, but the assigned names need not be.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef79#1{{}}\mathdef79{name map} & \href{../appendix/custom.html#binary-namemap}{\mathtt{namemap}} &::=& + \href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../appendix/custom.html#binary-namemap}{\mathtt{nameassoc}}) \\ +\def\mathdef79#1{{}}\mathdef79{name association} & \href{../appendix/custom.html#binary-namemap}{\mathtt{nameassoc}} &::=& + \href{../binary/modules.html#binary-index}{\mathtt{idx}}~\href{../binary/values.html#binary-name}{\mathtt{name}} \\ +\end{array}\end{split}\]
    +

    An indirect name map assigns names to a two-dimensional index space, where secondary indices are grouped by primary indices. +It consists of a vector of primary index/name map pairs in order of increasing index value, where each name map in turn maps secondary indices to names. +Each primary index must be unique, and likewise each secondary index per individual name map.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef79#1{{}}\mathdef79{indirect name map} & \href{../appendix/custom.html#binary-indirectnamemap}{\mathtt{indirectnamemap}} &::=& + \href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../appendix/custom.html#binary-indirectnamemap}{\mathtt{indirectnameassoc}}) \\ +\def\mathdef79#1{{}}\mathdef79{indirect name association} & \href{../appendix/custom.html#binary-indirectnamemap}{\mathtt{indirectnameassoc}} &::=& + \href{../binary/modules.html#binary-index}{\mathtt{idx}}~\href{../appendix/custom.html#binary-namemap}{\mathtt{namemap}} \\ +\end{array}\end{split}\]
    +
    +
    +

    Module Names

    +

    The module name subsection has the id 0. +It simply consists of a single name that is assigned to the module itself.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef79#1{{}}\mathdef79{module name subsection} & \href{../appendix/custom.html#binary-modulenamesec}{\mathtt{modulenamesubsec}} &::=& + \href{../appendix/custom.html#binary-namesubsection}{\mathtt{namesubsection}}_0(\href{../binary/values.html#binary-name}{\mathtt{name}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    Function Names

    +

    The function name subsection has the id 1. +It consists of a name map assigning function names to function indices.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef79#1{{}}\mathdef79{function name subsection} & \href{../appendix/custom.html#binary-funcnamesec}{\mathtt{funcnamesubsec}} &::=& + \href{../appendix/custom.html#binary-namesubsection}{\mathtt{namesubsection}}_1(\href{../appendix/custom.html#binary-namemap}{\mathtt{namemap}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    Local Names

    +

    The local name subsection has the id 2. +It consists of an indirect name map assigning local names to local indices grouped by function indices.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef79#1{{}}\mathdef79{local name subsection} & \href{../appendix/custom.html#binary-localnamesec}{\mathtt{localnamesubsec}} &::=& + \href{../appendix/custom.html#binary-namesubsection}{\mathtt{namesubsection}}_2(\href{../appendix/custom.html#binary-indirectnamemap}{\mathtt{indirectnamemap}}) \\ +\end{array}\end{split}\]
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/appendix/embedding.html b/core/appendix/embedding.html new file mode 100644 index 00000000..145be23a --- /dev/null +++ b/core/appendix/embedding.html @@ -0,0 +1,572 @@ + + + + + + + + + Embedding — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Embedding

    +

    A WebAssembly implementation will typically be embedded into a host environment. +An embedder implements the connection between such a host environment and the WebAssembly semantics as defined in the main body of this specification. +An embedder is expected to interact with the semantics in well-defined ways.

    +

    This section defines a suitable interface to the WebAssembly semantics in the form of entry points through which an embedder can access it. +The interface is intended to be complete, in the sense that an embedder does not need to reference other functional parts of the WebAssembly specification directly.

    +
    +

    Note

    +

    On the other hand, an embedder does not need to provide the host environment with access to all functionality defined in this interface. +For example, an implementation may not support parsing of the text format.

    +
    +
    +

    Types

    +

    In the description of the embedder interface, syntactic classes from the abstract syntax and the runtime’s abstract machine are used as names for variables that range over the possible objects from that class. +Hence, these syntactic classes can also be interpreted as types.

    +

    For numeric parameters, notation like \(n:\href{../syntax/values.html#syntax-int}{\mathit{u32}}\) is used to specify a symbolic name in addition to the respective value range.

    +
    +
    +

    Errors

    +

    Failure of an interface operation is indicated by an auxiliary syntactic class:

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef120#1{{}}\mathdef120{(error)} & \href{../appendix/embedding.html#embed-error}{\mathit{error}} &::=& \href{../appendix/embedding.html#embed-error}{\mathsf{error}} \\ +\end{array}\end{split}\]
    +

    In addition to the error conditions specified explicitly in this section, implementations may also return errors when specific implementation limitations are reached.

    +
    +

    Note

    +

    Errors are abstract and unspecific with this definition. +Implementations can refine it to carry suitable classifications and diagnostic messages.

    +
    +
    +
    +

    Pre- and Post-Conditions

    +

    Some operations state pre-conditions about their arguments or post-conditions about their results. +It is the embedder’s responsibility to meet the pre-conditions. +If it does, the post conditions are guaranteed by the semantics.

    +

    In addition to pre- and post-conditions explicitly stated with each operation, the specification adopts the following conventions for runtime objects (\(store\), \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\), \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}\), addresses):

    +
      +

    • Every runtime object passed as a parameter must be valid per an implicit pre-condition.

      • +

    • Every runtime object returned as a result is valid per an implicit post-condition.

      • +
    +
    +

    Note

    +

    As long as an embedder treats runtime objects as abstract and only creates and manipulates them through the interface defined here, all implicit pre-conditions are automatically met.

    +
    +
    +
    +

    Store

    +
    +

    \(\mathrm{store\_init}() : \href{../exec/runtime.html#syntax-store}{\mathit{store}}\)

    +
      +

    1. Return the empty store.

      2. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{store\_init}() &=& \{ \href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}~\epsilon,~ \href{../exec/runtime.html#syntax-store}{\mathsf{mems}}~\epsilon,~ \href{../exec/runtime.html#syntax-store}{\mathsf{tables}}~\epsilon,~ \href{../exec/runtime.html#syntax-store}{\mathsf{globals}}~\epsilon \} \\ +\end{array}\end{split}\]
    +
    +
    +
    +

    Modules

    +
    +

    \(\mathrm{module\_decode}(\href{../syntax/values.html#syntax-byte}{\mathit{byte}}^\ast) : \href{../syntax/modules.html#syntax-module}{\mathit{module}} ~|~ \href{../appendix/embedding.html#embed-error}{\mathit{error}}\)

    +
      +

    1. If there exists a derivation for the byte sequence \(\href{../syntax/values.html#syntax-byte}{\mathit{byte}}^\ast\) as a \(\href{../binary/modules.html#binary-module}{\mathtt{module}}\) according to the binary grammar for modules, yielding a module \(m\), then return \(m\).

      2. +

    2. Else, return \(\href{../appendix/embedding.html#embed-error}{\mathsf{error}}\).

      3. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{module\_decode}(b^\ast) &=& m && (\mathrel{\mbox{if}} \href{../binary/modules.html#binary-module}{\mathtt{module}} \stackrel\ast\Longrightarrow m{:}b^\ast) \\ +\mathrm{module\_decode}(b^\ast) &=& \href{../appendix/embedding.html#embed-error}{\mathsf{error}} && (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{module\_parse}(\href{../syntax/values.html#syntax-name}{\mathit{char}}^\ast) : \href{../syntax/modules.html#syntax-module}{\mathit{module}} ~|~ \href{../appendix/embedding.html#embed-error}{\mathit{error}}\)

    +
      +

    1. If there exists a derivation for the source \(\href{../syntax/values.html#syntax-name}{\mathit{char}}^\ast\) as a \(\href{../text/modules.html#text-module}{\mathtt{module}}\) according to the text grammar for modules, yielding a module \(m\), then return \(m\).

      2. +

    2. Else, return \(\href{../appendix/embedding.html#embed-error}{\mathsf{error}}\).

      3. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{module\_parse}(c^\ast) &=& m && (\mathrel{\mbox{if}} \href{../text/modules.html#text-module}{\mathtt{module}} \stackrel\ast\Longrightarrow m{:}c^\ast) \\ +\mathrm{module\_parse}(c^\ast) &=& \href{../appendix/embedding.html#embed-error}{\mathsf{error}} && (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{module\_validate}(\href{../syntax/modules.html#syntax-module}{\mathit{module}}) : \href{../appendix/embedding.html#embed-error}{\mathit{error}}^?\)

    +
      +

    1. If \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}\) is valid, then return nothing.

      2. +

    2. Else, return \(\href{../appendix/embedding.html#embed-error}{\mathsf{error}}\).

      3. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{module\_validate}(m) &=& \epsilon && (\mathrel{\mbox{if}} {} \href{../valid/modules.html#valid-module}{\vdash} m : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast \href{../syntax/types.html#syntax-functype}{\rightarrow} {\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}'}^\ast) \\ +\mathrm{module\_validate}(m) &=& \href{../appendix/embedding.html#embed-error}{\mathsf{error}} && (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{module\_instantiate}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../syntax/modules.html#syntax-module}{\mathit{module}}, \href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^\ast) : (\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}} ~|~ \href{../appendix/embedding.html#embed-error}{\mathit{error}})\)

    +
      +

    1. Try instantiating \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}\) in \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}\) with external values \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^\ast\) as imports:

      2. +
    +
    +
      +

    1. If it succeeds with a module instance \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\), then let \(\mathit{result}\) be \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\).

      2. +

    2. Else, let \(\mathit{result}\) be \(\href{../appendix/embedding.html#embed-error}{\mathsf{error}}\).

      3. +
    +
    +
      +

    1. Return the new store paired with \(\mathit{result}\).

      2. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{module\_instantiate}(S, m, \mathit{ev}^\ast) &=& (S', F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}) && (\mathrel{\mbox{if}} \href{../exec/modules.html#exec-instantiation}{\mathrm{instantiate}}(S, m, \mathit{ev}^\ast) \href{../exec/conventions.html#formal-notation}{\hookrightarrow}^\ast S'; F; \epsilon) \\ +\mathrm{module\_instantiate}(S, m, \mathit{ev}^\ast) &=& (S', \href{../appendix/embedding.html#embed-error}{\mathsf{error}}) && (\mathrel{\mbox{if}} \href{../exec/modules.html#exec-instantiation}{\mathrm{instantiate}}(S, m, \mathit{ev}^\ast) \href{../exec/conventions.html#formal-notation}{\hookrightarrow}^\ast S'; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}}) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The store may be modified even in case of an error.

    +
    +
    +
    +

    \(\mathrm{module\_imports}(\href{../syntax/modules.html#syntax-module}{\mathit{module}}) : (\href{../syntax/values.html#syntax-name}{\mathit{name}}, \href{../syntax/values.html#syntax-name}{\mathit{name}}, \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}})^\ast\)

    +
      +

    1. Pre-condition: \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}\) is valid with external import types \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast\) and external export types \({\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}'}^\ast\).

      2. +

    2. Let \(\href{../syntax/modules.html#syntax-import}{\mathit{import}}^\ast\) be the imports \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{imports}}\).

      3. +

    3. Assert: the length of \(\href{../syntax/modules.html#syntax-import}{\mathit{import}}^\ast\) equals the length of \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast\).

      4. +

    4. For each \(\href{../syntax/modules.html#syntax-import}{\mathit{import}}_i\) in \(\href{../syntax/modules.html#syntax-import}{\mathit{import}}^\ast\) and corresponding \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}_i\) in \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast\), do:

      5. +
    +
    +
      +

    1. Let \(\mathit{result}_i\) be the triple \((\href{../syntax/modules.html#syntax-import}{\mathit{import}}_i.\href{../syntax/modules.html#syntax-import}{\mathsf{module}}, \href{../syntax/modules.html#syntax-import}{\mathit{import}}_i.\href{../syntax/modules.html#syntax-import}{\mathsf{name}}, \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}_i)\).

      2. +
    +
    +
      +

    1. Return the concatenation of all \(\mathit{result}_i\), in index order.

      2. +

    2. Post-condition: each \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}_i\) is valid.

      3. +
    +
    +\[\begin{split}~ \\ +\begin{array}{lclll} +\mathrm{module\_imports}(m) &=& (\mathit{im}.\href{../syntax/modules.html#syntax-import}{\mathsf{module}}, \mathit{im}.\href{../syntax/modules.html#syntax-import}{\mathsf{name}}, \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}})^\ast \\ + && \qquad (\mathrel{\mbox{if}} \mathit{im}^\ast = m.\href{../syntax/modules.html#syntax-module}{\mathsf{imports}} \wedge {} \href{../valid/modules.html#valid-module}{\vdash} m : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast \href{../syntax/types.html#syntax-functype}{\rightarrow} {\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}'}^\ast) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{module\_exports}(\href{../syntax/modules.html#syntax-module}{\mathit{module}}) : (\href{../syntax/values.html#syntax-name}{\mathit{name}}, \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}})^\ast\)

    +
      +

    1. Pre-condition: \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}\) is valid with external import types \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast\) and external export types \({\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}'}^\ast\).

      2. +

    2. Let \(\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast\) be the exports \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{exports}}\).

      3. +

    3. Assert: the length of \(\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast\) equals the length of \({\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}'}^\ast\).

      4. +

    4. For each \(\href{../syntax/modules.html#syntax-export}{\mathit{export}}_i\) in \(\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast\) and corresponding \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}'_i\) in \({\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}'}^\ast\), do:

      5. +
    +
    +
      +

    1. Let \(\mathit{result}_i\) be the pair \((\href{../syntax/modules.html#syntax-export}{\mathit{export}}_i.\href{../syntax/modules.html#syntax-export}{\mathsf{name}}, \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}'_i)\).

      2. +
    +
    +
      +

    1. Return the concatenation of all \(\mathit{result}_i\), in index order.

      2. +

    2. Post-condition: each \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}'_i\) is valid.

      3. +
    +
    +\[\begin{split}~ \\ +\begin{array}{lclll} +\mathrm{module\_exports}(m) &=& (\mathit{ex}.\href{../syntax/modules.html#syntax-export}{\mathsf{name}}, \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}')^\ast \\ + && \qquad (\mathrel{\mbox{if}} \mathit{ex}^\ast = m.\href{../syntax/modules.html#syntax-module}{\mathsf{exports}} \wedge {} \href{../valid/modules.html#valid-module}{\vdash} m : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast \href{../syntax/types.html#syntax-functype}{\rightarrow} {\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}'}^\ast) \\ +\end{array}\end{split}\]
    +
    +
    +
    +

    Module Instances

    +
    +

    \(\mathrm{instance\_export}(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}, \href{../syntax/values.html#syntax-name}{\mathit{name}}) : \href{../exec/runtime.html#syntax-externval}{\mathit{externval}} ~|~ \href{../appendix/embedding.html#embed-error}{\mathit{error}}\)

    +
      +

    1. Assert: due to validity of the module instance \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\), all its export names are different.

      2. +

    2. If there exists an \(\href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}_i\) in \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{exports}}\) such that name \(\href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}_i.\href{../exec/runtime.html#syntax-exportinst}{\mathsf{name}}\) equals \(\href{../syntax/values.html#syntax-name}{\mathit{name}}\), then:

      +
        +

      1. Return the external value \(\href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}_i.\href{../exec/runtime.html#syntax-exportinst}{\mathsf{value}}\).

        2. +
      +
      3. +

    3. Else, return \(\href{../appendix/embedding.html#embed-error}{\mathsf{error}}\).

      4. +
    +
    +\[\begin{split}~ \\ +\begin{array}{lclll} +\mathrm{instance\_export}(m, \href{../syntax/values.html#syntax-name}{\mathit{name}}) &=& m.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{exports}}[i].\href{../exec/runtime.html#syntax-exportinst}{\mathsf{value}} && (\mathrel{\mbox{if}} m.\href{../syntax/modules.html#syntax-module}{\mathsf{exports}}[i].\href{../exec/runtime.html#syntax-exportinst}{\mathsf{name}} = \href{../syntax/values.html#syntax-name}{\mathit{name}}) \\ +\mathrm{instance\_export}(m, \href{../syntax/values.html#syntax-name}{\mathit{name}}) &=& \href{../appendix/embedding.html#embed-error}{\mathsf{error}} && (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +
    +

    Functions

    +
    +

    \(\mathrm{func\_alloc}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../syntax/types.html#syntax-functype}{\mathit{functype}}, \href{../exec/runtime.html#syntax-hostfunc}{\mathit{hostfunc}}) : (\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}})\)

    +
      +

    1. Pre-condition: \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\) is \(valid <valid-functype>\).

      2. +

    2. Let \(\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}\) be the result of allocating a host function in \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}\) with function type \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\) and host function code \(\href{../exec/runtime.html#syntax-hostfunc}{\mathit{hostfunc}}\).

      3. +

    3. Return the new store paired with \(\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}\).

      4. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{func\_alloc}(S, \mathit{ft}, \mathit{code}) &=& (S', \mathit{a}) && (\mathrel{\mbox{if}} \href{../exec/modules.html#alloc-hostfunc}{\mathrm{allochostfunc}}(S, \mathit{ft}, \mathit{code}) = S', \mathit{a}) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    This operation assumes that \(\href{../exec/runtime.html#syntax-hostfunc}{\mathit{hostfunc}}\) satisfies the pre- and post-conditions required for a function instance with type \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\).

    +

    Regular (non-host) function instances can only be created indirectly through module instantiation.

    +
    +
    +
    +

    \(\mathrm{func\_type}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}) : \href{../syntax/types.html#syntax-functype}{\mathit{functype}}\)

    +
      +

    1. Return \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a].\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}\).

      2. +

    2. Post-condition: the returned function type is valid.

      3. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{func\_type}(S, a) &=& S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a].\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}} \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{func\_invoke}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}, \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast) : (\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast ~|~ \href{../appendix/embedding.html#embed-error}{\mathit{error}})\)

    +
      +

    1. Try invoking the function \(\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}\) in \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}\) with values \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\) as arguments:

      2. +
    +
    +
      +

    1. If it succeeds with values \({\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}^\ast\) as results, then let \(\mathit{result}\) be \({\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}^\ast\).

      2. +

    2. Else it has trapped, hence let \(\mathit{result}\) be \(\href{../appendix/embedding.html#embed-error}{\mathsf{error}}\).

      3. +
    +
    +
      +

    1. Return the new store paired with \(\mathit{result}\).

      2. +
    +
    +\[\begin{split}~ \\ +\begin{array}{lclll} +\mathrm{func\_invoke}(S, a, v^\ast) &=& (S', {v'}^\ast) && (\mathrel{\mbox{if}} \href{../exec/modules.html#exec-invocation}{\mathrm{invoke}}(S, a, v^\ast) \href{../exec/conventions.html#formal-notation}{\hookrightarrow}^\ast S'; F; {v'}^\ast) \\ +\mathrm{func\_invoke}(S, a, v^\ast) &=& (S', \href{../appendix/embedding.html#embed-error}{\mathsf{error}}) && (\mathrel{\mbox{if}} \href{../exec/modules.html#exec-invocation}{\mathrm{invoke}}(S, a, v^\ast) \href{../exec/conventions.html#formal-notation}{\hookrightarrow}^\ast S'; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}}) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The store may be modified even in case of an error.

    +
    +
    +
    +
    +

    Tables

    +
    +

    \(\mathrm{table\_alloc}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}) : (\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}, \href{../exec/runtime.html#syntax-ref}{\mathit{ref}})\)

    +
      +

    1. Pre-condition: \(\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\) is \(valid <valid-tabletype>\).

      2. +

    2. Let \(\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}\) be the result of allocating a table in \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}\) with table type \(\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\) and initialization value \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}\).

      3. +

    3. Return the new store paired with \(\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}\).

      4. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{table\_alloc}(S, \mathit{tt}, r) &=& (S', \mathit{a}) && (\mathrel{\mbox{if}} \href{../exec/modules.html#alloc-table}{\mathrm{alloctable}}(S, \mathit{tt}, r) = S', \mathit{a}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{table\_type}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}) : \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\)

    +
      +

    1. Return \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}}\).

      2. +

    2. Post-condition: the returned table type is \(valid <valid-tabletype>\).

      3. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{table\_type}(S, a) &=& S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}} \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{table\_read}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}, i:\href{../syntax/values.html#syntax-int}{\mathit{u32}}) : \href{../exec/runtime.html#syntax-ref}{\mathit{ref}} ~|~ \href{../appendix/embedding.html#embed-error}{\mathit{error}}\)

    +
      +

    1. Let \(\mathit{ti}\) be the table instance \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}]\).

      2. +

    2. If \(i\) is larger than or equal to the length of \(\mathit{ti}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\), then return \(\href{../appendix/embedding.html#embed-error}{\mathsf{error}}\).

      3. +

    3. Else, return the reference value \(\mathit{ti}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}[i]\).

      4. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{table\_read}(S, a, i) &=& r && (\mathrel{\mbox{if}} S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}[i] = r) \\ +\mathrm{table\_read}(S, a, i) &=& \href{../appendix/embedding.html#embed-error}{\mathsf{error}} && (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{table\_write}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}, i:\href{../syntax/values.html#syntax-int}{\mathit{u32}}, \href{../exec/runtime.html#syntax-ref}{\mathit{ref}}) : \href{../exec/runtime.html#syntax-store}{\mathit{store}} ~|~ \href{../appendix/embedding.html#embed-error}{\mathit{error}}\)

    +
      +

    1. Let \(\mathit{ti}\) be the table instance \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}]\).

      2. +

    2. If \(i\) is larger than or equal to the length of \(\mathit{ti}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\), then return \(\href{../appendix/embedding.html#embed-error}{\mathsf{error}}\).

      3. +

    3. Replace \(\mathit{ti}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}[i]\) with the reference value \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}\).

      4. +

    4. Return the updated store.

      5. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{table\_write}(S, a, i, r) &=& S' && (\mathrel{\mbox{if}} S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}[i] = r) \\ +\mathrm{table\_write}(S, a, i, r) &=& \href{../appendix/embedding.html#embed-error}{\mathsf{error}} && (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{table\_size}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}) : \href{../syntax/values.html#syntax-int}{\mathit{u32}}\)

    +
      +

    1. Return the length of \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\).

      2. +
    +
    +\[\begin{split}~ \\ +\begin{array}{lclll} +\mathrm{table\_size}(S, a) &=& n && + (\mathrel{\mbox{if}} |S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}| = n) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{table\_grow}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}, n:\href{../syntax/values.html#syntax-int}{\mathit{u32}}, \href{../exec/runtime.html#syntax-ref}{\mathit{ref}}) : \href{../exec/runtime.html#syntax-store}{\mathit{store}} ~|~ \href{../appendix/embedding.html#embed-error}{\mathit{error}}\)

    +
      +

    1. Try growing the table instance \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}]\) by \(n\) elements with initialization value \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}\):

      +
        +

      1. If it succeeds, return the updated store.

        2. +

      2. Else, return \(\href{../appendix/embedding.html#embed-error}{\mathsf{error}}\).

        3. +
      +
      2. +
    +
    +\[\begin{split}~ \\ +\begin{array}{lclll} +\mathrm{table\_grow}(S, a, n, r) &=& S' && + (\mathrel{\mbox{if}} S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a] = \href{../exec/modules.html#grow-table}{\mathrm{growtable}}(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a], n, r)) \\ +\mathrm{table\_grow}(S, a, n, r) &=& \href{../appendix/embedding.html#embed-error}{\mathsf{error}} && (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +
    +

    Memories

    +
    +

    \(\mathrm{mem\_alloc}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}) : (\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}})\)

    +
      +

    1. Pre-condition: \(\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\) is \(valid <valid-memtype>\).

      2. +

    2. Let \(\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}\) be the result of allocating a memory in \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}\) with memory type \(\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\).

      3. +

    3. Return the new store paired with \(\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}\).

      4. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{mem\_alloc}(S, \mathit{mt}) &=& (S', \mathit{a}) && (\mathrel{\mbox{if}} \href{../exec/modules.html#alloc-mem}{\mathrm{allocmem}}(S, \mathit{mt}) = S', \mathit{a}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{mem\_type}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}) : \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\)

    +
      +

    1. Return \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a].\href{../exec/runtime.html#syntax-meminst}{\mathsf{type}}\).

      2. +

    2. Post-condition: the returned memory type is \(valid <valid-memtype>\).

      3. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{mem\_type}(S, a) &=& S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a].\href{../exec/runtime.html#syntax-meminst}{\mathsf{type}} \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{mem\_read}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}, i:\href{../syntax/values.html#syntax-int}{\mathit{u32}}) : \href{../syntax/values.html#syntax-byte}{\mathit{byte}} ~|~ \href{../appendix/embedding.html#embed-error}{\mathit{error}}\)

    +
      +

    1. Let \(\mathit{mi}\) be the memory instance \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}]\).

      2. +

    2. If \(i\) is larger than or equal to the length of \(\mathit{mi}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\), then return \(\href{../appendix/embedding.html#embed-error}{\mathsf{error}}\).

      3. +

    3. Else, return the byte \(\mathit{mi}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[i]\).

      4. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{mem\_read}(S, a, i) &=& b && (\mathrel{\mbox{if}} S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[i] = b) \\ +\mathrm{mem\_read}(S, a, i) &=& \href{../appendix/embedding.html#embed-error}{\mathsf{error}} && (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{mem\_write}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}, i:\href{../syntax/values.html#syntax-int}{\mathit{u32}}, \href{../syntax/values.html#syntax-byte}{\mathit{byte}}) : \href{../exec/runtime.html#syntax-store}{\mathit{store}} ~|~ \href{../appendix/embedding.html#embed-error}{\mathit{error}}\)

    +
      +

    1. Let \(\mathit{mi}\) be the memory instance \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}]\).

      2. +

    2. If \(\href{../syntax/values.html#syntax-int}{\mathit{u32}}\) is larger than or equal to the length of \(\mathit{mi}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\), then return \(\href{../appendix/embedding.html#embed-error}{\mathsf{error}}\).

      3. +

    3. Replace \(\mathit{mi}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[i]\) with \(\href{../syntax/values.html#syntax-byte}{\mathit{byte}}\).

      4. +

    4. Return the updated store.

      5. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{mem\_write}(S, a, i, b) &=& S' && (\mathrel{\mbox{if}} S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[i] = b) \\ +\mathrm{mem\_write}(S, a, i, b) &=& \href{../appendix/embedding.html#embed-error}{\mathsf{error}} && (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{mem\_size}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}) : \href{../syntax/values.html#syntax-int}{\mathit{u32}}\)

    +
      +

    1. Return the length of \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\) divided by the page size.

      2. +
    +
    +\[\begin{split}~ \\ +\begin{array}{lclll} +\mathrm{mem\_size}(S, a) &=& n && + (\mathrel{\mbox{if}} |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}| = n \cdot 64\,\mathrm{Ki}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{mem\_grow}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}, n:\href{../syntax/values.html#syntax-int}{\mathit{u32}}) : \href{../exec/runtime.html#syntax-store}{\mathit{store}} ~|~ \href{../appendix/embedding.html#embed-error}{\mathit{error}}\)

    +
      +

    1. Try growing the memory instance \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}]\) by \(n\) pages:

      +
        +

      1. If it succeeds, return the updated store.

        2. +

      2. Else, return \(\href{../appendix/embedding.html#embed-error}{\mathsf{error}}\).

        3. +
      +
      2. +
    +
    +\[\begin{split}~ \\ +\begin{array}{lclll} +\mathrm{mem\_grow}(S, a, n) &=& S' && + (\mathrel{\mbox{if}} S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a] = \href{../exec/modules.html#grow-mem}{\mathrm{growmem}}(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a], n)) \\ +\mathrm{mem\_grow}(S, a, n) &=& \href{../appendix/embedding.html#embed-error}{\mathsf{error}} && (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +
    +

    Globals

    +
    +

    \(\mathrm{global\_alloc}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}, \href{../exec/runtime.html#syntax-val}{\mathit{val}}) : (\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}})\)

    +
      +

    1. Pre-condition: \(\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}\) is \(valid <valid-globaltype>\).

      2. +

    2. Let \(\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}\) be the result of allocating a global in \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}\) with global type \(\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}\) and initialization value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\).

      3. +

    3. Return the new store paired with \(\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}\).

      4. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{global\_alloc}(S, \mathit{gt}, v) &=& (S', \mathit{a}) && (\mathrel{\mbox{if}} \href{../exec/modules.html#alloc-global}{\mathrm{allocglobal}}(S, \mathit{gt}, v) = S', \mathit{a}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{global\_type}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}) : \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}\)

    +
      +

    1. Return \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[a].\href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}}\).

      2. +

    2. Post-condition: the returned global type is \(valid <valid-globaltype>\).

      3. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{global\_type}(S, a) &=& S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[a].\href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}} \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{global\_read}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}) : \href{../exec/runtime.html#syntax-val}{\mathit{val}}\)

    +
      +

    1. Let \(\mathit{gi}\) be the global instance \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}]\).

      2. +

    2. Return the value \(\mathit{gi}.\href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}}\).

      3. +
    +
    +\[\begin{split}\begin{array}{lclll} +\mathrm{global\_read}(S, a) &=& v && (\mathrel{\mbox{if}} S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[a].\href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}} = v) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathrm{global\_write}(\href{../exec/runtime.html#syntax-store}{\mathit{store}}, \href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}, \href{../exec/runtime.html#syntax-val}{\mathit{val}}) : \href{../exec/runtime.html#syntax-store}{\mathit{store}} ~|~ \href{../appendix/embedding.html#embed-error}{\mathit{error}}\)

    +
      +

    1. Let \(\mathit{gi}\) be the global instance \(\href{../exec/runtime.html#syntax-store}{\mathit{store}}.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}]\).

      2. +

    2. Let \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t\) be the structure of the global type \(\mathit{gi}.\href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}}\).

      3. +

    3. If \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}\) is not \(\href{../syntax/types.html#syntax-mut}{\mathsf{var}}\), then return \(\href{../appendix/embedding.html#embed-error}{\mathsf{error}}\).

      4. +

    4. Replace \(\mathit{gi}.\href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}}\) with the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\).

      5. +

    5. Return the updated store.

      6. +
    +
    +\[\begin{split}~ \\ +\begin{array}{lclll} +\mathrm{global\_write}(S, a, v) &=& S' && (\mathrel{\mbox{if}} S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[a].\href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}} = \href{../syntax/types.html#syntax-mut}{\mathsf{var}}~t \wedge S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[a].\href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}} = v) \\ +\mathrm{global\_write}(S, a, v) &=& \href{../appendix/embedding.html#embed-error}{\mathsf{error}} && (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/appendix/implementation.html b/core/appendix/implementation.html new file mode 100644 index 00000000..7abf7cbe --- /dev/null +++ b/core/appendix/implementation.html @@ -0,0 +1,219 @@ + + + + + + + + + Implementation Limitations — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Implementation Limitations

    +

    Implementations typically impose additional restrictions on a number of aspects of a WebAssembly module or execution. +These may stem from:

    +
      +

    • physical resource limits,

      • +

    • constraints imposed by the embedder or its environment,

      • +

    • limitations of selected implementation strategies.

      • +
    +

    This section lists allowed limitations. +Where restrictions take the form of numeric limits, no minimum requirements are given, +nor are the limits assumed to be concrete, fixed numbers. +However, it is expected that all implementations have “reasonably” large limits to enable common applications.

    +
    +

    Note

    +

    A conforming implementation is not allowed to leave out individual features. +However, designated subsets of WebAssembly may be specified in the future.

    +
    +
    +

    Syntactic Limits

    +
    +

    Structure

    +

    An implementation may impose restrictions on the following dimensions of a module:

    + +

    If the limits of an implementation are exceeded for a given module, +then the implementation may reject the validation, compilation, or instantiation of that module with an embedder-specific error.

    +
    +

    Note

    +

    The last item allows embedders that operate in limited environments without support for +Unicode to limit the +names of imports and exports +to common subsets like ASCII.

    +
    +
    +
    +

    Binary Format

    +

    For a module given in binary format, additional limitations may be imposed on the following dimensions:

    + +
    +
    +

    Text Format

    +

    For a module given in text format, additional limitations may be imposed on the following dimensions:

    + +
    +
    +
    +

    Validation

    +

    An implementation may defer validation of individual functions until they are first invoked.

    +

    If a function turns out to be invalid, then the invocation, and every consecutive call to the same function, results in a trap.

    +
    +

    Note

    +

    This is to allow implementations to use interpretation or just-in-time compilation for functions. +The function must still be fully validated before execution of its body begins.

    +
    +
    +
    +

    Execution

    +

    Restrictions on the following dimensions may be imposed during execution of a WebAssembly program:

    + +

    If the runtime limits of an implementation are exceeded during execution of a computation, +then it may terminate that computation and report an embedder-specific error to the invoking code.

    +

    Some of the above limits may already be verified during instantiation, in which case an implementation may report exceedance in the same manner as for syntactic limits.

    +
    +

    Note

    +

    Concrete limits are usually not fixed but may be dependent on specifics, interdependent, vary over time, or depend on other implementation- or embedder-specific situations or events.

    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/appendix/index-instructions.html b/core/appendix/index-instructions.html new file mode 100644 index 00000000..8eaa5ffb --- /dev/null +++ b/core/appendix/index-instructions.html @@ -0,0 +1,3154 @@ + + + + + + + + + Index of Instructions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Index of Instructions

    + +++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Instruction

    Binary Opcode

    Type

    Validation

    Execution

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}\)

    \(\def\mathdef276#1{\mathtt{0x#1}}\mathdef276{00}\)

    \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\)

    validation

    execution

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{nop}}\)

    \(\def\mathdef277#1{\mathtt{0x#1}}\mathdef277{01}\)

    \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\)

    validation

    execution

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~\mathit{bt}\)

    \(\def\mathdef278#1{\mathtt{0x#1}}\mathdef278{02}\)

    \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\)

    validation

    execution

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}~\mathit{bt}\)

    \(\def\mathdef279#1{\mathtt{0x#1}}\mathdef279{03}\)

    \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\)

    validation

    execution

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}~\mathit{bt}\)

    \(\def\mathdef280#1{\mathtt{0x#1}}\mathdef280{04}\)

    \([t_1^\ast~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\)

    validation

    execution

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}\)

    \(\def\mathdef281#1{\mathtt{0x#1}}\mathdef281{05}\)

    (reserved)

    \(\def\mathdef282#1{\mathtt{0x#1}}\mathdef282{06}\)

    (reserved)

    \(\def\mathdef283#1{\mathtt{0x#1}}\mathdef283{07}\)

    (reserved)

    \(\def\mathdef284#1{\mathtt{0x#1}}\mathdef284{08}\)

    (reserved)

    \(\def\mathdef285#1{\mathtt{0x#1}}\mathdef285{09}\)

    (reserved)

    \(\def\mathdef286#1{\mathtt{0x#1}}\mathdef286{0A}\)

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\)

    \(\def\mathdef287#1{\mathtt{0x#1}}\mathdef287{0B}\)

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l\)

    \(\def\mathdef288#1{\mathtt{0x#1}}\mathdef288{0C}\)

    \([t_1^\ast~t^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\)

    validation

    execution

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_if}}~l\)

    \(\def\mathdef289#1{\mathtt{0x#1}}\mathdef289{0D}\)

    \([t^\ast~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t^\ast]\)

    validation

    execution

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}~l^\ast~l\)

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    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    validation

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    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_s}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_u}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_s}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_u}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_s}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_u}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_s}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_u}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_s}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_u}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{16}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{16}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{32}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\)

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    validation

    execution

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\href{../syntax/values.html#syntax-int}{\mathit{i32}}\)

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    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\href{../syntax/values.html#syntax-int}{\mathit{i64}}\)

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    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\href{../syntax/values.html#syntax-float}{\mathit{f32}}\)

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    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\href{../syntax/values.html#syntax-float}{\mathit{f64}}\)

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    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eqz}}\)

    \(\def\mathdef345#1{\mathtt{0x#1}}\mathdef345{45}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eq}}\)

    \(\def\mathdef346#1{\mathtt{0x#1}}\mathdef346{46}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ne}}\)

    \(\def\mathdef347#1{\mathtt{0x#1}}\mathdef347{47}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\mathsf{\_s}\)

    \(\def\mathdef348#1{\mathtt{0x#1}}\mathdef348{48}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\mathsf{\_u}\)

    \(\def\mathdef349#1{\mathtt{0x#1}}\mathdef349{49}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\mathsf{\_s}\)

    \(\def\mathdef350#1{\mathtt{0x#1}}\mathdef350{4A}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\mathsf{\_u}\)

    \(\def\mathdef351#1{\mathtt{0x#1}}\mathdef351{4B}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\mathsf{\_s}\)

    \(\def\mathdef352#1{\mathtt{0x#1}}\mathdef352{4C}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\mathsf{\_u}\)

    \(\def\mathdef353#1{\mathtt{0x#1}}\mathdef353{4D}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\mathsf{\_s}\)

    \(\def\mathdef354#1{\mathtt{0x#1}}\mathdef354{4E}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\mathsf{\_u}\)

    \(\def\mathdef355#1{\mathtt{0x#1}}\mathdef355{4F}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eqz}}\)

    \(\def\mathdef356#1{\mathtt{0x#1}}\mathdef356{50}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eq}}\)

    \(\def\mathdef357#1{\mathtt{0x#1}}\mathdef357{51}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ne}}\)

    \(\def\mathdef358#1{\mathtt{0x#1}}\mathdef358{52}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\mathsf{\_s}\)

    \(\def\mathdef359#1{\mathtt{0x#1}}\mathdef359{53}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\mathsf{\_u}\)

    \(\def\mathdef360#1{\mathtt{0x#1}}\mathdef360{54}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\mathsf{\_s}\)

    \(\def\mathdef361#1{\mathtt{0x#1}}\mathdef361{55}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\mathsf{\_u}\)

    \(\def\mathdef362#1{\mathtt{0x#1}}\mathdef362{56}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\mathsf{\_s}\)

    \(\def\mathdef363#1{\mathtt{0x#1}}\mathdef363{57}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\mathsf{\_u}\)

    \(\def\mathdef364#1{\mathtt{0x#1}}\mathdef364{58}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\mathsf{\_s}\)

    \(\def\mathdef365#1{\mathtt{0x#1}}\mathdef365{59}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\mathsf{\_u}\)

    \(\def\mathdef366#1{\mathtt{0x#1}}\mathdef366{5A}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eq}}\)

    \(\def\mathdef367#1{\mathtt{0x#1}}\mathdef367{5B}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ne}}\)

    \(\def\mathdef368#1{\mathtt{0x#1}}\mathdef368{5C}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\)

    \(\def\mathdef369#1{\mathtt{0x#1}}\mathdef369{5D}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\)

    \(\def\mathdef370#1{\mathtt{0x#1}}\mathdef370{5E}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\)

    \(\def\mathdef371#1{\mathtt{0x#1}}\mathdef371{5F}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\)

    \(\def\mathdef372#1{\mathtt{0x#1}}\mathdef372{60}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eq}}\)

    \(\def\mathdef373#1{\mathtt{0x#1}}\mathdef373{61}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ne}}\)

    \(\def\mathdef374#1{\mathtt{0x#1}}\mathdef374{62}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\)

    \(\def\mathdef375#1{\mathtt{0x#1}}\mathdef375{63}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\)

    \(\def\mathdef376#1{\mathtt{0x#1}}\mathdef376{64}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\)

    \(\def\mathdef377#1{\mathtt{0x#1}}\mathdef377{65}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\)

    \(\def\mathdef378#1{\mathtt{0x#1}}\mathdef378{66}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{clz}}\)

    \(\def\mathdef379#1{\mathtt{0x#1}}\mathdef379{67}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ctz}}\)

    \(\def\mathdef380#1{\mathtt{0x#1}}\mathdef380{68}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{popcnt}}\)

    \(\def\mathdef381#1{\mathtt{0x#1}}\mathdef381{69}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}\)

    \(\def\mathdef382#1{\mathtt{0x#1}}\mathdef382{6A}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sub}}\)

    \(\def\mathdef383#1{\mathtt{0x#1}}\mathdef383{6B}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}}\)

    \(\def\mathdef384#1{\mathtt{0x#1}}\mathdef384{6C}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\mathsf{\_s}\)

    \(\def\mathdef385#1{\mathtt{0x#1}}\mathdef385{6D}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\mathsf{\_u}\)

    \(\def\mathdef386#1{\mathtt{0x#1}}\mathdef386{6E}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rem}}\mathsf{\_s}\)

    \(\def\mathdef387#1{\mathtt{0x#1}}\mathdef387{6F}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rem}}\mathsf{\_u}\)

    \(\def\mathdef388#1{\mathtt{0x#1}}\mathdef388{70}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{and}}\)

    \(\def\mathdef389#1{\mathtt{0x#1}}\mathdef389{71}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{or}}\)

    \(\def\mathdef390#1{\mathtt{0x#1}}\mathdef390{72}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{xor}}\)

    \(\def\mathdef391#1{\mathtt{0x#1}}\mathdef391{73}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shl}}\)

    \(\def\mathdef392#1{\mathtt{0x#1}}\mathdef392{74}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shr}}\mathsf{\_s}\)

    \(\def\mathdef393#1{\mathtt{0x#1}}\mathdef393{75}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shr}}\mathsf{\_u}\)

    \(\def\mathdef394#1{\mathtt{0x#1}}\mathdef394{76}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rotl}}\)

    \(\def\mathdef395#1{\mathtt{0x#1}}\mathdef395{77}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rotr}}\)

    \(\def\mathdef396#1{\mathtt{0x#1}}\mathdef396{78}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{clz}}\)

    \(\def\mathdef397#1{\mathtt{0x#1}}\mathdef397{79}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ctz}}\)

    \(\def\mathdef398#1{\mathtt{0x#1}}\mathdef398{7A}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{popcnt}}\)

    \(\def\mathdef399#1{\mathtt{0x#1}}\mathdef399{7B}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}\)

    \(\def\mathdef400#1{\mathtt{0x#1}}\mathdef400{7C}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sub}}\)

    \(\def\mathdef401#1{\mathtt{0x#1}}\mathdef401{7D}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}}\)

    \(\def\mathdef402#1{\mathtt{0x#1}}\mathdef402{7E}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\mathsf{\_s}\)

    \(\def\mathdef403#1{\mathtt{0x#1}}\mathdef403{7F}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\mathsf{\_u}\)

    \(\def\mathdef404#1{\mathtt{0x#1}}\mathdef404{80}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rem}}\mathsf{\_s}\)

    \(\def\mathdef405#1{\mathtt{0x#1}}\mathdef405{81}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rem}}\mathsf{\_u}\)

    \(\def\mathdef406#1{\mathtt{0x#1}}\mathdef406{82}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{and}}\)

    \(\def\mathdef407#1{\mathtt{0x#1}}\mathdef407{83}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{or}}\)

    \(\def\mathdef408#1{\mathtt{0x#1}}\mathdef408{84}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{xor}}\)

    \(\def\mathdef409#1{\mathtt{0x#1}}\mathdef409{85}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shl}}\)

    \(\def\mathdef410#1{\mathtt{0x#1}}\mathdef410{86}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shr}}\mathsf{\_s}\)

    \(\def\mathdef411#1{\mathtt{0x#1}}\mathdef411{87}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shr}}\mathsf{\_u}\)

    \(\def\mathdef412#1{\mathtt{0x#1}}\mathdef412{88}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rotl}}\)

    \(\def\mathdef413#1{\mathtt{0x#1}}\mathdef413{89}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rotr}}\)

    \(\def\mathdef414#1{\mathtt{0x#1}}\mathdef414{8A}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{abs}}\)

    \(\def\mathdef415#1{\mathtt{0x#1}}\mathdef415{8B}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{neg}}\)

    \(\def\mathdef416#1{\mathtt{0x#1}}\mathdef416{8C}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ceil}}\)

    \(\def\mathdef417#1{\mathtt{0x#1}}\mathdef417{8D}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{floor}}\)

    \(\def\mathdef418#1{\mathtt{0x#1}}\mathdef418{8E}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\)

    \(\def\mathdef419#1{\mathtt{0x#1}}\mathdef419{8F}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{nearest}}\)

    \(\def\mathdef420#1{\mathtt{0x#1}}\mathdef420{90}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sqrt}}\)

    \(\def\mathdef421#1{\mathtt{0x#1}}\mathdef421{91}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}\)

    \(\def\mathdef422#1{\mathtt{0x#1}}\mathdef422{92}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sub}}\)

    \(\def\mathdef423#1{\mathtt{0x#1}}\mathdef423{93}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}}\)

    \(\def\mathdef424#1{\mathtt{0x#1}}\mathdef424{94}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\)

    \(\def\mathdef425#1{\mathtt{0x#1}}\mathdef425{95}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{min}}\)

    \(\def\mathdef426#1{\mathtt{0x#1}}\mathdef426{96}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{max}}\)

    \(\def\mathdef427#1{\mathtt{0x#1}}\mathdef427{97}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{copysign}}\)

    \(\def\mathdef428#1{\mathtt{0x#1}}\mathdef428{98}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{abs}}\)

    \(\def\mathdef429#1{\mathtt{0x#1}}\mathdef429{99}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{neg}}\)

    \(\def\mathdef430#1{\mathtt{0x#1}}\mathdef430{9A}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ceil}}\)

    \(\def\mathdef431#1{\mathtt{0x#1}}\mathdef431{9B}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{floor}}\)

    \(\def\mathdef432#1{\mathtt{0x#1}}\mathdef432{9C}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\)

    \(\def\mathdef433#1{\mathtt{0x#1}}\mathdef433{9D}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{nearest}}\)

    \(\def\mathdef434#1{\mathtt{0x#1}}\mathdef434{9E}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sqrt}}\)

    \(\def\mathdef435#1{\mathtt{0x#1}}\mathdef435{9F}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}\)

    \(\def\mathdef436#1{\mathtt{0x#1}}\mathdef436{A0}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sub}}\)

    \(\def\mathdef437#1{\mathtt{0x#1}}\mathdef437{A1}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}}\)

    \(\def\mathdef438#1{\mathtt{0x#1}}\mathdef438{A2}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\)

    \(\def\mathdef439#1{\mathtt{0x#1}}\mathdef439{A3}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{min}}\)

    \(\def\mathdef440#1{\mathtt{0x#1}}\mathdef440{A4}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{max}}\)

    \(\def\mathdef441#1{\mathtt{0x#1}}\mathdef441{A5}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{copysign}}\)

    \(\def\mathdef442#1{\mathtt{0x#1}}\mathdef442{A6}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{wrap}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}\)

    \(\def\mathdef443#1{\mathtt{0x#1}}\mathdef443{A7}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_s}\)

    \(\def\mathdef444#1{\mathtt{0x#1}}\mathdef444{A8}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_u}\)

    \(\def\mathdef445#1{\mathtt{0x#1}}\mathdef445{A9}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_s}\)

    \(\def\mathdef446#1{\mathtt{0x#1}}\mathdef446{AA}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_u}\)

    \(\def\mathdef447#1{\mathtt{0x#1}}\mathdef447{AB}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_s}\)

    \(\def\mathdef448#1{\mathtt{0x#1}}\mathdef448{AC}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_u}\)

    \(\def\mathdef449#1{\mathtt{0x#1}}\mathdef449{AD}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_s}\)

    \(\def\mathdef450#1{\mathtt{0x#1}}\mathdef450{AE}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_u}\)

    \(\def\mathdef451#1{\mathtt{0x#1}}\mathdef451{AF}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution, operator

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    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16x4\_u}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    validation

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    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32x2\_u}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    validation

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    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{\_splat}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    validation

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    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{\_splat}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

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    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{\_splat}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

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    validation

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    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}^{16}\)

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    validation

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

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    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

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    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

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    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_s}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_u}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef608#1{\mathtt{0x#1}}\mathdef608{FD}~~\def\mathdef609#1{\mathtt{0x#1}}\mathdef609{16}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef610#1{\mathtt{0x#1}}\mathdef610{FD}~~\def\mathdef611#1{\mathtt{0x#1}}\mathdef611{17}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_s}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef612#1{\mathtt{0x#1}}\mathdef612{FD}~~\def\mathdef613#1{\mathtt{0x#1}}\mathdef613{18}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_u}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef618#1{\mathtt{0x#1}}\mathdef618{FD}~~\def\mathdef619#1{\mathtt{0x#1}}\mathdef619{1B}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef622#1{\mathtt{0x#1}}\mathdef622{FD}~~\def\mathdef623#1{\mathtt{0x#1}}\mathdef623{1D}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef624#1{\mathtt{0x#1}}\mathdef624{FD}~~\def\mathdef625#1{\mathtt{0x#1}}\mathdef625{1E}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef626#1{\mathtt{0x#1}}\mathdef626{FD}~~\def\mathdef627#1{\mathtt{0x#1}}\mathdef627{1F}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef628#1{\mathtt{0x#1}}\mathdef628{FD}~~\def\mathdef629#1{\mathtt{0x#1}}\mathdef629{20}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef630#1{\mathtt{0x#1}}\mathdef630{FD}~~\def\mathdef631#1{\mathtt{0x#1}}\mathdef631{21}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef632#1{\mathtt{0x#1}}\mathdef632{FD}~~\def\mathdef633#1{\mathtt{0x#1}}\mathdef633{22}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}}\)

    \(\def\mathdef634#1{\mathtt{0x#1}}\mathdef634{FD}~~\def\mathdef635#1{\mathtt{0x#1}}\mathdef635{23}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}}\)

    \(\def\mathdef636#1{\mathtt{0x#1}}\mathdef636{FD}~~\def\mathdef637#1{\mathtt{0x#1}}\mathdef637{24}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_s}\)

    \(\def\mathdef638#1{\mathtt{0x#1}}\mathdef638{FD}~~\def\mathdef639#1{\mathtt{0x#1}}\mathdef639{25}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_u}\)

    \(\def\mathdef640#1{\mathtt{0x#1}}\mathdef640{FD}~~\def\mathdef641#1{\mathtt{0x#1}}\mathdef641{26}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_s}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_s}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_s}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}}\)

    \(\def\mathdef656#1{\mathtt{0x#1}}\mathdef656{FD}~~\def\mathdef657#1{\mathtt{0x#1}}\mathdef657{2E}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_s}\)

    \(\def\mathdef658#1{\mathtt{0x#1}}\mathdef658{FD}~~\def\mathdef659#1{\mathtt{0x#1}}\mathdef659{2F}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_u}\)

    \(\def\mathdef660#1{\mathtt{0x#1}}\mathdef660{FD}~~\def\mathdef661#1{\mathtt{0x#1}}\mathdef661{30}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_s}\)

    \(\def\mathdef662#1{\mathtt{0x#1}}\mathdef662{FD}~~\def\mathdef663#1{\mathtt{0x#1}}\mathdef663{31}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_u}\)

    \(\def\mathdef664#1{\mathtt{0x#1}}\mathdef664{FD}~~\def\mathdef665#1{\mathtt{0x#1}}\mathdef665{32}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_s}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_s}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}}\)

    \(\def\mathdef676#1{\mathtt{0x#1}}\mathdef676{FD}~~\def\mathdef677#1{\mathtt{0x#1}}\mathdef677{38}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_s}\)

    \(\def\mathdef678#1{\mathtt{0x#1}}\mathdef678{FD}~~\def\mathdef679#1{\mathtt{0x#1}}\mathdef679{39}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_u}\)

    \(\def\mathdef680#1{\mathtt{0x#1}}\mathdef680{FD}~~\def\mathdef681#1{\mathtt{0x#1}}\mathdef681{3A}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_s}\)

    \(\def\mathdef682#1{\mathtt{0x#1}}\mathdef682{FD}~~\def\mathdef683#1{\mathtt{0x#1}}\mathdef683{3B}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_u}\)

    \(\def\mathdef684#1{\mathtt{0x#1}}\mathdef684{FD}~~\def\mathdef685#1{\mathtt{0x#1}}\mathdef685{3C}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_s}\)

    \(\def\mathdef686#1{\mathtt{0x#1}}\mathdef686{FD}~~\def\mathdef687#1{\mathtt{0x#1}}\mathdef687{3D}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_u}\)

    \(\def\mathdef688#1{\mathtt{0x#1}}\mathdef688{FD}~~\def\mathdef689#1{\mathtt{0x#1}}\mathdef689{3E}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_s}\)

    \(\def\mathdef690#1{\mathtt{0x#1}}\mathdef690{FD}~~\def\mathdef691#1{\mathtt{0x#1}}\mathdef691{3F}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_u}\)

    \(\def\mathdef692#1{\mathtt{0x#1}}\mathdef692{FD}~~\def\mathdef693#1{\mathtt{0x#1}}\mathdef693{40}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}}\)

    \(\def\mathdef694#1{\mathtt{0x#1}}\mathdef694{FD}~~\def\mathdef695#1{\mathtt{0x#1}}\mathdef695{41}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}}\)

    \(\def\mathdef696#1{\mathtt{0x#1}}\mathdef696{FD}~~\def\mathdef697#1{\mathtt{0x#1}}\mathdef697{42}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\)

    \(\def\mathdef698#1{\mathtt{0x#1}}\mathdef698{FD}~~\def\mathdef699#1{\mathtt{0x#1}}\mathdef699{43}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\)

    \(\def\mathdef700#1{\mathtt{0x#1}}\mathdef700{FD}~~\def\mathdef701#1{\mathtt{0x#1}}\mathdef701{44}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\)

    \(\def\mathdef702#1{\mathtt{0x#1}}\mathdef702{FD}~~\def\mathdef703#1{\mathtt{0x#1}}\mathdef703{45}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\)

    \(\def\mathdef704#1{\mathtt{0x#1}}\mathdef704{FD}~~\def\mathdef705#1{\mathtt{0x#1}}\mathdef705{46}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}}\)

    \(\def\mathdef706#1{\mathtt{0x#1}}\mathdef706{FD}~~\def\mathdef707#1{\mathtt{0x#1}}\mathdef707{47}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}}\)

    \(\def\mathdef708#1{\mathtt{0x#1}}\mathdef708{FD}~~\def\mathdef709#1{\mathtt{0x#1}}\mathdef709{48}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\)

    \(\def\mathdef710#1{\mathtt{0x#1}}\mathdef710{FD}~~\def\mathdef711#1{\mathtt{0x#1}}\mathdef711{49}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\)

    \(\def\mathdef712#1{\mathtt{0x#1}}\mathdef712{FD}~~\def\mathdef713#1{\mathtt{0x#1}}\mathdef713{4A}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\)

    \(\def\mathdef714#1{\mathtt{0x#1}}\mathdef714{FD}~~\def\mathdef715#1{\mathtt{0x#1}}\mathdef715{4B}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\)

    \(\def\mathdef716#1{\mathtt{0x#1}}\mathdef716{FD}~~\def\mathdef717#1{\mathtt{0x#1}}\mathdef717{4C}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{not}}\)

    \(\def\mathdef718#1{\mathtt{0x#1}}\mathdef718{FD}~~\def\mathdef719#1{\mathtt{0x#1}}\mathdef719{4D}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{and}}\)

    \(\def\mathdef720#1{\mathtt{0x#1}}\mathdef720{FD}~~\def\mathdef721#1{\mathtt{0x#1}}\mathdef721{4E}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{andnot}}\)

    \(\def\mathdef722#1{\mathtt{0x#1}}\mathdef722{FD}~~\def\mathdef723#1{\mathtt{0x#1}}\mathdef723{4F}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{or}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{xor}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitselect}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{any\_true}}\)

    \(\def\mathdef730#1{\mathtt{0x#1}}\mathdef730{FD}~~\def\mathdef731#1{\mathtt{0x#1}}\mathdef731{53}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef732#1{\mathtt{0x#1}}\mathdef732{FD}~~\def\mathdef733#1{\mathtt{0x#1}}\mathdef733{54}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef734#1{\mathtt{0x#1}}\mathdef734{FD}~~\def\mathdef735#1{\mathtt{0x#1}}\mathdef735{55}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef736#1{\mathtt{0x#1}}\mathdef736{FD}~~\def\mathdef737#1{\mathtt{0x#1}}\mathdef737{56}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{64\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef738#1{\mathtt{0x#1}}\mathdef738{FD}~~\def\mathdef739#1{\mathtt{0x#1}}\mathdef739{57}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef740#1{\mathtt{0x#1}}\mathdef740{FD}~~\def\mathdef741#1{\mathtt{0x#1}}\mathdef741{58}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{16\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef742#1{\mathtt{0x#1}}\mathdef742{FD}~~\def\mathdef743#1{\mathtt{0x#1}}\mathdef743{59}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{32\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef744#1{\mathtt{0x#1}}\mathdef744{FD}~~\def\mathdef745#1{\mathtt{0x#1}}\mathdef745{5A}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{64\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef746#1{\mathtt{0x#1}}\mathdef746{FD}~~\def\mathdef747#1{\mathtt{0x#1}}\mathdef747{5B}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_zero}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    \(\def\mathdef748#1{\mathtt{0x#1}}\mathdef748{FD}~~\def\mathdef749#1{\mathtt{0x#1}}\mathdef749{5C}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{64\_zero}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{demote}}\mathsf{\_f64x2\_zero}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{promote}}\mathsf{\_low\_f32x4}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}}\)

    \(\def\mathdef756#1{\mathtt{0x#1}}\mathdef756{FD}~~\def\mathdef757#1{\mathtt{0x#1}}\mathdef757{60}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}}\)

    \(\def\mathdef758#1{\mathtt{0x#1}}\mathdef758{FD}~~\def\mathdef759#1{\mathtt{0x#1}}\mathdef759{61}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{popcnt}}\)

    \(\def\mathdef760#1{\mathtt{0x#1}}\mathdef760{FD}~~\def\mathdef761#1{\mathtt{0x#1}}\mathdef761{62}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}}\)

    \(\def\mathdef762#1{\mathtt{0x#1}}\mathdef762{FD}~~\def\mathdef763#1{\mathtt{0x#1}}\mathdef763{63}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}\)

    \(\def\mathdef764#1{\mathtt{0x#1}}\mathdef764{FD}~~\def\mathdef765#1{\mathtt{0x#1}}\mathdef765{64}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i16x8\_s}\)

    \(\def\mathdef766#1{\mathtt{0x#1}}\mathdef766{FD}~~\def\mathdef767#1{\mathtt{0x#1}}\mathdef767{65}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i16x8\_u}\)

    \(\def\mathdef768#1{\mathtt{0x#1}}\mathdef768{FD}~~\def\mathdef769#1{\mathtt{0x#1}}\mathdef769{66}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ceil}}\)

    \(\def\mathdef770#1{\mathtt{0x#1}}\mathdef770{FD}~~\def\mathdef771#1{\mathtt{0x#1}}\mathdef771{67}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{floor}}\)

    \(\def\mathdef772#1{\mathtt{0x#1}}\mathdef772{FD}~~\def\mathdef773#1{\mathtt{0x#1}}\mathdef773{68}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}}\)

    \(\def\mathdef774#1{\mathtt{0x#1}}\mathdef774{FD}~~\def\mathdef775#1{\mathtt{0x#1}}\mathdef775{69}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{nearest}}\)

    \(\def\mathdef776#1{\mathtt{0x#1}}\mathdef776{FD}~~\def\mathdef777#1{\mathtt{0x#1}}\mathdef777{6A}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shl}}\)

    \(\def\mathdef778#1{\mathtt{0x#1}}\mathdef778{FD}~~\def\mathdef779#1{\mathtt{0x#1}}\mathdef779{6B}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_s}\)

    \(\def\mathdef780#1{\mathtt{0x#1}}\mathdef780{FD}~~\def\mathdef781#1{\mathtt{0x#1}}\mathdef781{6C}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_u}\)

    \(\def\mathdef782#1{\mathtt{0x#1}}\mathdef782{FD}~~\def\mathdef783#1{\mathtt{0x#1}}\mathdef783{6D}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\)

    \(\def\mathdef784#1{\mathtt{0x#1}}\mathdef784{FD}~~\def\mathdef785#1{\mathtt{0x#1}}\mathdef785{6E}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\mathsf{\_sat\_s}\)

    \(\def\mathdef786#1{\mathtt{0x#1}}\mathdef786{FD}~~\def\mathdef787#1{\mathtt{0x#1}}\mathdef787{6F}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\mathsf{\_sat\_u}\)

    \(\def\mathdef788#1{\mathtt{0x#1}}\mathdef788{FD}~~\def\mathdef789#1{\mathtt{0x#1}}\mathdef789{70}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\)

    \(\def\mathdef790#1{\mathtt{0x#1}}\mathdef790{FD}~~\def\mathdef791#1{\mathtt{0x#1}}\mathdef791{71}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\mathsf{\_sat\_s}\)

    \(\def\mathdef792#1{\mathtt{0x#1}}\mathdef792{FD}~~\def\mathdef793#1{\mathtt{0x#1}}\mathdef793{72}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\mathsf{\_sat\_u}\)

    \(\def\mathdef794#1{\mathtt{0x#1}}\mathdef794{FD}~~\def\mathdef795#1{\mathtt{0x#1}}\mathdef795{73}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ceil}}\)

    \(\def\mathdef796#1{\mathtt{0x#1}}\mathdef796{FD}~~\def\mathdef797#1{\mathtt{0x#1}}\mathdef797{74}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{floor}}\)

    \(\def\mathdef798#1{\mathtt{0x#1}}\mathdef798{FD}~~\def\mathdef799#1{\mathtt{0x#1}}\mathdef799{75}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_s}\)

    \(\def\mathdef800#1{\mathtt{0x#1}}\mathdef800{FD}~~\def\mathdef801#1{\mathtt{0x#1}}\mathdef801{76}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_u}\)

    \(\def\mathdef802#1{\mathtt{0x#1}}\mathdef802{FD}~~\def\mathdef803#1{\mathtt{0x#1}}\mathdef803{77}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_s}\)

    \(\def\mathdef804#1{\mathtt{0x#1}}\mathdef804{FD}~~\def\mathdef805#1{\mathtt{0x#1}}\mathdef805{78}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

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    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{avgr}}\mathsf{\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

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    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_i8x16\_u}\)

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    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_i16x8\_s}\)

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    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_i16x8\_u}\)

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    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}}\)

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    validation

    execution, operator

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    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{q15mulr\_sat}}\mathsf{\_s}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}}\)

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    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}\)

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    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i32x4\_s}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i32x4\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i8x16\_s}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i8x16\_s}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i8x16\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i8x16\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shl}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_s}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\)

    \(\def\mathdef848#1{\mathtt{0x#1}}\mathdef848{FD}~~\def\mathdef849#1{\mathtt{0x#1}}\mathdef849{8E}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\mathsf{\_sat\_s}\)

    \(\def\mathdef850#1{\mathtt{0x#1}}\mathdef850{FD}~~\def\mathdef851#1{\mathtt{0x#1}}\mathdef851{8F}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\mathsf{\_sat\_u}\)

    \(\def\mathdef852#1{\mathtt{0x#1}}\mathdef852{FD}~~\def\mathdef853#1{\mathtt{0x#1}}\mathdef853{90}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\)

    \(\def\mathdef854#1{\mathtt{0x#1}}\mathdef854{FD}~~\def\mathdef855#1{\mathtt{0x#1}}\mathdef855{91}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\mathsf{\_sat\_s}\)

    \(\def\mathdef856#1{\mathtt{0x#1}}\mathdef856{FD}~~\def\mathdef857#1{\mathtt{0x#1}}\mathdef857{92}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\mathsf{\_sat\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{nearest}}\)

    \(\def\mathdef860#1{\mathtt{0x#1}}\mathdef860{FD}~~\def\mathdef861#1{\mathtt{0x#1}}\mathdef861{94}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}}\)

    \(\def\mathdef862#1{\mathtt{0x#1}}\mathdef862{FD}~~\def\mathdef863#1{\mathtt{0x#1}}\mathdef863{95}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_s}\)

    \(\def\mathdef864#1{\mathtt{0x#1}}\mathdef864{FD}~~\def\mathdef865#1{\mathtt{0x#1}}\mathdef865{96}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_u}\)

    \(\def\mathdef866#1{\mathtt{0x#1}}\mathdef866{FD}~~\def\mathdef867#1{\mathtt{0x#1}}\mathdef867{97}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_s}\)

    \(\def\mathdef868#1{\mathtt{0x#1}}\mathdef868{FD}~~\def\mathdef869#1{\mathtt{0x#1}}\mathdef869{98}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_u}\)

    \(\def\mathdef870#1{\mathtt{0x#1}}\mathdef870{FD}~~\def\mathdef871#1{\mathtt{0x#1}}\mathdef871{99}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{avgr}}\mathsf{\_u}\)

    \(\def\mathdef872#1{\mathtt{0x#1}}\mathdef872{FD}~~\def\mathdef873#1{\mathtt{0x#1}}\mathdef873{9B}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i8x16\_s}\)

    \(\def\mathdef874#1{\mathtt{0x#1}}\mathdef874{FD}~~\def\mathdef875#1{\mathtt{0x#1}}\mathdef875{9C}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i8x16\_s}\)

    \(\def\mathdef876#1{\mathtt{0x#1}}\mathdef876{FD}~~\def\mathdef877#1{\mathtt{0x#1}}\mathdef877{9D}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i8x16\_u}\)

    \(\def\mathdef878#1{\mathtt{0x#1}}\mathdef878{FD}~~\def\mathdef879#1{\mathtt{0x#1}}\mathdef879{9E}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i8x16\_u}\)

    \(\def\mathdef880#1{\mathtt{0x#1}}\mathdef880{FD}~~\def\mathdef881#1{\mathtt{0x#1}}\mathdef881{9F}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}}\)

    \(\def\mathdef882#1{\mathtt{0x#1}}\mathdef882{FD}~~\def\mathdef883#1{\mathtt{0x#1}}\mathdef883{A0}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}}\)

    \(\def\mathdef884#1{\mathtt{0x#1}}\mathdef884{FD}~~\def\mathdef885#1{\mathtt{0x#1}}\mathdef885{A1}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}\)

    \(\def\mathdef888#1{\mathtt{0x#1}}\mathdef888{FD}~~\def\mathdef889#1{\mathtt{0x#1}}\mathdef889{A4}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i16x8\_s}\)

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    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i16x8\_s}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i16x8\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i16x8\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shl}}\)

    \(\def\mathdef898#1{\mathtt{0x#1}}\mathdef898{FD}~~\def\mathdef899#1{\mathtt{0x#1}}\mathdef899{AB}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_s}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\)

    \(\def\mathdef904#1{\mathtt{0x#1}}\mathdef904{FD}~~\def\mathdef905#1{\mathtt{0x#1}}\mathdef905{AE}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\)

    \(\def\mathdef906#1{\mathtt{0x#1}}\mathdef906{FD}~~\def\mathdef907#1{\mathtt{0x#1}}\mathdef907{B1}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}}\)

    \(\def\mathdef908#1{\mathtt{0x#1}}\mathdef908{FD}~~\def\mathdef909#1{\mathtt{0x#1}}\mathdef909{B5}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_s}\)

    \(\def\mathdef910#1{\mathtt{0x#1}}\mathdef910{FD}~~\def\mathdef911#1{\mathtt{0x#1}}\mathdef911{B6}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_u}\)

    \(\def\mathdef912#1{\mathtt{0x#1}}\mathdef912{FD}~~\def\mathdef913#1{\mathtt{0x#1}}\mathdef913{B7}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_s}\)

    \(\def\mathdef914#1{\mathtt{0x#1}}\mathdef914{FD}~~\def\mathdef915#1{\mathtt{0x#1}}\mathdef915{B8}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_u}\)

    \(\def\mathdef916#1{\mathtt{0x#1}}\mathdef916{FD}~~\def\mathdef917#1{\mathtt{0x#1}}\mathdef917{B9}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

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    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{dot}}\mathsf{\_i16x8\_s}\)

    \(\def\mathdef918#1{\mathtt{0x#1}}\mathdef918{FD}~~\def\mathdef919#1{\mathtt{0x#1}}\mathdef919{BA}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i16x8\_s}\)

    \(\def\mathdef920#1{\mathtt{0x#1}}\mathdef920{FD}~~\def\mathdef921#1{\mathtt{0x#1}}\mathdef921{BC}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i16x8\_s}\)

    \(\def\mathdef922#1{\mathtt{0x#1}}\mathdef922{FD}~~\def\mathdef923#1{\mathtt{0x#1}}\mathdef923{BD}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i16x8\_u}\)

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    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i16x8\_u}\)

    \(\def\mathdef926#1{\mathtt{0x#1}}\mathdef926{FD}~~\def\mathdef927#1{\mathtt{0x#1}}\mathdef927{BF}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}}\)

    \(\def\mathdef928#1{\mathtt{0x#1}}\mathdef928{FD}~~\def\mathdef929#1{\mathtt{0x#1}}\mathdef929{C0}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}}\)

    \(\def\mathdef930#1{\mathtt{0x#1}}\mathdef930{FD}~~\def\mathdef931#1{\mathtt{0x#1}}\mathdef931{C1}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}}\)

    \(\def\mathdef932#1{\mathtt{0x#1}}\mathdef932{FD}~~\def\mathdef933#1{\mathtt{0x#1}}\mathdef933{C3}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}\)

    \(\def\mathdef934#1{\mathtt{0x#1}}\mathdef934{FD}~~\def\mathdef935#1{\mathtt{0x#1}}\mathdef935{C4}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i32x4\_s}\)

    \(\def\mathdef936#1{\mathtt{0x#1}}\mathdef936{FD}~~\def\mathdef937#1{\mathtt{0x#1}}\mathdef937{C7}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i32x4\_s}\)

    \(\def\mathdef938#1{\mathtt{0x#1}}\mathdef938{FD}~~\def\mathdef939#1{\mathtt{0x#1}}\mathdef939{C8}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i32x4\_u}\)

    \(\def\mathdef940#1{\mathtt{0x#1}}\mathdef940{FD}~~\def\mathdef941#1{\mathtt{0x#1}}\mathdef941{C9}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i32x4\_u}\)

    \(\def\mathdef942#1{\mathtt{0x#1}}\mathdef942{FD}~~\def\mathdef943#1{\mathtt{0x#1}}\mathdef943{CA}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shl}}\)

    \(\def\mathdef944#1{\mathtt{0x#1}}\mathdef944{FD}~~\def\mathdef945#1{\mathtt{0x#1}}\mathdef945{CB}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_s}\)

    \(\def\mathdef946#1{\mathtt{0x#1}}\mathdef946{FD}~~\def\mathdef947#1{\mathtt{0x#1}}\mathdef947{CC}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_u}\)

    \(\def\mathdef948#1{\mathtt{0x#1}}\mathdef948{FD}~~\def\mathdef949#1{\mathtt{0x#1}}\mathdef949{CD}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\)

    \(\def\mathdef950#1{\mathtt{0x#1}}\mathdef950{FD}~~\def\mathdef951#1{\mathtt{0x#1}}\mathdef951{CE}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\)

    \(\def\mathdef952#1{\mathtt{0x#1}}\mathdef952{FD}~~\def\mathdef953#1{\mathtt{0x#1}}\mathdef953{D1}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}}\)

    \(\def\mathdef954#1{\mathtt{0x#1}}\mathdef954{FD}~~\def\mathdef955#1{\mathtt{0x#1}}\mathdef955{D5}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}}\)

    \(\def\mathdef956#1{\mathtt{0x#1}}\mathdef956{FD}~~\def\mathdef957#1{\mathtt{0x#1}}\mathdef957{D6}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}}\)

    \(\def\mathdef958#1{\mathtt{0x#1}}\mathdef958{FD}~~\def\mathdef959#1{\mathtt{0x#1}}\mathdef959{D7}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_s}\)

    \(\def\mathdef960#1{\mathtt{0x#1}}\mathdef960{FD}~~\def\mathdef961#1{\mathtt{0x#1}}\mathdef961{D8}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_s}\)

    \(\def\mathdef962#1{\mathtt{0x#1}}\mathdef962{FD}~~\def\mathdef963#1{\mathtt{0x#1}}\mathdef963{D9}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_s}\)

    \(\def\mathdef964#1{\mathtt{0x#1}}\mathdef964{FD}~~\def\mathdef965#1{\mathtt{0x#1}}\mathdef965{DA}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_s}\)

    \(\def\mathdef966#1{\mathtt{0x#1}}\mathdef966{FD}~~\def\mathdef967#1{\mathtt{0x#1}}\mathdef967{DB}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i32x4\_s}\)

    \(\def\mathdef968#1{\mathtt{0x#1}}\mathdef968{FD}~~\def\mathdef969#1{\mathtt{0x#1}}\mathdef969{DC}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i32x4\_s}\)

    \(\def\mathdef970#1{\mathtt{0x#1}}\mathdef970{FD}~~\def\mathdef971#1{\mathtt{0x#1}}\mathdef971{DD}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i32x4\_u}\)

    \(\def\mathdef972#1{\mathtt{0x#1}}\mathdef972{FD}~~\def\mathdef973#1{\mathtt{0x#1}}\mathdef973{DE}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i32x4\_u}\)

    \(\def\mathdef974#1{\mathtt{0x#1}}\mathdef974{FD}~~\def\mathdef975#1{\mathtt{0x#1}}\mathdef975{DF}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}}\)

    \(\def\mathdef976#1{\mathtt{0x#1}}\mathdef976{FD}~~\def\mathdef977#1{\mathtt{0x#1}}\mathdef977{E0}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}}\)

    \(\def\mathdef978#1{\mathtt{0x#1}}\mathdef978{FD}~~\def\mathdef979#1{\mathtt{0x#1}}\mathdef979{E1}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sqrt}}\)

    \(\def\mathdef980#1{\mathtt{0x#1}}\mathdef980{FD}~~\def\mathdef981#1{\mathtt{0x#1}}\mathdef981{E3}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\)

    \(\def\mathdef982#1{\mathtt{0x#1}}\mathdef982{FD}~~\def\mathdef983#1{\mathtt{0x#1}}\mathdef983{E4}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\)

    \(\def\mathdef984#1{\mathtt{0x#1}}\mathdef984{FD}~~\def\mathdef985#1{\mathtt{0x#1}}\mathdef985{E5}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}}\)

    \(\def\mathdef986#1{\mathtt{0x#1}}\mathdef986{FD}~~\def\mathdef987#1{\mathtt{0x#1}}\mathdef987{E6}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{div}}\)

    \(\def\mathdef988#1{\mathtt{0x#1}}\mathdef988{FD}~~\def\mathdef989#1{\mathtt{0x#1}}\mathdef989{E7}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\)

    \(\def\mathdef990#1{\mathtt{0x#1}}\mathdef990{FD}~~\def\mathdef991#1{\mathtt{0x#1}}\mathdef991{E8}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\)

    \(\def\mathdef992#1{\mathtt{0x#1}}\mathdef992{FD}~~\def\mathdef993#1{\mathtt{0x#1}}\mathdef993{E9}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{pmin}}\)

    \(\def\mathdef994#1{\mathtt{0x#1}}\mathdef994{FD}~~\def\mathdef995#1{\mathtt{0x#1}}\mathdef995{EA}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{pmax}}\)

    \(\def\mathdef996#1{\mathtt{0x#1}}\mathdef996{FD}~~\def\mathdef997#1{\mathtt{0x#1}}\mathdef997{EB}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}}\)

    \(\def\mathdef998#1{\mathtt{0x#1}}\mathdef998{FD}~~\def\mathdef999#1{\mathtt{0x#1}}\mathdef999{EC}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}}\)

    \(\def\mathdef1000#1{\mathtt{0x#1}}\mathdef1000{FD}~~\def\mathdef1001#1{\mathtt{0x#1}}\mathdef1001{ED}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sqrt}}\)

    \(\def\mathdef1002#1{\mathtt{0x#1}}\mathdef1002{FD}~~\def\mathdef1003#1{\mathtt{0x#1}}\mathdef1003{EF}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\)

    \(\def\mathdef1004#1{\mathtt{0x#1}}\mathdef1004{FD}~~\def\mathdef1005#1{\mathtt{0x#1}}\mathdef1005{F0}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\)

    \(\def\mathdef1006#1{\mathtt{0x#1}}\mathdef1006{FD}~~\def\mathdef1007#1{\mathtt{0x#1}}\mathdef1007{F1}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}}\)

    \(\def\mathdef1008#1{\mathtt{0x#1}}\mathdef1008{FD}~~\def\mathdef1009#1{\mathtt{0x#1}}\mathdef1009{F2}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{div}}\)

    \(\def\mathdef1010#1{\mathtt{0x#1}}\mathdef1010{FD}~~\def\mathdef1011#1{\mathtt{0x#1}}\mathdef1011{F3}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\)

    \(\def\mathdef1012#1{\mathtt{0x#1}}\mathdef1012{FD}~~\def\mathdef1013#1{\mathtt{0x#1}}\mathdef1013{F4}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\)

    \(\def\mathdef1014#1{\mathtt{0x#1}}\mathdef1014{FD}~~\def\mathdef1015#1{\mathtt{0x#1}}\mathdef1015{F5}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{pmin}}\)

    \(\def\mathdef1016#1{\mathtt{0x#1}}\mathdef1016{FD}~~\def\mathdef1017#1{\mathtt{0x#1}}\mathdef1017{F6}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{pmax}}\)

    \(\def\mathdef1018#1{\mathtt{0x#1}}\mathdef1018{FD}~~\def\mathdef1019#1{\mathtt{0x#1}}\mathdef1019{F7}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_f32x4\_s}\)

    \(\def\mathdef1020#1{\mathtt{0x#1}}\mathdef1020{FD}~~\def\mathdef1021#1{\mathtt{0x#1}}\mathdef1021{F8}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_f32x4\_u}\)

    \(\def\mathdef1022#1{\mathtt{0x#1}}\mathdef1022{FD}~~\def\mathdef1023#1{\mathtt{0x#1}}\mathdef1023{F9}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{convert}}\mathsf{\_i32x4\_s}\)

    \(\def\mathdef1024#1{\mathtt{0x#1}}\mathdef1024{FD}~~\def\mathdef1025#1{\mathtt{0x#1}}\mathdef1025{FA}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{convert}}\mathsf{\_i32x4\_u}\)

    \(\def\mathdef1026#1{\mathtt{0x#1}}\mathdef1026{FD}~~\def\mathdef1027#1{\mathtt{0x#1}}\mathdef1027{FB}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}}\mathsf{\_sat\_f64x2\_s\_zero}\)

    \(\def\mathdef1028#1{\mathtt{0x#1}}\mathdef1028{FD}~~\def\mathdef1029#1{\mathtt{0x#1}}\mathdef1029{FC}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}}\mathsf{\_sat\_f64x2\_u\_zero}\)

    \(\def\mathdef1030#1{\mathtt{0x#1}}\mathdef1030{FD}~~\def\mathdef1031#1{\mathtt{0x#1}}\mathdef1031{FD}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{convert}}\mathsf{\_low\_i32x4\_s}\)

    \(\def\mathdef1032#1{\mathtt{0x#1}}\mathdef1032{FD}~~\def\mathdef1033#1{\mathtt{0x#1}}\mathdef1033{FE}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{convert}}\mathsf{\_low\_i32x4\_u}\)

    \(\def\mathdef1034#1{\mathtt{0x#1}}\mathdef1034{FD}~~\def\mathdef1035#1{\mathtt{0x#1}}\mathdef1035{FF}\)

    \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\)

    validation

    execution, operator

    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/appendix/index-rules.html b/core/appendix/index-rules.html new file mode 100644 index 00000000..2a244376 --- /dev/null +++ b/core/appendix/index-rules.html @@ -0,0 +1,358 @@ + + + + + + + + + Index of Semantic Rules — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Index of Semantic Rules

    +
    +

    Typing of Static Constructs

    + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Construct

    Judgement

    Limits

    \(\href{../valid/types.html#valid-limits}{\vdash} \href{../syntax/types.html#syntax-limits}{\mathit{limits}} : k\)

    Function type

    \(\href{../valid/types.html#valid-functype}{\vdash} \href{../syntax/types.html#syntax-functype}{\mathit{functype}} \mathrel{\mbox{ok}}\)

    Block type

    \(\href{../valid/types.html#valid-blocktype}{\vdash} \href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}} \mathrel{\mbox{ok}}\)

    Table type

    \(\href{../valid/types.html#valid-tabletype}{\vdash} \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} \mathrel{\mbox{ok}}\)

    Memory type

    \(\href{../valid/types.html#valid-memtype}{\vdash} \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} \mathrel{\mbox{ok}}\)

    Global type

    \(\href{../valid/types.html#valid-globaltype}{\vdash} \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} \mathrel{\mbox{ok}}\)

    External type

    \(\href{../valid/types.html#valid-externtype}{\vdash} \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}} \mathrel{\mbox{ok}}\)

    Instruction

    \(S;C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}} : \href{../syntax/types.html#syntax-stacktype}{\mathit{stacktype}}\)

    Instruction sequence

    \(S;C \href{../valid/instructions.html#valid-instr-seq}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast : \href{../syntax/types.html#syntax-stacktype}{\mathit{stacktype}}\)

    Expression

    \(C \href{../valid/instructions.html#valid-expr}{\vdash} \href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} : \href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}}\)

    Function

    \(C \href{../valid/modules.html#valid-func}{\vdash} \href{../syntax/modules.html#syntax-func}{\mathit{func}} : \href{../syntax/types.html#syntax-functype}{\mathit{functype}}\)

    Table

    \(C \href{../valid/modules.html#valid-table}{\vdash} \href{../syntax/modules.html#syntax-table}{\mathit{table}} : \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\)

    Memory

    \(C \href{../valid/modules.html#valid-mem}{\vdash} \href{../syntax/modules.html#syntax-mem}{\mathit{mem}} : \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\)

    Global

    \(C \href{../valid/modules.html#valid-global}{\vdash} \href{../syntax/modules.html#syntax-global}{\mathit{global}} : \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}\)

    Element segment

    \(C \href{../valid/modules.html#valid-elem}{\vdash} \href{../syntax/modules.html#syntax-elem}{\mathit{elem}} : \href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}\)

    Element mode

    \(C \href{../valid/modules.html#valid-elemmode}{\vdash} \href{../syntax/modules.html#syntax-elemmode}{\mathit{elemmode}} : \href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}\)

    Data segment

    \(C \href{../valid/modules.html#valid-data}{\vdash} \href{../syntax/modules.html#syntax-data}{\mathit{data}} \mathrel{\mbox{ok}}\)

    Data mode

    \(C \href{../valid/modules.html#valid-datamode}{\vdash} \href{../syntax/modules.html#syntax-datamode}{\mathit{datamode}} \mathrel{\mbox{ok}}\)

    Start function

    \(C \href{../valid/modules.html#valid-start}{\vdash} \href{../syntax/modules.html#syntax-start}{\mathit{start}} \mathrel{\mbox{ok}}\)

    Export

    \(C \href{../valid/modules.html#valid-export}{\vdash} \href{../syntax/modules.html#syntax-export}{\mathit{export}} : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}\)

    Export description

    \(C \href{../valid/modules.html#valid-exportdesc}{\vdash} \href{../syntax/modules.html#syntax-exportdesc}{\mathit{exportdesc}} : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}\)

    Import

    \(C \href{../valid/modules.html#valid-import}{\vdash} \href{../syntax/modules.html#syntax-import}{\mathit{import}} : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}\)

    Import description

    \(C \href{../valid/modules.html#valid-importdesc}{\vdash} \href{../syntax/modules.html#syntax-importdesc}{\mathit{importdesc}} : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}\)

    Module

    \(\href{../valid/modules.html#valid-module}{\vdash} \href{../syntax/modules.html#syntax-module}{\mathit{module}} : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast \href{../syntax/types.html#syntax-functype}{\rightarrow} \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast\)

    +
    +
    +

    Typing of Runtime Constructs

    + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Construct

    Judgement

    Value

    \(S \href{../appendix/properties.html#valid-val}{\vdash} \href{../exec/runtime.html#syntax-val}{\mathit{val}} : \href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}\)

    Result

    \(S \href{../appendix/properties.html#valid-result}{\vdash} \href{../exec/runtime.html#syntax-result}{\mathit{result}} : \href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}}\)

    External value

    \(S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathit{externval}} : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}\)

    Function instance

    \(S \href{../appendix/properties.html#valid-funcinst}{\vdash} \href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}} : \href{../syntax/types.html#syntax-functype}{\mathit{functype}}\)

    Table instance

    \(S \href{../appendix/properties.html#valid-tableinst}{\vdash} \href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}} : \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\)

    Memory instance

    \(S \href{../appendix/properties.html#valid-meminst}{\vdash} \href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}} : \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\)

    Global instance

    \(S \href{../appendix/properties.html#valid-globalinst}{\vdash} \href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}} : \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}\)

    Element instance

    \(S \href{../appendix/properties.html#valid-eleminst}{\vdash} \href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}} \mathrel{\mbox{ok}}\)

    Data instance

    \(S \href{../appendix/properties.html#valid-datainst}{\vdash} \href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}} \mathrel{\mbox{ok}}\)

    Export instance

    \(S \href{../appendix/properties.html#valid-exportinst}{\vdash} \href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}} \mathrel{\mbox{ok}}\)

    Module instance

    \(S \href{../appendix/properties.html#valid-moduleinst}{\vdash} \href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}} : C\)

    Store

    \(\href{../appendix/properties.html#valid-store}{\vdash} \href{../exec/runtime.html#syntax-store}{\mathit{store}} \mathrel{\mbox{ok}}\)

    Configuration

    \(\href{../appendix/properties.html#valid-config}{\vdash} \href{../exec/runtime.html#syntax-config}{\mathit{config}} \mathrel{\mbox{ok}}\)

    Thread

    \(S;\href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}}^? \href{../appendix/properties.html#valid-thread}{\vdash} \href{../exec/runtime.html#syntax-thread}{\mathit{thread}} : \href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}}\)

    Frame

    \(S \href{../appendix/properties.html#valid-frame}{\vdash} \href{../exec/runtime.html#syntax-frame}{\mathit{frame}} : C\)

    +
    +
    +

    Constantness

    + ++++ + + + + + + + + + + + + + +

    Construct

    Judgement

    Constant expression

    \(C \href{../valid/instructions.html#valid-constant}{\vdash} \href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \href{../valid/instructions.html#valid-constant}{\mathrel{\mbox{const}}}\)

    Constant instruction

    \(C \href{../valid/instructions.html#valid-constant}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}} \href{../valid/instructions.html#valid-constant}{\mathrel{\mbox{const}}}\)

    +
    +
    +

    Matching

    + ++++ + + + + + + + + + + + + + +

    Construct

    Judgement

    External type

    \(\href{../exec/modules.html#match-externtype}{\vdash} \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}_1 \href{../exec/modules.html#match-externtype}{\leq} \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}_2\)

    Limits

    \(\href{../exec/modules.html#match-limits}{\vdash} \href{../syntax/types.html#syntax-limits}{\mathit{limits}}_1 \href{../exec/modules.html#match-limits}{\leq} \href{../syntax/types.html#syntax-limits}{\mathit{limits}}_2\)

    +
    +
    +

    Store Extension

    + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Construct

    Judgement

    Function instance

    \(\href{../appendix/properties.html#extend-funcinst}{\vdash} \href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}_1 \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}_2\)

    Table instance

    \(\href{../appendix/properties.html#extend-tableinst}{\vdash} \href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}_1 \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}_2\)

    Memory instance

    \(\href{../appendix/properties.html#extend-meminst}{\vdash} \href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}_1 \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}_2\)

    Global instance

    \(\href{../appendix/properties.html#extend-globalinst}{\vdash} \href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}_1 \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}_2\)

    Element instance

    \(\href{../appendix/properties.html#extend-eleminst}{\vdash} \href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}_1 \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}_2\)

    Data instance

    \(\href{../appendix/properties.html#extend-datainst}{\vdash} \href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}_1 \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}_2\)

    Store

    \(\href{../appendix/properties.html#extend-store}{\vdash} \href{../exec/runtime.html#syntax-store}{\mathit{store}}_1 \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-store}{\mathit{store}}_2\)

    +
    +
    +

    Execution

    + ++++ + + + + + + + + + + + + + +

    Construct

    Judgement

    Instruction

    \(S;F;\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast \href{../exec/conventions.html#formal-notation}{\hookrightarrow} S';F';{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}'}^\ast\)

    Expression

    \(S;F;\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \href{../exec/conventions.html#formal-notation}{\hookrightarrow} S';F';\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}'\)

    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/appendix/index-types.html b/core/appendix/index-types.html new file mode 100644 index 00000000..c67f84ac --- /dev/null +++ b/core/appendix/index-types.html @@ -0,0 +1,178 @@ + + + + + + + + + Index of Types — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Index of Types

    + +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Category

    Constructor

    Binary Opcode

    Type index

    \(x\)

    (positive number as \(\href{../binary/values.html#binary-int}{\def\mathdef1084#1{{\mathtt{s}#1}}\mathdef1084{\mathtt{32}}}\) or \(\href{../binary/values.html#binary-int}{\def\mathdef1080#1{{\mathtt{u}#1}}\mathdef1080{\mathtt{32}}}\))

    Number type

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\)

    \(\def\mathdef1114#1{\mathtt{0x#1}}\mathdef1114{7F}\) (-1 as \(\href{../binary/values.html#binary-int}{\def\mathdef1083#1{{\mathtt{s}#1}}\mathdef1083{\mathtt{7}}}\))

    Number type

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}\)

    \(\def\mathdef1115#1{\mathtt{0x#1}}\mathdef1115{7E}\) (-2 as \(\href{../binary/values.html#binary-int}{\def\mathdef1083#1{{\mathtt{s}#1}}\mathdef1083{\mathtt{7}}}\))

    Number type

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\)

    \(\def\mathdef1116#1{\mathtt{0x#1}}\mathdef1116{7D}\) (-3 as \(\href{../binary/values.html#binary-int}{\def\mathdef1083#1{{\mathtt{s}#1}}\mathdef1083{\mathtt{7}}}\))

    Number type

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\)

    \(\def\mathdef1117#1{\mathtt{0x#1}}\mathdef1117{7C}\) (-4 as \(\href{../binary/values.html#binary-int}{\def\mathdef1083#1{{\mathtt{s}#1}}\mathdef1083{\mathtt{7}}}\))

    Vector type

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\)

    \(\def\mathdef1118#1{\mathtt{0x#1}}\mathdef1118{7B}\) (-5 as \(\href{../binary/values.html#binary-int}{\def\mathdef1083#1{{\mathtt{s}#1}}\mathdef1083{\mathtt{7}}}\))

    (reserved)

    \(\def\mathdef1119#1{\mathtt{0x#1}}\mathdef1119{7A}\) .. \(\def\mathdef1120#1{\mathtt{0x#1}}\mathdef1120{71}\)

    Reference type

    \(\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}\)

    \(\def\mathdef1121#1{\mathtt{0x#1}}\mathdef1121{70}\) (-16 as \(\href{../binary/values.html#binary-int}{\def\mathdef1083#1{{\mathtt{s}#1}}\mathdef1083{\mathtt{7}}}\))

    Reference type

    \(\href{../syntax/types.html#syntax-reftype}{\mathsf{externref}}\)

    \(\def\mathdef1122#1{\mathtt{0x#1}}\mathdef1122{6F}\) (-17 as \(\href{../binary/values.html#binary-int}{\def\mathdef1083#1{{\mathtt{s}#1}}\mathdef1083{\mathtt{7}}}\))

    (reserved)

    \(\def\mathdef1123#1{\mathtt{0x#1}}\mathdef1123{6E}\) .. \(\def\mathdef1124#1{\mathtt{0x#1}}\mathdef1124{61}\)

    Function type

    \([\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}^\ast]\)

    \(\def\mathdef1125#1{\mathtt{0x#1}}\mathdef1125{60}\) (-32 as \(\href{../binary/values.html#binary-int}{\def\mathdef1083#1{{\mathtt{s}#1}}\mathdef1083{\mathtt{7}}}\))

    (reserved)

    \(\def\mathdef1126#1{\mathtt{0x#1}}\mathdef1126{5F}\) .. \(\def\mathdef1127#1{\mathtt{0x#1}}\mathdef1127{41}\)

    Result type

    \([\epsilon]\)

    \(\def\mathdef1128#1{\mathtt{0x#1}}\mathdef1128{40}\) (-64 as \(\href{../binary/values.html#binary-int}{\def\mathdef1083#1{{\mathtt{s}#1}}\mathdef1083{\mathtt{7}}}\))

    Table type

    \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}\)

    (none)

    Memory type

    \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}\)

    (none)

    Global type

    \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}\)

    (none)

    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/appendix/index.html b/core/appendix/index.html new file mode 100644 index 00000000..b4c366f3 --- /dev/null +++ b/core/appendix/index.html @@ -0,0 +1,152 @@ + + + + + + + + + Appendix — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Appendix

    +
    + +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/appendix/properties.html b/core/appendix/properties.html new file mode 100644 index 00000000..2544f7b2 --- /dev/null +++ b/core/appendix/properties.html @@ -0,0 +1,741 @@ + + + + + + + + + Soundness — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Soundness

    +

    The type system of WebAssembly is sound, implying both type safety and memory safety with respect to the WebAssembly semantics. For example:

    +
      +

    • All types declared and derived during validation are respected at run time; +e.g., every local or global variable will only contain type-correct values, every instruction will only be applied to operands of the expected type, and every function invocation always evaluates to a result of the right type (if it does not trap or diverge).

      • +

    • No memory location will be read or written except those explicitly defined by the program, i.e., as a local, a global, an element in a table, or a location within a linear memory.

      • +

    • There is no undefined behavior, +i.e., the execution rules cover all possible cases that can occur in a valid program, and the rules are mutually consistent.

      • +
    +

    Soundness also is instrumental in ensuring additional properties, most notably, encapsulation of function and module scopes: no locals can be accessed outside their own function and no module components can be accessed outside their own module unless they are explicitly exported or imported.

    +

    The typing rules defining WebAssembly validation only cover the static components of a WebAssembly program. +In order to state and prove soundness precisely, the typing rules must be extended to the dynamic components of the abstract runtime, that is, the store, configurations, and administrative instructions. 1

    +
    +

    Results

    +

    Results can be classified by result types as follows.

    +
    +

    Results \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\)

    +
      +

    • For each value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}_i\) in \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\):

      +
        +

      • The value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}_i\) is valid with some value type \(t_i\).

        • +
      +
      • +

    • Let \(t^\ast\) be the concatenation of all \(t_i\).

      • +

    • Then the result is valid with result type \([t^\ast]\).

      • +
    +
    +\[\frac{ + (S \href{../appendix/properties.html#valid-val}{\vdash} \href{../exec/runtime.html#syntax-val}{\mathit{val}} : t)^\ast +}{ + S \href{../appendix/properties.html#valid-result}{\vdash} \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast : [t^\ast] +}\]
    +
    +
    +

    Results \(\href{../exec/runtime.html#syntax-trap}{\mathsf{trap}}\)

    + +
    +\[\frac{ +}{ + S \href{../appendix/properties.html#valid-result}{\vdash} \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} : [t^\ast] +}\]
    +
    +
    +
    +

    Store Validity

    +

    The following typing rules specify when a runtime store \(S\) is valid. +A valid store must consist of +function, table, memory, global, and module instances that are themselves valid, relative to \(S\).

    +

    To that end, each kind of instance is classified by a respective function, table, memory, or global type. +Module instances are classified by module contexts, which are regular contexts repurposed as module types describing the index spaces defined by a module.

    +
    +

    Store \(S\)

    +
      +

    • Each function instance \(\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}_i\) in \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}\) must be valid with some function type \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}_i\).

      • +

    • Each table instance \(\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}_i\) in \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}\) must be valid with some table type \(\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}_i\).

      • +

    • Each memory instance \(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}_i\) in \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}\) must be valid with some memory type \(\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}_i\).

      • +

    • Each global instance \(\href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}_i\) in \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}\) must be valid with some global type \(\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}_i\).

      • +

    • Each element instance \(\href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}_i\) in \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}\) must be valid.

      • +

    • Each data instance \(\href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}_i\) in \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}\) must be valid.

      • +

    • Then the store is valid.

      • +
    +
    +\[\begin{split}~\\[-1ex] +\frac{ + \begin{array}{@{}c@{}} + (S \href{../appendix/properties.html#valid-funcinst}{\vdash} \href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}} : \href{../syntax/types.html#syntax-functype}{\mathit{functype}})^\ast + \qquad + (S \href{../appendix/properties.html#valid-tableinst}{\vdash} \href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}} : \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}})^\ast + \\ + (S \href{../appendix/properties.html#valid-meminst}{\vdash} \href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}} : \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}})^\ast + \qquad + (S \href{../appendix/properties.html#valid-globalinst}{\vdash} \href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}} : \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}})^\ast + \\ + (S \href{../appendix/properties.html#valid-eleminst}{\vdash} \href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}} \mathrel{\mbox{ok}})^\ast + \qquad + (S \href{../appendix/properties.html#valid-datainst}{\vdash} \href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}} \mathrel{\mbox{ok}})^\ast + \\ + S = \{ + \href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}~\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}^\ast, + \href{../exec/runtime.html#syntax-store}{\mathsf{tables}}~\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}^\ast, + \href{../exec/runtime.html#syntax-store}{\mathsf{mems}}~\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}^\ast, + \href{../exec/runtime.html#syntax-store}{\mathsf{globals}}~\href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}^\ast, + \href{../exec/runtime.html#syntax-store}{\mathsf{elems}}~\href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}^\ast, + \href{../exec/runtime.html#syntax-store}{\mathsf{datas}}~\href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}^\ast \} + \end{array} +}{ + \href{../appendix/properties.html#valid-store}{\vdash} S \mathrel{\mbox{ok}} +}\end{split}\]
    +
    +
    +

    Function Instances \(\{\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{module}}~\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{code}}~\href{../syntax/modules.html#syntax-func}{\mathit{func}}\}\)

    +
      +

    • The function type \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\) must be valid.

      • +

    • The module instance \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\) must be valid with some context \(C\).

      • +

    • Under context \(C\), the function \(\href{../syntax/modules.html#syntax-func}{\mathit{func}}\) must be valid with function type \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\).

      • +

    • Then the function instance is valid with function type \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\).

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-functype}{\vdash} \href{../syntax/types.html#syntax-functype}{\mathit{functype}} \mathrel{\mbox{ok}} + \qquad + S \href{../appendix/properties.html#valid-moduleinst}{\vdash} \href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}} : C + \qquad + C \href{../valid/modules.html#valid-func}{\vdash} \href{../syntax/modules.html#syntax-func}{\mathit{func}} : \href{../syntax/types.html#syntax-functype}{\mathit{functype}} +}{ + S \href{../appendix/properties.html#valid-funcinst}{\vdash} \{\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{module}}~\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{code}}~\href{../syntax/modules.html#syntax-func}{\mathit{func}}\} : \href{../syntax/types.html#syntax-functype}{\mathit{functype}} +}\]
    +
    +
    +

    Host Function Instances \(\{\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{hostcode}}~\mathit{hf}\}\)

    +
      +

    • The function type \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\) must be valid.

      • +

    • Let \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\) be the function type \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\).

      • +

    • For every valid store \(S_1\) extending \(S\) and every sequence \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\) of values whose types coincide with \(t_1^\ast\):

      +
        +

      • Executing \(\mathit{hf}\) in store \(S_1\) with arguments \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\) has a non-empty set of possible outcomes.

        • +

      • For every element \(R\) of this set:

        +
          +

        • Either \(R\) must be \(\bot\) (i.e., divergence).

          • +

        • Or \(R\) consists of a valid store \(S_2\) extending \(S_1\) and a result \(\href{../exec/runtime.html#syntax-result}{\mathit{result}}\) whose type coincides with \([t_2^\ast]\).

          • +
        +
        • +
      +
      • +

    • Then the function instance is valid with function type \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\).

      • +
    +
    +\[\begin{split}\frac{ + \begin{array}[b]{@{}l@{}} + \href{../valid/types.html#valid-functype}{\vdash} [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] \mathrel{\mbox{ok}} \\ + \end{array} + \quad + \begin{array}[b]{@{}l@{}} + \forall S_1, \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast,~ + {\href{../appendix/properties.html#valid-store}{\vdash} S_1 \mathrel{\mbox{ok}}} \wedge + {\href{../appendix/properties.html#extend-store}{\vdash} S \href{../appendix/properties.html#extend}{\preceq} S_1} \wedge + {S_1 \href{../appendix/properties.html#valid-result}{\vdash} \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast : [t_1^\ast]} + \Longrightarrow {} \\ \qquad + \mathit{hf}(S_1; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast) \supset \emptyset \wedge {} \\ \qquad + \forall R \in \mathit{hf}(S_1; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast),~ + R = \bot \vee {} \\ \qquad\qquad + \exists S_2, \href{../exec/runtime.html#syntax-result}{\mathit{result}},~ + {\href{../appendix/properties.html#valid-store}{\vdash} S_2 \mathrel{\mbox{ok}}} \wedge + {\href{../appendix/properties.html#extend-store}{\vdash} S_1 \href{../appendix/properties.html#extend}{\preceq} S_2} \wedge + {S_2 \href{../appendix/properties.html#valid-result}{\vdash} \href{../exec/runtime.html#syntax-result}{\mathit{result}} : [t_2^\ast]} \wedge + R = (S_2; \href{../exec/runtime.html#syntax-result}{\mathit{result}}) + \end{array} +}{ + S \href{../appendix/properties.html#valid-funcinst}{\vdash} \{\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~[t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast], \href{../exec/runtime.html#syntax-funcinst}{\mathsf{hostcode}}~\mathit{hf}\} : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\end{split}\]
    +
    +

    Note

    +

    This rule states that, if appropriate pre-conditions about store and arguments are satisfied, then executing the host function must satisfy appropriate post-conditions about store and results. +The post-conditions match the ones in the execution rule for invoking host functions.

    +

    Any store under which the function is invoked is assumed to be an extension of the current store. +That way, the function itself is able to make sufficient assumptions about future stores.

    +
    +
    +
    +

    Table Instances \(\{ \href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}}~(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t), \href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}~\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast \}\)

    +
      +

    • The table type \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t\) must be valid.

      • +

    • The length of \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast\) must equal \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}.\href{../syntax/types.html#syntax-limits}{\mathsf{min}}\).

      • +

    • For each reference \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}_i\) in the table’s elements \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^n\):

      + +
      • +

    • Then the table instance is valid with table type \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t\).

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-tabletype}{\vdash} \href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t \mathrel{\mbox{ok}} + \qquad + n = \href{../syntax/types.html#syntax-limits}{\mathit{limits}}.\href{../syntax/types.html#syntax-limits}{\mathsf{min}} + \qquad + (S \vdash \href{../exec/runtime.html#syntax-ref}{\mathit{ref}} : t)^n +}{ + S \href{../appendix/properties.html#valid-tableinst}{\vdash} \{ \href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}}~(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t), \href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}~\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^n \} : \href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t +}\]
    +
    +
    +

    Memory Instances \(\{ \href{../exec/runtime.html#syntax-meminst}{\mathsf{type}}~\href{../syntax/types.html#syntax-limits}{\mathit{limits}}, \href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}~b^\ast \}\)

    +
      +

    • The memory type \(\{\href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m^?\}\) must be valid.

      • +

    • The length of \(b^\ast\) must equal \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}.\href{../syntax/types.html#syntax-limits}{\mathsf{min}}\) multiplied by the page size \(64\,\mathrm{Ki}\).

      • +

    • Then the memory instance is valid with memory type \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}\).

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-memtype}{\vdash} \href{../syntax/types.html#syntax-limits}{\mathit{limits}} \mathrel{\mbox{ok}} + \qquad + n = \href{../syntax/types.html#syntax-limits}{\mathit{limits}}.\href{../syntax/types.html#syntax-limits}{\mathsf{min}} \cdot 64\,\mathrm{Ki} +}{ + S \href{../appendix/properties.html#valid-meminst}{\vdash} \{ \href{../exec/runtime.html#syntax-meminst}{\mathsf{type}}~\href{../syntax/types.html#syntax-limits}{\mathit{limits}}, \href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}~b^n \} : \href{../syntax/types.html#syntax-limits}{\mathit{limits}} +}\]
    +
    +
    +

    Global Instances \(\{ \href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}}~(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t), \href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}} \}\)

    +
      +

    • The global type \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t\) must be valid.

      • +

    • The value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) must be valid with value type \(t\).

      • +

    • Then the global instance is valid with global type \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t\).

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-globaltype}{\vdash} \href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t \mathrel{\mbox{ok}} + \qquad + S \href{../appendix/properties.html#valid-val}{\vdash} \href{../exec/runtime.html#syntax-val}{\mathit{val}} : t +}{ + S \href{../appendix/properties.html#valid-globalinst}{\vdash} \{ \href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}}~(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t), \href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}} \} : \href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t +}\]
    +
    +
    +

    Element Instances \(\{ \href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}~\mathit{fa}^\ast \}\)

    +
      +

    • For each reference \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}_i\) in the elements \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^n\):

      + +
      • +

    • Then the table instance is valid.

      • +
    +
    +\[\frac{ + (S \vdash \href{../exec/runtime.html#syntax-ref}{\mathit{ref}} : t)^\ast +}{ + S \href{../appendix/properties.html#valid-eleminst}{\vdash} \{ \href{../exec/runtime.html#syntax-eleminst}{\mathsf{type}}~t, \href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}~\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast \} \mathrel{\mbox{ok}} +}\]
    +
    +
    +

    Data Instances \(\{ \href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}~b^\ast \}\)

    +
      +

    • The data instance is valid.

      • +
    +
    +\[\frac{ +}{ + S \href{../appendix/properties.html#valid-datainst}{\vdash} \{ \href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}~b^\ast \} \mathrel{\mbox{ok}} +}\]
    +
    +
    +

    Export Instances \(\{ \href{../exec/runtime.html#syntax-exportinst}{\mathsf{name}}~\href{../syntax/values.html#syntax-name}{\mathit{name}}, \href{../exec/runtime.html#syntax-exportinst}{\mathsf{value}}~\href{../exec/runtime.html#syntax-externval}{\mathit{externval}} \}\)

    +
      +

    • The external value \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}\) must be valid with some external type \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}\).

      • +

    • Then the export instance is valid.

      • +
    +
    +\[\frac{ + S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathit{externval}} : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}} +}{ + S \href{../appendix/properties.html#valid-exportinst}{\vdash} \{ \href{../exec/runtime.html#syntax-exportinst}{\mathsf{name}}~\href{../syntax/values.html#syntax-name}{\mathit{name}}, \href{../exec/runtime.html#syntax-exportinst}{\mathsf{value}}~\href{../exec/runtime.html#syntax-externval}{\mathit{externval}} \} \mathrel{\mbox{ok}} +}\]
    +
    +
    +

    Module Instances \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\)

    +
      +

    • Each function type \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}_i\) in \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{types}}\) must be valid.

      • +

    • For each function address \(\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}_i\) in \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}}\), the external value \(\href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}_i\) must be valid with some external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}'_i\).

      • +

    • For each table address \(\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}_i\) in \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}\), the external value \(\href{../exec/runtime.html#syntax-externval}{\mathsf{table}}~\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}_i\) must be valid with some external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}_i\).

      • +

    • For each memory address \(\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}_i\) in \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}\), the external value \(\href{../exec/runtime.html#syntax-externval}{\mathsf{mem}}~\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}_i\) must be valid with some external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}_i\).

      • +

    • For each global address \(\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}_i\) in \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{globaladdrs}}\), the external value \(\href{../exec/runtime.html#syntax-externval}{\mathsf{global}}~\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}_i\) must be valid with some external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}_i\).

      • +

    • For each element address \(\href{../exec/runtime.html#syntax-elemaddr}{\mathit{elemaddr}}_i\) in \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{elemaddrs}}\), the element instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}[\href{../exec/runtime.html#syntax-elemaddr}{\mathit{elemaddr}}_i]\) must be valid.

      • +

    • For each data address \(\href{../exec/runtime.html#syntax-dataaddr}{\mathit{dataaddr}}_i\) in \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{dataaddrs}}\), the data instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}[\href{../exec/runtime.html#syntax-dataaddr}{\mathit{dataaddr}}_i]\) must be valid.

      • +

    • Each export instance \(\href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}_i\) in \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{exports}}\) must be valid.

      • +

    • For each export instance \(\href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}_i\) in \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{exports}}\), the name \(\href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}_i.\href{../exec/runtime.html#syntax-exportinst}{\mathsf{name}}\) must be different from any other name occurring in \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{exports}}\).

      • +

    • Let \({\href{../syntax/types.html#syntax-functype}{\mathit{functype}}'}^\ast\) be the concatenation of all \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}'_i\) in order.

      • +

    • Let \(\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}^\ast\) be the concatenation of all \(\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}_i\) in order.

      • +

    • Let \(\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}^\ast\) be the concatenation of all \(\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}_i\) in order.

      • +

    • Let \(\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}^\ast\) be the concatenation of all \(\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}_i\) in order.

      • +
    • +
      Then the module instance is valid with context
      +
      \(\{\href{../valid/conventions.html#context}{\mathsf{types}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}^\ast, \href{../valid/conventions.html#context}{\mathsf{funcs}}~{\href{../syntax/types.html#syntax-functype}{\mathit{functype}}'}^\ast, \href{../valid/conventions.html#context}{\mathsf{tables}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}^\ast, \href{../valid/conventions.html#context}{\mathsf{mems}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}^\ast, \href{../valid/conventions.html#context}{\mathsf{globals}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}^\ast\}\).
      +
      +
      • +
    +
    +\[\begin{split}~\\[-1ex] +\frac{ + \begin{array}{@{}c@{}} + (\href{../valid/types.html#valid-functype}{\vdash} \href{../syntax/types.html#syntax-functype}{\mathit{functype}} \mathrel{\mbox{ok}})^\ast + \\ + (S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} : \href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}')^\ast + \qquad + (S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathsf{table}}~\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}} : \href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}})^\ast + \\ + (S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathsf{mem}}~\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}} : \href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}})^\ast + \qquad + (S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathsf{global}}~\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}} : \href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}})^\ast + \\ + (S \href{../appendix/properties.html#valid-eleminst}{\vdash} S.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}[\href{../exec/runtime.html#syntax-elemaddr}{\mathit{elemaddr}}] \mathrel{\mbox{ok}})^\ast + \qquad + (S \href{../appendix/properties.html#valid-datainst}{\vdash} S.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}[\href{../exec/runtime.html#syntax-dataaddr}{\mathit{dataaddr}}] \mathrel{\mbox{ok}})^\ast + \\ + (S \href{../appendix/properties.html#valid-exportinst}{\vdash} \href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}} \mathrel{\mbox{ok}})^\ast + \qquad + (\href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}.\href{../exec/runtime.html#syntax-exportinst}{\mathsf{name}})^\ast ~\mbox{disjoint} + \end{array} +}{ + S \href{../appendix/properties.html#valid-moduleinst}{\vdash} \{ + \begin{array}[t]{@{}l@{~}l@{}} + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{types}} & \href{../syntax/types.html#syntax-functype}{\mathit{functype}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}} & \href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}} & \href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}} & \href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{globaladdrs}} & \href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{elemaddrs}} & \href{../exec/runtime.html#syntax-elemaddr}{\mathit{elemaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{dataaddrs}} & \href{../exec/runtime.html#syntax-dataaddr}{\mathit{dataaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{exports}} & \href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}^\ast ~\} : \{ + \begin{array}[t]{@{}l@{~}l@{}} + \href{../valid/conventions.html#context}{\mathsf{types}} & \href{../syntax/types.html#syntax-functype}{\mathit{functype}}^\ast, \\ + \href{../valid/conventions.html#context}{\mathsf{funcs}} & {\href{../syntax/types.html#syntax-functype}{\mathit{functype}}'}^\ast, \\ + \href{../valid/conventions.html#context}{\mathsf{tables}} & \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}^\ast, \\ + \href{../valid/conventions.html#context}{\mathsf{mems}} & \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}^\ast, \\ + \href{../valid/conventions.html#context}{\mathsf{globals}} & \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}^\ast ~\} + \end{array} + \end{array} +}\end{split}\]
    +
    +
    +
    +

    Configuration Validity

    +

    To relate the WebAssembly type system to its execution semantics, the typing rules for instructions must be extended to configurations \(S;T\), +which relates the store to execution threads.

    +

    Configurations and threads are classified by their result type. +In addition to the store \(S\), threads are typed under a return type \(\href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}}^?\), which controls whether and with which type a \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}\) instruction is allowed. +This type is absent (\(\epsilon\)) except for instruction sequences inside an administrative \(\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}\) instruction.

    +

    Finally, frames are classified with frame contexts, which extend the module contexts of a frame’s associated module instance with the locals that the frame contains.

    +
    +

    Configurations \(S;T\)

    + +
    +\[\frac{ + \href{../appendix/properties.html#valid-store}{\vdash} S \mathrel{\mbox{ok}} + \qquad + S; \epsilon \href{../appendix/properties.html#valid-thread}{\vdash} T : [t^\ast] +}{ + \href{../appendix/properties.html#valid-config}{\vdash} S; T : [t^\ast] +}\]
    +
    +
    +

    Threads \(F;\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\)

    +
      +

    • Let \(\href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}}^?\) be the current allowed return type.

      • +

    • The frame \(F\) must be valid with a context \(C\).

      • +

    • Let \(C'\) be the same context as \(C\), but with \(\href{../valid/conventions.html#context}{\mathsf{return}}\) set to \(\href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}}^?\).

      • +

    • Under context \(C'\), +the instruction sequence \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) must be valid with some type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t^\ast]\).

      • +

    • Then the thread is valid with the result type \([t^\ast]\).

      • +
    +
    +\[\frac{ + S \href{../appendix/properties.html#valid-frame}{\vdash} F : C + \qquad + S; C,\href{../valid/conventions.html#context}{\mathsf{return}}~\href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}}^? \href{../valid/instructions.html#valid-instr-seq}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t^\ast] +}{ + S; \href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}}^? \href{../appendix/properties.html#valid-thread}{\vdash} F; \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast : [t^\ast] +}\]
    +
    +
    +

    Frames \(\{\href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast, \href{../exec/runtime.html#syntax-frame}{\mathsf{module}}~\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\}\)

    +
      +

    • The module instance \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\) must be valid with some module context \(C\).

      • +

    • Each value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}_i\) in \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\) must be valid with some value type \(t_i\).

      • +

    • Let \(t^\ast\) the concatenation of all \(t_i\) in order.

      • +

    • Let \(C'\) be the same context as \(C\), but with the value types \(t^\ast\) prepended to the \(\href{../valid/conventions.html#context}{\mathsf{locals}}\) vector.

      • +

    • Then the frame is valid with frame context \(C'\).

      • +
    +
    +\[\frac{ + S \href{../appendix/properties.html#valid-moduleinst}{\vdash} \href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}} : C + \qquad + (S \href{../appendix/properties.html#valid-val}{\vdash} \href{../exec/runtime.html#syntax-val}{\mathit{val}} : t)^\ast +}{ + S \href{../appendix/properties.html#valid-frame}{\vdash} \{\href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast, \href{../exec/runtime.html#syntax-frame}{\mathsf{module}}~\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\} : (C, \href{../valid/conventions.html#context}{\mathsf{locals}}~t^\ast) +}\]
    +
    +
    +
    +

    Administrative Instructions

    +

    Typing rules for administrative instructions are specified as follows. +In addition to the context \(C\), typing of these instructions is defined under a given store \(S\). +To that end, all previous typing judgements \(C \vdash \mathit{prop}\) are generalized to include the store, as in \(S; C \vdash \mathit{prop}\), by implicitly adding \(S\) to all rules – \(S\) is never modified by the pre-existing rules, but it is accessed in the extra rules for administrative instructions given below.

    +
    +

    \(\href{../exec/runtime.html#syntax-trap}{\mathsf{trap}}\)

    +
      +

    • The instruction is valid with type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\), for any sequences of value types \(t_1^\ast\) and \(t_2^\ast\).

      • +
    +
    +\[\frac{ +}{ + S; C \href{../appendix/properties.html#valid-instr-admin}{\vdash} \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +
    +
    +

    \(\href{../exec/runtime.html#syntax-ref.extern}{\mathsf{ref{.}extern}}~\href{../exec/runtime.html#syntax-externaddr}{\mathit{externaddr}}\)

    +
      +

    • The instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-reftype}{\mathsf{externref}}]\).

      • +
    +
    +\[\frac{ +}{ + S; C \href{../appendix/properties.html#valid-instr-admin}{\vdash} \href{../exec/runtime.html#syntax-ref.extern}{\mathsf{ref{.}extern}}~\href{../exec/runtime.html#syntax-externaddr}{\mathit{externaddr}} : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-reftype}{\mathsf{externref}}] +}\]
    +
    +
    +

    \(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}\)

    +
      +

    • The external function value \(\href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}\) must be valid with external function type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{func}} \href{../syntax/types.html#syntax-functype}{\mathit{functype}}\).

      • +

    • Then the instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}]\).

      • +
    +
    +\[\frac{ + S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} : \href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}} +}{ + S; C \href{../appendix/properties.html#valid-instr-admin}{\vdash} \href{../exec/runtime.html#syntax-ref}{\mathsf{ref}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}] +}\]
    +
    +
    +

    \(\href{../exec/runtime.html#syntax-invoke}{\mathsf{invoke}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}\)

    +
      +

    • The external function value \(\href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}\) must be valid with external function type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{func}} ([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast])\).

      • +

    • Then the instruction is valid with type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +
    +
    +\[\frac{ + S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} : \href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~[t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}{ + S; C \href{../appendix/properties.html#valid-instr-admin}{\vdash} \href{../exec/runtime.html#syntax-invoke}{\mathsf{invoke}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +
    +
    +

    \(\href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_0^\ast\}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\)

    +
      +

    • The instruction sequence \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_0^\ast\) must be valid with some type \([t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^*]\).

      • +

    • Let \(C'\) be the same context as \(C\), but with the result type \([t_1^n]\) prepended to the \(\href{../valid/conventions.html#context}{\mathsf{labels}}\) vector.

      • +

    • Under context \(C'\), +the instruction sequence \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) must be valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^*]\).

      • +

    • Then the compound instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^*]\).

      • +
    +
    +\[\frac{ + S; C \href{../valid/instructions.html#valid-instr-seq}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_0^\ast : [t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^*] + \qquad + S; C,\href{../valid/conventions.html#context}{\mathsf{labels}}\,[t_1^n] \href{../valid/instructions.html#valid-instr-seq}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^*] +}{ + S; C \href{../appendix/properties.html#valid-instr-admin}{\vdash} \href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_0^\ast\}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^*] +}\]
    +
    +
    +

    \(\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}_n\{F\}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\)

    +
      +

    • Under the return type \([t^n]\), +the thread \(F; \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) must be valid with result type \([t^n]\).

      • +

    • Then the compound instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t^n]\).

      • +
    +
    +\[\frac{ + S; [t^n] \href{../valid/instructions.html#valid-instr-seq}{\vdash} F; \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast : [t^n] +}{ + S; C \href{../appendix/properties.html#valid-instr-admin}{\vdash} \href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}_n\{F\}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t^n] +}\]
    +
    +
    +
    +

    Store Extension

    +

    Programs can mutate the store and its contained instances. +Any such modification must respect certain invariants, such as not removing allocated instances or changing immutable definitions. +While these invariants are inherent to the execution semantics of WebAssembly instructions and modules, +host functions do not automatically adhere to them. Consequently, the required invariants must be stated as explicit constraints on the invocation of host functions. +Soundness only holds when the embedder ensures these constraints.

    +

    The necessary constraints are codified by the notion of store extension: +a store state \(S'\) extends state \(S\), written \(S \href{../appendix/properties.html#extend}{\preceq} S'\), when the following rules hold.

    +
    +

    Note

    +

    Extension does not imply that the new store is valid, which is defined separately above.

    +
    +
    +

    Store \(S\)

    +
      +

    • The length of \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}\) must not shrink.

      • +

    • The length of \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}\) must not shrink.

      • +

    • The length of \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}\) must not shrink.

      • +

    • The length of \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}\) must not shrink.

      • +

    • The length of \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}\) must not shrink.

      • +

    • The length of \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}\) must not shrink.

      • +

    • For each function instance \(\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}_i\) in the original \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}\), the new function instance must be an extension of the old.

      • +

    • For each table instance \(\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}_i\) in the original \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}\), the new table instance must be an extension of the old.

      • +

    • For each memory instance \(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}_i\) in the original \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}\), the new memory instance must be an extension of the old.

      • +

    • For each global instance \(\href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}_i\) in the original \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}\), the new global instance must be an extension of the old.

      • +

    • For each element instance \(\href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}_i\) in the original \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}\), the new global instance must be an extension of the old.

      • +

    • For each data instance \(\href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}_i\) in the original \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}\), the new global instance must be an extension of the old.

      • +
    +
    +\[\begin{split}\frac{ + \begin{array}{@{}ccc@{}} + S_1.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}} = \href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}_1^\ast & + S_2.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}} = {\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}'_1}^\ast~\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}_2^\ast & + (\href{../appendix/properties.html#extend-funcinst}{\vdash} \href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}_1 \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}'_1)^\ast \\ + S_1.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}} = \href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}_1^\ast & + S_2.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}} = {\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}'_1}^\ast~\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}_2^\ast & + (\href{../appendix/properties.html#extend-tableinst}{\vdash} \href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}_1 \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}'_1)^\ast \\ + S_1.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}} = \href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}_1^\ast & + S_2.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}} = {\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}'_1}^\ast~\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}_2^\ast & + (\href{../appendix/properties.html#extend-meminst}{\vdash} \href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}_1 \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}'_1)^\ast \\ + S_1.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}} = \href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}_1^\ast & + S_2.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}} = {\href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}'_1}^\ast~\href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}_2^\ast & + (\href{../appendix/properties.html#extend-globalinst}{\vdash} \href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}_1 \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}'_1)^\ast \\ + S_1.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}} = \href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}_1^\ast & + S_2.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}} = {\href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}'_1}^\ast~\href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}_2^\ast & + (\href{../appendix/properties.html#extend-eleminst}{\vdash} \href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}_1 \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}'_1)^\ast \\ + S_1.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}} = \href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}_1^\ast & + S_2.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}} = {\href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}'_1}^\ast~\href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}_2^\ast & + (\href{../appendix/properties.html#extend-datainst}{\vdash} \href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}_1 \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}'_1)^\ast \\ + \end{array} +}{ + \href{../appendix/properties.html#extend-store}{\vdash} S_1 \href{../appendix/properties.html#extend}{\preceq} S_2 +}\end{split}\]
    +
    +
    +

    Function Instance \(\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}\)

    +
      +

    • A function instance must remain unchanged.

      • +
    +
    +\[\frac{ +}{ + \href{../appendix/properties.html#extend-funcinst}{\vdash} \href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}} \href{../appendix/properties.html#extend}{\preceq} \href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}} +}\]
    +
    +
    +

    Table Instance \(\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}\)

    +
      +

    • The table type \(\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}}\) must remain unchanged.

      • +

    • The length of \(\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\) must not shrink.

      • +
    +
    +\[\frac{ + n_1 \leq n_2 +}{ + \href{../appendix/properties.html#extend-tableinst}{\vdash} \{\href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}}~\mathit{tt}, \href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}~(\mathit{fa}_1^?)^{n_1}\} \href{../appendix/properties.html#extend}{\preceq} \{\href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}}~\mathit{tt}, \href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}~(\mathit{fa}_2^?)^{n_2}\} +}\]
    +
    +
    +

    Memory Instance \(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}\)

    +
      +

    • The memory type \(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{type}}\) must remain unchanged.

      • +

    • The length of \(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\) must not shrink.

      • +
    +
    +\[\frac{ + n_1 \leq n_2 +}{ + \href{../appendix/properties.html#extend-meminst}{\vdash} \{\href{../exec/runtime.html#syntax-meminst}{\mathsf{type}}~\mathit{mt}, \href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}~b_1^{n_1}\} \href{../appendix/properties.html#extend}{\preceq} \{\href{../exec/runtime.html#syntax-meminst}{\mathsf{type}}~\mathit{mt}, \href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}~b_2^{n_2}\} +}\]
    +
    +
    +

    Global Instance \(\href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}\)

    +
      +

    • The global type \(\href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}.\href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}}\) must remain unchanged.

      • +

    • Let \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t\) be the structure of \(\href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}.\href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}}\).

      • +

    • If \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}\) is \(\href{../syntax/types.html#syntax-mut}{\mathsf{const}}\), then the value \(\href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}.\href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}}\) must remain unchanged.

      • +
    +
    +\[\frac{ + \href{../syntax/types.html#syntax-mut}{\mathit{mut}} = \href{../syntax/types.html#syntax-mut}{\mathsf{var}} \vee \href{../exec/runtime.html#syntax-val}{\mathit{val}}_1 = \href{../exec/runtime.html#syntax-val}{\mathit{val}}_2 +}{ + \href{../appendix/properties.html#extend-globalinst}{\vdash} \{\href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}}~(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t), \href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}_1\} \href{../appendix/properties.html#extend}{\preceq} \{\href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}}~(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t), \href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}_2\} +}\]
    +
    +
    +

    Element Instance \(\href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}\)

    +
      +

    • The vector \(\href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}.\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}\) must either remain unchanged or shrink to length \(0\).

      • +
    +
    +\[\frac{ + \mathit{fa}_1^\ast = \mathit{fa}_2^\ast \vee \mathit{fa}_2^\ast = \epsilon +}{ + \href{../appendix/properties.html#extend-eleminst}{\vdash} \{\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}~\mathit{fa}_1^\ast\} \href{../appendix/properties.html#extend}{\preceq} \{\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}~\mathit{fa}_2^\ast\} +}\]
    +
    +
    +

    Data Instance \(\href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}\)

    +
      +

    • The vector \(\href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}.\href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}\) must either remain unchanged or shrink to length \(0\).

      • +
    +
    +\[\frac{ + b_1^\ast = b_2^\ast \vee b_2^\ast = \epsilon +}{ + \href{../appendix/properties.html#extend-datainst}{\vdash} \{\href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}~b_1^\ast\} \href{../appendix/properties.html#extend}{\preceq} \{\href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}~b_2^\ast\} +}\]
    +
    +
    +
    +

    Theorems

    +

    Given the definition of valid configurations, +the standard soundness theorems hold. 2

    +

    Theorem (Preservation). +If a configuration \(S;T\) is valid with result type \([t^\ast]\) (i.e., \(\href{../appendix/properties.html#valid-config}{\vdash} S;T : [t^\ast]\)), +and steps to \(S';T'\) (i.e., \(S;T \href{../exec/conventions.html#formal-notation}{\hookrightarrow} S';T'\)), +then \(S';T'\) is a valid configuration with the same result type (i.e., \(\href{../appendix/properties.html#valid-config}{\vdash} S';T' : [t^\ast]\)). +Furthermore, \(S'\) is an extension of \(S\) (i.e., \(\href{../appendix/properties.html#extend-store}{\vdash} S \href{../appendix/properties.html#extend}{\preceq} S'\)).

    +

    A terminal thread is one whose sequence of instructions is a result. +A terminal configuration is a configuration whose thread is terminal.

    +

    Theorem (Progress). +If a configuration \(S;T\) is valid (i.e., \(\href{../appendix/properties.html#valid-config}{\vdash} S;T : [t^\ast]\) for some result type \([t^\ast]\)), +then either it is terminal, +or it can step to some configuration \(S';T'\) (i.e., \(S;T \href{../exec/conventions.html#formal-notation}{\hookrightarrow} S';T'\)).

    +

    From Preservation and Progress the soundness of the WebAssembly type system follows directly.

    +

    Corollary (Soundness). +If a configuration \(S;T\) is valid (i.e., \(\href{../appendix/properties.html#valid-config}{\vdash} S;T : [t^\ast]\) for some result type \([t^\ast]\)), +then it either diverges or takes a finite number of steps to reach a terminal configuration \(S';T'\) (i.e., \(S;T \href{../exec/conventions.html#formal-notation}{\hookrightarrow}^\ast S';T'\)) that is valid with the same result type (i.e., \(\href{../appendix/properties.html#valid-config}{\vdash} S';T' : [t^\ast]\)) +and where \(S'\) is an extension of \(S\) (i.e., \(\href{../appendix/properties.html#extend-store}{\vdash} S \href{../appendix/properties.html#extend}{\preceq} S'\)).

    +

    In other words, every thread in a valid configuration either runs forever, traps, or terminates with a result that has the expected type. +Consequently, given a valid store, no computation defined by instantiation or invocation of a valid module can “crash” or otherwise (mis)behave in ways not covered by the execution semantics given in this specification.

    +
    +
    1
    +

    The formalization and theorems are derived from the following article: +Andreas Haas, Andreas Rossberg, Derek Schuff, Ben Titzer, Dan Gohman, Luke Wagner, Alon Zakai, JF Bastien, Michael Holman. Bringing the Web up to Speed with WebAssembly. Proceedings of the 38th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2017). ACM 2017.

    +
    +
    2
    +

    A machine-verified version of the formalization and soundness proof is described in the following article: +Conrad Watt. Mechanising and Verifying the WebAssembly Specification. Proceedings of the 7th ACM SIGPLAN Conference on Certified Programs and Proofs (CPP 2018). ACM 2018.

    +
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/bikeshed/index.html b/core/bikeshed/index.html new file mode 100644 index 00000000..e04eefb1 --- /dev/null +++ b/core/bikeshed/index.html @@ -0,0 +1,17117 @@ + + + + + WebAssembly Core Specification + + + + + + + + + + + + + + + + + + + +
    +

    +

    WebAssembly Core Specification

    +

    Editor’s Draft,

    +
    + More details about this document +
    +
    +
    This version: +
    https://webassembly.github.io/spec/core/bikeshed/ +
    Latest published version: +
    https://www.w3.org/TR/wasm-core-2/ +
    Editor: +
    Andreas Rossberg (Dfinity Stiftung) +
    Issue Tracking: +
    GitHub Issues +
    +
    +
    +
    +

    Copyright © 2022 W3C® (MIT, ERCIM, Keio, Beihang). W3C liability, trademark and permissive document license rules apply.

    +
    +
    +
    +

    Abstract

    +

    This document describes version 2.0 of the core WebAssembly standard, a safe, portable, low-level code format designed for efficient execution and compact representation.

    + This is part of a collection of related documents: +the Core WebAssembly Specification, +the WebAssembly JS Interface, +and the WebAssembly Web API. +
    +

    Status of this document

    +
    +

    This is a public copy of the editors’ draft. + It is provided for discussion only and may change at any moment. + Its publication here does not imply endorsement of its contents by W3C. + Don’t cite this document other than as work in progress.

    +

    GitHub Issues are preferred for discussion of this specification. + All issues and comments are archived.

    +

    This document was produced by the WebAssembly Working Group.

    +

    This document was produced by a group operating under + the W3C Patent Policy. + W3C maintains a public list of any patent disclosures made in connection with the deliverables of the group; + that page also includes instructions for disclosing a patent. + An individual who has actual knowledge of a patent which the individual believes contains Essential Claim(s) must disclose the information in accordance with section 6 of the W3C Patent Policy.

    +

    This document is governed by the 2 November 2021 W3C Process Document.

    +

    +
    +
    + +
    +

    + WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + +
    +
    +
    +
    +

    WebAssembly Specification

    +
    +
    Release 2.0 + stringref (Draft 2022-04-27)
    +
    +
    +
    Editor: Andreas Rossberg
    +
    +
    +
    Latest Draft: https://webassembly.github.io/stringref/core/
    +
    Issue Tracker: https://github.com/webassembly/stringref/issues/
    +
    +
    + +
    + +

    1. Introduction

    +
    + +
    +

    1.1. Introduction

    +

    WebAssembly (abbreviated Wasm 1) is a safe, portable, low-level code format designed for efficient execution and compact representation. +Its main goal is to enable high performance applications on the Web, but it does not make any Web-specific assumptions or provide Web-specific features, so it can be employed in other environments as well.

    +

    WebAssembly is an open standard developed by a W3C Community Group.

    +

    This document describes version 2.0 + stringref (Draft 2022-04-27) of the core WebAssembly standard. +It is intended that it will be superseded by new incremental releases with additional features in the future.

    +
    + +

    1.1.1. Design Goals

    +

    The design goals of WebAssembly are the following:

    +
      +
    • +

      Fast, safe, and portable semantics:

      +
        +
      • +

        Fast: executes with near native code performance, taking advantage of capabilities common to all contemporary hardware.

        +
      • +

        Safe: code is validated and executes in a memory-safe 2, sandboxed environment preventing data corruption or security breaches.

        +
      • +

        Well-defined: fully and precisely defines valid programs and their behavior in a way that is easy to reason about informally and formally.

        +
      • +

        Hardware-independent: can be compiled on all modern architectures, desktop or mobile devices and embedded systems alike.

        +
      • +

        Language-independent: does not privilege any particular language, programming model, or object model.

        +
      • +

        Platform-independent: can be embedded in browsers, run as a stand-alone VM, or integrated in other environments.

        +
      • +

        Open: programs can interoperate with their environment in a simple and universal manner.

        +
      +
    • +

      Efficient and portable representation:

      +
        +
      • +

        Compact: has a binary format that is fast to transmit by being smaller than typical text or native code formats.

        +
      • +

        Modular: programs can be split up in smaller parts that can be transmitted, cached, and consumed separately.

        +
      • +

        Efficient: can be decoded, validated, and compiled in a fast single pass, equally with either just-in-time (JIT) or ahead-of-time (AOT) compilation.

        +
      • +

        Streamable: allows decoding, validation, and compilation to begin as soon as possible, before all data has been seen.

        +
      • +

        Parallelizable: allows decoding, validation, and compilation to be split into many independent parallel tasks.

        +
      • +

        Portable: makes no architectural assumptions that are not broadly supported across modern hardware.

        +
      +
    +

    WebAssembly code is also intended to be easy to inspect and debug, especially in environments like web browsers, but such features are beyond the scope of this specification.

    +
    +
    1 +
    +

    A contraction of “WebAssembly”, not an acronym, hence not using all-caps.

    +
    2 +
    +

    No program can break WebAssembly’s memory model. Of course, it cannot guarantee that an unsafe language compiling to WebAssembly does not corrupt its own memory layout, e.g. inside WebAssembly’s linear memory.

    +
    +
    +
    + +

    1.1.2. Scope

    +

    At its core, WebAssembly is a virtual instruction set architecture (virtual ISA). +As such, it has many use cases and can be embedded in many different environments. +To encompass their variety and enable maximum reuse, the WebAssembly specification is split and layered into several documents.

    +

    This document is concerned with the core ISA layer of WebAssembly. +It defines the instruction set, binary encoding, validation, and execution semantics, as well as a textual representation. +It does not, however, define how WebAssembly programs can interact with a specific environment they execute in, nor how they are invoked from such an environment.

    +

    Instead, this specification is complemented by additional documents defining interfaces to specific embedding environments such as the Web. +These will each define a WebAssembly application programming interface (API) suitable for a given environment.

    +
    +
    + +

    1.1.3. Security Considerations

    +

    WebAssembly provides no ambient access to the computing environment in which code is executed. +Any interaction with the environment, such as I/O, access to resources, or operating system calls, can only be performed by invoking functions provided by the embedder and imported into a WebAssembly module. +An embedder can establish security policies suitable for a respective environment by controlling or limiting which functional capabilities it makes available for import. +Such considerations are an embedder’s responsibility and the subject of API definitions for a specific environment.

    +

    Because WebAssembly is designed to be translated into machine code running directly on the host’s hardware, it is potentially vulnerable to side channel attacks on the hardware level. +In environments where this is a concern, an embedder may have to put suitable mitigations into place to isolate WebAssembly computations.

    +
    +
    + +

    1.1.4. Dependencies

    +

    WebAssembly depends on two existing standards:

    + +

    However, to make this specification self-contained, relevant aspects of the aforementioned standards are defined and formalized as part of this specification, +such as the binary representation and rounding of floating-point values, and the value range and UTF-8 encoding of Unicode characters.

    +
    +

    Note

    +

    The aforementioned standards are the authoritative source of all respective definitions. +Formalizations given in this specification are intended to match these definitions. +Any discrepancy in the syntax or semantics described is to be considered an error.

    +
    +
    +
    + +
    +

    1.2. Overview

    +
    + +

    1.2.1. Concepts

    +

    WebAssembly encodes a low-level, assembly-like programming language. +This language is structured around the following concepts.

    +
    +
    Values +
    +

    WebAssembly provides only four basic number types. +These are integers and [IEEE-754-2019] numbers, +each in 32 and 64 bit width. +32 bit integers also serve as Booleans and as memory addresses. +The usual operations on these types are available, +including the full matrix of conversions between them. +There is no distinction between signed and unsigned integer types. +Instead, integers are interpreted by respective operations +as either unsigned or signed in two’s complement representation.

    +

    In addition to these basic number types, there is a single 128 bit wide +vector type representing different types of packed data. +The supported representations are 4 32-bit, or 2 64-bit [IEEE-754-2019] numbers, or different widths of packed integer values +specifically 2 64-bit integers, 4 32-bit integers, 8 +16-bit integers, or 16 8-bit integers.

    +

    Finally, values can consist of opaque references that represent pointers towards different sorts of entities. +Unlike with other types, their size or representation is not observable.

    +
    +
    +
    Instructions +
    +

    The computational model of WebAssembly is based on a stack machine. +Code consists of sequences of instructions that are executed in order. +Instructions manipulate values on an implicit operand stack 1 and fall into two main categories. Simple instructions perform basic operations on data. +They pop arguments from the operand stack and push results back to it. Control instructions alter control flow. +Control flow is structured, meaning it is expressed with well-nested constructs such as blocks, loops, and conditionals. +Branches can only target such constructs.

    +
    +
    +
    Traps +
    +

    Under some conditions, certain instructions may produce a trap, +which immediately aborts execution. +Traps cannot be handled by WebAssembly code, +but are reported to the outside environment, +where they typically can be caught.

    +
    +
    +
    Functions +
    +

    Code is organized into separate functions. +Each function takes a sequence of values as parameters +and returns a sequence of values as results. +Functions can call each other, including recursively, +resulting in an implicit call stack that cannot be accessed directly. +Functions may also declare mutable local variables that are usable as virtual registers.

    +
    +
    +
    Tables +
    +

    A table is an array of opaque values of a particular element type. +It allows programs to select such values indirectly through a dynamic index operand. +Currently, the only available element type is an untyped function reference. +Thereby, a program can call functions indirectly through a dynamic index into a table. +For example, this allows emulating function pointers by way of table indices.

    +
    +
    +
    Linear Memory +
    +

    A linear memory is a contiguous, mutable array of raw bytes. +Such a memory is created with an initial size but can be grown dynamically. +A program can load and store values from/to a linear memory at any byte address (including unaligned). +Integer loads and stores can specify a storage size which is smaller than the size of the respective value type. +A trap occurs if an access is not within the bounds of the current memory size.

    +
    +
    +
    Modules +
    +

    A WebAssembly binary takes the form of a module that contains definitions for functions, tables, and linear memories, +as well as mutable or immutable global variables. +Definitions can also be imported, specifying a module/name pair and a suitable type. +Each definition can optionally be exported under one or more names. +In addition to definitions, modules can define initialization data for their memories or tables +that takes the form of segments copied to given offsets. +They can also define a start function that is automatically executed.

    +
    +
    +
    Embedder +
    +

    A WebAssembly implementation will typically be embedded into a host environment. +This environment defines how loading of modules is initiated, +how imports are provided (including host-side definitions), and how exports can be accessed. +However, the details of any particular embedding are beyond the scope of this specification, and will instead be provided by complementary, environment-specific API definitions.

    +
    +
    +
    1 +
    +

    In practice, implementations need not maintain an actual operand stack. Instead, the stack can be viewed as a set of anonymous registers that are implicitly referenced by instructions. The type system ensures that the stack height, and thus any referenced register, is always known statically.

    +
    +
    +
    + +

    1.2.2. Semantic Phases

    +

    Conceptually, the semantics of WebAssembly is divided into three phases. +For each part of the language, the specification specifies each of them.

    +
    +
    Decoding +
    +

    WebAssembly modules are distributed in a binary format. Decoding processes that format and converts it into an internal representation of a module. +In this specification, this representation is modelled by abstract syntax, but a real implementation could compile directly to machine code instead.

    +
    +
    +
    Validation +
    +

    A decoded module has to be valid. +Validation checks a number of well-formedness conditions to guarantee that the module is meaningful and safe. +In particular, it performs type checking of functions and the instruction sequences in their bodies, ensuring for example that the operand stack is used consistently.

    +
    + +
    +
    Execution +
    +

    Finally, a valid module can be executed. +Execution can be further divided into two phases:

    +

    Instantiation. +A module instance is the dynamic representation of a module, +complete with its own state and execution stack. +Instantiation executes the module body itself, given definitions for all its imports. +It initializes globals, memories and tables and invokes the module’s start function if defined. +It returns the instances of the module’s exports.

    +

    Invocation. +Once instantiated, further WebAssembly computations can be initiated by invoking an exported function on a module instance. +Given the required arguments, that executes the respective function and returns its results.

    +

    Instantiation and invocation are operations within the embedding environment.

    +
    +
    +
    +
    +
    + +
    + +

    2. Structure

    +
    + +
    + +

    2.1. Conventions

    +

    WebAssembly is a programming language that has multiple concrete representations +(its binary format and the text format). +Both map to a common structure. +For conciseness, this structure is described in the form of an abstract syntax. +All parts of this specification are defined in terms of this abstract syntax.

    +
    + +

    2.1.1. Grammar Notation

    +

    The following conventions are adopted in defining grammar rules for abstract syntax.

    +
      +
    • +

      Terminal symbols (atoms) are written in sans-serif font: .

      +
    • +

      Nonterminal symbols are written in italic font: .

      +
    • +

      is a sequence of iterations of .

      +
    • +

      is a possibly empty sequence of iterations of . +(This is a shorthand for used where is not relevant.)

      +
    • +

      is a non-empty sequence of iterations of . +(This is a shorthand for where .)

      +
    • +

      is an optional occurrence of . +(This is a shorthand for where .)

      +
    • +

      Productions are written .

      +
    • +

      Large productions may be split into multiple definitions, indicated by ending the first one with explicit ellipses, , and starting continuations with ellipses, .

      +
    • +

      Some productions are augmented with side conditions in parentheses, “”, that provide a shorthand for a combinatorial expansion of the production into many separate cases.

      +
    • +

      If the same meta variable or non-terminal symbol appears multiple times in a production, then all those occurrences must have the same instantiation. +(This is a shorthand for a side condition requiring multiple different variables to be equal.)

      +
    +
    +
    + +

    2.1.2. Auxiliary Notation

    +

    When dealing with syntactic constructs the following notation is also used:

    +
      +
    • +

      denotes the empty sequence.

      +
    • +

      denotes the length of a sequence .

      +
    • +

      denotes the -th element of a sequence , starting from .

      +
    • +

      denotes the sub-sequence of a sequence .

      +
    • +

      denotes the same sequence as , +except that the -th element is replaced with .

      +
    • +

      denotes the same sequence as , +except that the sub-sequence is replaced with .

      +
    • +

      denotes the flat sequence formed by concatenating all sequences in .

      +
    +

    Moreover, the following conventions are employed:

    +
      +
    • +

      The notation , where is a non-terminal symbol, is treated as a meta variable ranging over respective sequences of (similarly for , , ).

      +
    • +

      When given a sequence , +then the occurrences of in a sequence written are assumed to be in point-wise correspondence with (similarly for , , ). +This implicitly expresses a form of mapping syntactic constructions over a sequence.

      +
    +

    Productions of the following form are interpreted as records that map a fixed set of fields to “values” , respectively:

    +
    +

    The following notation is adopted for manipulating such records:

    +
      +
    • +

      denotes the contents of the component of .

      +
    • +

      denotes the same record as , +except that the contents of the component is replaced with .

      +
    • +

      denotes the composition of two records with the same fields of sequences by appending each sequence point-wise:

      +
      +
    • +

      denotes the composition of a sequence of records, respectively; if the sequence is empty, then all fields of the resulting record are empty.

      +
    +

    The update notation for sequences and records generalizes recursively to nested components accessed by “paths” :

    +
      +
    • +

      is short for .

      +
    • +

      is short for .

      +
    +

    where is shortened to .

    +
    +
    + +

    2.1.3. Vectors

    +

    Vectors are bounded sequences of the form (or ), +where the can either be values or complex constructions. +A vector can have at most elements.

    +
    +
    +
    + +
    + +

    2.2. Values

    +

    WebAssembly programs operate on primitive numeric values. +Moreover, in the definition of programs, immutable sequences of values occur to represent more complex data, such as text strings or other vectors.

    +
    + +

    2.2.1. Bytes

    +

    The simplest form of value are raw uninterpreted bytes. +In the abstract syntax they are represented as hexadecimal literals.

    +
    +
    +
    2.2.1.1. Conventions
    +
      +
    • +

      The meta variable ranges over bytes.

      +
    • +

      Bytes are sometimes interpreted as natural numbers .

      +
    +
    +
    +
    + +

    2.2.2. Integers

    +

    Different classes of integers with different value ranges are distinguished by their bit width and by whether they are unsigned or signed.

    +
    +

    The latter class defines uninterpreted integers, whose signedness interpretation can vary depending on context. +In the abstract syntax, they are represented as unsigned values. +However, some operations convert them to signed based on a two’s complement interpretation.

    +
    +

    Note

    +

    The main integer types occurring in this specification are , , , , , , , . +However, other sizes occur as auxiliary constructions, e.g., in the definition of floating-point numbers.

    +
    +
    +
    2.2.2.1. Conventions
    +
      +
    • +

      The meta variables range over integers.

      +
    • +

      Numbers may be denoted by simple arithmetics, as in the grammar above. +In order to distinguish arithmetics like from sequences like , the latter is distinguished with parentheses.

      +
    +
    +
    +
    + +

    2.2.3. Floating-Point

    +

    Floating-point data represents 32 or 64 bit values that correspond to the respective binary formats of the [IEEE-754-2019] standard (Section 3.3).

    +

    Every value has a sign and a magnitude. +Magnitudes can either be expressed as normal numbers of the form , where is the exponent and is the significand whose most significant bit is , +or as a subnormal number where the exponent is fixed to the smallest possible value and is ; among the subnormals are positive and negative zero values. +Since the significands are binary values, normals are represented in the form , where is the bit width of ; similarly for subnormals.

    +

    Possible magnitudes also include the special values (infinity) and (NaN, not a number). +NaN values have a payload that describes the mantissa bits in the underlying binary representation. +No distinction is made between signalling and quiet NaNs.

    +
    +

    where and with

    +
    +

    A canonical NaN is a floating-point value where is a payload whose most significant bit is while all others are :

    +
    +

    An arithmetic NaN is a floating-point value with , such that the most significant bit is while all others are arbitrary.

    +
    +

    Note

    +

    In the abstract syntax, subnormals are distinguished by the leading 0 of the significand. The exponent of subnormals has the same value as the smallest possible exponent of a normal number. Only in the binary representation the exponent of a subnormal is encoded differently than the exponent of any normal number.

    +
    +
    +
    2.2.3.1. Conventions
    +
      +
    • +

      The meta variable ranges over floating-point values where clear from context.

      +
    +
    +
    +
    + +

    2.2.4. Vectors

    +

    Numeric vectors are 128-bit values that are processed by vector instructions (also known as SIMD instructions, single instruction multiple data). +They are represented in the abstract syntax using . The interpretation of lane types (integer or floating-point numbers) and lane sizes are determined by the specific instruction operating on them.

    +
    +
    + +

    2.2.5. Names

    +

    Names are sequences of characters, which are scalar values as defined by [UNICODE] (Section 2.4).

    +
    +

    Due to the limitations of the binary format, +the length of a name is bounded by the length of its UTF-8 encoding.

    +
    +
    2.2.5.1. Convention
    +
      +
    • +

      Characters (Unicode scalar values) are sometimes used interchangeably with natural numbers .

      +
    +
    +
    +
    + +
    + +

    2.3. Types

    +

    Various entities in WebAssembly are classified by types. +Types are checked during validation, instantiation, and possibly execution.

    +
    + +

    2.3.1. Number Types

    +

    Number types classify numeric values.

    +
    +

    The types and classify 32 and 64 bit integers, respectively. +Integers are not inherently signed or unsigned, their interpretation is determined by individual operations.

    +

    The types and classify 32 and 64 bit floating-point data, respectively. +They correspond to the respective binary floating-point representations, also known as single and double precision, as defined by the [IEEE-754-2019] standard (Section 3.3).

    +

    Number types are transparent, meaning that their bit patterns can be observed. +Values of number type can be stored in memories.

    +
    + +
    2.3.1.1. Conventions
    +
      +
    • +

      The notation denotes the bit width of a number type . +That is, and .

      +
    +
    +
    +
    + +

    2.3.2. Vector Types

    +

    Vector types classify vectors of numeric values processed by vector instructions (also known as SIMD instructions, single instruction multiple data).

    +
    +

    The type corresponds to a 128 bit vector of packed integer or floating-point data. The packed data +can be interpreted as signed or unsigned integers, single or double precision floating-point +values, or a single 128 bit type. The interpretation is determined by individual operations.

    +

    Vector types, like number types are transparent, meaning that their bit patterns can be observed. +Values of vector type can be stored in memories.

    +
    +
    2.3.2.1. Conventions
    +
      +
    • +

      The notation for bit width extends to vector types as well, that is, .

      +
    +
    +
    +
    + +

    2.3.3. Reference Types

    +

    Reference types classify first-class references to objects in the runtime store.

    +
    +

    The type denotes the infinite union of all references to functions, regardless of their function types.

    +

    The type denotes the infinite union of all references to objects owned by the embedder and that can be passed into WebAssembly under this type.

    +

    Reference types are opaque, meaning that neither their size nor their bit pattern can be observed. +Values of reference type can be stored in tables.

    +
    +
    + +

    2.3.4. Value Types

    +

    Value types classify the individual values that WebAssembly code can compute with and the values that a variable accepts. +They are either number types, vector types, or reference types.

    +
    +
    +
    2.3.4.1. Conventions
    +
      +
    • +

      The meta variable ranges over value types or subclasses thereof where clear from context.

      +
    +
    +
    +
    + +

    2.3.5. Result Types

    +

    Result types classify the result of executing instructions or functions, +which is a sequence of values, written with brackets.

    +
    +
    +
    + +

    2.3.6. Function Types

    +

    Function types classify the signature of functions, +mapping a vector of parameters to a vector of results. +They are also used to classify the inputs and outputs of instructions.

    +
    +
    +
    + +

    2.3.7. Limits

    +

    Limits classify the size range of resizeable storage associated with memory types and table types.

    +
    +

    If no maximum is given, the respective storage can grow to any size.

    +
    +
    + +

    2.3.8. Memory Types

    +

    Memory types classify linear memories and their size range.

    +
    +

    The limits constrain the minimum and optionally the maximum size of a memory. +The limits are given in units of page size.

    +
    +
    + +

    2.3.9. Table Types

    +

    Table types classify tables over elements of reference type within a size range.

    +
    +

    Like memories, tables are constrained by limits for their minimum and optionally maximum size. +The limits are given in numbers of entries.

    +
    +

    Note

    +

    In future versions of WebAssembly, additional element types may be introduced.

    +
    +
    +
    + +

    2.3.10. Global Types

    +

    Global types classify global variables, which hold a value and can either be mutable or immutable.

    +
    +
    +
    + +

    2.3.11. External Types

    +

    External types classify imports and external values with their respective types.

    +
    +
    +
    2.3.11.1. Conventions
    +

    The following auxiliary notation is defined for sequences of external types. +It filters out entries of a specific kind in an order-preserving fashion:

    + +
    +
    +
    + +
    + +

    2.4. Instructions

    +

    WebAssembly code consists of sequences of instructions. +Its computational model is based on a stack machine in that instructions manipulate values on an implicit operand stack, +consuming (popping) argument values and producing or returning (pushing) result values.

    +

    In addition to dynamic operands from the stack, some instructions also have static immediate arguments, +typically indices or type annotations, +which are part of the instruction itself.

    +

    Some instructions are structured in that they bracket nested sequences of instructions.

    +

    The following sections group instructions into a number of different categories.

    +
    + +

    2.4.1. Numeric Instructions

    +

    Numeric instructions provide basic operations over numeric values of specific type. +These operations closely match respective operations available in hardware.

    +
    +

    Numeric instructions are divided by number type. +For each type, several subcategories can be distinguished:

    +
      +
    • +

      Constants: return a static constant.

      +
    • +

      Unary Operations: consume one operand and produce one result of the respective type.

      +
    • +

      Binary Operations: consume two operands and produce one result of the respective type.

      +
    • +

      Tests: consume one operand of the respective type and produce a Boolean integer result.

      +
    • +

      Comparisons: consume two operands of the respective type and produce a Boolean integer result.

      +
    • +

      Conversions: consume a value of one type and produce a result of another +(the source type of the conversion is the one after the “”).

      +
    +

    Some integer instructions come in two flavors, +where a signedness annotation distinguishes whether the operands are to be interpreted as unsigned or signed integers. +For the other integer instructions, the use of two’s complement for the signed interpretation means that they behave the same regardless of signedness.

    +
    + +
    2.4.1.1. Conventions
    +

    Occasionally, it is convenient to group operators together according to the following grammar shorthands:

    +
    +
    +
    +
    + +

    2.4.2. Vector Instructions

    +

    Vector instructions (also known as SIMD instructions, single data multiple value) provide basic operations over values of vector type.

    +
    +

    Vector instructions have a naming convention involving a prefix that +determines how their operands will be interpreted. +This prefix describes the shape of the operand, +written , and consisting of a packed numeric type and the number of lanes of that type. +Operations are performed point-wise on the values of each lane.

    +
    +

    Note

    +

    For example, the shape interprets the operand +as four values, packed into an . +The bitwidth of the numeric type times always is 128.

    +
    +

    Instructions prefixed with do not involve a specific interpretation, and treat the as an value or a vector of 128 individual bits.

    +

    Vector instructions can be grouped into several subcategories:

    +
      +
    • +

      Constants: return a static constant.

      +
    • +

      Unary Operations: consume one operand and produce one result.

      +
    • +

      Binary Operations: consume two operands and produce one result.

      +
    • +

      Ternary Operations: consume three operands and produce one result.

      +
    • +

      Tests: consume one operand and produce a Boolean integer result.

      +
    • +

      Shifts: consume a operand and a operand, producing one result.

      +
    • +

      Splats: consume a value of numeric type and produce a result of a specified shape.

      +
    • +

      Extract lanes: consume a operand and return the numeric value in a given lane.

      +
    • +

      Replace lanes: consume a operand and a numeric value for a given lane, and produce a result.

      +
    +

    Some vector instructions have a signedness annotation which distinguishes whether the elements in the operands are to be interpreted as unsigned or signed integers. +For the other vector instructions, the use of two’s complement for the signed interpretation means that they behave the same regardless of signedness.

    +
    + +
    2.4.2.1. Conventions
    +

    Occasionally, it is convenient to group operators together according to the following grammar shorthands:

    +
    +
    +
    +
    + +

    2.4.3. Reference Instructions

    +

    Instructions in this group are concerned with accessing references.

    +
    +

    These instruction produce a null value, check for a null value, or produce a reference to a given function, respectively.

    +
    +
    + +

    2.4.4. Parametric Instructions

    +

    Instructions in this group can operate on operands of any value type.

    +
    +

    The instruction simply throws away a single operand.

    +

    The instruction selects one of its first two operands based on whether its third operand is zero or not. +It may include a value type determining the type of these operands. If missing, the operands must be of numeric type.

    +
    +

    Note

    +

    In future versions of WebAssembly, the type annotation on may allow for more than a single value being selected at the same time.

    +
    +
    +
    + +

    2.4.5. Variable Instructions

    +

    Variable instructions are concerned with access to local or global variables.

    +
    +

    These instructions get or set the values of variables, respectively. +The instruction is like but also returns its argument.

    +
    +
    + +

    2.4.6. Table Instructions

    +

    Instructions in this group are concerned with tables table.

    +
    +

    The and instructions load or store an element in a table, respectively.

    +

    The instruction returns the current size of a table. +The instruction grows table by a given delta and returns the previous size, or if enough space cannot be allocated. +It also takes an initialization value for the newly allocated entries.

    +

    The instruction sets all entries in a range to a given value.

    +

    The instruction copies elements from a source table region to a possibly overlapping destination region; the first index denotes the destination. +The instruction copies elements from a passive element segment into a table. +The instruction prevents further use of a passive element segment. This instruction is intended to be used as an optimization hint. After an element segment is dropped its elements can no longer be retrieved, so the memory used by this segment may be freed.

    +

    An additional instruction that accesses a table is the control instruction .

    +
    +
    + +

    2.4.7. Memory Instructions

    +

    Instructions in this group are concerned with linear memory.

    +
    +

    Memory is accessed with and instructions for the different number types. +They all take a memory immediate that contains an address offset and the expected alignment (expressed as the exponent of a power of 2). +Integer loads and stores can optionally specify a storage size that is smaller than the bit width of the respective value type. +In the case of loads, a sign extension mode is then required to select appropriate behavior.

    +

    Vector loads can specify a shape that is half the bit width of . Each lane is half its usual size, and the sign extension mode then specifies how the smaller lane is extended to the larger lane. +Alternatively, vector loads can perform a splat, such that only a single lane of the specified storage size is loaded, and the result is duplicated to all lanes.

    +

    The static address offset is added to the dynamic address operand, yielding a 33 bit effective address that is the zero-based index at which the memory is accessed. +All values are read and written in little endian byte order. +A trap results if any of the accessed memory bytes lies outside the address range implied by the memory’s current size.

    +
    +

    Note

    +

    Future version of WebAssembly might provide memory instructions with 64 bit address ranges.

    +
    +

    The instruction returns the current size of a memory. +The instruction grows memory by a given delta and returns the previous size, or if enough memory cannot be allocated. +Both instructions operate in units of page size.

    +

    The instruction sets all values in a region to a given byte. +The instruction copies data from a source memory region to a possibly overlapping destination region. +The instruction copies data from a passive data segment into a memory. +The instruction prevents further use of a passive data segment. This instruction is intended to be used as an optimization hint. After a data segment is dropped its data can no longer be retrieved, so the memory used by this segment may be freed.

    +
    +

    Note

    +

    In the current version of WebAssembly, +all memory instructions implicitly operate on memory index . +This restriction may be lifted in future versions.

    +
    +
    +
    + +

    2.4.8. Control Instructions

    +

    Instructions in this group affect the flow of control.

    +
    +

    The instruction does nothing.

    +

    The instruction causes an unconditional trap.

    +

    The , and instructions are structured instructions. +They bracket nested sequences of instructions, called blocks, terminated with, or separated by, or pseudo-instructions. +As the grammar prescribes, they must be well-nested.

    +

    A structured instruction can consume input and produce output on the operand stack according to its annotated block type. +It is given either as a type index that refers to a suitable function type, or as an optional value type inline, which is a shorthand for the function type .

    +

    Each structured control instruction introduces an implicit label. +Labels are targets for branch instructions that reference them with label indices. +Unlike with other index spaces, indexing of labels is relative by nesting depth, +that is, label refers to the innermost structured control instruction enclosing the referring branch instruction, +while increasing indices refer to those farther out. +Consequently, labels can only be referenced from within the associated structured control instruction. +This also implies that branches can only be directed outwards, +“breaking” from the block of the control construct they target. +The exact effect depends on that control construct. +In case of or it is a forward jump, +resuming execution after the matching . +In case of it is a backward jump to the beginning of the loop.

    +
    +

    Note

    +

    This enforces structured control flow. +Intuitively, a branch targeting a or behaves like a statement in most C-like languages, +while a branch targeting a behaves like a statement.

    +
    +

    Branch instructions come in several flavors: performs an unconditional branch, performs a conditional branch, +and performs an indirect branch through an operand indexing into the label vector that is an immediate to the instruction, or to a default target if the operand is out of bounds. +The instruction is a shortcut for an unconditional branch to the outermost block, which implicitly is the body of the current function. +Taking a branch unwinds the operand stack up to the height where the targeted structured control instruction was entered. +However, branches may additionally consume operands themselves, which they push back on the operand stack after unwinding. +Forward branches require operands according to the output of the targeted block’s type, i.e., represent the values produced by the terminated block. +Backward branches require operands according to the input of the targeted block’s type, i.e., represent the values consumed by the restarted block.

    +

    The instruction invokes another function, consuming the necessary arguments from the stack and returning the result values of the call. +The instruction calls a function indirectly through an operand indexing into a table that is denoted by a table index and must have type . +Since it may contain functions of heterogeneous type, +the callee is dynamically checked against the function type indexed by the instruction’s second immediate, and the call is aborted with a trap if it does not match.

    +
    +
    + +

    2.4.9. Expressions

    +

    Function bodies, initialization values for globals, and offsets of element or data segments are given as expressions, which are sequences of instructions terminated by an marker.

    +
    +

    In some places, validation restricts expressions to be constant, which limits the set of allowable instructions.

    +
    +
    + +
    + +

    2.5. Modules

    +

    WebAssembly programs are organized into modules, +which are the unit of deployment, loading, and compilation. +A module collects definitions for types, functions, tables, memories, and globals. +In addition, it can declare imports and exports and provide initialization in the form of data and element segments, or a start function.

    +
    +

    Each of the vectors – and thus the entire module – may be empty.

    +
    + +

    2.5.1. Indices

    +

    Definitions are referenced with zero-based indices. +Each class of definition has its own index space, as distinguished by the following classes.

    +
    +

    The index space for functions, tables, memories and globals includes respective imports declared in the same module. +The indices of these imports precede the indices of other definitions in the same index space.

    +

    Element indices reference element segments and data indices reference data segments.

    +

    The index space for locals is only accessible inside a function and includes the parameters of that function, which precede the local variables.

    +

    Label indices reference structured control instructions inside an instruction sequence.

    +
    + +
    2.5.1.1. Conventions
    +
      +
    • +

      The meta variable ranges over label indices.

      +
    • +

      The meta variables range over indices in any of the other index spaces.

      +
    • +

      The notation denotes the set of indices from index space occurring free in . We sometimes reinterpret this set as the vector of its elements.

      +
    +
    +

    Note

    +

    For example, if is , then , or equivalently, the vector .

    +
    +
    +
    +
    + +

    2.5.2. Types

    +

    The component of a module defines a vector of function types.

    +

    All function types used in a module must be defined in this component. +They are referenced by type indices.

    +
    +

    Note

    +

    Future versions of WebAssembly may add additional forms of type definitions.

    +
    +
    +
    + +

    2.5.3. Functions

    +

    The component of a module defines a vector of functions with the following structure:

    +
    +

    The of a function declares its signature by reference to a type defined in the module. +The parameters of the function are referenced through 0-based local indices in the function’s body; they are mutable.

    +

    The declare a vector of mutable local variables and their types. +These variables are referenced through local indices in the function’s body. +The index of the first local is the smallest index not referencing a parameter.

    +

    The is an instruction sequence that upon termination must produce a stack matching the function type’s result type.

    +

    Functions are referenced through function indices, +starting with the smallest index not referencing a function import.

    +
    +
    + +

    2.5.4. Tables

    +

    The component of a module defines a vector of tables described by their table type:

    +
    +

    A table is a vector of opaque values of a particular reference type. +The size in the limits of the table type specifies the initial size of that table, while its , if present, restricts the size to which it can grow later.

    +

    Tables can be initialized through element segments.

    +

    Tables are referenced through table indices, +starting with the smallest index not referencing a table import. +Most constructs implicitly reference table index .

    +
    +
    + +

    2.5.5. Memories

    +

    The component of a module defines a vector of linear memories (or memories for short) as described by their memory type:

    +
    +

    A memory is a vector of raw uninterpreted bytes. +The size in the limits of the memory type specifies the initial size of that memory, while its , if present, restricts the size to which it can grow later. +Both are in units of page size.

    +

    Memories can be initialized through data segments.

    +

    Memories are referenced through memory indices, +starting with the smallest index not referencing a memory import. +Most constructs implicitly reference memory index .

    +
    +

    Note

    +

    In the current version of WebAssembly, at most one memory may be defined or imported in a single module, +and all constructs implicitly reference this memory . +This restriction may be lifted in future versions.

    +
    +
    +
    + +

    2.5.6. Globals

    +

    The component of a module defines a vector of global variables (or globals for short):

    +
    +

    Each global stores a single value of the given global type. +Its also specifies whether a global is immutable or mutable. +Moreover, each global is initialized with an value given by a constant initializer expression.

    +

    Globals are referenced through global indices, +starting with the smallest index not referencing a global import.

    +
    +
    + +

    2.5.7. Element Segments

    +

    The initial contents of a table is uninitialized. Element segments can be used to initialize a subrange of a table from a static vector of elements.

    +

    The component of a module defines a vector of element segments. +Each element segment defines a reference type and a corresponding list of constant element expressions.

    +

    Element segments have a mode that identifies them as either passive, active, or declarative. +A passive element segment’s elements can be copied to a table using the instruction. +An active element segment copies its elements into a table during instantiation, as specified by a table index and a constant expression defining an offset into that table. +A declarative element segment is not available at runtime but merely serves to forward-declare references that are formed in code with instructions like .

    +
    +

    The is given by a constant expression.

    +

    Element segments are referenced through element indices.

    +
    +

    Note

    +

    In the current version of WebAssembly, only tables of element type can be initialized with an element segment. +This limitation may be lifted in the future.

    +
    +
    +
    + +

    2.5.8. Data Segments

    +

    The initial contents of a memory are zero bytes. Data segments can be used to initialize a range of memory from a static vector of bytes.

    +

    The component of a module defines a vector of data segments.

    +

    Like element segments, data segments have a mode that identifies them as either passive or active. +A passive data segment’s contents can be copied into a memory using the instruction. +An active data segment copies its contents into a memory during instantiation, as specified by a memory index and a constant expression defining an offset into that memory.

    +
    +

    Data segments are referenced through data indices.

    +
    +

    Note

    +

    In the current version of WebAssembly, at most one memory is allowed in a module. +Consequently, the only valid is .

    +
    +
    +
    + +

    2.5.9. Start Function

    +

    The component of a module declares the function index of a start function that is automatically invoked when the module is instantiated, after tables and memories have been initialized.

    +
    +
    +

    Note

    +

    The start function is intended for initializing the state of a module. +The module and its exports are not accessible before this initialization has completed.

    +
    +
    +
    + +

    2.5.10. Exports

    +

    The component of a module defines a set of exports that become accessible to the host environment once the module has been instantiated.

    +
    +

    Each export is labeled by a unique name. +Exportable definitions are functions, tables, memories, and globals, +which are referenced through a respective descriptor.

    +
    +
    2.5.10.1. Conventions
    +

    The following auxiliary notation is defined for sequences of exports, filtering out indices of a specific kind in an order-preserving fashion:

    + +
    +
    +
    + +

    2.5.11. Imports

    +

    The component of a module defines a set of imports that are required for instantiation.

    +
    +

    Each import is labeled by a two-level name space, consisting of a name and a for an entity within that module. +Importable definitions are functions, tables, memories, and globals. +Each import is specified by a descriptor with a respective type that a definition provided during instantiation is required to match.

    +

    Every import defines an index in the respective index space. +In each index space, the indices of imports go before the first index of any definition contained in the module itself.

    +
    +

    Note

    +

    Unlike export names, import names are not necessarily unique. +It is possible to import the same / pair multiple times; +such imports may even have different type descriptions, including different kinds of entities. +A module with such imports can still be instantiated depending on the specifics of how an embedder allows resolving and supplying imports. +However, embedders are not required to support such overloading, +and a WebAssembly module itself cannot implement an overloaded name.

    +
    +
    +
    +
    +
    + +
    + +

    3. Validation

    +
    + +
    + +

    3.1. Conventions

    +

    Validation checks that a WebAssembly module is well-formed. +Only valid modules can be instantiated.

    +

    Validity is defined by a type system over the abstract syntax of a module and its contents. +For each piece of abstract syntax, there is a typing rule that specifies the constraints that apply to it. +All rules are given in two equivalent forms:

    +
      +
    1. +

      In prose, describing the meaning in intuitive form.

      +
    2. +

      In formal notation, describing the rule in mathematical form. 1

      +
    +
    +

    Note

    +

    The prose and formal rules are equivalent, +so that understanding of the formal notation is not required to read this specification. +The formalism offers a more concise description in notation that is used widely in programming languages semantics and is readily amenable to mathematical proof.

    +
    +

    In both cases, the rules are formulated in a declarative manner. +That is, they only formulate the constraints, they do not define an algorithm. +The skeleton of a sound and complete algorithm for type-checking instruction sequences according to this specification is provided in the appendix.

    +
    + +

    3.1.1. Contexts

    +

    Validity of an individual definition is specified relative to a context, +which collects relevant information about the surrounding module and the definitions in scope:

    +
      +
    • +

      Types: the list of types defined in the current module.

      +
    • +

      Functions: the list of functions declared in the current module, represented by their function type.

      +
    • +

      Tables: the list of tables declared in the current module, represented by their table type.

      +
    • +

      Memories: the list of memories declared in the current module, represented by their memory type.

      +
    • +

      Globals: the list of globals declared in the current module, represented by their global type.

      +
    • +

      Element Segments: the list of element segments declared in the current module, represented by their element type.

      +
    • +

      Data Segments: the list of data segments declared in the current module, each represented by an entry.

      +
    • +

      Locals: the list of locals declared in the current function (including parameters), represented by their value type.

      +
    • +

      Labels: the stack of labels accessible from the current position, represented by their result type.

      +
    • +

      Return: the return type of the current function, represented as an optional result type that is absent when no return is allowed, as in free-standing expressions.

      +
    • +

      References: the list of function indices that occur in the module outside functions and can hence be used to form references inside them.

      +
    +

    In other words, a context contains a sequence of suitable types for each index space, +describing each defined entry in that space. +Locals, labels and return type are only used for validating instructions in function bodies, and are left empty elsewhere. +The label stack is the only part of the context that changes as validation of an instruction sequence proceeds.

    +

    More concretely, contexts are defined as records with abstract syntax:

    +
    +

    In addition to field access written the following notation is adopted for manipulating contexts:

    +
      +
    • +

      When spelling out a context, empty fields are omitted.

      +
    • +

      denotes the same context as but with the elements prepended to its component sequence.

      +
    +
    +

    Note

    +

    We use indexing notation like to look up indices in their respective index space in the context. +Context extension notation is primarily used to locally extend relative index spaces, such as label indices. +Accordingly, the notation is defined to append at the front of the respective sequence, introducing a new relative index and shifting the existing ones.

    +
    +
    +
    + +

    3.1.2. Prose Notation

    +

    Validation is specified by stylised rules for each relevant part of the abstract syntax. +The rules not only state constraints defining when a phrase is valid, +they also classify it with a type. +The following conventions are adopted in stating these rules.

    +
      +
    • +

      A phrase is said to be “valid with type ” +if and only if all constraints expressed by the respective rules are met. +The form of depends on what is.

      +
      +

      Note

      +

      For example, if is a function, +then is a function type; +for an that is a global, is a global type; +and so on.

      +
      +
    • +

      The rules implicitly assume a given context .

      +
    • +

      In some places, this context is locally extended to a context with additional entries. +The formulation “Under context , … statement …” is adopted to express that the following statement must apply under the assumptions embodied in the extended context.

      +
    +
    +
    + +

    3.1.3. Formal Notation

    +
    +

    Note

    +

    This section gives a brief explanation of the notation for specifying typing rules formally. +For the interested reader, a more thorough introduction can be found in respective text books. 2

    +
    +

    The proposition that a phrase has a respective type is written . +In general, however, typing is dependent on a context . +To express this explicitly, the complete form is a judgement , +which says that holds under the assumptions encoded in .

    +

    The formal typing rules use a standard approach for specifying type systems, rendering them into deduction rules. +Every rule has the following general form:

    +
    +

    Such a rule is read as a big implication: if all premises hold, then the conclusion holds. +Some rules have no premises; they are axioms whose conclusion holds unconditionally. +The conclusion always is a judgment , +and there is one respective rule for each relevant construct of the abstract syntax.

    +
    +

    Note

    +

    For example, the typing rule for the instruction can be given as an axiom:

    +
    +

    The instruction is always valid with type ] +(saying that it consumes two values and produces one), +independent of any side conditions.

    +

    An instruction like can be typed as follows:

    +
    +

    Here, the premise enforces that the immediate local index exists in the context. +The instruction produces a value of its respective type (and does not consume any values). +If does not exist then the premise does not hold, +and the instruction is ill-typed.

    +

    Finally, a structured instruction requires +a recursive rule, where the premise is itself a typing judgement:

    +
    +

    A instruction is only valid when the instruction sequence in its body is. +Moreover, the result type must match the block’s annotation . +If so, then the instruction has the same type as the body. +Inside the body an additional label of the corresponding result type is available, +which is expressed by extending the context with the additional label information for the premise.

    +
    +
    +
    1 +
    +

    The semantics is derived from the following article: +Andreas Haas, Andreas Rossberg, Derek Schuff, Ben Titzer, Dan Gohman, Luke Wagner, Alon Zakai, JF Bastien, Michael Holman. Bringing the Web up to Speed with WebAssembly. Proceedings of the 38th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2017). ACM 2017.

    +
    2 +
    +

    For example: Benjamin Pierce. Types and Programming Languages. The MIT Press 2002

    +
    +
    +
    + +
    +

    3.2. Types

    +

    Most types are universally valid. +However, restrictions apply to limits, which must be checked during validation. +Moreover, block types are converted to plain function types for ease of processing.

    +
    + +

    3.2.1. Limits

    +

    Limits must have meaningful bounds that are within a given range.

    +
    +
    3.2.1.1.
    +
      +
    • +

      The value of must not be larger than .

      +
    • +

      If the maximum is not empty, then:

      +
        +
      • +

        Its value must not be larger than .

        +
      • +

        Its value must not be smaller than .

        +
      +
    • +

      Then the limit is valid within range .

      +
    +
    +
    +
    +
    + +

    3.2.2. Block Types

    +

    Block types may be expressed in one of two forms, both of which are converted to plain function types by the following rules.

    +
    +
    3.2.2.1.
    + +
    +
    +
    +
    3.2.2.2.
    + +
    +
    +
    +
    + +

    3.2.3. Function Types

    +

    Function types are always valid.

    +
    +
    3.2.3.1.
    +
      +
    • +

      The function type is valid.

      +
    +
    +
    +
    +
    + +

    3.2.4. Table Types

    +
    +
    3.2.4.1.
    +
      +
    • +

      The limits must be valid within range .

      +
    • +

      Then the table type is valid.

      +
    +
    +
    +
    +
    + +

    3.2.5. Memory Types

    +
    +
    3.2.5.1.
    +
      +
    • +

      The limits must be valid within range .

      +
    • +

      Then the memory type is valid.

      +
    +
    +
    +
    +
    + +

    3.2.6. Global Types

    +
    +
    3.2.6.1.
    +
      +
    • +

      The global type is valid.

      +
    +
    +
    +
    +
    + +

    3.2.7. External Types

    +
    +
    3.2.7.1.
    + +
    +
    +
    +
    3.2.7.2.
    + +
    +
    +
    +
    3.2.7.3.
    + +
    +
    +
    +
    3.2.7.4.
    + +
    +
    +
    +
    + +

    3.2.8. Import Subtyping

    +

    When instantiating a module, external values must be provided whose types are matched against the respective external types classifying each import. +In some cases, this allows for a simple form of subtyping, as defined here.

    +
    + +
    3.2.8.1. Limits
    +

    Limits match limits if and only if:

    +
      +
    • +

      is larger than or equal to .

      +
    • +

      Either:

      +
        +
      • +

        is empty.

        +
      +
    • +

      Or:

      +
        +
      • +

        Both and are non-empty.

        +
      • +

        is smaller than or equal to .

        +
      +
    +
    + +
    +
    + +
    3.2.8.2. Functions
    +

    An external type matches if and only if:

    + +
    +
    +
    + +
    3.2.8.3. Tables
    +

    An external type matches if and only if:

    + +
    +
    +
    + +
    3.2.8.4. Memories
    +

    An external type matches if and only if:

    + +
    +
    +
    + +
    3.2.8.5. Globals
    +

    An external type matches if and only if:

    + +
    +
    +
    +
    + +
    + +

    3.3. Instructions

    +

    Instructions are classified by stack types that describe how instructions manipulate the operand stack.

    +
    +

    The types describe the required input stack with operand types that an instruction pops off +and the provided output stack with result values of types that it pushes back. +Stack types are akin to function types, +except that they allow individual operands to be classified as (bottom), indicating that the type is unconstrained. +As an auxiliary notion, an operand type matches another operand type , if is either or equal to . +This is extended to stack types in a point-wise manner.

    +
    +
    +
    +

    Note

    +

    For example, the instruction has type , +consuming two values and producing one.

    +
    +

    Typing extends to instruction sequences . +Such a sequence has a function type if the accumulative effect of executing the instructions is consuming values of types off the operand stack and pushing new values of types .

    +

    For some instructions, the typing rules do not fully constrain the type, +and therefore allow for multiple types. +Such instructions are called polymorphic. +Two degrees of polymorphism can be distinguished:

    + +

    In both cases, the unconstrained types or type sequences can be chosen arbitrarily, as long as they meet the constraints imposed for the surrounding parts of the program.

    +
    +

    Note

    +

    For example, the instruction is valid with type , for any possible number type . Consequently, both instruction sequences

    +
    +

    and

    +
    +

    are valid, with in the typing of being instantiated to or , respectively.

    +

    The instruction is valid with type for any possible sequences of value types and . +Consequently,

    +
    +

    is valid by assuming type for the instruction. +In contrast,

    +
    +

    is invalid, because there is no possible type to pick for the instruction that would make the sequence well-typed.

    +
    +

    The Appendix describes a type checking algorithm that efficiently implements validation of instruction sequences as prescribed by the rules given here.

    +
    + +

    3.3.1. Numeric Instructions

    +
    + +
    3.3.1.1.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.1.2.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.1.3.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.1.4.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.1.5.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.1.6.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    +
    + +

    3.3.2. Reference Instructions

    +
    + +
    3.3.2.1.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +

    Note

    +

    In future versions of WebAssembly, there may be reference types for which no null reference is allowed.

    +
    +
    +
    + +
    3.3.2.2.
    + +
    +
    +
    + +
    3.3.2.3.
    +
      +
    • +

      The function must be defined in the context.

      +
    • +

      The function index must be contained in .

      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    +
    + +

    3.3.3. Vector Instructions

    +

    Vector instructions can have a prefix to describe the shape of the operand. Packed numeric types, and , are not value type, we define an auxiliary function to map such packed types into value types:

    +
    +

    We also define an auxiliary function to get number of packed numeric types in a , dimension:

    +
    +
    + +
    3.3.3.1.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.3.2.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.3.3.
    + +
    +
    +
    + +
    3.3.3.4.
    + +
    +
    +
    + +
    3.3.3.5.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.3.6.
    + +
    +
    +
    + +
    3.3.3.7.
    + +
    +
    +
    + +
    3.3.3.8.
    + +
    +
    +
    + +
    3.3.3.9.
    + +
    +
    +
    + +
    3.3.3.10.
    + +
    +
    +
    + +
    3.3.3.11.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.3.12.
    + +
    +
    +
    + +
    3.3.3.13.
    + +
    +
    +
    + +
    3.3.3.14.
    + +
    +
    +
    + +
    3.3.3.15.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.3.16.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.3.17.
    + +
    +
    +
    + +
    3.3.3.18.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.3.19.
    + +
    +
    +
    + +
    3.3.3.20.
    + +
    +
    +
    + +
    3.3.3.21.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    +
    + +

    3.3.4. Parametric Instructions

    +
    + +
    3.3.4.1.
    +
      +
    • +

      The instruction is valid with type , for any value type .

      +
    +
    +
    +

    Note

    +

    Both and without annotation are value-polymorphic instructions.

    +
    +
    +
    + +
    3.3.4.2.
    +
      +
    • +

      If is present, then:

      +
        +
      • +

        The length of must be .

        +
      • +

        Then the instruction is valid with type .

        +
      +
    • +

      Else:

      + +
    +
    +
    +

    Note

    +

    In future versions of WebAssembly, may allow more than one value per choice.

    +
    +
    +
    +
    + +

    3.3.5. Variable Instructions

    +
    + +
    3.3.5.1.
    +
      +
    • +

      The local must be defined in the context.

      +
    • +

      Let be the value type .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.5.2.
    +
      +
    • +

      The local must be defined in the context.

      +
    • +

      Let be the value type .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.5.3.
    +
      +
    • +

      The local must be defined in the context.

      +
    • +

      Let be the value type .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.5.4.
    +
      +
    • +

      The global must be defined in the context.

      +
    • +

      Let be the global type .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.5.5.
    +
      +
    • +

      The global must be defined in the context.

      +
    • +

      Let be the global type .

      +
    • +

      The mutability must be .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    +
    + +

    3.3.6. Table Instructions

    +
    + +
    3.3.6.1.
    + +
    +
    +
    + +
    3.3.6.2.
    + +
    +
    +
    + +
    3.3.6.3.
    +
      +
    • +

      The table must be defined in the context.

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.6.4.
    + +
    +
    +
    + +
    3.3.6.5.
    + +
    +
    +
    + +
    3.3.6.6.
    + +
    +
    +
    + +
    3.3.6.7.
    + +
    +
    +
    + +
    3.3.6.8.
    +
      +
    • +

      The element segment must be defined in the context.

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    +
    + +

    3.3.7. Memory Instructions

    +
    + +
    3.3.7.1.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      The alignment must not be larger than the bit width of divided by .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.7.2.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      The alignment must not be larger than .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    +
    3.3.7.3.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      The alignment must not be larger than the bit width of divided by .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.7.4.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      The alignment must not be larger than .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.7.5.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      The alignment must not be larger than .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.7.6.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      The alignment must not be larger than .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.7.7.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      The alignment must not be larger than .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.7.8.
    +
      +
    • +

      The lane index must be smaller than .

      +
    • +

      The memory must be defined in the context.

      +
    • +

      The alignment must not be larger than .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.7.9.
    +
      +
    • +

      The lane index must be smaller than .

      +
    • +

      The memory must be defined in the context.

      +
    • +

      The alignment must not be larger than .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.7.10.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.7.11.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.7.12.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.7.13.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.7.14.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      The data segment must be defined in the context.

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.7.15.
    +
      +
    • +

      The data segment must be defined in the context.

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    +
    + +

    3.3.8. Control Instructions

    +
    + +
    3.3.8.1.
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.8.2.
    +
      +
    • +

      The instruction is valid with type , for any sequences of value types and .

      +
    +
    +
    +

    Note

    +

    The instruction is stack-polymorphic.

    +
    +
    +
    + +
    3.3.8.3.
    +
      +
    • +

      The block type must be valid as some function type .

      +
    • +

      Let be the same context as , but with the result type prepended to the vector.

      +
    • +

      Under context , +the instruction sequence must be valid with type .

      +
    • +

      Then the compound instruction is valid with type .

      +
    +
    +
    +

    Note

    +

    The notation inserts the new label type at index , shifting all others.

    +
    +
    +
    + +
    3.3.8.4.
    +
      +
    • +

      The block type must be valid as some function type .

      +
    • +

      Let be the same context as , but with the result type prepended to the vector.

      +
    • +

      Under context , +the instruction sequence must be valid with type .

      +
    • +

      Then the compound instruction is valid with type .

      +
    +
    +
    +

    Note

    +

    The notation inserts the new label type at index , shifting all others.

    +
    +
    +
    + +
    3.3.8.5.
    +
      +
    • +

      The block type must be valid as some function type .

      +
    • +

      Let be the same context as , but with the result type prepended to the vector.

      +
    • +

      Under context , +the instruction sequence must be valid with type .

      +
    • +

      Under context , +the instruction sequence must be valid with type .

      +
    • +

      Then the compound instruction is valid with type .

      +
    +
    +
    +

    Note

    +

    The notation inserts the new label type at index , shifting all others.

    +
    +
    +
    + +
    3.3.8.6.
    +
      +
    • +

      The label must be defined in the context.

      +
    • +

      Let be the result type .

      +
    • +

      Then the instruction is valid with type , for any sequences of value types and .

      +
    +
    +
    +

    Note

    +

    The label index space in the context contains the most recent label first, so that performs a relative lookup as expected.

    +

    The instruction is stack-polymorphic.

    +
    +
    +
    + +
    3.3.8.7.
    +
      +
    • +

      The label must be defined in the context.

      +
    • +

      Let be the result type .

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +

    Note

    +

    The label index space in the context contains the most recent label first, so that performs a relative lookup as expected.

    +
    +
    +
    + +
    3.3.8.8.
    +
      +
    • +

      The label must be defined in the context.

      +
    • +

      For all in , +the label must be defined in the context.

      +
    • +

      There must be a result type , such that:

      +
        +
      • +

        For each operand type in and corresponding type in , matches .

        +
      • +

        For all in , +and for each operand type in and corresponding type in , matches .

        +
      +
    • +

      Then the instruction is valid with type , for any sequences of value types and .

      +
    +
    +
    +

    Note

    +

    The label index space in the context contains the most recent label first, so that performs a relative lookup as expected.

    +

    The instruction is stack-polymorphic.

    +
    +
    +
    + +
    3.3.8.9.
    +
      +
    • +

      The return type must not be absent in the context.

      +
    • +

      Let be the result type of .

      +
    • +

      Then the instruction is valid with type , for any sequences of value types and .

      +
    +
    +
    +

    Note

    +

    The instruction is stack-polymorphic.

    +

    is absent (set to ) when validating an expression that is not a function body. +This differs from it being set to the empty result type (), +which is the case for functions not returning anything.

    +
    +
    +
    + +
    3.3.8.10.
    +
      +
    • +

      The function must be defined in the context.

      +
    • +

      Then the instruction is valid with type .

      +
    +
    +
    +
    + +
    3.3.8.11.
    + +
    +
    +
    +
    + +

    3.3.9. Instruction Sequences

    +

    Typing of instruction sequences is defined recursively.

    +
    +
    3.3.9.1. Empty Instruction Sequence:
    +
      +
    • +

      The empty instruction sequence is valid with type , +for any sequence of operand types .

      +
    +
    +
    +
    +
    3.3.9.2. Non-empty Instruction Sequence:
    +
      +
    • +

      The instruction sequence must be valid with type , +for some sequences of value types and .

      +
    • +

      The instruction must be valid with type , +for some sequences of value types and .

      +
    • +

      There must be a sequence of value types , +such that where the type sequence is as long as .

      +
    • +

      For each operand type in and corresponding type in , matches .

      +
    • +

      Then the combined instruction sequence is valid with type .

      +
    +
    +
    +
    +
    + +

    3.3.10. Expressions

    +

    Expressions are classified by result types of the form .

    +
    +
    3.3.10.1.
    + +
    +
    +
    + +
    3.3.10.2. Constant Expressions
    + +
    +
    +
    +
    +

    Note

    +

    Currently, constant expressions occurring as initializers of globals are further constrained in that contained instructions are only allowed to refer to imported globals. +This is enforced in the validation rule for modules by constraining the context accordingly.

    +

    The definition of constant expression may be extended in future versions of WebAssembly.

    +
    +
    +
    +
    + +
    +

    3.4. Modules

    +

    Modules are valid when all the components they contain are valid. +Furthermore, most definitions are themselves classified with a suitable type.

    +
    + +

    3.4.1. Functions

    +

    Functions are classified by function types of the form .

    +
    +
    3.4.1.1.
    +
      +
    • +

      The type must be defined in the context.

      +
    • +

      Let be the function type .

      +
    • +

      Let be the same context as , +but with:

      + +
    • +

      Under the context , +the expression must be valid with type .

      +
    • +

      Then the function definition is valid with type .

      +
    +
    +
    +
    +
    + +

    3.4.2. Tables

    +

    Tables are classified by table types.

    +
    +
    3.4.2.1.
    + +
    +
    +
    +
    + +

    3.4.3. Memories

    +

    Memories are classified by memory types.

    +
    +
    3.4.3.1.
    + +
    +
    +
    +
    + +

    3.4.4. Globals

    +

    Globals are classified by global types of the form .

    +
    +
    3.4.4.1.
    + +
    +
    +
    +
    + +

    3.4.5. Element Segments

    +

    Element segments are classified by the reference type of their elements.

    +
    +
    3.4.5.1.
    +
      +
    • +

      For each in ,

      +
        +
      • +

        The expression must be valid.

        +
      • +

        The expression must be constant.

        +
      +
    • +

      The element mode must be valid with reference type .

      +
    • +

      Then the element segment is valid with reference type .

      +
    +
    +
    +
    + +
    3.4.5.2.
    + +
    +
    +
    +
    3.4.5.3.
    + +
    +
    +
    +
    3.4.5.4.
    + +
    +
    +
    +
    + +

    3.4.6. Data Segments

    +

    Data segments are not classified by any type but merely checked for well-formedness.

    +
    +
    3.4.6.1.
    +
      +
    • +

      The data mode must be valid.

      +
    • +

      Then the data segment is valid.

      +
    +
    +
    +
    + +
    3.4.6.2.
    +
      +
    • +

      The data mode is valid.

      +
    +
    +
    +
    +
    3.4.6.3.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      The expression must be valid with result type .

      +
    • +

      The expression must be constant.

      +
    • +

      Then the data mode is valid.

      +
    +
    +
    +
    +
    + +

    3.4.7. Start Function

    +

    Start function declarations are not classified by any type.

    +
    +
    3.4.7.1.
    +
      +
    • +

      The function must be defined in the context.

      +
    • +

      The type of must be .

      +
    • +

      Then the start function is valid.

      +
    +
    +
    +
    +
    + +

    3.4.8. Exports

    +

    Exports and export descriptions are classified by their external type.

    +
    +
    3.4.8.1.
    + +
    +
    +
    +
    3.4.8.2.
    +
      +
    • +

      The function must be defined in the context.

      +
    • +

      Then the export description is valid with external type .

      +
    +
    +
    +
    +
    3.4.8.3.
    + +
    +
    +
    +
    3.4.8.4.
    +
      +
    • +

      The memory must be defined in the context.

      +
    • +

      Then the export description is valid with external type .

      +
    +
    +
    +
    +
    3.4.8.5.
    + +
    +
    +
    +
    + +

    3.4.9. Imports

    +

    Imports and import descriptions are classified by external types.

    +
    +
    3.4.9.1.
    + +
    +
    +
    +
    3.4.9.2.
    +
      +
    • +

      The function must be defined in the context.

      +
    • +

      Let be the function type .

      +
    • +

      Then the import description is valid with type .

      +
    +
    +
    +
    +
    3.4.9.3.
    + +
    +
    +
    +
    3.4.9.4.
    +
      +
    • +

      The memory type must be valid.

      +
    • +

      Then the import description is valid with type .

      +
    +
    +
    +
    +
    3.4.9.5.
    + +
    +
    +
    +
    + +

    3.4.10. Modules

    +

    Modules are classified by their mapping from the external types of their imports to those of their exports.

    +

    A module is entirely closed, +that is, its components can only refer to definitions that appear in the module itself. +Consequently, no initial context is required. +Instead, the context for validation of the module’s content is constructed from the definitions in the module.

    + +
    +
    +

    Note

    +

    Most definitions in a module – particularly functions – are mutually recursive. +Consequently, the definition of the context in this rule is recursive: +it depends on the outcome of validation of the function, table, memory, and global definitions contained in the module, +which itself depends on . +However, this recursion is just a specification device. +All types needed to construct can easily be determined from a simple pre-pass over the module that does not perform any actual validation.

    +

    Globals, however, are not recursive. +The effect of defining the limited context for validating the module’s globals is that their initialization expressions can only access functions and imported globals and nothing else.

    +
    +
    +

    Note

    +

    The restriction on the number of memories may be lifted in future versions of WebAssembly.

    +
    +
    +
    +
    +
    + +
    + +

    4. Execution

    +
    + +
    + +

    4.1. Conventions

    +

    WebAssembly code is executed when instantiating a module or invoking an exported function on the resulting module instance.

    +

    Execution behavior is defined in terms of an abstract machine that models the program state. +It includes a stack, which records operand values and control constructs, and an abstract store containing global state.

    +

    For each instruction, there is a rule that specifies the effect of its execution on the program state. +Furthermore, there are rules describing the instantiation of a module. +As with validation, all rules are given in two equivalent forms:

    +
      +
    1. +

      In prose, describing the execution in intuitive form.

      +
    2. +

      In formal notation, describing the rule in mathematical form. 1

      +
    +
    +

    Note

    +

    As with validation, the prose and formal rules are equivalent, +so that understanding of the formal notation is not required to read this specification. +The formalism offers a more concise description in notation that is used widely in programming languages semantics and is readily amenable to mathematical proof.

    +
    +
    + +

    4.1.1. Prose Notation

    +

    Execution is specified by stylised, step-wise rules for each instruction of the abstract syntax. +The following conventions are adopted in stating these rules.

    +
      +
    • +

      The execution rules implicitly assume a given store .

      +
    • +

      The execution rules also assume the presence of an implicit stack that is modified by pushing or popping values, labels, and frames.

      +
    • +

      Certain rules require the stack to contain at least one frame. +The most recent frame is referred to as the current frame.

      +
    • +

      Both the store and the current frame are mutated by replacing some of their components. +Such replacement is assumed to apply globally.

      +
    • +

      The execution of an instruction may trap, +in which case the entire computation is aborted and no further modifications to the store are performed by it. (Other computations can still be initiated afterwards.)

      +
    • +

      The execution of an instruction may also end in a jump to a designated target, +which defines the next instruction to execute.

      +
    • +

      Execution can enter and exit instruction sequences that form blocks.

      +
    • +

      Instruction sequences are implicitly executed in order, unless a trap or jump occurs.

      +
    • +

      In various places the rules contain assertions expressing crucial invariants about the program state.

      +
    +
    +
    + +

    4.1.2. Formal Notation

    +
    +

    Note

    +

    This section gives a brief explanation of the notation for specifying execution formally. +For the interested reader, a more thorough introduction can be found in respective text books. 2

    +
    +

    The formal execution rules use a standard approach for specifying operational semantics, rendering them into reduction rules. +Every rule has the following general form:

    +
    +

    A configuration is a syntactic description of a program state. +Each rule specifies one step of execution. +As long as there is at most one reduction rule applicable to a given configuration, reduction – and thereby execution – is deterministic. +WebAssembly has only very few exceptions to this, which are noted explicitly in this specification.

    +

    For WebAssembly, a configuration typically is a tuple consisting of the current store , the call frame of the current function, and the sequence of instructions that is to be executed. +(A more precise definition is given later.)

    +

    To avoid unnecessary clutter, the store and the frame are omitted from reduction rules that do not touch them.

    +

    There is no separate representation of the stack. +Instead, it is conveniently represented as part of the configuration’s instruction sequence. +In particular, values are defined to coincide with instructions, +and a sequence of instructions can be interpreted as an operand “stack” that grows to the right.

    +
    +

    Note

    +

    For example, the reduction rule for the instruction can be given as follows:

    +
    +

    Per this rule, two instructions and the instruction itself are removed from the instruction stream and replaced with one new instruction. +This can be interpreted as popping two value off the stack and pushing the result.

    +

    When no result is produced, an instruction reduces to the empty sequence:

    +
    +
    +

    Labels and frames are similarly defined to be part of an instruction sequence.

    +

    The order of reduction is determined by the definition of an appropriate evaluation context.

    +

    Reduction terminates when no more reduction rules are applicable. Soundness of the WebAssembly type system guarantees that this is only the case when the original instruction sequence has either been reduced to a sequence of instructions, which can be interpreted as the values of the resulting operand stack, +or if a trap occurred.

    +
    +

    Note

    +

    For example, the following instruction sequence,

    +
    +

    terminates after three steps:

    +
    +

    where and and .

    +
    +
    +
    1 +
    +

    The semantics is derived from the following article: +Andreas Haas, Andreas Rossberg, Derek Schuff, Ben Titzer, Dan Gohman, Luke Wagner, Alon Zakai, JF Bastien, Michael Holman. Bringing the Web up to Speed with WebAssembly. Proceedings of the 38th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2017). ACM 2017.

    +
    2 +
    +

    For example: Benjamin Pierce. Types and Programming Languages. The MIT Press 2002

    +
    +
    +
    + +
    + +

    4.2. Runtime Structure

    +

    Store, stack, and other runtime structure forming the WebAssembly abstract machine, such as values or module instances, are made precise in terms of additional auxiliary syntax.

    +
    + +

    4.2.1. Values

    +

    WebAssembly computations manipulate values of either the four basic number types, i.e., integers and floating-point data of 32 or 64 bit width each, of vectors of 128 bit width, or of reference type.

    +

    In most places of the semantics, values of different types can occur. +In order to avoid ambiguities, values are therefore represented with an abstract syntax that makes their type explicit. +It is convenient to reuse the same notation as for the instructions and producing them.

    +

    References other than null are represented with additional administrative instructions. +They either are function references, pointing to a specific function address, +or external references pointing to an uninterpreted form of extern address that can be defined by the embedder to represent its own objects.

    +
    +
    +

    Note

    +

    Future versions of WebAssembly may add additional forms of reference.

    +
    +

    Each value type has an associated default value; +it is the respective value for number types and null for reference types.

    +
    +
    +
    4.2.1.1. Convention
    +
      +
    • +

      The meta variable ranges over reference values where clear from context.

      +
    +
    +
    +
    + +

    4.2.2. Results

    +

    A result is the outcome of a computation. +It is either a sequence of values or a trap.

    +
    +
    +

    Note

    +

    In the current version of WebAssembly, a result can consist of at most one value.

    +
    +
    +
    + +

    4.2.3. Store

    +

    The store represents all global state that can be manipulated by WebAssembly programs. +It consists of the runtime representation of all instances of functions, tables, memories, and globals, element segments, and data segments that have been allocated during the life time of the abstract machine. 1

    +

    It is an invariant of the semantics that no element or data instance is addressed from anywhere else but the owning module instances.

    +

    Syntactically, the store is defined as a record listing the existing instances of each category:

    +
    +
    +
    1 +
    +

    In practice, implementations may apply techniques like garbage collection to remove objects from the store that are no longer referenced. +However, such techniques are not semantically observable, +and hence outside the scope of this specification.

    +
    +
    +
    4.2.3.1. Convention
    +
      +
    • +

      The meta variable ranges over stores where clear from context.

      +
    +
    +
    +
    + +

    4.2.4. Addresses

    +

    Function instances, table instances, memory instances, and global instances, element instances, and data instances in the store are referenced with abstract addresses. +These are simply indices into the respective store component. +In addition, an embedder may supply an uninterpreted set of host addresses.

    +
    +

    An embedder may assign identity to exported store objects corresponding to their addresses, +even where this identity is not observable from within WebAssembly code itself +(such as for function instances or immutable globals).

    +
    +

    Note

    +

    Addresses are dynamic, globally unique references to runtime objects, +in contrast to indices, +which are static, module-local references to their original definitions. +A memory address denotes the abstract address of a memory instance in the store, +not an offset inside a memory instance.

    +

    There is no specific limit on the number of allocations of store objects, +hence logical addresses can be arbitrarily large natural numbers.

    +
    +
    +
    + +

    4.2.5. Module Instances

    +

    A module instance is the runtime representation of a module. +It is created by instantiating a module, +and collects runtime representations of all entities that are imported, defined, or exported by the module.

    +
    +

    Each component references runtime instances corresponding to respective declarations from the original module – whether imported or defined – in the order of their static indices. Function instances, table instances, memory instances, and global instances are referenced with an indirection through their respective addresses in the store.

    +

    It is an invariant of the semantics that all export instances in a given module instance have different names.

    +
    +
    + +

    4.2.6. Function Instances

    +

    A function instance is the runtime representation of a function. +It effectively is a closure of the original function over the runtime module instance of its originating module. +The module instance is used to resolve references to other definitions during execution of the function.

    +
    +

    A host function is a function expressed outside WebAssembly but passed to a module as an import. +The definition and behavior of host functions are outside the scope of this specification. +For the purpose of this specification, it is assumed that when invoked, +a host function behaves non-deterministically, +but within certain constraints that ensure the integrity of the runtime.

    +
    +

    Note

    +

    Function instances are immutable, and their identity is not observable by WebAssembly code. +However, the embedder might provide implicit or explicit means for distinguishing their addresses.

    +
    +
    +
    + +

    4.2.7. Table Instances

    +

    A table instance is the runtime representation of a table. +It records its type and holds a vector of reference values.

    +
    +

    Table elements can be mutated through table instructions, the execution of an active element segment, or by external means provided by the embedder.

    +

    It is an invariant of the semantics that all table elements have a type equal to the element type of . +It also is an invariant that the length of the element vector never exceeds the maximum size of , if present.

    +
    +
    + +

    4.2.8. Memory Instances

    +

    A memory instance is the runtime representation of a linear memory. +It records its type and holds a vector of bytes.

    +
    +

    The length of the vector always is a multiple of the WebAssembly page size, which is defined to be the constant – abbreviated .

    +

    The bytes can be mutated through memory instructions, the execution of an active data segment, or by external means provided by the embedder.

    +

    It is an invariant of the semantics that the length of the byte vector, divided by page size, never exceeds the maximum size of , if present.

    +
    +
    + +

    4.2.9. Global Instances

    +

    A global instance is the runtime representation of a global variable. +It records its type and holds an individual value.

    +
    +

    The value of mutable globals can be mutated through variable instructions or by external means provided by the embedder.

    +

    It is an invariant of the semantics that the value has a type equal to the value type of .

    +
    +
    + +

    4.2.10. Element Instances

    +

    An element instance is the runtime representation of an element segment. +It holds a vector of references and their common type.

    +
    +
    +
    + +

    4.2.11. Data Instances

    +

    An data instance is the runtime representation of a data segment. +It holds a vector of bytes.

    +
    +
    +
    + +

    4.2.12. Export Instances

    +

    An export instance is the runtime representation of an export. +It defines the export’s name and the associated external value.

    +
    +
    +
    + +

    4.2.13. External Values

    +

    An external value is the runtime representation of an entity that can be imported or exported. +It is an address denoting either a function instance, table instance, memory instance, or global instances in the shared store.

    +
    +
    +
    4.2.13.1. Conventions
    +

    The following auxiliary notation is defined for sequences of external values. +It filters out entries of a specific kind in an order-preserving fashion:

    + +
    +
    +
    + +

    4.2.14. Stack

    +

    Besides the store, most instructions interact with an implicit stack. +The stack contains three kinds of entries:

    + +

    These entries can occur on the stack in any order during the execution of a program. +Stack entries are described by abstract syntax as follows.

    +
    +

    Note

    +

    It is possible to model the WebAssembly semantics using separate stacks for operands, control constructs, and calls. +However, because the stacks are interdependent, additional book keeping about associated stack heights would be required. +For the purpose of this specification, an interleaved representation is simpler.

    +
    +
    +
    4.2.14.1. Values
    +

    Values are represented by themselves.

    +
    +
    +
    4.2.14.2. Labels
    +

    Labels carry an argument arity and their associated branch target, which is expressed syntactically as an instruction sequence:

    +
    +

    Intuitively, is the continuation to execute when the branch is taken, in place of the original control construct.

    +
    +

    Note

    +

    For example, a loop label has the form

    +
    +

    When performing a branch to this label, this executes the loop, effectively restarting it from the beginning. +Conversely, a simple block label has the form

    +
    +

    When branching, the empty continuation ends the targeted block, such that execution can proceed with consecutive instructions.

    +
    +
    +
    +
    4.2.14.3. Activations and Frames
    +

    Activation frames carry the return arity of the respective function, +hold the values of its locals (including arguments) in the order corresponding to their static local indices, +and a reference to the function’s own module instance:

    +
    +

    The values of the locals are mutated by respective variable instructions.

    +
    +
    + +
    4.2.14.4. Conventions
    +
      +
    • +

      The meta variable ranges over labels where clear from context.

      +
    • +

      The meta variable ranges over frames where clear from context.

      +
    • +

      The following auxiliary definition takes a block type and looks up the function type that it denotes in the current frame:

      +
    +
    +
    +
    +
    + +

    4.2.15. Administrative Instructions

    +
    +

    Note

    +

    This section is only relevant for the formal notation.

    +
    +

    In order to express the reduction of traps, calls, and control instructions, the syntax of instructions is extended to include the following administrative instructions:

    +
    +

    The instruction represents the occurrence of a trap. +Traps are bubbled up through nested instruction sequences, ultimately reducing the entire program to a single instruction, signalling abrupt termination.

    +

    The instruction represents function reference values. Similarly, represents external references.

    +

    The instruction represents the imminent invocation of a function instance, identified by its address. +It unifies the handling of different forms of calls.

    +

    The and instructions model labels and frames “on the stack”. +Moreover, the administrative syntax maintains the nesting structure of the original structured control instruction or function body and their instruction sequences with an marker. +That way, the end of the inner instruction sequence is known when part of an outer sequence.

    +
    +

    Note

    +

    For example, the reduction rule for is:

    +
    +

    This replaces the block with a label instruction, +which can be interpreted as “pushing” the label on the stack. +When is reached, i.e., the inner instruction sequence has been reduced to the empty sequence – or rather, a sequence of instructions representing the resulting values – then the instruction is eliminated courtesy of its own reduction rule:

    +
    +

    This can be interpreted as removing the label from the stack and only leaving the locally accumulated operand values.

    +
    +
    + +
    4.2.15.1. Block Contexts
    +

    In order to specify the reduction of branches, the following syntax of block contexts is defined, indexed by the count of labels surrounding a hole that marks the place where the next step of computation is taking place:

    +
    +

    This definition allows to index active labels surrounding a branch or return instruction.

    +
    +

    Note

    +

    For example, the reduction of a simple branch can be defined as follows:

    +
    +

    Here, the hole of the context is instantiated with a branch instruction. +When a branch occurs, +this rule replaces the targeted label and associated instruction sequence with the label’s continuation. +The selected label is identified through the label index , which corresponds to the number of surrounding instructions that must be hopped over – which is exactly the count encoded in the index of a block context.

    +
    +
    +
    + +
    4.2.15.2. Configurations
    +

    A configuration consists of the current store and an executing thread.

    +

    A thread is a computation over instructions that operates relative to a current frame referring to the module instance in which the computation runs, i.e., where the current function originates from.

    +
    +
    +

    Note

    +

    The current version of WebAssembly is single-threaded, +but configurations with multiple threads may be supported in the future.

    +
    +
    +
    + +
    4.2.15.3. Evaluation Contexts
    +

    Finally, the following definition of evaluation context and associated structural rules enable reduction inside instruction sequences and administrative forms as well as the propagation of traps:

    +
    +
    +

    Reduction terminates when a thread’s instruction sequence has been reduced to a result, +that is, either a sequence of values or to a .

    +
    +

    Note

    +

    The restriction on evaluation contexts rules out contexts like and for which .

    +

    For an example of reduction under evaluation contexts, consider the following instruction sequence.

    +
    +

    This can be decomposed into where

    +
    +

    Moreover, this is the only possible choice of evaluation context where the contents of the hole matches the left-hand side of a reduction rule.

    +
    +
    +
    +
    + +
    + +

    4.3. Numerics

    +

    Numeric primitives are defined in a generic manner, by operators indexed over a bit width .

    +

    Some operators are non-deterministic, because they can return one of several possible results (such as different NaN values). +Technically, each operator thus returns a set of allowed values. +For convenience, deterministic results are expressed as plain values, which are assumed to be identified with a respective singleton set.

    +

    Some operators are partial, because they are not defined on certain inputs. +Technically, an empty set of results is returned for these inputs.

    +

    In formal notation, each operator is defined by equational clauses that apply in decreasing order of precedence. +That is, the first clause that is applicable to the given arguments defines the result. +In some cases, similar clauses are combined into one by using the notation or . +When several of these placeholders occur in a single clause, then they must be resolved consistently: either the upper sign is chosen for all of them or the lower sign.

    +
    +

    Note

    +

    For example, the operator is defined as follows:

    +
    +

    This definition is to be read as a shorthand for the following expansion of each clause into two separate ones:

    +
    +
    +

    Numeric operators are lifted to input sequences by applying the operator element-wise, returning a sequence of results. When there are multiple inputs, they must be of equal length.

    +
    +
    +

    Note

    +

    For example, the unary operator , when given a sequence of floating-point values, return a sequence of floating-point results:

    +
    +

    The binary operator , when given two sequences of integers of the same length, , return a sequence of integer results:

    +
    +
    +

    Conventions:

    +
      +
    • +

      The meta variable is used to range over single bits.

      +
    • +

      The meta variable is used to range over (signless) magnitudes of floating-point values, including and .

      +
    • +

      The meta variable is used to range over (signless) rational magnitudes, excluding or .

      +
    • +

      The notation denotes the inverse of a bijective function .

      +
    • +

      Truncation of rational values is written , with the usual mathematical definition:

      +
      +
    + +
      +
    • +

      Saturation of integers is written and . The arguments to these two functions range over arbitrary signed integers.

      +
        +
      • +

        Unsigned saturation, clamps to between and :

        +
        +
      • +

        Signed saturation, clamps to between and :

        +
      +
      +
    +
    + +

    4.3.1. Representations

    +

    Numbers have an underlying binary representation as a sequence of bits:

    +
    +

    Each of these functions is a bijection, hence they are invertible.

    +
    + +
    4.3.1.1. Integers
    +

    Integers are represented as base two unsigned numbers:

    +
    +

    Boolean operators like , , or are lifted to bit sequences of equal length by applying them pointwise.

    +
    +
    + +
    4.3.1.2. Floating-Point
    +

    Floating-point values are represented in the respective binary format defined by [IEEE-754-2019] (Section 3.4):

    +
    +

    where and .

    +
    +
    + +
    4.3.1.3. Storage
    +

    When a number is stored into memory, it is converted into a sequence of bytes in little endian byte order:

    +
    +

    Again these functions are invertable bijections.

    +
    +
    + +
    4.3.1.4. Vectors
    +

    Numeric vectors have the same underlying representation as an . They can also be interpreted as a sequence of numeric values packed into a with a particular .

    +
    +

    These functions are bijections, so they are invertible.

    +
    +
    +
    + +

    4.3.2. Integer Operations

    +
    + +
    4.3.2.1. Sign Interpretation
    +

    Integer operators are defined on values. +Operators that use a signed interpretation convert the value using the following definition, which takes the two’s complement when the value lies in the upper half of the value range (i.e., its most significant bit is ):

    +
    +

    This function is bijective, and hence invertible.

    +
    +
    + +
    4.3.2.2. Boolean Interpretation
    +

    The integer result of predicates – i.e., tests and relational operators – is defined with the help of the following auxiliary function producing the value or depending on a condition.

    +
    +
    +
    + +
    4.3.2.3.
    +
      +
    • +

      Return the result of adding and modulo .

      +
    +
    +
    +
    + +
    4.3.2.4.
    +
      +
    • +

      Return the result of subtracting from modulo .

      +
    +
    +
    +
    + +
    4.3.2.5.
    +
      +
    • +

      Return the result of multiplying and modulo .

      +
    +
    +
    +
    + +
    4.3.2.6.
    +
      +
    • +

      If is , then the result is undefined.

      +
    • +

      Else, return the result of dividing by , truncated toward zero.

      +
    +
    +
    +

    Note

    +

    This operator is partial.

    +
    +
    +
    + +
    4.3.2.7.
    +
      +
    • +

      Let be the signed interpretation of .

      +
    • +

      Let be the signed interpretation of .

      +
    • +

      If is , then the result is undefined.

      +
    • +

      Else if divided by is , then the result is undefined.

      +
    • +

      Else, return the result of dividing by , truncated toward zero.

      +
    +
    +
    +

    Note

    +

    This operator is partial. +Besides division by , the result of is not representable as an -bit signed integer.

    +
    +
    +
    + +
    4.3.2.8.
    +
      +
    • +

      If is , then the result is undefined.

      +
    • +

      Else, return the remainder of dividing by .

      +
    +
    +
    +

    Note

    +

    This operator is partial.

    +

    As long as both operators are defined, +it holds that .

    +
    +
    +
    + +
    4.3.2.9.
    +
      +
    • +

      Let be the signed interpretation of .

      +
    • +

      Let be the signed interpretation of .

      +
    • +

      If is , then the result is undefined.

      +
    • +

      Else, return the remainder of dividing by , with the sign of the dividend .

      +
    +
    +
    +

    Note

    +

    This operator is partial.

    +

    As long as both operators are defined, +it holds that .

    +
    +
    +
    + +
    4.3.2.10.
    +
      +
    • +

      Return the bitwise negation of .

      +
    +
    +
    +
    + +
    4.3.2.11.
    +
      +
    • +

      Return the bitwise conjunction of and .

      +
    +
    +
    +
    + +
    4.3.2.12.
    +
      +
    • +

      Return the bitwise conjunction of and the bitwise negation of .

      +
    +
    +
    +
    + +
    4.3.2.13.
    +
      +
    • +

      Return the bitwise disjunction of and .

      +
    +
    +
    +
    + +
    4.3.2.14.
    +
      +
    • +

      Return the bitwise exclusive disjunction of and .

      +
    +
    +
    +
    + +
    4.3.2.15.
    +
      +
    • +

      Let be modulo .

      +
    • +

      Return the result of shifting left by bits, modulo .

      +
    +
    +
    +
    + +
    4.3.2.16.
    +
      +
    • +

      Let be modulo .

      +
    • +

      Return the result of shifting right by bits, extended with bits.

      +
    +
    +
    +
    + +
    4.3.2.17.
    +
      +
    • +

      Let be modulo .

      +
    • +

      Return the result of shifting right by bits, extended with the most significant bit of the original value.

      +
    +
    +
    +
    + +
    4.3.2.18.
    +
      +
    • +

      Let be modulo .

      +
    • +

      Return the result of rotating left by bits.

      +
    +
    +
    +
    + +
    4.3.2.19.
    +
      +
    • +

      Let be modulo .

      +
    • +

      Return the result of rotating right by bits.

      +
    +
    +
    +
    + +
    4.3.2.20.
    +
      +
    • +

      Return the count of leading zero bits in ; all bits are considered leading zeros if is .

      +
    +
    +
    +
    + +
    4.3.2.21.
    +
      +
    • +

      Return the count of trailing zero bits in ; all bits are considered trailing zeros if is .

      +
    +
    +
    +
    + +
    4.3.2.22.
    +
      +
    • +

      Return the count of non-zero bits in .

      +
    +
    +
    +
    + +
    4.3.2.23.
    +
      +
    • +

      Return if is zero, otherwise.

      +
    +
    +
    +
    + +
    4.3.2.24.
    +
      +
    • +

      Return if equals , otherwise.

      +
    +
    +
    +
    + +
    4.3.2.25.
    +
      +
    • +

      Return if does not equal , otherwise.

      +
    +
    +
    +
    + +
    4.3.2.26.
    +
      +
    • +

      Return if is less than , otherwise.

      +
    +
    +
    +
    + +
    4.3.2.27.
    + +
    +
    +
    + +
    4.3.2.28.
    +
      +
    • +

      Return if is greater than , otherwise.

      +
    +
    +
    +
    + +
    4.3.2.29.
    + +
    +
    +
    + +
    4.3.2.30.
    +
      +
    • +

      Return if is less than or equal to , otherwise.

      +
    +
    +
    +
    + +
    4.3.2.31.
    + +
    +
    +
    + +
    4.3.2.32.
    +
      +
    • +

      Return if is greater than or equal to , otherwise.

      +
    +
    +
    +
    + +
    4.3.2.33.
    + +
    +
    +
    + +
    4.3.2.34.
    + +
    +
    +
    + +
    4.3.2.35.
    +
      +
    • +

      Let be the bitwise conjunction of and .

      +
    • +

      Let be the bitwise negation of .

      +
    • +

      Let be the bitwise conjunction of and .

      +
    • +

      Return the bitwise disjunction of and .

      +
    +
    +
    +
    + +
    4.3.2.36.
    +
      +
    • +

      Let be the signed interpretation of .

      +
    • +

      If greater than or equal to , then return .

      +
    • +

      Else return the negation of j, modulo .

      +
    +
    +
    +
    + +
    4.3.2.37.
    +
      +
    • +

      Return the result of negating , modulo .

      +
    +
    +
    +
    + +
    4.3.2.38.
    +
      +
    • +

      Return if is , return otherwise.

      +
    +
    +
    +
    + +
    4.3.2.39.
    +
      +
    • +

      Return if is , return otherwise.

      +
    +
    +
    +
    + +
    4.3.2.40.
    +
      +
    • +

      Return if is , return otherwise.

      +
    +
    +
    +
    + +
    4.3.2.41.
    +
      +
    • +

      Return if is , return otherwise.

      +
    +
    +
    +
    + +
    4.3.2.42.
    +
      +
    • +

      Let be the result of adding and .

      +
    • +

      Return .

      +
    +
    +
    +
    + +
    4.3.2.43.
    +
      +
    • +

      Let be the signed interpretation of

      +
    • +

      Let be the signed interpretation of

      +
    • +

      Let be the result of adding and .

      +
    • +

      Return .

      +
    +
    +
    +
    + +
    4.3.2.44.
    +
      +
    • +

      Let be the result of subtracting from .

      +
    • +

      Return .

      +
    +
    +
    +
    + +
    4.3.2.45.
    +
      +
    • +

      Let be the signed interpretation of

      +
    • +

      Let be the signed interpretation of

      +
    • +

      Let be the result of subtracting from .

      +
    • +

      Return .

      +
    +
    +
    +
    + +
    4.3.2.46.
    +
      +
    • +

      Let be the result of adding , , and .

      +
    • +

      Return the result of dividing by , truncated toward zero.

      +
    +
    +
    +
    + +
    4.3.2.47.
    +
      +
    • +

      Return the result of .

      +
    +
    +
    +
    +
    + +

    4.3.3. Floating-Point Operations

    +

    Floating-point arithmetic follows the [IEEE-754-2019] standard, +with the following qualifications:

    +
      +
    • +

      All operators use round-to-nearest ties-to-even, except where otherwise specified. +Non-default directed rounding attributes are not supported.

      +
    • +

      Following the recommendation that operators propagate NaN payloads from their operands is permitted but not required.

      +
    • +

      All operators use “non-stop” mode, and floating-point exceptions are not otherwise observable. +In particular, neither alternate floating-point exception handling attributes nor operators on status flags are supported. +There is no observable difference between quiet and signalling NaNs.

      +
    +
    +

    Note

    +

    Some of these limitations may be lifted in future versions of WebAssembly.

    +
    +
    + +
    4.3.3.1. Rounding
    +

    Rounding always is round-to-nearest ties-to-even, in correspondence with [IEEE-754-2019] (Section 4.3.1).

    +

    An exact floating-point number is a rational number that is exactly representable as a floating-point number of given bit width .

    +

    A limit number for a given floating-point bit width is a positive or negative number whose magnitude is the smallest power of that is not exactly representable as a floating-point number of width (that magnitude is for and for ).

    +

    A candidate number is either an exact floating-point number or a positive or negative limit number for the given bit width .

    +

    A candidate pair is a pair of candidate numbers, such that no candidate number exists that lies between the two.

    +

    A real number is converted to a floating-point value of bit width as follows:

    +
      +
    • +

      If is , then return .

      +
    • +

      Else if is an exact floating-point number, then return .

      +
    • +

      Else if greater than or equal to the positive limit, then return .

      +
    • +

      Else if is less than or equal to the negative limit, then return .

      +
    • +

      Else if and are a candidate pair such that , then:

      +
        +
      • +

        If , then let be .

        +
      • +

        Else if , then let be .

        +
      • +

        Else if and the significand of is even, then let be .

        +
      • +

        Else, let be .

        +
      +
    • +

      If is , then:

      +
        +
      • +

        If , then return .

        +
      • +

        Else, return .

        +
      +
    • +

      Else if is a limit number, then:

      +
        +
      • +

        If , then return .

        +
      • +

        Else, return .

        +
      +
    • +

      Else, return .

      +
    +
    +

    where:

    +
    +
    +
    + +
    4.3.3.2. NaN Propagation
    +

    When the result of a floating-point operator other than , , or is a NaN, +then its sign is non-deterministic and the payload is computed as follows:

    +
      +
    • +

      If the payload of all NaN inputs to the operator is canonical (including the case that there are no NaN inputs), then the payload of the output is canonical as well.

      +
    • +

      Otherwise the payload is picked non-deterministically among all arithmetic NaNs; that is, its most significant bit is and all others are unspecified.

      +
    +

    This non-deterministic result is expressed by the following auxiliary function producing a set of allowed outputs from a set of inputs:

    +
    +
    +
    + +
    4.3.3.3.
    +
      +
    • +

      If either or is a NaN, then return an element of .

      +
    • +

      Else if both and are infinities of opposite signs, then return an element of .

      +
    • +

      Else if both and are infinities of equal sign, then return that infinity.

      +
    • +

      Else if one of or is an infinity, then return that infinity.

      +
    • +

      Else if both and are zeroes of opposite sign, then return positive zero.

      +
    • +

      Else if both and are zeroes of equal sign, then return that zero.

      +
    • +

      Else if one of or is a zero, then return the other operand.

      +
    • +

      Else if both and are values with the same magnitude but opposite signs, then return positive zero.

      +
    • +

      Else return the result of adding and , rounded to the nearest representable value.

      +
    +
    +
    +
    + +
    4.3.3.4.
    +
      +
    • +

      If either or is a NaN, then return an element of .

      +
    • +

      Else if both and are infinities of equal signs, then return an element of .

      +
    • +

      Else if both and are infinities of opposite sign, then return .

      +
    • +

      Else if is an infinity, then return that infinity.

      +
    • +

      Else if is an infinity, then return that infinity negated.

      +
    • +

      Else if both and are zeroes of equal sign, then return positive zero.

      +
    • +

      Else if both and are zeroes of opposite sign, then return .

      +
    • +

      Else if is a zero, then return .

      +
    • +

      Else if is a zero, then return negated.

      +
    • +

      Else if both and are the same value, then return positive zero.

      +
    • +

      Else return the result of subtracting from , rounded to the nearest representable value.

      +
    +
    +
    +

    Note

    +

    Up to the non-determinism regarding NaNs, it always holds that .

    +
    +
    +
    + +
    4.3.3.5.
    +
      +
    • +

      If either or is a NaN, then return an element of .

      +
    • +

      Else if one of and is a zero and the other an infinity, then return an element of .

      +
    • +

      Else if both and are infinities of equal sign, then return positive infinity.

      +
    • +

      Else if both and are infinities of opposite sign, then return negative infinity.

      +
    • +

      Else if one of or is an infinity and the other a value with equal sign, then return positive infinity.

      +
    • +

      Else if one of or is an infinity and the other a value with opposite sign, then return negative infinity.

      +
    • +

      Else if both and are zeroes of equal sign, then return positive zero.

      +
    • +

      Else if both and are zeroes of opposite sign, then return negative zero.

      +
    • +

      Else return the result of multiplying and , rounded to the nearest representable value.

      +
    +
    +
    +
    + +
    4.3.3.6.
    +
      +
    • +

      If either or is a NaN, then return an element of .

      +
    • +

      Else if both and are infinities, then return an element of .

      +
    • +

      Else if both and are zeroes, then return an element of .

      +
    • +

      Else if is an infinity and a value with equal sign, then return positive infinity.

      +
    • +

      Else if is an infinity and a value with opposite sign, then return negative infinity.

      +
    • +

      Else if is an infinity and a value with equal sign, then return positive zero.

      +
    • +

      Else if is an infinity and a value with opposite sign, then return negative zero.

      +
    • +

      Else if is a zero and a value with equal sign, then return positive zero.

      +
    • +

      Else if is a zero and a value with opposite sign, then return negative zero.

      +
    • +

      Else if is a zero and a value with equal sign, then return positive infinity.

      +
    • +

      Else if is a zero and a value with opposite sign, then return negative infinity.

      +
    • +

      Else return the result of dividing by , rounded to the nearest representable value.

      +
    +
    +
    +
    + +
    4.3.3.7.
    +
      +
    • +

      If either or is a NaN, then return an element of .

      +
    • +

      Else if one of or is a negative infinity, then return negative infinity.

      +
    • +

      Else if one of or is a positive infinity, then return the other value.

      +
    • +

      Else if both and are zeroes of opposite signs, then return negative zero.

      +
    • +

      Else return the smaller value of and .

      +
    +
    +
    +
    + +
    4.3.3.8.
    +
      +
    • +

      If either or is a NaN, then return an element of .

      +
    • +

      Else if one of or is a positive infinity, then return positive infinity.

      +
    • +

      Else if one of or is a negative infinity, then return the other value.

      +
    • +

      Else if both and are zeroes of opposite signs, then return positive zero.

      +
    • +

      Else return the larger value of and .

      +
    +
    +
    +
    + +
    4.3.3.9.
    +
      +
    • +

      If and have the same sign, then return .

      +
    • +

      Else return with negated sign.

      +
    +
    +
    +
    + +
    4.3.3.10.
    +
      +
    • +

      If is a NaN, then return with positive sign.

      +
    • +

      Else if is an infinity, then return positive infinity.

      +
    • +

      Else if is a zero, then return positive zero.

      +
    • +

      Else if is a positive value, then .

      +
    • +

      Else return negated.

      +
    +
    +
    +
    + +
    4.3.3.11.
    +
      +
    • +

      If is a NaN, then return with negated sign.

      +
    • +

      Else if is an infinity, then return that infinity negated.

      +
    • +

      Else if is a zero, then return that zero negated.

      +
    • +

      Else return negated.

      +
    +
    +
    +
    + +
    4.3.3.12.
    +
      +
    • +

      If is a NaN, then return an element of .

      +
    • +

      Else if is negative infinity, then return an element of .

      +
    • +

      Else if is positive infinity, then return positive infinity.

      +
    • +

      Else if is a zero, then return that zero.

      +
    • +

      Else if has a negative sign, then return an element of .

      +
    • +

      Else return the square root of .

      +
    +
    +
    +
    + +
    4.3.3.13.
    +
      +
    • +

      If is a NaN, then return an element of .

      +
    • +

      Else if is an infinity, then return .

      +
    • +

      Else if is a zero, then return .

      +
    • +

      Else if is smaller than but greater than , then return negative zero.

      +
    • +

      Else return the smallest integral value that is not smaller than .

      +
    +
    +
    +
    + +
    4.3.3.14.
    +
      +
    • +

      If is a NaN, then return an element of .

      +
    • +

      Else if is an infinity, then return .

      +
    • +

      Else if is a zero, then return .

      +
    • +

      Else if is greater than but smaller than , then return positive zero.

      +
    • +

      Else return the largest integral value that is not larger than .

      +
    +
    +
    +
    + +
    4.3.3.15.
    +
      +
    • +

      If is a NaN, then return an element of .

      +
    • +

      Else if is an infinity, then return .

      +
    • +

      Else if is a zero, then return .

      +
    • +

      Else if is greater than but smaller than , then return positive zero.

      +
    • +

      Else if is smaller than but greater than , then return negative zero.

      +
    • +

      Else return the integral value with the same sign as and the largest magnitude that is not larger than the magnitude of .

      +
    +
    +
    +
    + +
    4.3.3.16.
    +
      +
    • +

      If is a NaN, then return an element of .

      +
    • +

      Else if is an infinity, then return .

      +
    • +

      Else if is a zero, then return .

      +
    • +

      Else if is greater than but smaller than or equal to , then return positive zero.

      +
    • +

      Else if is smaller than but greater than or equal to , then return negative zero.

      +
    • +

      Else return the integral value that is nearest to ; if two values are equally near, return the even one.

      +
    +
    +
    +
    + +
    4.3.3.17.
    +
      +
    • +

      If either or is a NaN, then return .

      +
    • +

      Else if both and are zeroes, then return .

      +
    • +

      Else if both and are the same value, then return .

      +
    • +

      Else return .

      +
    +
    +
    +
    + +
    4.3.3.18.
    +
      +
    • +

      If either or is a NaN, then return .

      +
    • +

      Else if both and are zeroes, then return .

      +
    • +

      Else if both and are the same value, then return .

      +
    • +

      Else return .

      +
    +
    +
    +
    + +
    4.3.3.19.
    +
      +
    • +

      If either or is a NaN, then return .

      +
    • +

      Else if and are the same value, then return .

      +
    • +

      Else if is positive infinity, then return .

      +
    • +

      Else if is negative infinity, then return .

      +
    • +

      Else if is positive infinity, then return .

      +
    • +

      Else if is negative infinity, then return .

      +
    • +

      Else if both and are zeroes, then return .

      +
    • +

      Else if is smaller than , then return .

      +
    • +

      Else return .

      +
    +
    +
    +
    + +
    4.3.3.20.
    +
      +
    • +

      If either or is a NaN, then return .

      +
    • +

      Else if and are the same value, then return .

      +
    • +

      Else if is positive infinity, then return .

      +
    • +

      Else if is negative infinity, then return .

      +
    • +

      Else if is positive infinity, then return .

      +
    • +

      Else if is negative infinity, then return .

      +
    • +

      Else if both and are zeroes, then return .

      +
    • +

      Else if is larger than , then return .

      +
    • +

      Else return .

      +
    +
    +
    +
    + +
    4.3.3.21.
    +
      +
    • +

      If either or is a NaN, then return .

      +
    • +

      Else if and are the same value, then return .

      +
    • +

      Else if is positive infinity, then return .

      +
    • +

      Else if is negative infinity, then return .

      +
    • +

      Else if is positive infinity, then return .

      +
    • +

      Else if is negative infinity, then return .

      +
    • +

      Else if both and are zeroes, then return .

      +
    • +

      Else if is smaller than or equal to , then return .

      +
    • +

      Else return .

      +
    +
    +
    +
    + +
    4.3.3.22.
    +
      +
    • +

      If either or is a NaN, then return .

      +
    • +

      Else if and are the same value, then return .

      +
    • +

      Else if is positive infinity, then return .

      +
    • +

      Else if is negative infinity, then return .

      +
    • +

      Else if is positive infinity, then return .

      +
    • +

      Else if is negative infinity, then return .

      +
    • +

      Else if both and are zeroes, then return .

      +
    • +

      Else if is smaller than or equal to , then return .

      +
    • +

      Else return .

      +
    +
    +
    +
    + +
    4.3.3.23.
    +
      +
    • +

      If is less than then return .

      +
    • +

      Else return .

      +
    +
    +
    +
    + +
    4.3.3.24.
    +
      +
    • +

      If is less than then return .

      +
    • +

      Else return .

      +
    +
    +
    +
    +
    + +

    4.3.4. Conversions

    +
    + +
    4.3.4.1.
    +
      +
    • +

      Return .

      +
    +
    +
    +

    Note

    +

    In the abstract syntax, unsigned extension just reinterprets the same value.

    +
    +
    +
    + +
    4.3.4.2.
    +
      +
    • +

      Let be the signed interpretation of of size .

      +
    • +

      Return the two’s complement of relative to size .

      +
    +
    +
    +
    + +
    4.3.4.3.
    +
      +
    • +

      Return modulo .

      +
    +
    +
    +
    + +
    4.3.4.4.
    +
      +
    • +

      If is a NaN, then the result is undefined.

      +
    • +

      Else if is an infinity, then the result is undefined.

      +
    • +

      Else if is a number and is a value within range of the target type, then return that value.

      +
    • +

      Else the result is undefined.

      +
    +
    +
    +

    Note

    +

    This operator is partial. +It is not defined for NaNs, infinities, or values for which the result is out of range.

    +
    +
    +
    + +
    4.3.4.5.
    +
      +
    • +

      If is a NaN, then the result is undefined.

      +
    • +

      Else if is an infinity, then the result is undefined.

      +
    • +

      If is a number and is a value within range of the target type, then return that value.

      +
    • +

      Else the result is undefined.

      +
    +
    +
    +

    Note

    +

    This operator is partial. +It is not defined for NaNs, infinities, or values for which the result is out of range.

    +
    +
    +
    + +
    4.3.4.6.
    +
      +
    • +

      If is a NaN, then return .

      +
    • +

      Else if is negative infinity, then return .

      +
    • +

      Else if is positive infinity, then return .

      +
    • +

      Else, return .

      +
    +
    +
    +
    + +
    4.3.4.7.
    +
      +
    • +

      If is a NaN, then return .

      +
    • +

      Else if is negative infinity, then return .

      +
    • +

      Else if is positive infinity, then return .

      +
    • +

      Else, return .

      +
    +
    +
    +
    + +
    4.3.4.8.
    +
      +
    • +

      If is a canonical NaN, then return an element of (i.e., a canonical NaN of size ).

      +
    • +

      Else if is a NaN, then return an element of (i.e., any arithmetic NaN of size ).

      +
    • +

      Else, return .

      +
    +
    +
    +
    + +
    4.3.4.9.
    +
      +
    • +

      If is a canonical NaN, then return an element of (i.e., a canonical NaN of size ).

      +
    • +

      Else if is a NaN, then return an element of (i.e., any NaN of size ).

      +
    • +

      Else if is an infinity, then return that infinity.

      +
    • +

      Else if is a zero, then return that zero.

      +
    • +

      Else, return .

      +
    +
    +
    +
    + +
    4.3.4.10.
    +
      +
    • +

      Return .

      +
    +
    +
    +
    + +
    4.3.4.11.
    + +
    +
    +
    + +
    4.3.4.12.
    +
      +
    • +

      Let be the bit sequence .

      +
    • +

      Return the constant for which .

      +
    +
    +
    +
    + +
    4.3.4.13.
    + +
    +
    +
    + +
    4.3.4.14.
    + +
    +
    +
    +
    + +
    + +

    4.4. Instructions

    +

    WebAssembly computation is performed by executing individual instructions.

    +
    + +

    4.4.1. Numeric Instructions

    +

    Numeric instructions are defined in terms of the generic numeric operators. +The mapping of numeric instructions to their underlying operators is expressed by the following definition:

    +
    +

    And for conversion operators:

    +
    +

    Where the underlying operators are partial, the corresponding instruction will trap when the result is not defined. +Where the underlying operators are non-deterministic, because they may return one of multiple possible NaN values, so are the corresponding instructions.

    +
    +

    Note

    +

    For example, the result of instruction applied to operands invokes , +which maps to the generic via the above definition. +Similarly, applied to invokes , +which maps to the generic .

    +
    +
    + +
    4.4.1.1.
    +
      +
    1. +

      Push the value to the stack.

      +
    +
    +

    Note

    +

    No formal reduction rule is required for this instruction, since instructions already are values.

    +
    +
    +
    + +
    4.4.1.2.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      If is defined, then:

      +
        +
      1. +

        Let be a possible result of computing .

        +
      2. +

        Push the value to the stack.

        +
      +
    4. +

      Else:

      +
        +
      1. +

        Trap.

        +
      +
    +
    +
    +
    + +
    4.4.1.3.
    +
      +
    1. +

      Assert: due to validation, two values of value type are on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Pop the value from the stack.

      +
    4. +

      If is defined, then:

      +
        +
      1. +

        Let be a possible result of computing .

        +
      2. +

        Push the value to the stack.

        +
      +
    5. +

      Else:

      +
        +
      1. +

        Trap.

        +
      +
    +
    +
    +
    + +
    4.4.1.4.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Let be the result of computing .

      +
    4. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.1.5.
    +
      +
    1. +

      Assert: due to validation, two values of value type are on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Pop the value from the stack.

      +
    4. +

      Let be the result of computing .

      +
    5. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.1.6.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      If is defined:

      +
        +
      1. +

        Let be a possible result of computing .

        +
      2. +

        Push the value to the stack.

        +
      +
    4. +

      Else:

      +
        +
      1. +

        Trap.

        +
      +
    +
    +
    +
    +
    + +

    4.4.2. Reference Instructions

    +
    + +
    4.4.2.1.
    +
      +
    1. +

      Push the value to the stack.

      +
    +
    +

    Note

    +

    No formal reduction rule is required for this instruction, since the instruction is already a value.

    +
    +
    +
    + +
    4.4.2.2.
    +
      +
    1. +

      Assert: due to validation, a reference value is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      If is , then:

      +
        +
      1. +

        Push the value to the stack.

        +
      +
    4. +

      Else:

      +
        +
      1. +

        Push the value to the stack.

        +
      +
    +
    +
    +
    + +
    4.4.2.3.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the function address .

      +
    4. +

      Push the value to the stack.

      +
    +
    +
    +
    +
    + +

    4.4.3. Vector Instructions

    +

    Most vector instructions are defined in terms of generic numeric operators applied lane-wise based on the shape.

    +
    +
    +

    Note

    +

    For example, the result of instruction applied to operands invokes , which maps to , +where and are sequences resulting from invoking and respectively.

    +
    +
    + +
    4.4.3.1.
    +
      +
    1. +

      Push the value to the stack.

      +
    +
    +

    Note

    +

    No formal reduction rule is required for this instruction, since instructions coincide with values.

    +
    +
    +
    + +
    4.4.3.2.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Let be the result of computing .

      +
    4. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.3.3.
    +
      +
    1. +

      Assert: due to validation, two values of value type are on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Pop the value from the stack.

      +
    4. +

      Let be the result of computing .

      +
    5. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.3.4.
    +
      +
    1. +

      Assert: due to validation, three values of value type are on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Pop the value from the stack.

      +
    4. +

      Pop the value from the stack.

      +
    5. +

      Let be the result of computing .

      +
    6. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.3.5.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Let be the result of computing .

      +
    4. +

      Push the value onto the stack.

      +
    +
    +
    +
    + +
    4.4.3.6.
    +
      +
    1. +

      Assert: due to validation, two values of value type are on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Let be the sequence .

      +
    4. +

      Pop the value from the stack.

      +
    5. +

      Let be the sequence .

      +
    6. +

      Let be the concatenation of the two sequences

      +
    7. +

      Let be the result of .

      +
    8. +

      Push the value onto the stack.

      +
    +
    +
    +
    + +
    4.4.3.7.
    +
      +
    1. +

      Assert: due to validation, two values of value type are on the top of the stack.

      +
    2. +

      Assert: due to validation, for all in it holds that .

      +
    3. +

      Pop the value from the stack.

      +
    4. +

      Let be the sequence .

      +
    5. +

      Pop the value from the stack.

      +
    6. +

      Let be the sequence .

      +
    7. +

      Let be the concatenation of the two sequences .

      +
    8. +

      Let be the result of .

      +
    9. +

      Push the value onto the stack.

      +
    +
    +
    +
    + +
    4.4.3.8.
    +
      +
    1. +

      Let be the type .

      +
    2. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    3. +

      Pop the value from the stack.

      +
    4. +

      Let be the integer .

      +
    5. +

      Let be the result of .

      +
    6. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.3.9.
    +
      +
    1. +

      Assert: due to validation, .

      +
    2. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    3. +

      Pop the value from the stack.

      +
    4. +

      Let be the sequence .

      +
    5. +

      Let be the type .

      +
    6. +

      Let be the result of computing .

      +
    7. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.3.10.
    +
      +
    1. +

      Assert: due to validation, .

      +
    2. +

      Let be the type .

      +
    3. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    4. +

      Pop the value from the stack.

      +
    5. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    6. +

      Pop the value from the stack.

      +
    7. +

      Let be the sequence .

      +
    8. +

      Let be the result of computing

      +
    9. +

      Push on the stack.

      +
    +
    +
    +
    + +
    4.4.3.11.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Let be the result of computing .

      +
    4. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.3.12.
    +
      +
    1. +

      Assert: due to validation, two values of value type are on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Pop the value from the stack.

      +
    4. +

      If is defined:

      +
        +
      1. +

        Let be a possible result of computing .

        +
      2. +

        Push the value to the stack.

        +
      +
    5. +

      Else:

      +
        +
      1. +

        Trap.

        +
      +
    +
    +
    +
    + +
    4.4.3.13.
    +
      +
    1. +

      Assert: due to validation, two values of value type are on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Pop the value from the stack.

      +
    4. +

      Let be the sequence .

      +
    5. +

      Let be the sequence .

      +
    6. +

      Let be the result of computing .

      +
    7. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.3.14.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    4. +

      Pop the value from the stack.

      +
    5. +

      Let be the sequence .

      +
    6. +

      Let be .

      +
    7. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.3.15.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Let be the sequence

      +
    4. +

      Let be the result of computing .

      +
    5. +

      Push the value onto the stack.

      +
    +
    +
    +
    + +
    4.4.3.16.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Let be the sequence .

      +
    4. +

      Let be the bit width of value type .

      +
    5. +

      Let be the sequence as a result of computing .

      +
    6. +

      Let be the integer .

      +
    7. +

      Push the value onto the stack.

      +
    +
    +
    +
    + +
    4.4.3.17.
    +
      +
    1. +

      Assert: due to syntax, .

      +
    2. +

      Assert: due to validation, two values of value type are on the top of the stack.

      +
    3. +

      Pop the value from the stack.

      +
    4. +

      Let be the result of computing .

      +
    5. +

      Pop the value from the stack.

      +
    6. +

      Let be the result of computing .

      +
    7. +

      Let be the result of .

      +
    8. +

      Push the value onto the stack.

      +
    +
    +
    +
    + +
    4.4.3.18.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Let be the sequence .

      +
    4. +

      Let be the result of computing

      +
    5. +

      Push the value onto the stack.

      +
    +
    +
    +
    +
    4.4.3.19.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      If is , then:

      +
        +
      1. +

        Let be the sequence .

        +
      +
    4. +

      Else:

      +
        +
      1. +

        Let be the sequence .

        +
      +
    5. +

      Let be the result of computing .

      +
    6. +

      Let be the result of computing .

      +
    7. +

      Push the value onto the stack.

      +
    +
    +

    where:

    +
    +
    +
    +
    4.4.3.20.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Let be the sequence .

      +
    4. +

      Let be the result of computing concatenated with the vector .

      +
    5. +

      Let be the result of computing .

      +
    6. +

      Push the value onto the stack.

      +
    +
    +
    +
    + +
    4.4.3.21.
    +
      +
    1. +

      Assert: due to validation, two values of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Pop the value from the stack.

      +
    4. +

      Let be the result of computing

      +
    5. +

      Let be the result of computing .

      +
    6. +

      Let be the result of computing .

      +
    7. +

      Push the value onto the stack.

      +
    +
    +
    +
    + +
    4.4.3.22.
    +
      +
    1. +

      Assert: due to validation, two values of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Pop the value from the stack.

      +
    4. +

      If is , then:

      +
        +
      1. +

        Let be the sequence .

        +
      2. +

        Let be the sequence .

        +
      +
    5. +

      Else:

      +
        +
      1. +

        Let be the sequence .

        +
      2. +

        Let be the sequence .

        +
      +
    6. +

      Let be the result of computing

      +
    7. +

      Push the value onto the stack.

      +
    +
    +

    where:

    +
    +
    +
    + +
    4.4.3.23.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Let be the sequence .

      +
    4. +

      Let be the result of computing .

      +
    5. +

      Let c be the result of computing .

      +
    6. +

      Push the value to the stack.

      +
    +
    +
    +
    +
    + +

    4.4.4. Parametric Instructions

    +
    + +
    4.4.4.1.
    +
      +
    1. +

      Assert: due to validation, a value is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    +
    +
    +
    + +
    4.4.4.2.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Assert: due to validation, two more values (of the same value type) are on the top of the stack.

      +
    4. +

      Pop the value from the stack.

      +
    5. +

      Pop the value from the stack.

      +
    6. +

      If is not , then:

      +
        +
      1. +

        Push the value back to the stack.

        +
      +
    7. +

      Else:

      +
        +
      1. +

        Push the value back to the stack.

        +
      +
    +
    +
    +

    Note

    +

    In future versions of WebAssembly, may allow more than one value per choice.

    +
    +
    +
    +
    + +

    4.4.5. Variable Instructions

    +
    + +
    4.4.5.1.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the value .

      +
    4. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.5.2.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Assert: due to validation, a value is on the top of the stack.

      +
    4. +

      Pop the value from the stack.

      +
    5. +

      Replace with the value .

      +
    +
    +
    +
    + +
    4.4.5.3.
    +
      +
    1. +

      Assert: due to validation, a value is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      Push the value to the stack.

      +
    4. +

      Push the value to the stack.

      +
    5. +

      Execute the instruction .

      +
    +
    +
    +
    + +
    4.4.5.4.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the global address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the global instance .

      +
    6. +

      Let be the value .

      +
    7. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.5.5.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the global address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the global instance .

      +
    6. +

      Assert: due to validation, a value is on the top of the stack.

      +
    7. +

      Pop the value from the stack.

      +
    8. +

      Replace with the value .

      +
    +
    +
    +

    Note

    +

    Validation ensures that the global is, in fact, marked as mutable.

    +
    +
    +
    +
    + +

    4.4.6. Table Instructions

    +
    + +
    4.4.6.1.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the table address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the table instance .

      +
    6. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    7. +

      Pop the value from the stack.

      +
    8. +

      If is not smaller than the length of , then:

      +
        +
      1. +

        Trap.

        +
      +
    9. +

      Let be the value .

      +
    10. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.6.2.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the table address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the table instance .

      +
    6. +

      Assert: due to validation, a reference value is on the top of the stack.

      +
    7. +

      Pop the value from the stack.

      +
    8. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    9. +

      Pop the value from the stack.

      +
    10. +

      If is not smaller than the length of , then:

      +
        +
      1. +

        Trap.

        +
      +
    11. +

      Replace the element with .

      +
    +
    +
    +
    + +
    4.4.6.3.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the table address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the table instance .

      +
    6. +

      Let be the length of .

      +
    7. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.6.4.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the table address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the table instance .

      +
    6. +

      Let be the length of .

      +
    7. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    8. +

      Pop the value from the stack.

      +
    9. +

      Assert: due to validation, a reference value is on the top of the stack.

      +
    10. +

      Pop the value from the stack.

      +
    11. +

      Either, try growing by entries with initialization value :

      +
    +
    +
    +
      +
    1. +

      If it succeeds, push the value to the stack.

      +
    2. +

      Else, push the value to the stack.

      +
    +
    +
    +
      +
    1. +

      Or, push the value to the stack.

      +
    +
    +
    +

    Note

    +

    The instruction is non-deterministic. +It may either succeed, returning the old table size , +or fail, returning . +Failure must occur if the referenced table instance has a maximum size defined that would be exceeded. +However, failure can occur in other cases as well. +In practice, the choice depends on the resources available to the embedder.

    +
    +
    +
    + +
    4.4.6.5.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the table address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the table instance .

      +
    6. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    7. +

      Pop the value from the stack.

      +
    8. +

      Assert: due to validation, a reference value is on the top of the stack.

      +
    9. +

      Pop the value from the stack.

      +
    10. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    11. +

      Pop the value from the stack.

      +
    12. +

      If is larger than the length of , then:

      +
        +
      1. +

        Trap.

        +
      +
    +
      +
    1. +

      If is , then:

      +
        +
      1. +

        Return.

        +
      +
    2. +

      Push the value to the stack.

      +
    3. +

      Push the value to the stack.

      +
    4. +

      Execute the instruction .

      +
    5. +

      Push the value to the stack.

      +
    6. +

      Push the value to the stack.

      +
    7. +

      Push the value to the stack.

      +
    8. +

      Execute the instruction .

      +
    +
    +
    +
    + +
    4.4.6.6.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the table address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the table instance .

      +
    6. +

      Assert: due to validation, exists.

      +
    7. +

      Let be the table address .

      +
    8. +

      Assert: due to validation, exists.

      +
    9. +

      Let be the table instance .

      +
    10. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    11. +

      Pop the value from the stack.

      +
    12. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    13. +

      Pop the value from the stack.

      +
    14. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    15. +

      Pop the value from the stack.

      +
    16. +

      If is larger than the length of or is larger than the length of , then:

      +
        +
      1. +

        Trap.

        +
      +
    17. +

      If , then:

      +
    +
    +
    +
      +
    1. +

      Return.

      +
    +
    +
    +
      +
    1. +

      If , then:

      +
    +
    +
    +
      +
    1. +

      Push the value to the stack.

      +
    2. +

      Push the value to the stack.

      +
    3. +

      Execute the instruction .

      +
    4. +

      Execute the instruction .

      +
    5. +

      Assert: due to the earlier check against the table size, .

      +
    6. +

      Push the value to the stack.

      +
    7. +

      Assert: due to the earlier check against the table size, .

      +
    8. +

      Push the value to the stack.

      +
    +
    +
    +
      +
    1. +

      Else:

      +
    +
    +
    +
      +
    1. +

      Assert: due to the earlier check against the table size, .

      +
    2. +

      Push the value to the stack.

      +
    3. +

      Assert: due to the earlier check against the table size, .

      +
    4. +

      Push the value to the stack.

      +
    +
      +
    1. +

      Execute the instruction .

      +
    +
      +
    1. +

      Execute the instruction .

      +
    2. +

      Push the value to the stack.

      +
    3. +

      Push the value to the stack.

      +
    +
    +
    +
      +
    1. +

      Push the value to the stack.

      +
    2. +

      Execute the instruction .

      +
    +
    +
    +
    + +
    4.4.6.7.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the table address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the table instance .

      +
    6. +

      Assert: due to validation, exists.

      +
    7. +

      Let be the element address .

      +
    8. +

      Assert: due to validation, exists.

      +
    9. +

      Let be the element instance .

      +
    10. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    11. +

      Pop the value from the stack.

      +
    12. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    13. +

      Pop the value from the stack.

      +
    14. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    15. +

      Pop the value from the stack.

      +
    16. +

      If is larger than the length of or is larger than the length of , then:

      +
        +
      1. +

        Trap.

        +
      +
    17. +

      If , then:

      +
        +
      1. +

        Return.

        +
      +
    18. +

      Let be the reference value .

      +
    19. +

      Push the value to the stack.

      +
    20. +

      Push the value to the stack.

      +
    21. +

      Execute the instruction .

      +
    22. +

      Assert: due to the earlier check against the table size, .

      +
    23. +

      Push the value to the stack.

      +
    24. +

      Assert: due to the earlier check against the segment size, .

      +
    25. +

      Push the value to the stack.

      +
    26. +

      Push the value to the stack.

      +
    27. +

      Execute the instruction .

      +
    +
    +
    +
    + +
    4.4.6.8.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the element address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Replace with the element instance .

      +
    +
    +
    +
    +
    + +

    4.4.7. Memory Instructions

    +
    +

    Note

    +

    The alignment in load and store instructions does not affect the semantics. +It is an indication that the offset at which the memory is accessed is intended to satisfy the property . +A WebAssembly implementation can use this hint to optimize for the intended use. +Unaligned access violating that property is still allowed and must succeed regardless of the annotation. +However, it may be substantially slower on some hardware.

    +
    +
    + +
    4.4.7.1. and
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the memory address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the memory instance .

      +
    6. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    7. +

      Pop the value from the stack.

      +
    8. +

      Let be the integer .

      +
    9. +

      If is not part of the instruction, then:

      +
        +
      1. +

        Let be the bit width of number type .

        +
      +
    10. +

      If is larger than the length of , then:

      +
        +
      1. +

        Trap.

        +
      +
    11. +

      Let be the byte sequence .

      +
    12. +

      If and are part of the instruction, then:

      +
        +
      1. +

        Let be the integer for which .

        +
      2. +

        Let be the result of computing .

        +
      +
    13. +

      Else:

      +
        +
      1. +

        Let be the constant for which .

        +
      +
    14. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.7.2.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the memory address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the memory instance .

      +
    6. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    7. +

      Pop the value from the stack.

      +
    8. +

      Let be the integer .

      +
    9. +

      If is larger than the length of , then:

      +
      +
      +
        +
      1. +

        Trap.

        +
      +
      +
      +
    10. +

      Let be the byte sequence .

      +
    11. +

      Let be the integer for which .

      +
    12. +

      Let be the integer .

      +
    13. +

      Let be the result of .

      +
    14. +

      Let be the result of computing .

      +
    15. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.7.3.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the memory address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the memory instance .

      +
    6. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    7. +

      Pop the value from the stack.

      +
    8. +

      Let be the integer .

      +
    9. +

      If is larger than the length of , then:

      +
      +
      +
        +
      1. +

        Trap.

        +
      +
      +
      +
    10. +

      Let be the byte sequence .

      +
    11. +

      Let be the integer for which .

      +
    12. +

      Let be the integer .

      +
    13. +

      Let be the result of computing .

      +
    14. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.7.4.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the memory address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the memory instance .

      +
    6. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    7. +

      Pop the value from the stack.

      +
    8. +

      Let be the integer .

      +
    9. +

      If is larger than the length of , then:

      +
      +
      +
        +
      1. +

        Trap.

        +
      +
      +
      +
    10. +

      Let be the byte sequence .

      +
    11. +

      Let be the integer for which .

      +
    12. +

      Let be the result of .

      +
    13. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.7.5.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the memory address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the memory instance .

      +
    6. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    7. +

      Pop the value from the stack.

      +
    8. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    9. +

      Pop the value from the stack.

      +
    10. +

      Let be the integer .

      +
    11. +

      If is larger than the length of , then:

      +
        +
      1. +

        Trap.

        +
      +
    12. +

      Let be the byte sequence .

      +
    13. +

      Let be the constant for which .

      +
    14. +

      Let be .

      +
    15. +

      Let be the result of computing .

      +
    16. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.7.6. and
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the memory address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the memory instance .

      +
    6. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    7. +

      Pop the value from the stack.

      +
    8. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    9. +

      Pop the value from the stack.

      +
    10. +

      Let be the integer .

      +
    11. +

      If is not part of the instruction, then:

      +
        +
      1. +

        Let be the bit width of number type .

        +
      +
    12. +

      If is larger than the length of , then:

      +
        +
      1. +

        Trap.

        +
      +
    13. +

      If is part of the instruction, then:

      +
        +
      1. +

        Let be the result of computing .

        +
      2. +

        Let be the byte sequence .

        +
      +
    14. +

      Else:

      +
        +
      1. +

        Let be the byte sequence .

        +
      +
    15. +

      Replace the bytes with .

      +
    +
    +
    +
    + +
    4.4.7.7.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the memory address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the memory instance .

      +
    6. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    7. +

      Pop the value from the stack.

      +
    8. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    9. +

      Pop the value from the stack.

      +
    10. +

      Let be the integer .

      +
    11. +

      If is larger than the length of , then:

      +
        +
      1. +

        Trap.

        +
      +
    12. +

      Let be .

      +
    13. +

      Let be the byte sequence .

      +
    14. +

      Replace the bytes with .

      +
    +
    +
    +
    + +
    4.4.7.8.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the memory address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the memory instance .

      +
    6. +

      Let be the length of divided by the page size.

      +
    7. +

      Push the value to the stack.

      +
    +
    +
    +
    + +
    4.4.7.9.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the memory address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the memory instance .

      +
    6. +

      Let be the length of divided by the page size.

      +
    7. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    8. +

      Pop the value from the stack.

      +
    9. +

      Let be the value , for which is .

      +
    10. +

      Either, try growing by pages:

      +
    +
    +
    +
      +
    1. +

      If it succeeds, push the value to the stack.

      +
    2. +

      Else, push the value to the stack.

      +
    +
    +
    +
      +
    1. +

      Or, push the value to the stack.

      +
    +
    +
    +

    Note

    +

    The instruction is non-deterministic. +It may either succeed, returning the old memory size , +or fail, returning . +Failure must occur if the referenced memory instance has a maximum size defined that would be exceeded. +However, failure can occur in other cases as well. +In practice, the choice depends on the resources available to the embedder.

    +
    +
    +
    + +
    4.4.7.10.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the memory address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the memory instance .

      +
    6. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    7. +

      Pop the value from the stack.

      +
    8. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    9. +

      Pop the value from the stack.

      +
    10. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    11. +

      Pop the value from the stack.

      +
    12. +

      If is larger than the length of , then:

      +
        +
      1. +

        Trap.

        +
      +
    13. +

      If , then:

      +
        +
      1. +

        Return.

        +
      +
    14. +

      Push the value to the stack.

      +
    15. +

      Push the value to the stack.

      +
    16. +

      Execute the instruction .

      +
    17. +

      Assert: due to the earlier check against the memory size, .

      +
    18. +

      Push the value to the stack.

      +
    19. +

      Push the value to the stack.

      +
    20. +

      Push the value to the stack.

      +
    21. +

      Execute the instruction .

      +
    +
    +
    +
    + +
    4.4.7.11.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the memory address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the memory instance .

      +
    6. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    7. +

      Pop the value from the stack.

      +
    8. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    9. +

      Pop the value from the stack.

      +
    10. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    11. +

      Pop the value from the stack.

      +
    12. +

      If is larger than the length of or is larger than the length of , then:

      +
        +
      1. +

        Trap.

        +
      +
    13. +

      If , then:

      +
    +
    +
    +
      +
    1. +

      Return.

      +
    +
    +
    +
      +
    1. +

      If , then:

      +
    +
    +
    +
      +
    1. +

      Push the value to the stack.

      +
    2. +

      Push the value to the stack.

      +
    3. +

      Execute the instruction .

      +
    4. +

      Execute the instruction .

      +
    5. +

      Assert: due to the earlier check against the memory size, .

      +
    6. +

      Push the value to the stack.

      +
    7. +

      Assert: due to the earlier check against the memory size, .

      +
    8. +

      Push the value to the stack.

      +
    +
    +
    +
      +
    1. +

      Else:

      +
    +
    +
    +
      +
    1. +

      Assert: due to the earlier check against the memory size, .

      +
    2. +

      Push the value to the stack.

      +
    3. +

      Assert: due to the earlier check against the memory size, .

      +
    4. +

      Push the value to the stack.

      +
    5. +

      Execute the instruction .

      +
    6. +

      Execute the instruction .

      +
    7. +

      Push the value to the stack.

      +
    8. +

      Push the value to the stack.

      +
    +
    +
    +
      +
    1. +

      Push the value to the stack.

      +
    2. +

      Execute the instruction .

      +
    +
    +
    +
    + +
    4.4.7.12.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the memory address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the memory instance .

      +
    6. +

      Assert: due to validation, exists.

      +
    7. +

      Let be the data address .

      +
    8. +

      Assert: due to validation, exists.

      +
    9. +

      Let be the data instance .

      +
    10. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    11. +

      Pop the value from the stack.

      +
    12. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    13. +

      Pop the value from the stack.

      +
    14. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    15. +

      Pop the value from the stack.

      +
    16. +

      If is larger than the length of or is larger than the length of , then:

      +
        +
      1. +

        Trap.

        +
      +
    17. +

      If , then:

      +
        +
      1. +

        Return.

        +
      +
    18. +

      Let be the byte .

      +
    19. +

      Push the value to the stack.

      +
    20. +

      Push the value to the stack.

      +
    21. +

      Execute the instruction .

      +
    22. +

      Assert: due to the earlier check against the memory size, .

      +
    23. +

      Push the value to the stack.

      +
    24. +

      Assert: due to the earlier check against the memory size, .

      +
    25. +

      Push the value to the stack.

      +
    26. +

      Push the value to the stack.

      +
    27. +

      Execute the instruction .

      +
    +
    +
    +
    + +
    4.4.7.13.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the data address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Replace with the data instance .

      +
    +
    +
    +
    +
    + +

    4.4.8. Control Instructions

    +
    + +
    4.4.8.1.
    +
      +
    1. +

      Do nothing.

      +
    +
    +
    +
    + +
    4.4.8.2.
    +
      +
    1. +

      Trap.

      +
    +
    +
    +
    + +
    4.4.8.3.
    +
      +
    1. +

      Assert: due to validation, is defined.

      +
    2. +

      Let be the function type .

      +
    3. +

      Let be the label whose arity is and whose continuation is the end of the block.

      +
    4. +

      Assert: due to validation, there are at least values on the top of the stack.

      +
    5. +

      Pop the values from the stack.

      +
    6. +

      Enter the block with label .

      +
    +
    +
    +
    + +
    4.4.8.4.
    +
      +
    1. +

      Assert: due to validation, is defined.

      +
    2. +

      Let be the function type .

      +
    3. +

      Let be the label whose arity is and whose continuation is the start of the loop.

      +
    4. +

      Assert: due to validation, there are at least values on the top of the stack.

      +
    5. +

      Pop the values from the stack.

      +
    6. +

      Enter the block with label .

      +
    +
    +
    +
    + +
    4.4.8.5.
    +
      +
    1. +

      Assert: due to validation, is defined.

      +
    2. +

      Let be the function type .

      +
    3. +

      Let be the label whose arity is and whose continuation is the end of the instruction.

      +
    4. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    5. +

      Pop the value from the stack.

      +
    6. +

      Assert: due to validation, there are at least values on the top of the stack.

      +
    7. +

      Pop the values from the stack.

      +
    8. +

      If is non-zero, then:

      +
        +
      1. +

        Enter the block with label .

        +
      +
    9. +

      Else:

      +
        +
      1. +

        Enter the block with label .

        +
      +
    +
    +
    +
    + +
    4.4.8.6.
    +
      +
    1. +

      Assert: due to validation, the stack contains at least labels.

      +
    2. +

      Let be the -th label appearing on the stack, starting from the top and counting from zero.

      +
    3. +

      Let be the arity of .

      +
    4. +

      Assert: due to validation, there are at least values on the top of the stack.

      +
    5. +

      Pop the values from the stack.

      +
    6. +

      Repeat times:

      +
        +
      1. +

        While the top of the stack is a value, do:

        +
          +
        1. +

          Pop the value from the stack.

          +
        +
      2. +

        Assert: due to validation, the top of the stack now is a label.

        +
      3. +

        Pop the label from the stack.

        +
      +
    7. +

      Push the values to the stack.

      +
    8. +

      Jump to the continuation of .

      +
    +
    +
    +
    + +
    4.4.8.7.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      If is non-zero, then:

      +
        +
      1. +

        Execute the instruction .

        +
      +
    4. +

      Else:

      +
        +
      1. +

        Do nothing.

        +
      +
    +
    +
    +
    + +
    4.4.8.8.
    +
      +
    1. +

      Assert: due to validation, a value of value type is on the top of the stack.

      +
    2. +

      Pop the value from the stack.

      +
    3. +

      If is smaller than the length of , then:

      +
        +
      1. +

        Let be the label .

        +
      2. +

        Execute the instruction .

        +
      +
    4. +

      Else:

      +
        +
      1. +

        Execute the instruction .

        +
      +
    +
    +
    +
    + +
    4.4.8.9.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Let be the arity of .

      +
    3. +

      Assert: due to validation, there are at least values on the top of the stack.

      +
    4. +

      Pop the results from the stack.

      +
    5. +

      Assert: due to validation, the stack contains at least one frame.

      +
    6. +

      While the top of the stack is not a frame, do:

      +
        +
      1. +

        Pop the top element from the stack.

        +
      +
    7. +

      Assert: the top of the stack is the frame .

      +
    8. +

      Pop the frame from the stack.

      +
    9. +

      Push to the stack.

      +
    10. +

      Jump to the instruction after the original call that pushed the frame.

      +
    +
    +
    +
    + +
    4.4.8.10.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the function address .

      +
    4. +

      Invoke the function instance at address .

      +
    +
    +
    +
    + +
    4.4.8.11.
    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Assert: due to validation, exists.

      +
    3. +

      Let be the table address .

      +
    4. +

      Assert: due to validation, exists.

      +
    5. +

      Let be the table instance .

      +
    6. +

      Assert: due to validation, exists.

      +
    7. +

      Let be the function type .

      +
    8. +

      Assert: due to validation, a value with value type is on the top of the stack.

      +
    9. +

      Pop the value from the stack.

      +
    10. +

      If is not smaller than the length of , then:

      +
        +
      1. +

        Trap.

        +
      +
    11. +

      Let be the reference .

      +
    12. +

      If is , then:

      +
        +
      1. +

        Trap.

        +
      +
    13. +

      Assert: due to validation of table mutation, is a function reference.

      +
    14. +

      Let be the function reference .

      +
    15. +

      Assert: due to validation of table mutation, exists.

      +
    16. +

      Let be the function instance .

      +
    17. +

      Let be the function type .

      +
    18. +

      If and differ, then:

      +
        +
      1. +

        Trap.

        +
      +
    19. +

      Invoke the function instance at address .

      +
    +
    +
    +
    +
    + +

    4.4.9. Blocks

    +

    The following auxiliary rules define the semantics of executing an instruction sequence that forms a block.

    +
    + +
    4.4.9.1. Entering with label
    +
      +
    1. +

      Push to the stack.

      +
    2. +

      Jump to the start of the instruction sequence .

      +
    +
    +

    Note

    +

    No formal reduction rule is needed for entering an instruction sequence, +because the label is embedded in the administrative instruction that structured control instructions reduce to directly.

    +
    +
    +
    + +
    4.4.9.2. Exiting with label
    +

    When the end of a block is reached without a jump or trap aborting it, then the following steps are performed.

    +
      +
    1. +

      Let be the number of values on the top of the stack.

      +
    2. +

      Pop the values from the stack.

      +
    3. +

      Assert: due to validation, the label is now on the top of the stack.

      +
    4. +

      Pop the label from the stack.

      +
    5. +

      Push back to the stack.

      +
    6. +

      Jump to the position after the of the structured control instruction associated with the label .

      +
    +
    +
    +

    Note

    +

    This semantics also applies to the instruction sequence contained in a instruction. +Therefore, execution of a loop falls off the end, unless a backwards branch is performed explicitly.

    +
    +
    +
    +
    + +

    4.4.10. Function Calls

    +

    The following auxiliary rules define the semantics of invoking a function instance through one of the call instructions and returning from it.

    +
    + +
    4.4.10.1. Invocation of function address
    +
      +
    1. +

      Assert: due to validation, exists.

      +
    2. +

      Let be the function instance, .

      +
    3. +

      Let be the function type .

      +
    4. +

      Let be the list of value types .

      +
    5. +

      Let be the expression .

      +
    6. +

      Assert: due to validation, values are on the top of the stack.

      +
    7. +

      Pop the values from the stack.

      +
    8. +

      Let be the list of zero values of types .

      +
    9. +

      Let be the frame .

      +
    10. +

      Push the activation of with arity to the stack.

      +
    11. +

      Let be the label whose arity is and whose continuation is the end of the function.

      +
    12. +

      Enter the instruction sequence with label .

      +
    +
    +
    +
    + +
    4.4.10.2. Returning from a function
    +

    When the end of a function is reached without a jump (i.e., ) or trap aborting it, then the following steps are performed.

    +
      +
    1. +

      Let be the current frame.

      +
    2. +

      Let be the arity of the activation of .

      +
    3. +

      Assert: due to validation, there are values on the top of the stack.

      +
    4. +

      Pop the results from the stack.

      +
    5. +

      Assert: due to validation, the frame is now on the top of the stack.

      +
    6. +

      Pop the frame from the stack.

      +
    7. +

      Push back to the stack.

      +
    8. +

      Jump to the instruction after the original call.

      +
    +
    +
    +
    + +
    4.4.10.3. Host Functions
    +

    Invoking a host function has non-deterministic behavior. +It may either terminate with a trap or return regularly. +However, in the latter case, it must consume and produce the right number and types of WebAssembly values on the stack, +according to its function type.

    +

    A host function may also modify the store. +However, all store modifications must result in an extension of the original store, i.e., they must only modify mutable contents and must not have instances removed. +Furthermore, the resulting store must be valid, i.e., all data and code in it is well-typed.

    +
    +

    Here, denotes the implementation-defined execution of host function in current store with arguments . +It yields a set of possible outcomes, where each element is either a pair of a modified store and a result or the special value indicating divergence. +A host function is non-deterministic if there is at least one argument for which the set of outcomes is not singular.

    +

    For a WebAssembly implementation to be sound in the presence of host functions, +every host function instance must be valid, +which means that it adheres to suitable pre- and post-conditions: +under a valid store , and given arguments matching the ascribed parameter types , +executing the host function must yield a non-empty set of possible outcomes each of which is either divergence or consists of a valid store that is an extension of and a result matching the ascribed return types . +All these notions are made precise in the Appendix.

    +
    +

    Note

    +

    A host function can call back into WebAssembly by invoking a function exported from a module. +However, the effects of any such call are subsumed by the non-deterministic behavior allowed for the host function.

    +
    +
    +
    +
    + +

    4.4.11. Expressions

    +

    An expression is evaluated relative to a current frame pointing to its containing module instance.

    +
      +
    1. +

      Jump to the start of the instruction sequence of the expression.

      +
    2. +

      Execute the instruction sequence.

      +
    3. +

      Assert: due to validation, the top of the stack contains a value.

      +
    4. +

      Pop the value from the stack.

      +
    +

    The value is the result of the evaluation.

    +
    +
    +

    Note

    +

    Evaluation iterates this reduction rule until reaching a value. +Expressions constituting function bodies are executed during function invocation.

    +
    +
    +
    + +
    +

    4.5. Modules

    +

    For modules, the execution semantics primarily defines instantiation, which allocates instances for a module and its contained definitions, initializes tables and memories from contained element and data segments, and invokes the start function if present. It also includes invocation of exported functions.

    +

    Instantiation depends on a number of auxiliary notions for type-checking imports and allocating instances.

    +
    + +

    4.5.1. External Typing

    +

    For the purpose of checking external values against imports, +such values are classified by external types. +The following auxiliary typing rules specify this typing relation relative to a store in which the referenced instances live.

    +
    + +
    4.5.1.1.
    + +
    +
    +
    + +
    4.5.1.2.
    + +
    +
    +
    + +
    4.5.1.3.
    + +
    +
    +
    + +
    4.5.1.4.
    + +
    +
    +
    +
    + +

    4.5.2. Value Typing

    +

    For the purpose of checking argument values against the parameter types of exported functions, +values are classified by value types. +The following auxiliary typing rules specify this typing relation relative to a store in which possibly referenced addresses live.

    +
    + +
    4.5.2.1. Numeric Values
    + +
    +
    +
    + +
    4.5.2.2. Null References
    + +
    +
    +
    +
    4.5.2.3. Function References
    + +
    +
    +
    +
    4.5.2.4. External References
    + +
    +
    +
    +
    + +

    4.5.3. Allocation

    +

    New instances of functions, tables, memories, and globals are allocated in a store , as defined by the following auxiliary functions.

    +
    + +
    4.5.3.1. Functions
    +
      +
    1. +

      Let be the function to allocate and its module instance.

      +
    2. +

      Let be the first free function address in .

      +
    3. +

      Let be the function type .

      +
    4. +

      Let be the function instance .

      +
    5. +

      Append to the of .

      +
    6. +

      Return .

      +
    +
    +
    +
    + +
    4.5.3.2. Host Functions
    +
      +
    1. +

      Let be the host function to allocate and its function type.

      +
    2. +

      Let be the first free function address in .

      +
    3. +

      Let be the function instance .

      +
    4. +

      Append to the of .

      +
    5. +

      Return .

      +
    +
    +
    +

    Note

    +

    Host functions are never allocated by the WebAssembly semantics itself, +but may be allocated by the embedder.

    +
    +
    +
    + +
    4.5.3.3. Tables
    +
      +
    1. +

      Let be the table type to allocate and the initialization value.

      +
    2. +

      Let be the structure of table type .

      +
    3. +

      Let be the first free table address in .

      +
    4. +

      Let be the table instance with elements set to .

      +
    5. +

      Append to the of .

      +
    6. +

      Return .

      +
    +
    +
    +
    + +
    4.5.3.4. Memories
    +
      +
    1. +

      Let be the memory type to allocate.

      +
    2. +

      Let be the structure of memory type .

      +
    3. +

      Let be the first free memory address in .

      +
    4. +

      Let be the memory instance that contains pages of zeroed bytes.

      +
    5. +

      Append to the of .

      +
    6. +

      Return .

      +
    +
    +
    +
    + +
    4.5.3.5. Globals
    +
      +
    1. +

      Let be the global type to allocate and the value to initialize the global with.

      +
    2. +

      Let be the first free global address in .

      +
    3. +

      Let be the global instance .

      +
    4. +

      Append to the of .

      +
    5. +

      Return .

      +
    +
    +
    +
    + +
    4.5.3.6. Element segments
    +
      +
    1. +

      Let be the elements’ type and the vector of references to allocate.

      +
    2. +

      Let be the first free element address in .

      +
    3. +

      Let be the element instance .

      +
    4. +

      Append to the of .

      +
    5. +

      Return .

      +
    +
    +
    +
    + +
    4.5.3.7. Data segments
    +
      +
    1. +

      Let be the vector of bytes to allocate.

      +
    2. +

      Let be the first free data address in .

      +
    3. +

      Let be the data instance .

      +
    4. +

      Append to the of .

      +
    5. +

      Return .

      +
    +
    +
    +
    + +
    4.5.3.8. Growing tables
    +
      +
    1. +

      Let be the table instance to grow, the number of elements by which to grow it, and the initialization value.

      +
    2. +

      Let be added to the length of .

      +
    3. +

      If is larger than or equal to , then fail.

      +
    4. +

      Let be the structure of table type .

      +
    5. +

      Let be with updated to .

      +
    6. +

      If is not valid, then fail.

      +
    7. +

      Append to .

      +
    8. +

      Set to the table type .

      +
    +
    +
    +
    + +
    4.5.3.9. Growing memories
    +
      +
    1. +

      Let be the memory instance to grow and the number of pages by which to grow it.

      +
    2. +

      Assert: The length of is divisible by the page size .

      +
    3. +

      Let be added to the length of divided by the page size .

      +
    4. +

      If is larger than , then fail.

      +
    5. +

      Let be the structure of memory type .

      +
    6. +

      Let be with updated to .

      +
    7. +

      If is not valid, then fail.

      +
    8. +

      Append times bytes with value to .

      +
    9. +

      Set to the memory type .

      +
    +
    +
    +
    + +
    4.5.3.10. Modules
    +

    The allocation function for modules requires a suitable list of external values that are assumed to match the import vector of the module, +a list of initialization values for the module’s globals, +and list of reference vectors for the module’s element segments.

    +
      +
    1. +

      Let be the module to allocate and the vector of external values providing the module’s imports, the initialization values of the module’s globals, and the reference vectors of the module’s element segments.

      +
    2. +

      For each function in , do:

      +
        +
      1. +

        Let be the function address resulting from allocating for the module instance defined below.

        +
      +
    3. +

      For each table in , do:

      +
        +
      1. +

        Let be the table type .

        +
      +

      b. Let be the table address resulting from allocating with initialization value .

      +
    4. +

      For each memory in , do:

      +
        +
      1. +

        Let be the memory address resulting from allocating .

        +
      +
    5. +

      For each global in , do:

      +
        +
      1. +

        Let be the global address resulting from allocating with initializer value .

        +
      +
    6. +

      For each element segment in , do:

      +
        +
      1. +

        Let be the element address resulting from allocating a element instance of reference type with contents .

        +
      +
    7. +

      For each data segment in , do:

      +
        +
      1. +

        Let be the data address resulting from allocating a data instance with contents .

        +
      +
    8. +

      Let be the concatenation of the function addresses in index order.

      +
    9. +

      Let be the concatenation of the table addresses in index order.

      +
    10. +

      Let be the concatenation of the memory addresses in index order.

      +
    11. +

      Let be the concatenation of the global addresses in index order.

      +
    12. +

      Let be the concatenation of the element addresses in index order.

      +
    13. +

      Let be the concatenation of the data addresses in index order.

      +
    14. +

      Let be the list of function addresses extracted from , concatenated with .

      +
    15. +

      Let be the list of table addresses extracted from , concatenated with .

      +
    16. +

      Let be the list of memory addresses extracted from , concatenated with .

      +
    17. +

      Let be the list of global addresses extracted from , concatenated with .

      +
    18. +

      For each export in , do:

      +
        +
      1. +

        If is a function export for function index , then let be the external value .

        +
      2. +

        Else, if is a table export for table index , then let be the external value .

        +
      3. +

        Else, if is a memory export for memory index , then let be the external value .

        +
      4. +

        Else, if is a global export for global index , then let be the external value .

        +
      5. +

        Let be the export instance .

        +
      +
    19. +

      Let be the concatenation of the export instances in index order.

      +
    20. +

      Let be the module instance .

      +
    21. +

      Return .

      +
    +
    +

    where:

    +
    +

    Here, the notation is shorthand for multiple allocations of object kind , defined as follows:

    +
    +

    Moreover, if the dots are a sequence (as for globals or tables), then the elements of this sequence are passed to the allocation function pointwise.

    +
    +

    Note

    +

    The definition of module allocation is mutually recursive with the allocation of its associated functions, because the resulting module instance is passed to the function allocator as an argument, in order to form the necessary closures. +In an implementation, this recursion is easily unraveled by mutating one or the other in a secondary step.

    +
    +
    +
    +
    + +

    4.5.4. Instantiation

    +

    Given a store , a module is instantiated with a list of external values supplying the required imports as follows.

    +

    Instantiation checks that the module is valid and the provided imports match the declared types, +and may fail with an error otherwise. +Instantiation can also result in a trap from executing the start function. +It is up to the embedder to define how such conditions are reported.

    +
      +
    1. +

      If is not valid, then:

      +
        +
      1. +

        Fail.

        +
      +
    2. +

      Assert: is valid with external types classifying its imports.

      +
    3. +

      If the number of imports is not equal to the number of provided external values, then:

      +
        +
      1. +

        Fail.

        +
      +
    4. +

      For each external value in and external type in , do:

      +
        +
      1. +

        If is not valid with an external type in store , then:

        +
          +
        1. +

          Fail.

          +
        +
      2. +

        If does not match , then:

        +
          +
        1. +

          Fail.

          +
        +
      +
    +
      +
    1. +

      Let be the auxiliary module instance that only consists of the imported globals and the imported and allocated functions from the final module instance , defined below.

      +
    2. +

      Let be the auxiliary frame .

      +
    3. +

      Push the frame to the stack.

      +
    4. +

      Let be the vector of global initialization values determined by and . These may be calculated as follows.

      +
        +
      1. +

        For each global in , do:

        +
          +
        1. +

          Let be the result of evaluating the initializer expression .

          +
        +
      2. +

        Assert: due to validation, the frame is now on the top of the stack.

        +
      3. +

        Let be the concatenation of in index order.

        +
      +
    5. +

      Let be the list of reference vectors determined by the element segments in . These may be calculated as follows.

      +
      +
      +
        +
      1. +

        For each element segment in , and for each element expression in , do:

        +
          +
        1. +

          Let be the result of evaluating the initializer expression .

          +
        +
      2. +

        Let be the concatenation of function elements in order of index .

        +
      3. +

        Let be the concatenation of function element vectors in order of index .

        +
      +
      +
      +
    6. +

      Pop the frame from the stack.

      +
    7. +

      Let be a new module instance allocated from in store with imports , global initializer values , and element segment contents , and let be the extended store produced by module allocation.

      +
    8. +

      Let be the auxiliary frame .

      +
    9. +

      Push the frame to the stack.

      +
    10. +

      For each element segment in whose mode is of the form , do:

      +
        +
      1. +

        Let be the length of the vector .

        +
      2. +

        Execute the instruction sequence .

        +
      3. +

        Execute the instruction .

        +
      4. +

        Execute the instruction .

        +
      5. +

        Execute the instruction .

        +
      6. +

        Execute the instruction .

        +
      +
    11. +

      For each data segment in whose mode is of the form , do:

      +
        +
      1. +

        Assert: is .

        +
      2. +

        Let be the length of the vector .

        +
      3. +

        Execute the instruction sequence .

        +
      4. +

        Execute the instruction .

        +
      5. +

        Execute the instruction .

        +
      6. +

        Execute the instruction .

        +
      7. +

        Execute the instruction .

        +
      +
    12. +

      If the start function is not empty, then:

      +
        +
      1. +

        Let be the start function .

        +
      2. +

        Execute the instruction .

        +
      +
    13. +

      Assert: due to validation, the frame is now on the top of the stack.

      +
    14. +

      Pop the frame from the stack.

      +
    +
    +

    where:

    +
    +
    +

    Note

    +

    Module allocation and the evaluation of global initializers and element segments are mutually recursive because the global initialization values and element segment contents are passed to the module allocator while depending on the module instance and store returned by allocation. +However, this recursion is just a specification device. +In practice, the initialization values can be determined beforehand by staging module allocation such that first, the module’s own are pre-allocated in the store, then the initializer expressions are evaluated, then the rest of the module instance is allocated, and finally the new function instances’ fields are set to that module instance. +This is possible because validation ensures that initialization expressions cannot actually call a function, only take their reference.

    +

    All failure conditions are checked before any observable mutation of the store takes place. +Store mutation is not atomic; +it happens in individual steps that may be interleaved with other threads.

    +

    Evaluation of constant expressions does not affect the store.

    +
    +
    +
    + +

    4.5.5. Invocation

    +

    Once a module has been instantiated, any exported function can be invoked externally via its function address in the store and an appropriate list of argument values.

    +

    Invocation may fail with an error if the arguments do not fit the function type. +Invocation can also result in a trap. +It is up to the embedder to define how such conditions are reported.

    +
    +

    Note

    +

    If the embedder API performs type checks itself, either statically or dynamically, before performing an invocation, then no failure other than traps can occur.

    +
    +

    The following steps are performed:

    +
      +
    1. +

      Assert: exists.

      +
    2. +

      Let be the function instance .

      +
    3. +

      Let be the function type .

      +
    4. +

      If the length of the provided argument values is different from the number of expected arguments, then:

      +
        +
      1. +

        Fail.

        +
      +
    5. +

      For each value type in and corresponding value in , do:

      +
        +
      1. +

        If is not valid with value type , then:

        +
          +
        1. +

          Fail.

          +
        +
      +
    6. +

      Let be the dummy frame .

      +
    7. +

      Push the frame to the stack.

      +
    8. +

      Push the values to the stack.

      +
    9. +

      Invoke the function instance at address .

      +
    +

    Once the function has returned, the following steps are executed:

    +
      +
    1. +

      Assert: due to validation, values are on the top of the stack.

      +
    2. +

      Pop from the stack.

      +
    +

    The values are returned as the results of the invocation.

    +
    +
    +
    +
    +
    + +
    + +

    5. Binary Format

    +
    + +
    + +

    5.1. Conventions

    +

    The binary format for WebAssembly modules is a dense linear encoding of their abstract syntax. 1

    +

    The format is defined by an attribute grammar whose only terminal symbols are bytes. +A byte sequence is a well-formed encoding of a module if and only if it is generated by the grammar.

    +

    Each production of this grammar has exactly one synthesized attribute: the abstract syntax that the respective byte sequence encodes. +Thus, the attribute grammar implicitly defines a decoding function +(i.e., a parsing function for the binary format).

    +

    Except for a few exceptions, the binary grammar closely mirrors the grammar of the abstract syntax.

    +
    +

    Note

    +

    Some phrases of abstract syntax have multiple possible encodings in the binary format. +For example, numbers may be encoded as if they had optional leading zeros. +Implementations of decoders must support all possible alternatives; +implementations of encoders can pick any allowed encoding.

    +
    +

    The recommended extension for files containing WebAssembly modules in binary format is “” +and the recommended Media Type is “”.

    +
    +
    1 +
    +

    Additional encoding layers – for example, introducing compression – may be defined on top of the basic representation defined here. +However, such layers are outside the scope of the current specification.

    +
    +
    + +

    5.1.1. Grammar

    +

    The following conventions are adopted in defining grammar rules for the binary format. +They mirror the conventions used for abstract syntax. +In order to distinguish symbols of the binary syntax from symbols of the abstract syntax, font is adopted for the former.

    +
      +
    • +

      Terminal symbols are bytes expressed in hexadecimal notation: .

      +
    • +

      Nonterminal symbols are written in typewriter font: .

      +
    • +

      is a sequence of iterations of .

      +
    • +

      is a possibly empty sequence of iterations of . +(This is a shorthand for used where is not relevant.)

      +
    • +

      is an optional occurrence of . +(This is a shorthand for where .)

      +
    • +

      denotes the same language as the nonterminal , but also binds the variable to the attribute synthesized for .

      +
    • +

      Productions are written , where each is the attribute that is synthesized for in the given case, usually from attribute variables bound in .

      +
    • +

      Some productions are augmented by side conditions in parentheses, which restrict the applicability of the production. They provide a shorthand for a combinatorial expansion of the production into many separate cases.

      +
    • +

      If the same meta variable or non-terminal symbol appears multiple times in a production (in the syntax or in an attribute), then all those occurrences must have the same instantiation. +(This is a shorthand for a side condition requiring multiple different variables to be equal.)

      +
    +
    +

    Note

    +

    For example, the binary grammar for number types is given as follows:

    +
    +

    Consequently, the byte encodes the type , encodes the type , and so forth. +No other byte value is allowed as the encoding of a number type.

    +

    The binary grammar for limits is defined as follows:

    +
    +

    That is, a limits pair is encoded as either the byte followed by the encoding of a value, +or the byte followed by two such encodings. +The variables and name the attributes of the respective nonterminals, which in this case are the actual unsigned integers those decode into. +The attribute of the complete production then is the abstract syntax for the limit, expressed in terms of the former values.

    +
    +
    +
    + +

    5.1.2. Auxiliary Notation

    +

    When dealing with binary encodings the following notation is also used:

    +
      +
    • +

      denotes the empty byte sequence.

      +
    • +

      is the length of the byte sequence generated from the production in a derivation.

      +
    +
    +
    + +

    5.1.3. Vectors

    +

    Vectors are encoded with their length followed by the encoding of their element sequence.

    +
    +
    +
    + +
    + +

    5.2. Values

    +
    + +

    5.2.1. Bytes

    +

    Bytes encode themselves.

    +
    +
    +
    + +

    5.2.2. Integers

    +

    All integers are encoded using the LEB128 variable-length integer encoding, in either unsigned or signed variant.

    +

    Unsigned integers are encoded in unsigned LEB128 format. +As an additional constraint, the total number of bytes encoding a value of type must not exceed bytes.

    +
    +

    Signed integers are encoded in signed LEB128 format, which uses a two’s complement representation. +As an additional constraint, the total number of bytes encoding a value of type must not exceed bytes.

    +
    +

    Uninterpreted integers are encoded as signed integers.

    +
    +
    +

    Note

    +

    The side conditions in the productions for non-terminal bytes of the and encodings restrict the encoding’s length. +However, “trailing zeros” are still allowed within these bounds. +For example, and are both well-formed encodings for the value as a . +Similarly, either of and and are well-formed encodings of the value as a .

    +

    The side conditions on the value of terminal bytes further enforce that +any unused bits in these bytes must be for positive values and for negative ones. +For example, is malformed as a encoding. +Similarly, both and are malformed as encodings.

    +
    +
    +
    + +

    5.2.3. Floating-Point

    +

    Floating-point values are encoded directly by their [IEEE-754-2019] (Section 3.4) bit pattern in little endian byte order:

    +
    +
    +
    + +

    5.2.4. Names

    +

    Names are encoded as a vector of bytes containing the [UNICODE] (Section 3.9) UTF-8 encoding of the name’s character sequence.

    +
    +

    The auxiliary function expressing this encoding is defined as follows:

    +
    +
    +

    Note

    +

    Unlike in some other formats, name strings are not 0-terminated.

    +
    +
    +
    + +
    + +

    5.3. Types

    +
    +

    Note

    +

    In some places, possible types include both type constructors or types denoted by type indices. +Thus, the binary format for type constructors corresponds to the encodings of small negative values, such that they can unambiguously occur in the same place as (positive) type indices.

    +
    +
    + +

    5.3.1. Number Types

    +

    Number types are encoded by a single byte.

    +
    +
    +
    + +

    5.3.2. Vector Types

    +

    Vector types are also encoded by a single byte.

    +
    +
    +
    + +

    5.3.3. Reference Types

    +

    Reference types are also encoded by a single byte.

    +
    +
    +
    + +

    5.3.4. Value Types

    +

    Value types are encoded with their respective encoding as a number type, vector type, or reference type.

    +
    +
    +

    Note

    +

    Value types can occur in contexts where type indices are also allowed, such as in the case of block types. +Thus, the binary format for types corresponds to the signed LEB128 encoding of small negative values, so that they can coexist with (positive) type indices in the future.

    +
    +
    +
    + +

    5.3.5. Result Types

    +

    Result types are encoded by the respective vectors of value types `.

    +
    +
    +
    + +

    5.3.6. Function Types

    +

    Function types are encoded by the byte followed by the respective vectors of parameter and result types.

    +
    +
    +
    + +

    5.3.7. Limits

    +

    Limits are encoded with a preceding flag indicating whether a maximum is present.

    +
    +
    +
    + +

    5.3.8. Memory Types

    +

    Memory types are encoded with their limits.

    +
    +
    +
    + +

    5.3.9. Table Types

    +

    Table types are encoded with their limits and the encoding of their element reference type.

    +
    +
    +
    + +

    5.3.10. Global Types

    +

    Global types are encoded by their value type and a flag for their mutability.

    +
    +
    +
    + +
    + +

    5.4. Instructions

    +

    Instructions are encoded by opcodes. +Each opcode is represented by a single byte, +and is followed by the instruction’s immediate arguments, where present. +The only exception are structured control instructions, which consist of several opcodes bracketing their nested instruction sequences.

    +
    +

    Note

    +

    Gaps in the byte code ranges for encoding instructions are reserved for future extensions.

    +
    +
    + +

    5.4.1. Control Instructions

    +

    Control instructions have varying encodings. For structured instructions, the instruction sequences forming nested blocks are terminated with explicit opcodes for and .

    +

    Block types are encoded in special compressed form, by either the byte indicating the empty type, as a single value type, or as a type index encoded as a positive signed integer.

    +
    +
    +

    Note

    +

    The opcode in the encoding of an instruction can be omitted if the following instruction sequence is empty.

    +

    Unlike any other occurrence, the type index in a block type is encoded as a positive signed integer, so that its signed LEB128 bit pattern cannot collide with the encoding of value types or the special code , which correspond to the LEB128 encoding of negative integers. +To avoid any loss in the range of allowed indices, it is treated as a 33 bit signed integer.

    +
    +
    +
    + +

    5.4.2. Reference Instructions

    +

    Reference instructions are represented by single byte codes.

    +
    +
    +
    + +

    5.4.3. Parametric Instructions

    +

    Parametric instructions are represented by single byte codes, possibly followed by a type annotation.

    +
    +
    +
    + +

    5.4.4. Variable Instructions

    +

    Variable instructions are represented by byte codes followed by the encoding of the respective index.

    +
    +
    +
    + +

    5.4.5. Table Instructions

    +

    Table instructions are represented either by a single byte or a one byte prefix followed by a variable-length unsigned integer.

    +
    +
    +
    + +

    5.4.6. Memory Instructions

    +

    Each variant of memory instruction is encoded with a different byte code. Loads and stores are followed by the encoding of their immediate.

    +
    +
    +

    Note

    +

    In future versions of WebAssembly, the additional zero bytes occurring in the encoding of the , , , and instructions may be used to index additional memories.

    +
    +
    +
    + +

    5.4.7. Numeric Instructions

    +

    All variants of numeric instructions are represented by separate byte codes.

    +

    The instructions are followed by the respective literal.

    +
    +

    All other numeric instructions are plain opcodes without any immediates.

    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +

    The saturating truncation instructions all have a one byte prefix, +whereas the actual opcode is encoded by a variable-length unsigned integer.

    +
    +
    +
    + +

    5.4.8. Vector Instructions

    +

    All variants of vector instructions are represented by separate byte codes. +They all have a one byte prefix, whereas the actual opcode is encoded by a variable-length unsigned integer.

    +

    Vector loads and stores are followed by the encoding of their immediate.

    +
    +

    The instruction is followed by 16 immediate bytes, which are converted into a in byte order:

    +
    +

    The instruction is also followed by the encoding of 16 immediates.

    +
    +

    and instructions are followed by the encoding of a immediate.

    +
    +

    All other vector instructions are plain opcodes without any immediates.

    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    + +

    5.4.9. Expressions

    +

    Expressions are encoded by their instruction sequence terminated with an explicit opcode for .

    +
    +
    +
    + +
    +

    5.5. Modules

    +

    The binary encoding of modules is organized into sections. +Most sections correspond to one component of a module record, +except that function definitions are split into two sections, separating their type declarations in the function section from their bodies in the code section.

    +
    +

    Note

    +

    This separation enables parallel and streaming compilation of the functions in a module.

    +
    +
    + +

    5.5.1. Indices

    +

    All indices are encoded with their respective value.

    +
    +
    +
    + +

    5.5.2. Sections

    +

    Each section consists of

    +
      +
    • +

      a one-byte section id,

      +
    • +

      the size of the contents, in bytes,

      +
    • +

      the actual contents, whose structure is depended on the section id.

      +
    +

    Every section is optional; an omitted section is equivalent to the section being present with empty contents.

    +

    The following parameterized grammar rule defines the generic structure of a section with id and contents described by the grammar .

    +
    +

    For most sections, the contents encodes a vector. +In these cases, the empty result is interpreted as the empty vector.

    +
    +

    Note

    +

    Other than for unknown custom sections, +the is not required for decoding, but can be used to skip sections when navigating through a binary. +The module is malformed if the size does not match the length of the binary contents .

    +
    +

    The following section ids are used:

    + + + + + + + + + + + + + + + + + + + + +
    +

    Id

    +     		+

    Section

    +
    +

    0

    +     		+

    custom section

    +
    +

    1

    +     		+

    type section

    +
    +

    2

    +     		+

    import section

    +
    +

    3

    +     		+

    function section

    +
    +

    4

    +     		+

    table section

    +
    +

    5

    +     		+

    memory section

    +
    +

    6

    +     		+

    global section

    +
    +

    7

    +     		+

    export section

    +
    +

    8

    +     		+

    start section

    +
    +

    9

    +     		+

    element section

    +
    +

    10

    +     		+

    code section

    +
    +

    11

    +     		+

    data section

    +
    +

    12

    +     		+

    data count section

    +
    +
    +
    + +

    5.5.3. Custom Section

    +

    Custom sections have the id 0. +They are intended to be used for debugging information or third-party extensions, and are ignored by the WebAssembly semantics. +Their contents consist of a name further identifying the custom section, followed by an uninterpreted sequence of bytes for custom use.

    +
    +
    +

    Note

    +

    If an implementation interprets the data of a custom section, then errors in that data, or the placement of the section, must not invalidate the module.

    +
    +
    +
    + +

    5.5.4. Type Section

    +

    The type section has the id 1. +It decodes into a vector of function types that represent the component of a module.

    +
    +
    +
    + +

    5.5.5. Import Section

    +

    The import section has the id 2. +It decodes into a vector of imports that represent the component of a module.

    +
    +
    +
    + +

    5.5.6. Function Section

    +

    The function section has the id 3. +It decodes into a vector of type indices that represent the fields of the functions in the component of a module. +The and fields of the respective functions are encoded separately in the code section.

    +
    +
    +
    + +

    5.5.7. Table Section

    +

    The table section has the id 4. +It decodes into a vector of tables that represent the component of a module.

    +
    +
    +
    + +

    5.5.8. Memory Section

    +

    The memory section has the id 5. +It decodes into a vector of memories that represent the component of a module.

    +
    +
    +
    + +

    5.5.9. Global Section

    +

    The global section has the id 6. +It decodes into a vector of globals that represent the component of a module.

    +
    +
    +
    + +

    5.5.10. Export Section

    +

    The export section has the id 7. +It decodes into a vector of exports that represent the component of a module.

    +
    +
    +
    + +

    5.5.11. Start Section

    +

    The start section has the id 8. +It decodes into an optional start function that represents the component of a module.

    +
    +
    +
    + +

    5.5.12. Element Section

    +

    The element section has the id 9. +It decodes into a vector of element segments that represent the component of a module.

    +
    +
    +

    Note

    +

    The initial byte can be interpreted as a bitfield. +Bit 0 indicates a passive or declarative segment, +bit 1 indicates the presence of an explicit table index for an active segment and otherwise distinguishes passive from declarative segments, +bit 2 indicates the use of element type and element expressions instead of element kind and element indices.

    +

    Additional element kinds may be added in future versions of WebAssembly.

    +
    +
    +
    + +

    5.5.13. Code Section

    +

    The code section has the id 10. +It decodes into a vector of code entries that are pairs of value type vectors and expressions. +They represent the and field of the functions in the component of a module. +The fields of the respective functions are encoded separately in the function section.

    +

    The encoding of each code entry consists of

    +
      +
    • +

      the size of the function code in bytes,

      +
    • +

      the actual function code, which in turn consists of

      +
        +
      • +

        the declaration of locals,

        +
      • +

        the function body as an expression.

        +
      +
    +

    Local declarations are compressed into a vector whose entries consist of

    + +

    denoting count locals of the same value type.

    +
    +

    Here, ranges over pairs . +The meta function concatenates all sequences in . +Any code for which the length of the resulting sequence is out of bounds of the maximum size of a vector is malformed.

    +
    +

    Note

    +

    Like with sections, the code is not needed for decoding, but can be used to skip functions when navigating through a binary. +The module is malformed if a size does not match the length of the respective function code.

    +
    +
    +
    + +

    5.5.14. Data Section

    +

    The data section has the id 11. +It decodes into a vector of data segments that represent the component of a module.

    +
    +
    +

    Note

    +

    The initial byte can be interpreted as a bitfield. +Bit 0 indicates a passive segment, +bit 1 indicates the presence of an explicit memory index for an active segment.

    +

    In the current version of WebAssembly, at most one memory may be defined or +imported in a single module, so all valid active data +segments have a value of .

    +
    +
    +
    + +

    5.5.15. Data Count Section

    +

    The data count section has the id 12. +It decodes into an optional u32 that represents the number of data segments in the data section. If this count does not match the length of the data segment vector, the module is malformed.

    +
    +
    +

    Note

    +

    The data count section is used to simplify single-pass validation. Since the +data section occurs after the code section, the and instructions would not be able to check whether the data +segment index is valid until the data section is read. The data count section +occurs before the code section, so a single-pass validator can use this count +instead of deferring validation.

    +
    +
    +
    + +

    5.5.16. Modules

    +

    The encoding of a module starts with a preamble containing a 4-byte magic number (the string ) and a version field. +The current version of the WebAssembly binary format is 1.

    +

    The preamble is followed by a sequence of sections. Custom sections may be inserted at any place in this sequence, +while other sections must occur at most once and in the prescribed order. +All sections can be empty.

    +

    The lengths of vectors produced by the (possibly empty) function and code section must match up.

    +

    Similarly, the optional data count must match the length of the data segment vector. +Furthermore, it must be present if any occurs in the code section.

    +
    +

    where for each in ,

    +
    +
    +

    Note

    +

    The version of the WebAssembly binary format may increase in the future +if backward-incompatible changes have to be made to the format. +However, such changes are expected to occur very infrequently, if ever. +The binary format is intended to be forward-compatible, +such that future extensions can be made without incrementing its version.

    +
    +
    +
    +
    +
    + +
    + +

    6. Text Format

    +
    + +
    + +

    6.1. Conventions

    +

    The textual format for WebAssembly modules is a rendering of their abstract syntax into S-expressions.

    +

    Like the binary format, the text format is defined by an attribute grammar. +A text string is a well-formed description of a module if and only if it is generated by the grammar. +Each production of this grammar has at most one synthesized attribute: the abstract syntax that the respective character sequence expresses. +Thus, the attribute grammar implicitly defines a parsing function. +Some productions also take a context as an inherited attribute +that records bound identifiers.

    +

    Except for a few exceptions, the core of the text grammar closely mirrors the grammar of the abstract syntax. +However, it also defines a number of abbreviations that are “syntactic sugar” over the core syntax.

    +

    The recommended extension for files containing WebAssembly modules in text format is “”. +Files with this extension are assumed to be encoded in UTF-8, as per [UNICODE] (Section 2.5).

    +
    + +

    6.1.1. Grammar

    +

    The following conventions are adopted in defining grammar rules of the text format. +They mirror the conventions used for abstract syntax and for the binary format. +In order to distinguish symbols of the textual syntax from symbols of the abstract syntax, font is adopted for the former.

    +
      +
    • +

      Terminal symbols are either literal strings of characters enclosed in quotes +or expressed as [UNICODE] scalar values: , . +(All characters written literally are unambiguously drawn from the 7-bit ASCII subset of Unicode.)

      +
    • +

      Nonterminal symbols are written in typewriter font: .

      +
    • +

      is a sequence of iterations of .

      +
    • +

      is a possibly empty sequence of iterations of . +(This is a shorthand for used where is not relevant.)

      +
    • +

      is a sequence of one or more iterations of . +(This is a shorthand for where .)

      +
    • +

      is an optional occurrence of . +(This is a shorthand for where .)

      +
    • +

      denotes the same language as the nonterminal , but also binds the variable to the attribute synthesized for .

      +
    • +

      Productions are written , where each is the attribute that is synthesized for in the given case, usually from attribute variables bound in .

      +
    • +

      Some productions are augmented by side conditions in parentheses, which restrict the applicability of the production. They provide a shorthand for a combinatorial expansion of the production into many separate cases.

      +
    • +

      If the same meta variable or non-terminal symbol appears multiple times in a production (in the syntax or in an attribute), then all those occurrences must have the same instantiation.

      +
    +
      +
    • +

      A distinction is made between lexical and syntactic productions. For the latter, arbitrary white space is allowed in any place where the grammar contains spaces. The productions defining lexical syntax and the syntax of values are considered lexical, all others are syntactic.

      +
    +
    +

    Note

    +

    For example, the textual grammar for number types is given as follows:

    +
    +

    The textual grammar for limits is defined as follows:

    +
    +

    The variables and name the attributes of the respective nonterminals, which in this case are the actual unsigned integers those parse into. +The attribute of the complete production then is the abstract syntax for the limit, expressed in terms of the former values.

    +
    +
    +
    + +

    6.1.2. Abbreviations

    +

    In addition to the core grammar, which corresponds directly to the abstract syntax, the textual syntax also defines a number of abbreviations that can be used for convenience and readability.

    +

    Abbreviations are defined by rewrite rules specifying their expansion into the core syntax:

    +
    +

    These expansions are assumed to be applied, recursively and in order of appearance, before applying the core grammar rules to construct the abstract syntax.

    +
    +
    + +

    6.1.3. Contexts

    +

    The text format allows the use of symbolic identifiers in place of indices. +To resolve these identifiers into concrete indices, +some grammar production are indexed by an identifier context as a synthesized attribute that records the declared identifiers in each index space. +In addition, the context records the types defined in the module, so that parameter indices can be computed for functions.

    +

    It is convenient to define identifier contexts as records with abstract syntax as follows:

    +
    +

    For each index space, such a context contains the list of identifiers assigned to the defined indices. +Unnamed indices are associated with empty () entries in these lists.

    +

    An identifier context is well-formed if no index space contains duplicate identifiers.

    +
    +
    6.1.3.1. Conventions
    +

    To avoid unnecessary clutter, empty components are omitted when writing out identifier contexts. +For example, the record is shorthand for an identifier context whose components are all empty.

    +
    +
    +
    + +

    6.1.4. Vectors

    +

    Vectors are written as plain sequences, but with a restriction on the length of these sequence.

    +
    +
    +
    + +
    + +

    6.2. Lexical Format

    +
    + +

    6.2.1. Characters

    +

    The text format assigns meaning to source text, which consists of a sequence of characters. +Characters are assumed to be represented as valid [UNICODE] (Section 2.4) scalar values.

    +
    +
    +

    Note

    +

    While source text may contain any Unicode character in comments or string literals, +the rest of the grammar is formed exclusively from the characters supported by the 7-bit ASCII subset of Unicode.

    +
    +
    +
    + +

    6.2.2. Tokens

    +

    The character stream in the source text is divided, from left to right, into a sequence of tokens, as defined by the following grammar.

    +
    +

    Tokens are formed from the input character stream according to the longest match rule. +That is, the next token always consists of the longest possible sequence of characters that is recognized by the above lexical grammar. +Tokens can be separated by white space, +but except for strings, they cannot themselves contain whitespace.

    +

    The set of keyword tokens is defined implicitly, by all occurrences of a terminal symbol in literal form, such as , in a syntactic production of this chapter.

    +

    Any token that does not fall into any of the other categories is considered reserved, and cannot occur in source text.

    +
    +

    Note

    +

    The effect of defining the set of reserved tokens is that all tokens must be separated by either parentheses or white space. +For example, is a single reserved token. +Consequently, it is not recognized as two separate tokens and , but instead disallowed. +This property of tokenization is not affected by the fact that the definition of reserved tokens overlaps with other token classes.

    +
    +
    +
    + +

    6.2.3. White Space

    +

    White space is any sequence of literal space characters, formatting characters, or comments. +The allowed formatting characters correspond to a subset of the ASCII format effectors, namely, horizontal tabulation (), line feed (), and carriage return ().

    +
    +

    The only relevance of white space is to separate tokens. It is otherwise ignored.

    +
    +
    + +

    6.2.4. Comments

    +

    A comment can either be a line comment, started with a double semicolon and extending to the end of the line, +or a block comment, enclosed in delimiters . +Block comments can be nested.

    +
    +

    Here, the pseudo token indicates the end of the input. +The look-ahead restrictions on the productions for disambiguate the grammar such that only well-bracketed uses of block comment delimiters are allowed.

    +
    +

    Note

    +

    Any formatting and control characters are allowed inside comments.

    +
    +
    +
    + +
    + +

    6.3. Values

    +

    The grammar productions in this section define lexical syntax, +hence no white space is allowed.

    +
    + +

    6.3.1. Integers

    +

    All integers can be written in either decimal or hexadecimal notation. +In both cases, digits can optionally be separated by underscores.

    +
    +

    The allowed syntax for integer literals depends on size and signedness. +Moreover, their value must lie within the range of the respective type.

    +
    +

    Uninterpreted integers can be written as either signed or unsigned, and are normalized to unsigned in the abstract syntax.

    +
    +
    +
    + +

    6.3.2. Floating-Point

    +

    Floating-point values can be represented in either decimal or hexadecimal notation.

    +
    +

    The value of a literal must not lie outside the representable range of the corresponding [IEEE-754-2019] type +(that is, a numeric value must not overflow to ), +but it may be rounded to the nearest representable value.

    +
    +

    Note

    +

    Rounding can be prevented by using hexadecimal notation with no more significant bits than supported by the required type.

    +
    +

    Floating-point values may also be written as constants for infinity or canonical NaN (not a number). +Furthermore, arbitrary NaN values may be expressed by providing an explicit payload value.

    +
    +
    +
    + +

    6.3.3. Strings

    +

    Strings denote sequences of bytes that can represent both textual and binary data. +They are enclosed in quotation marks +and may contain any character other than ASCII control characters, quotation marks (), or backslash (), +except when expressed with an escape sequence.

    +
    +

    Each character in a string literal represents the byte sequence corresponding to its UTF-8 [UNICODE] (Section 2.5) encoding, +except for hexadecimal escape sequences , which represent raw bytes of the respective value.

    +
    +
    +
    + +

    6.3.4. Names

    +

    Names are strings denoting a literal character sequence. +A name string must form a valid UTF-8 encoding as defined by [UNICODE] (Section 2.5) and is interpreted as a string of Unicode scalar values.

    +
    +
    +

    Note

    +

    Presuming the source text is itself encoded correctly, +strings that do not contain any uses of hexadecimal byte escapes are always valid names.

    +
    +
    +
    + +

    6.3.5. Identifiers

    +

    Indices can be given in both numeric and symbolic form. +Symbolic identifiers that stand in lieu of indices start with , followed by any sequence of printable ASCII characters that does not contain a space, quotation mark, comma, semicolon, or bracket.

    +
    +
    + +
    6.3.5.1. Conventions
    +

    The expansion rules of some abbreviations require insertion of a fresh identifier. +That may be any syntactically valid identifier that does not already occur in the given source text.

    +
    +
    +
    + +
    + +

    6.4. Types

    +
    + +

    6.4.1. Number Types

    +
    +
    +
    + +

    6.4.2. Vector Types

    +
    +
    +
    + +

    6.4.3. Reference Types

    +
    +
    +
    + +

    6.4.4. Value Types

    +
    +
    +
    + +

    6.4.5. Function Types

    +
    +
    +

    Note

    +

    The optional identifier names for parameters in a function type only have documentation purpose. +They cannot be referenced from anywhere.

    +
    +
    +
    6.4.5.1. Abbreviations
    +

    Multiple anonymous parameters or results may be combined into a single declaration:

    +
    +
    +
    +
    + +

    6.4.6. Limits

    +
    +
    +
    + +

    6.4.7. Memory Types

    +
    +
    +
    + +

    6.4.8. Table Types

    +
    +
    +
    + +

    6.4.9. Global Types

    +
    +
    +
    + +
    + +

    6.5. Instructions

    +

    Instructions are syntactically distinguished into plain and structured instructions.

    +
    +

    In addition, as a syntactic abbreviation, instructions can be written as S-expressions in folded form, to group them visually.

    +
    + +

    6.5.1. Labels

    +

    Structured control instructions can be annotated with a symbolic label identifier. +They are the only symbolic identifiers that can be bound locally in an instruction sequence. +The following grammar handles the corresponding update to the identifier context by composing the context with an additional label entry.

    +
    +
    +

    Note

    +

    The new label entry is inserted at the beginning of the label list in the identifier context. +This effectively shifts all existing labels up by one, +mirroring the fact that control instructions are indexed relatively not absolutely.

    +
    +
    +
    + +

    6.5.2. Control Instructions

    +

    Structured control instructions can bind an optional symbolic label identifier. +The same label identifier may optionally be repeated after the corresponding and pseudo instructions, to indicate the matching delimiters.

    +

    Their block type is given as a type use, analogous to the type of functions. +However, the special case of a type use that is syntactically empty or consists of only a single result is not regarded as an abbreviation for an inline function type, but is parsed directly into an optional value type.

    +
    +
    +

    Note

    +

    The side condition stating that the identifier context must only contain unnamed entries in the rule for block types enforces that no identifier can be bound in any declaration for a block type.

    +
    +

    All other control instruction are represented verbatim.

    +
    +
    +

    Note

    +

    The side condition stating that the identifier context must only contain unnamed entries in the rule for enforces that no identifier can be bound in any declaration appearing in the type annotation.

    +
    +
    +
    6.5.2.1. Abbreviations
    +

    The keyword of an instruction can be omitted if the following instruction sequence is empty.

    +
    +

    Also, for backwards compatibility, the table index to can be omitted, defaulting to .

    +
    +
    +
    +
    + +

    6.5.3. Reference Instructions

    +
    +
    +
    + +

    6.5.4. Parametric Instructions

    +
    +
    +
    + +

    6.5.5. Variable Instructions

    +
    +
    +
    + +

    6.5.6. Table Instructions

    +
    +
    +
    6.5.6.1. Abbreviations
    +

    For backwards compatibility, all may be omitted from table instructions, defaulting to .

    +
    +
    +
    +
    + +

    6.5.7. Memory Instructions

    +

    The offset and alignment immediates to memory instructions are optional. +The offset defaults to , the alignment to the storage size of the respective memory access, which is its natural alignment. +Lexically, an or phrase is considered a single keyword token, so no white space is allowed around the .

    +
    +
    +
    + +

    6.5.8. Numeric Instructions

    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    + +

    6.5.9. Vector Instructions

    +

    Vector memory instructions have optional offset and alignment immediates, like the memory instructions.

    +
    +

    Vector constant instructions have a mandatory shape descriptor, which determines how the following values are parsed.

    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    + +

    6.5.10. Folded Instructions

    +

    Instructions can be written as S-expressions by grouping them into folded form. In that notation, an instruction is wrapped in parentheses and optionally includes nested folded instructions to indicate its operands.

    +

    In the case of block instructions, the folded form omits the delimiter. +For instructions, both branches have to be wrapped into nested S-expressions, headed by the keywords and .

    +

    The set of all phrases defined by the following abbreviations recursively forms the auxiliary syntactic class . +Such a folded instruction can appear anywhere a regular instruction can.

    +
    +
    +

    Note

    +

    For example, the instruction sequence

    +
    +

    can be folded into

    +
    +

    Folded instructions are solely syntactic sugar, +no additional syntactic or type-based checking is implied.

    +
    +
    +
    + +

    6.5.11. Expressions

    +

    Expressions are written as instruction sequences. +No explicit keyword is included, since they only occur in bracketed positions.

    +
    +
    +
    + +
    +

    6.6. Modules

    +
    + +

    6.6.1. Indices

    +

    Indices can be given either in raw numeric form or as symbolic identifiers when bound by a respective construct. +Such identifiers are looked up in the suitable space of the identifier context .

    +
    +
    +
    + +

    6.6.2. Types

    +

    Type definitions can bind a symbolic type identifier.

    +
    +
    +
    + +

    6.6.3. Type Uses

    +

    A type use is a reference to a type definition. +It may optionally be augmented by explicit inlined parameter and result declarations. +That allows binding symbolic identifiers to name the local indices of parameters. +If inline declarations are given, then their types must match the referenced function type.

    +
    +

    The synthesized attribute of a is a pair consisting of both the used type index and the updated identifier context including possible parameter identifiers. +The following auxiliary function extracts optional identifiers from parameters:

    +
    +
    +

    Note

    +

    Both productions overlap for the case that the function type is . +However, in that case, they also produce the same results, so that the choice is immaterial.

    +

    The well-formedness condition on ensures that the parameters do not contain duplicate identifier.

    +
    +
    + +
    6.6.3.1. Abbreviations
    +

    A may also be replaced entirely by inline parameter and result declarations. +In that case, a type index is automatically inserted:

    +
    +

    where is the smallest existing type index whose definition in the current module is the function type . +If no such index exists, then a new type definition of the form

    +
    +

    is inserted at the end of the module.

    +

    Abbreviations are expanded in the order they appear, such that previously inserted type definitions are reused by consecutive expansions.

    +
    +
    +
    + +

    6.6.4. Imports

    +

    The descriptors in imports can bind a symbolic function, table, memory, or global identifier.

    +
    +
    +
    6.6.4.1. Abbreviations
    +

    As an abbreviation, imports may also be specified inline with function, table, memory, or global definitions; see the respective sections.

    +
    +
    +
    + +

    6.6.5. Functions

    +

    Function definitions can bind a symbolic function identifier, and local identifiers for its parameters and locals.

    +
    +

    The definition of the local identifier context uses the following auxiliary function to extract optional identifiers from locals:

    +
    +
    +

    Note

    +

    The well-formedness condition on ensures that parameters and locals do not contain duplicate identifiers.

    +
    + +
    + +
    6.6.5.1. Abbreviations
    +

    Multiple anonymous locals may be combined into a single declaration:

    +
    +

    Functions can be defined as imports or exports inline:

    +
    +
    +

    Note

    +

    The latter abbreviation can be applied repeatedly, if “” contains additional export clauses. +Consequently, a function declaration can contain any number of exports, possibly followed by an import.

    +
    +
    +
    +
    + +

    6.6.6. Tables

    +

    Table definitions can bind a symbolic table identifier.

    +
    + +
    + +
    6.6.6.1. Abbreviations
    +

    An element segment can be given inline with a table definition, in which case its offset is and the limits of the table type are inferred from the length of the given segment:

    +
    +
    +

    Tables can be defined as imports or exports inline:

    +
    +
    +

    Note

    +

    The latter abbreviation can be applied repeatedly, if “” contains additional export clauses. +Consequently, a table declaration can contain any number of exports, possibly followed by an import.

    +
    +
    +
    +
    + +

    6.6.7. Memories

    +

    Memory definitions can bind a symbolic memory identifier.

    +
    + +
    + +
    6.6.7.1. Abbreviations
    +

    A data segment can be given inline with a memory definition, in which case its offset is the limits of the memory type are inferred from the length of the data, rounded up to page size:

    +
    +

    Memories can be defined as imports or exports inline:

    +
    +
    +

    Note

    +

    The latter abbreviation can be applied repeatedly, if “” contains additional export clauses. +Consequently, a memory declaration can contain any number of exports, possibly followed by an import.

    +
    +
    +
    +
    + +

    6.6.8. Globals

    +

    Global definitions can bind a symbolic global identifier.

    +
    + +
    + +
    6.6.8.1. Abbreviations
    +

    Globals can be defined as imports or exports inline:

    +
    +
    +

    Note

    +

    The latter abbreviation can be applied repeatedly, if “” contains additional export clauses. +Consequently, a global declaration can contain any number of exports, possibly followed by an import.

    +
    +
    +
    +
    + +

    6.6.9. Exports

    +

    The syntax for exports mirrors their abstract syntax directly.

    +
    +
    +
    6.6.9.1. Abbreviations
    +

    As an abbreviation, exports may also be specified inline with function, table, memory, or global definitions; see the respective sections.

    +
    +
    +
    + +

    6.6.10. Start Function

    +

    A start function is defined in terms of its index.

    +
    +
    +

    Note

    +

    At most one start function may occur in a module, +which is ensured by a suitable side condition on the grammar.

    +
    +
    +
    + +

    6.6.11. Element Segments

    +

    Element segments allow for an optional table index to identify the table to initialize.

    +
    +
    +
    6.6.11.1. Abbreviations
    +

    As an abbreviation, a single instruction may occur in place of the offset of an active element segment or as an element expression:

    +
    +

    Also, the element list may be written as just a sequence of function indices:

    +
    +

    A table use can be omitted, defaulting to . +Furthermore, for backwards compatibility with earlier versions of WebAssembly, if the table use is omitted, the keyword can be omitted as well.

    +
    +

    As another abbreviation, element segments may also be specified inline with table definitions; see the respective section.

    +
    +
    +
    + +

    6.6.12. Data Segments

    +

    Data segments allow for an optional memory index to identify the memory to initialize. +The data is written as a string, which may be split up into a possibly empty sequence of individual string literals.

    +
    +
    +

    Note

    +

    In the current version of WebAssembly, the only valid memory index is 0 +or a symbolic memory identifier resolving to the same value.

    +
    +
    +
    6.6.12.1. Abbreviations
    +

    As an abbreviation, a single instruction may occur in place of the offset of an active data segment:

    +
    +

    Also, a memory use can be omitted, defaulting to .

    +
    +

    As another abbreviation, data segments may also be specified inline with memory definitions; see the respective section.

    +
    +
    +
    + +

    6.6.13. Modules

    +

    A module consists of a sequence of fields that can occur in any order. +All definitions and their respective bound identifiers scope over the entire module, including the text preceding them.

    +

    A module may optionally bind an identifier that names the module. +The name serves a documentary role only.

    +
    +

    Note

    +

    Tools may include the module name in the name section of the binary format.

    +
    +
    +

    The following restrictions are imposed on the composition of modules: is defined if and only if

    + +
    +

    Note

    +

    The first condition ensures that there is at most one start function. +The second condition enforces that all imports must occur before any regular definition of a function, table, memory, or global, +thereby maintaining the ordering of the respective index spaces.

    +

    The well-formedness condition on in the grammar for ensures that no namespace contains duplicate identifiers.

    +
    +

    The definition of the initial identifier context uses the following auxiliary definition which maps each relevant definition to a singular context with one (possibly empty) identifier:

    +
    +
    +
    6.6.13.1. Abbreviations
    +

    In a source file, the toplevel surrounding the module body may be omitted.

    +
    +
    +
    +
    +
    +
    + +
    + +

    A Appendix

    +
    + +
    + +

    A.1 Embedding

    +

    A WebAssembly implementation will typically be embedded into a host environment. +An embedder implements the connection between such a host environment and the WebAssembly semantics as defined in the main body of this specification. +An embedder is expected to interact with the semantics in well-defined ways.

    +

    This section defines a suitable interface to the WebAssembly semantics in the form of entry points through which an embedder can access it. +The interface is intended to be complete, in the sense that an embedder does not need to reference other functional parts of the WebAssembly specification directly.

    +
    +

    Note

    +

    On the other hand, an embedder does not need to provide the host environment with access to all functionality defined in this interface. +For example, an implementation may not support parsing of the text format.

    +
    +
    +

    Types

    +

    In the description of the embedder interface, syntactic classes from the abstract syntax and the runtime’s abstract machine are used as names for variables that range over the possible objects from that class. +Hence, these syntactic classes can also be interpreted as types.

    +

    For numeric parameters, notation like is used to specify a symbolic name in addition to the respective value range.

    +
    +
    + +

    Errors

    +

    Failure of an interface operation is indicated by an auxiliary syntactic class:

    +
    +

    In addition to the error conditions specified explicitly in this section, implementations may also return errors when specific implementation limitations are reached.

    +
    +

    Note

    +

    Errors are abstract and unspecific with this definition. +Implementations can refine it to carry suitable classifications and diagnostic messages.

    +
    +
    +
    +

    Pre- and Post-Conditions

    +

    Some operations state pre-conditions about their arguments or post-conditions about their results. +It is the embedder’s responsibility to meet the pre-conditions. +If it does, the post conditions are guaranteed by the semantics.

    +

    In addition to pre- and post-conditions explicitly stated with each operation, the specification adopts the following conventions for runtime objects (, , , addresses):

    +
      +
    • +

      Every runtime object passed as a parameter must be valid per an implicit pre-condition.

      +
    • +

      Every runtime object returned as a result is valid per an implicit post-condition.

      +
    +
    +

    Note

    +

    As long as an embedder treats runtime objects as abstract and only creates and manipulates them through the interface defined here, all implicit pre-conditions are automatically met.

    +
    +
    +
    + +

    Store

    +
    + +
    +
      +
    1. +

      Return the empty store.

      +
    +
    +
    +
    +
    + +

    Modules

    +
    + +
    +
      +
    1. +

      If there exists a derivation for the byte sequence as a according to the binary grammar for modules, yielding a module , then return .

      +
    2. +

      Else, return .

      +
    +
    +
    +
    + +
    +
      +
    1. +

      If there exists a derivation for the source as a according to the text grammar for modules, yielding a module , then return .

      +
    2. +

      Else, return .

      +
    +
    +
    +
    + +
    +
      +
    1. +

      If is valid, then return nothing.

      +
    2. +

      Else, return .

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Try instantiating in with external values as imports:

      +
    +
    +
    +
      +
    1. +

      If it succeeds with a module instance , then let be .

      +
    2. +

      Else, let be .

      +
    +
    +
    +
      +
    1. +

      Return the new store paired with .

      +
    +
    +
    +

    Note

    +

    The store may be modified even in case of an error.

    +
    +
    +
    + +
    +
      +
    1. +

      Pre-condition: is valid with external import types and external export types .

      +
    2. +

      Let be the imports .

      +
    3. +

      Assert: the length of equals the length of .

      +
    4. +

      For each in and corresponding in , do:

      +
    +
    +
    +
      +
    1. +

      Let be the triple .

      +
    +
    +
    +
      +
    1. +

      Return the concatenation of all , in index order.

      +
    2. +

      Post-condition: each is valid.

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Pre-condition: is valid with external import types and external export types .

      +
    2. +

      Let be the exports .

      +
    3. +

      Assert: the length of equals the length of .

      +
    4. +

      For each in and corresponding in , do:

      +
    +
    +
    +
      +
    1. +

      Let be the pair .

      +
    +
    +
    +
      +
    1. +

      Return the concatenation of all , in index order.

      +
    2. +

      Post-condition: each is valid.

      +
    +
    +
    +
    +
    + +

    Module Instances

    +
    + +
    +
      +
    1. +

      Assert: due to validity of the module instance , all its export names are different.

      +
    2. +

      If there exists an in such that name equals , then:

      +
        +
      1. +

        Return the external value .

        +
      +
    3. +

      Else, return .

      +
    +
    +
    +
    +
    + +

    Functions

    +
    + +
    +
      +
    1. +

      Pre-condition: is .

      +
    2. +

      Let be the result of allocating a host function in with function type and host function code .

      +
    3. +

      Return the new store paired with .

      +
    +
    +
    +

    Note

    +

    This operation assumes that satisfies the pre- and post-conditions required for a function instance with type .

    +

    Regular (non-host) function instances can only be created indirectly through module instantiation.

    +
    +
    +
    + +
    +
      +
    1. +

      Return .

      +
    2. +

      Post-condition: the returned function type is valid.

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Try invoking the function in with values as arguments:

      +
    +
    +
    +
      +
    1. +

      If it succeeds with values as results, then let be .

      +
    2. +

      Else it has trapped, hence let be .

      +
    +
    +
    +
      +
    1. +

      Return the new store paired with .

      +
    +
    +
    +

    Note

    +

    The store may be modified even in case of an error.

    +
    +
    +
    +
    + +

    Tables

    +
    + +
    +
      +
    1. +

      Pre-condition: is .

      +
    2. +

      Let be the result of allocating a table in with table type and initialization value .

      +
    3. +

      Return the new store paired with .

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Return .

      +
    2. +

      Post-condition: the returned table type is .

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Let be the table instance .

      +
    2. +

      If is larger than or equal to the length of , then return .

      +
    3. +

      Else, return the reference value .

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Let be the table instance .

      +
    2. +

      If is larger than or equal to the length of , then return .

      +
    3. +

      Replace with the reference value .

      +
    4. +

      Return the updated store.

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Return the length of .

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Try growing the table instance by elements with initialization value :

      +
        +
      1. +

        If it succeeds, return the updated store.

        +
      2. +

        Else, return .

        +
      +
    +
    +
    +
    +
    + +

    Memories

    +
    + +
    +
      +
    1. +

      Pre-condition: is .

      +
    2. +

      Let be the result of allocating a memory in with memory type .

      +
    3. +

      Return the new store paired with .

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Return .

      +
    2. +

      Post-condition: the returned memory type is .

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Let be the memory instance .

      +
    2. +

      If is larger than or equal to the length of , then return .

      +
    3. +

      Else, return the byte .

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Let be the memory instance .

      +
    2. +

      If is larger than or equal to the length of , then return .

      +
    3. +

      Replace with .

      +
    4. +

      Return the updated store.

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Return the length of divided by the page size.

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Try growing the memory instance by pages:

      +
        +
      1. +

        If it succeeds, return the updated store.

        +
      2. +

        Else, return .

        +
      +
    +
    +
    +
    +
    + +

    Globals

    +
    + +
    +
      +
    1. +

      Pre-condition: is .

      +
    2. +

      Let be the result of allocating a global in with global type and initialization value .

      +
    3. +

      Return the new store paired with .

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Return .

      +
    2. +

      Post-condition: the returned global type is .

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Let be the global instance .

      +
    2. +

      Return the value .

      +
    +
    +
    +
    + +
    +
      +
    1. +

      Let be the global instance .

      +
    2. +

      Let be the structure of the global type .

      +
    3. +

      If is not , then return .

      +
    4. +

      Replace with the value .

      +
    5. +

      Return the updated store.

      +
    +
    +
    +
    +
    + +
    + +

    A.2 Implementation Limitations

    +

    Implementations typically impose additional restrictions on a number of aspects of a WebAssembly module or execution. +These may stem from:

    +
      +
    • +

      physical resource limits,

      +
    • +

      constraints imposed by the embedder or its environment,

      +
    • +

      limitations of selected implementation strategies.

      +
    +

    This section lists allowed limitations. +Where restrictions take the form of numeric limits, no minimum requirements are given, +nor are the limits assumed to be concrete, fixed numbers. +However, it is expected that all implementations have “reasonably” large limits to enable common applications.

    +
    +

    Note

    +

    A conforming implementation is not allowed to leave out individual features. +However, designated subsets of WebAssembly may be specified in the future.

    +
    +
    +

    Syntactic Limits

    +
    + +
    Structure
    +

    An implementation may impose restrictions on the following dimensions of a module:

    + +

    If the limits of an implementation are exceeded for a given module, +then the implementation may reject the validation, compilation, or instantiation of that module with an embedder-specific error.

    +
    +

    Note

    +

    The last item allows embedders that operate in limited environments without support for [UNICODE] to limit the +names of imports and exports to common subsets like ASCII.

    +
    +
    +
    + +
    Binary Format
    +

    For a module given in binary format, additional limitations may be imposed on the following dimensions:

    +
      +
    • +

      the size of a module

      +
    • +

      the size of any section

      +
    • +

      the size of an individual function’s code

      +
    • +

      the number of sections

      +
    +
    +
    + +
    Text Format
    +

    For a module given in text format, additional limitations may be imposed on the following dimensions:

    + +
    +
    +
    + +

    Validation

    +

    An implementation may defer validation of individual functions until they are first invoked.

    +

    If a function turns out to be invalid, then the invocation, and every consecutive call to the same function, results in a trap.

    +
    +

    Note

    +

    This is to allow implementations to use interpretation or just-in-time compilation for functions. +The function must still be fully validated before execution of its body begins.

    +
    +
    +
    + +

    Execution

    +

    Restrictions on the following dimensions may be imposed during execution of a WebAssembly program:

    + +

    If the runtime limits of an implementation are exceeded during execution of a computation, +then it may terminate that computation and report an embedder-specific error to the invoking code.

    +

    Some of the above limits may already be verified during instantiation, in which case an implementation may report exceedance in the same manner as for syntactic limits.

    +
    +

    Note

    +

    Concrete limits are usually not fixed but may be dependent on specifics, interdependent, vary over time, or depend on other implementation- or embedder-specific situations or events.

    +
    +
    +
    + +
    + +

    A.3 Validation Algorithm

    +

    The specification of WebAssembly validation is purely declarative. +It describes the constraints that must be met by a module or instruction sequence to be valid.

    +

    This section sketches the skeleton of a sound and complete algorithm for effectively validating code, i.e., sequences of instructions. +(Other aspects of validation are straightforward to implement.)

    +

    In fact, the algorithm is expressed over the flat sequence of opcodes as occurring in the binary format, and performs only a single pass over it. +Consequently, it can be integrated directly into a decoder.

    +

    The algorithm is expressed in typed pseudo code whose semantics is intended to be self-explanatory.

    +
    + +

    Data Structures

    +

    Types are representable as an enumeration.

    +
    +
    +
    type val_type = I32 | I64 | F32 | F64 | V128 | Funcref | Externref
+
+func is_num(t : val_type | Unknown) : bool =
+  return t = I32 || t = I64 || t = F32 || t = F64 || t = Unknown
+
+func is_vec(t : val_type | Unknown) : bool =
+  return t = V128 || t = Unknown
+
+func is_ref(t : val_type | Unknown) : bool =
+  return t = Funcref || t = Externref || t = Unknown
+
    +
    +
    +

    The algorithm uses two separate stacks: the value stack and the control stack. +The former tracks the types of operand values on the stack, +the latter surrounding structured control instructions and their associated blocks.

    +
    +
    +
    type val_stack = stack(val_type | Unknown)
+
+type ctrl_stack = stack(ctrl_frame)
+type ctrl_frame = {
+  opcode : opcode
+  start_types : list(val_type)
+  end_types : list(val_type)
+  height : nat
+  unreachable : bool
+}
+
    +
    +
    +

    For each value, the value stack records its value type, or Unknown when the type is not known.

    +

    For each entered block, the control stack records a control frame with the originating opcode, the types on the top of the operand stack at the start and end of the block (used to check its result as well as branches), the height of the operand stack at the start of the block (used to check that operands do not underflow the current block), and a flag recording whether the remainder of the block is unreachable (used to handle stack-polymorphic typing after branches).

    +

    For the purpose of presenting the algorithm, the operand and control stacks are simply maintained as global variables:

    +
    +
    +
    var vals : val_stack
+var ctrls : ctrl_stack
+
    +
    +
    +

    However, these variables are not manipulated directly by the main checking function, but through a set of auxiliary functions:

    +
    +
    +
    func push_val(type : val_type | Unknown) =
+  vals.push(type)
+
+func pop_val() : val_type | Unknown =
+  if (vals.size() = ctrls[0].height && ctrls[0].unreachable) return Unknown
+  error_if(vals.size() = ctrls[0].height)
+  return vals.pop()
+
+func pop_val(expect : val_type | Unknown) : val_type | Unknown =
+  let actual = pop_val()
+  error_if(actual =/= expect && actual =/= Unknown && expect =/= Unknown)
+  return actual
+
+func push_vals(types : list(val_type)) = foreach (t in types) push_val(t)
+func pop_vals(types : list(val_type)) : list(val_type) =
+  var popped := []
+  foreach (t in reverse(types)) popped.prepend(pop_val(t))
+  return popped
+
    +
    +
    +

    Pushing an operand value simply pushes the respective type to the value stack.

    +

    Popping an operand value checks that the value stack does not underflow the current block and then removes one type. +But first, a special case is handled where the block contains no known values, but has been marked as unreachable. +That can occur after an unconditional branch, when the stack is typed polymorphically. +In that case, an unknown type is returned.

    +

    A second function for popping an operand value takes an expected type, which the actual operand type is checked against. +The types may differ in case one of them is Unknown. +The function returns the actual type popped from the stack.

    +

    Finally, there are accumulative functions for pushing or popping multiple operand types.

    +
    +

    Note

    +

    The notation stack[i] is meant to index the stack from the top, +so that, e.g., ctrls[0] accesses the element pushed last.

    +
    +

    The control stack is likewise manipulated through auxiliary functions:

    +
    +
    +
    func push_ctrl(opcode : opcode, in : list(val_type), out : list(val_type)) =
+  let frame = ctrl_frame(opcode, in, out, vals.size(), false)
+  ctrls.push(frame)
+  push_vals(in)
+
+func pop_ctrl() : ctrl_frame =
+  error_if(ctrls.is_empty())
+  let frame = ctrls[0]
+  pop_vals(frame.end_types)
+  error_if(vals.size() =/= frame.height)
+  ctrls.pop()
+  return frame
+
+func label_types(frame : ctrl_frame) : list(val_types) =
+  return (if frame.opcode == loop then frame.start_types else frame.end_types)
+
+func unreachable() =
+  vals.resize(ctrls[0].height)
+  ctrls[0].unreachable := true
+
    +
    +
    +

    Pushing a control frame takes the types of the label and result values. +It allocates a new frame record recording them along with the current height of the operand stack and marks the block as reachable.

    +

    Popping a frame first checks that the control stack is not empty. +It then verifies that the operand stack contains the right types of values expected at the end of the exited block and pops them off the operand stack. +Afterwards, it checks that the stack has shrunk back to its initial height.

    +

    The type of the label associated with a control frame is either that of the stack at the start or the end of the frame, determined by the opcode that it originates from.

    +

    Finally, the current frame can be marked as unreachable. +In that case, all existing operand types are purged from the value stack, in order to allow for the stack-polymorphism logic in pop_val to take effect.

    +
    +

    Note

    +

    Even with the unreachable flag set, consecutive operands are still pushed to and popped from the operand stack. +That is necessary to detect invalid examples like . +However, a polymorphic stack cannot underflow, but instead generates Unknown types as needed.

    +
    +
    +
    + +

    Validation of Opcode Sequences

    +

    The following function shows the validation of a number of representative instructions that manipulate the stack. +Other instructions are checked in a similar manner.

    +
    +

    Note

    +

    Various instructions not shown here will additionally require the presence of a validation context for checking uses of indices. +That is an easy addition and therefore omitted from this presentation.

    +
    +
    +
    +
    func validate(opcode) =
+  switch (opcode)
+    case (i32.add)
+      pop_val(I32)
+      pop_val(I32)
+      push_val(I32)
+
+   case (drop)
+      pop_val()
+
+   case (select)
+      pop_val(I32)
+      let t1 = pop_val()
+      let t2 = pop_val()
+      error_if(not ((is_num(t1) && is_num(t2)) || (is_vec(t1) && is_vec(t2))))
+      error_if(t1 =/= t2 && t1 =/= Unknown && t2 =/= Unknown)
+      push_val(if (t1 = Unknown) t2 else t1)
+
+   case (select t)
+      pop_val(I32)
+      pop_val(t)
+      pop_val(t)
+      push_val(t)
+
+   case (unreachable)
+      unreachable()
+
+   case (block t1*->t2*)
+      pop_vals([t1*])
+      push_ctrl(block, [t1*], [t2*])
+
+   case (loop t1*->t2*)
+      pop_vals([t1*])
+      push_ctrl(loop, [t1*], [t2*])
+
+   case (if t1*->t2*)
+      pop_val(I32)
+      pop_vals([t1*])
+      push_ctrl(if, [t1*], [t2*])
+
+   case (end)
+      let frame = pop_ctrl()
+      push_vals(frame.end_types)
+
+   case (else)
+      let frame = pop_ctrl()
+      error_if(frame.opcode =/= if)
+      push_ctrl(else, frame.start_types, frame.end_types)
+
+   case (br n)
+      error_if(ctrls.size() < n)
+      pop_vals(label_types(ctrls[n]))
+      unreachable()
+
+   case (br_if n)
+      error_if(ctrls.size() < n)
+      pop_val(I32)
+      pop_vals(label_types(ctrls[n]))
+      push_vals(label_types(ctrls[n]))
+
+   case (br_table n* m)
+      pop_val(I32)
+      error_if(ctrls.size() < m)
+      let arity = label_types(ctrls[m]).size()
+      foreach (n in n*)
+        error_if(ctrls.size() < n)
+        error_if(label_types(ctrls[n]).size() =/= arity)
+        push_vals(pop_vals(label_types(ctrls[n])))
+      pop_vals(label_types(ctrls[m]))
+      unreachable()
+
    +
    +
    +
    +

    Note

    +

    It is an invariant under the current WebAssembly instruction set that an operand of Unknown type is never duplicated on the stack. +This would change if the language were extended with stack instructions like dup. +Under such an extension, the above algorithm would need to be refined by replacing the Unknown type with proper type variables to ensure that all uses are consistent.

    +
    +
    +
    + +
    + +

    A.4 Custom Sections

    +

    This appendix defines dedicated custom sections for WebAssembly’s binary format. +Such sections do not contribute to, or otherwise affect, the WebAssembly semantics, and like any custom section they may be ignored by an implementation. +However, they provide useful meta data that implementations can make use of to improve user experience or take compilation hints.

    +

    Currently, only one dedicated custom section is defined, the name section.

    +
    + +

    Name Section

    +

    The name section is a custom section whose name string is itself . +The name section should appear only once in a module, and only after the data section.

    +

    The purpose of this section is to attach printable names to definitions in a module, which e.g. can be used by a debugger or when parts of the module are to be rendered in text form.

    +
    +

    Note

    +

    All names are represented in [UNICODE] encoded in UTF-8. +Names need not be unique.

    +
    +
    + +
    Subsections
    +

    The data of a name section consists of a sequence of subsections. +Each subsection consists of a

    +
      +
    • +

      a one-byte subsection id,

      +
    • +

      the size of the contents, in bytes,

      +
    • +

      the actual contents, whose structure is dependent on the subsection id.

      +
    +
    +

    The following subsection ids are used:

    + + + + + + + + + + +
    +

    Id

    +     		+

    Subsection

    +
    +

    0

    +     		+

    module name

    +
    +

    1

    +     		+

    function names

    +
    +

    2

    +     		+

    local names

    +
    +

    Each subsection may occur at most once, and in order of increasing id.

    +
    +
    + +
    Name Maps
    +

    A name map assigns names to indices in a given index space. +It consists of a vector of index/name pairs in order of increasing index value. +Each index must be unique, but the assigned names need not be.

    +
    +

    An indirect name map assigns names to a two-dimensional index space, where secondary indices are grouped by primary indices. +It consists of a vector of primary index/name map pairs in order of increasing index value, where each name map in turn maps secondary indices to names. +Each primary index must be unique, and likewise each secondary index per individual name map.

    +
    +
    +
    + +
    Module Names
    +

    The module name subsection has the id 0. +It simply consists of a single name that is assigned to the module itself.

    +
    +
    +
    + +
    Function Names
    +

    The function name subsection has the id 1. +It consists of a name map assigning function names to function indices.

    +
    +
    +
    + +
    Local Names
    +

    The local name subsection has the id 2. +It consists of an indirect name map assigning local names to local indices grouped by function indices.

    +
    +
    +
    +
    + +
    + +

    A.5 Soundness

    +

    The type system of WebAssembly is sound, implying both type safety and memory safety with respect to the WebAssembly semantics. For example:

    +
      +
    • +

      All types declared and derived during validation are respected at run time; +e.g., every local or global variable will only contain type-correct values, every instruction will only be applied to operands of the expected type, and every function invocation always evaluates to a result of the right type (if it does not trap or diverge).

      +
    • +

      No memory location will be read or written except those explicitly defined by the program, i.e., as a local, a global, an element in a table, or a location within a linear memory.

      +
    • +

      There is no undefined behavior, +i.e., the execution rules cover all possible cases that can occur in a valid program, and the rules are mutually consistent.

      +
    +

    Soundness also is instrumental in ensuring additional properties, most notably, encapsulation of function and module scopes: no locals can be accessed outside their own function and no module components can be accessed outside their own module unless they are explicitly exported or imported.

    +

    The typing rules defining WebAssembly validation only cover the static components of a WebAssembly program. +In order to state and prove soundness precisely, the typing rules must be extended to the dynamic components of the abstract runtime, that is, the store, configurations, and administrative instructions. 1

    +
    + +

    Results

    +

    Results can be classified by result types as follows.

    +
    +
    Results
    +
      +
    • +

      For each value in :

      + +
    • +

      Let be the concatenation of all .

      +
    • +

      Then the result is valid with result type .

      +
    +
    +
    +
    +
    Results
    + +
    +
    +
    +
    + +

    Store Validity

    +

    The following typing rules specify when a runtime store is valid. +A valid store must consist of function, table, memory, global, and module instances that are themselves valid, relative to .

    +

    To that end, each kind of instance is classified by a respective function, table, memory, or global type. +Module instances are classified by module contexts, which are regular contexts repurposed as module types describing the index spaces defined by a module.

    +
    + +
    Store
    + +
    +
    +
    + +
    Function Instances
    + +
    +
    +
    + +
    Host Function Instances
    + +
    +
    +

    Note

    +

    This rule states that, if appropriate pre-conditions about store and arguments are satisfied, then executing the host function must satisfy appropriate post-conditions about store and results. +The post-conditions match the ones in the execution rule for invoking host functions.

    +

    Any store under which the function is invoked is assumed to be an extension of the current store. +That way, the function itself is able to make sufficient assumptions about future stores.

    +
    +
    +
    + +
    Table Instances
    + +
    +
    +
    + +
    Memory Instances
    + +
    +
    +
    + +
    Global Instances
    + +
    +
    +
    + +
    Element Instances
    + +
    +
    +
    + +
    Data Instances
    +
      +
    • +

      The data instance is valid.

      +
    +
    +
    +
    + +
    Export Instances
    + +
    +
    +
    + +
    Module Instances
    + +
    +
    +
    +
    + +

    Configuration Validity

    +

    To relate the WebAssembly type system to its execution semantics, the typing rules for instructions must be extended to configurations , +which relates the store to execution threads.

    +

    Configurations and threads are classified by their result type. +In addition to the store , threads are typed under a return type , which controls whether and with which type a instruction is allowed. +This type is absent () except for instruction sequences inside an administrative instruction.

    +

    Finally, frames are classified with frame contexts, which extend the module contexts of a frame’s associated module instance with the locals that the frame contains.

    +
    + +
    Configurations
    + +
    +
    +
    + +
    Threads
    + +
    +
    +
    + +
    Frames
    + +
    +
    +
    +
    + +

    Administrative Instructions

    +

    Typing rules for administrative instructions are specified as follows. +In addition to the context , typing of these instructions is defined under a given store . +To that end, all previous typing judgements are generalized to include the store, as in , by implicitly adding to all rules – is never modified by the pre-existing rules, but it is accessed in the extra rules for administrative instructions given below.

    +
    + +
    +
      +
    • +

      The instruction is valid with type , for any sequences of value types and .

      +
    +
    +
    +
    + +
    +
      +
    • +

      The instruction is valid with type .

      +
    +
    +
    +
    + +
    + +
    +
    +
    + +
    + +
    +
    +
    + +
    +
      +
    • +

      The instruction sequence must be valid with some type .

      +
    • +

      Let be the same context as , but with the result type prepended to the vector.

      +
    • +

      Under context , +the instruction sequence must be valid with type .

      +
    • +

      Then the compound instruction is valid with type .

      +
    +
    +
    +
    + +
    +
      +
    • +

      Under the return type , +the thread must be valid with result type .

      +
    • +

      Then the compound instruction is valid with type .

      +
    +
    +
    +
    +
    + +

    Store Extension

    +

    Programs can mutate the store and its contained instances. +Any such modification must respect certain invariants, such as not removing allocated instances or changing immutable definitions. +While these invariants are inherent to the execution semantics of WebAssembly instructions and modules, host functions do not automatically adhere to them. Consequently, the required invariants must be stated as explicit constraints on the invocation of host functions. +Soundness only holds when the embedder ensures these constraints.

    +

    The necessary constraints are codified by the notion of store extension: +a store state extends state , written , when the following rules hold.

    +
    +

    Note

    +

    Extension does not imply that the new store is valid, which is defined separately above.

    +
    +
    + +
    Store
    + +
    +
    +
    + +
    Function Instance
    +
      +
    • +

      A function instance must remain unchanged.

      +
    +
    +
    +
    + +
    Table Instance
    + +
    +
    +
    + +
    Memory Instance
    + +
    +
    +
    + +
    Global Instance
    + +
    +
    +
    + +
    Element Instance
    +
      +
    • +

      The vector must either remain unchanged or shrink to length .

      +
    +
    +
    +
    + +
    Data Instance
    +
      +
    • +

      The vector must either remain unchanged or shrink to length .

      +
    +
    +
    +
    +
    + +

    Theorems

    +

    Given the definition of valid configurations, +the standard soundness theorems hold. 2

    +

    Theorem (Preservation). If a configuration is valid with result type (i.e., ), +and steps to (i.e., ), +then is a valid configuration with the same result type (i.e., ). +Furthermore, is an extension of (i.e., ).

    +

    A terminal thread is one whose sequence of instructions is a result. +A terminal configuration is a configuration whose thread is terminal.

    +

    Theorem (Progress). If a configuration is valid (i.e., for some result type ), +then either it is terminal, +or it can step to some configuration (i.e., ).

    +

    From Preservation and Progress the soundness of the WebAssembly type system follows directly.

    +

    Corollary (Soundness). If a configuration is valid (i.e., for some result type ), +then it either diverges or takes a finite number of steps to reach a terminal configuration (i.e., ) that is valid with the same result type (i.e., ) +and where is an extension of (i.e., ).

    +

    In other words, every thread in a valid configuration either runs forever, traps, or terminates with a result that has the expected type. +Consequently, given a valid store, no computation defined by instantiation or invocation of a valid module can “crash” or otherwise (mis)behave in ways not covered by the execution semantics given in this specification.

    +
    +
    1 +
    +

    The formalization and theorems are derived from the following article: +Andreas Haas, Andreas Rossberg, Derek Schuff, Ben Titzer, Dan Gohman, Luke Wagner, Alon Zakai, JF Bastien, Michael Holman. Bringing the Web up to Speed with WebAssembly. Proceedings of the 38th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2017). ACM 2017.

    +
    2 +
    +

    A machine-verified version of the formalization and soundness proof is described in the following article: +Conrad Watt. Mechanising and Verifying the WebAssembly Specification. Proceedings of the 7th ACM SIGPLAN Conference on Certified Programs and Proofs (CPP 2018). ACM 2018.

    +
    +
    +
    + +
    + +

    Change History

    +

    Since the original release 1.0 of the WebAssembly specification, a number of proposals for extensions have been integrated. +The following sections provide an overview of what has changed.

    +
    +

    Release 2.0

    +
    + +
    Sign extension instructions
    +

    Added new numeric instructions for performing sign extension within integer representations 1.

    + +
    +
    + +
    Non-trapping float-to-int conversions
    +

    Added new conversion instructions that avoid trapping when converting a floating-point number to an integer 2.

    + +
    +
    + +
    Multiple values
    +

    Generalized the result type of blocks and functions to allow for multiple values; in addition, introduced the ability to have block parameters 3.

    + +
    +
    + +
    Reference types
    +

    Added and as new value types and respective instructions 4.

    + +
    +
    + +
    Table instructions
    +

    Added instructions to directly access and modify tables 4.

    + +
    +
    + +
    Multiple tables
    +

    Added the ability to use multiple tables per module 4.

    + +
    +
    + +
    Bulk memory and table instructions
    +

    Added instructions that modify ranges of memory or table entries 4 5

    + +
    +
    + +
    Vector instructions
    +

    Added vector type and instructions that manipulate multiple numeric values in parallel (also known as SIMD, single instruction multiple data) 6

    +
      +
    • +

      New value type:

      +
    • +

      New memory instructions: , , , , , ,

      +
    • +

      New constant vector instruction:

      +
    • +

      New unary vector instructions: , , , , , , , , , ,

      +
    • +

      New binary vector instructions: , , , , , , , , , , , , , , , , , , , , , , , , , , ,

      +
    • +

      New ternary vector instruction:

      +
    • +

      New test vector instructions: ,

      +
    • +

      New relational vector instructions: , , , , , , , , , , ,

      +
    • +

      New conversion vector instructions:, , , , ,

      +
    • +

      New lane access vector instructions: , , ,

      +
    • +

      New lane splitting/combining vector instructions: , ,

      +
    • +

      New byte reordering vector instructions: ,

      +
    • +

      New injection/projection vector instructions: , ,

      +
    +
    +
    1 +
    +

    https://github.com/WebAssembly/spec/tree/main/proposals/sign-extension-ops/

    +
    2 +
    +

    https://github.com/WebAssembly/spec/tree/main/proposals/nontrapping-float-to-int-conversion/

    +
    3 +
    +

    https://github.com/WebAssembly/spec/tree/main/proposals/multi-value/

    +
    4(1,2,3,4) +
    +

    https://github.com/WebAssembly/spec/tree/main/proposals/reference-types/

    +
    5 +
    +

    https://github.com/WebAssembly/spec/tree/main/proposals/bulk-memory-operations/

    +
    6 +
    +

    https://github.com/WebAssembly/spec/tree/main/proposals/simd/

    +
    +
    +
    +
    +
    +
    + +
    + +

    A.6 Index of Types

    + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    Category

    +     		+

    Constructor

    +     		+

    Binary Opcode

    +
    +

    Type index

    +     		+

    +     		+

    (positive number as or )

    +
    +

    Number type

    +     		+

    +     		+

    (-1 as )

    +
    +

    Number type

    +     		+

    +     		+

    (-2 as )

    +
    +

    Number type

    +     		+

    +     		+

    (-3 as )

    +
    +

    Number type

    +     		+

    +     		+

    (-4 as )

    +
    +

    Vector type

    +     		+

    +     		+

    (-5 as )

    +
    +

    (reserved)

    +     		+ +

    ..

    +
    +

    Reference type

    +     		+

    +     		+

    (-16 as )

    +
    +

    Reference type

    +     		+

    +     		+

    (-17 as )

    +
    +

    (reserved)

    +     		+ +

    ..

    +
    +

    Function type

    +     		+

    +     		+

    (-32 as )

    +
    +

    (reserved)

    +     		+ +

    ..

    +
    +

    Result type

    +     		+

    +     		+

    (-64 as )

    +
    +

    Table type

    +     		+

    +     		+

    (none)

    +
    +

    Memory type

    +     		+

    +     		+

    (none)

    +
    +

    Global type

    +     		+

    +     		+

    (none)

    +
    +
    + +
    + +

    A.7 Index of Instructions

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    Instruction

    +     		+

    Binary Opcode

    +     		+

    Type

    +     		+

    Validation

    +     		+

    Execution

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution

    +
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    +     		+

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    validation

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    validation

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    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution

    +
    +

    +     		+

    +     		+ + +
    +

    (reserved)

    +     		+

    +     		+ + +
    +

    (reserved)

    +     		+

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    +
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    +     		+

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    (reserved)

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    +     		+

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    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +

    +     		+

    +     		+

    +     		+

    validation

    +     		+

    execution, operator

    +
    +
    + +
    + +

    A.8 Index of Semantic Rules

    +
    + +

    Typing of Static Constructs

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    Construct

    +     		+

    Judgement

    +
    +

    Limits

    +     		+

    +
    +

    Function type

    +     		+

    +
    +

    Block type

    +     		+

    +
    +

    Table type

    +     		+

    +
    +

    Memory type

    +     		+

    +
    +

    Global type

    +     		+

    +
    +

    External type

    +     		+

    +
    +

    Instruction

    +     		+

    +
    +

    Instruction sequence

    +     		+

    +
    +

    Expression

    +     		+

    +
    +

    Function

    +     		+

    +
    +

    Table

    +     		+

    +
    +

    Memory

    +     		+

    +
    +

    Global

    +     		+

    +
    +

    Element segment

    +     		+

    +
    +

    Element mode

    +     		+

    +
    +

    Data segment

    +     		+

    +
    +

    Data mode

    +     		+

    +
    +

    Start function

    +     		+

    +
    +

    Export

    +     		+

    +
    +

    Export description

    +     		+

    +
    +

    Import

    +     		+

    +
    +

    Import description

    +     		+

    +
    +

    Module

    +     		+

    +
    +
    +
    + +

    Typing of Runtime Constructs

    + + + + + + + + + + + + + + + + + + + + + + +
    +

    Construct

    +     		+

    Judgement

    +
    +

    Value

    +     		+

    +
    +

    Result

    +     		+

    +
    +

    External value

    +     		+

    +
    +

    Function instance

    +     		+

    +
    +

    Table instance

    +     		+

    +
    +

    Memory instance

    +     		+

    +
    +

    Global instance

    +     		+

    +
    +

    Element instance

    +     		+

    +
    +

    Data instance

    +     		+

    +
    +

    Export instance

    +     		+

    +
    +

    Module instance

    +     		+

    +
    +

    Store

    +     		+

    +
    +

    Configuration

    +     		+

    +
    +

    Thread

    +     		+

    +
    +

    Frame

    +     		+

    +
    +
    +
    +

    Constantness

    + + + + + + + + + +
    +

    Construct

    +     		+

    Judgement

    +
    +

    Constant expression

    +     		+

    +
    +

    Constant instruction

    +     		+

    +
    +
    +
    +

    Matching

    + + + + + + + + + +
    +

    Construct

    +     		+

    Judgement

    +
    +

    External type

    +     		+

    +
    +

    Limits

    +     		+

    +
    +
    +
    +

    Store Extension

    + + + + + + + + + + + + + + +
    +

    Construct

    +     		+

    Judgement

    +
    +

    Function instance

    +     		+

    +
    +

    Table instance

    +     		+

    +
    +

    Memory instance

    +     		+

    +
    +

    Global instance

    +     		+

    +
    +

    Element instance

    +     		+

    +
    +

    Data instance

    +     		+

    +
    +

    Store

    +     		+

    +
    +
    +
    +

    Execution

    + + + + + + + + + +
    +

    Construct

    +     		+

    Judgement

    +
    +

    Instruction

    +     		+

    +
    +

    Expression

    +     		+

    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    +
    + + +
    +
    +

    Conformance

    +

    Document conventions

    +

    Conformance requirements are expressed + with a combination of descriptive assertions + and RFC 2119 terminology. + The key words “MUST”, “MUST NOT”, “REQUIRED”, “SHALL”, “SHALL NOT”, “SHOULD”, “SHOULD NOT”, “RECOMMENDED”, “MAY”, and “OPTIONAL” + in the normative parts of this document + are to be interpreted as described in RFC 2119. + However, for readability, + these words do not appear in all uppercase letters in this specification.

    +

    All of the text of this specification is normative + except sections explicitly marked as non-normative, examples, and notes. [RFC2119]

    +

    Examples in this specification are introduced with the words “for example” + or are set apart from the normative text + with class="example", + like this:

    +
    + +

    This is an example of an informative example.

    +
    +

    Informative notes begin with the word “Note” + and are set apart from the normative text + with class="note", + like this:

    +

    Note, this is an informative note.

    +

    Conformant Algorithms

    +

    Requirements phrased in the imperative as part of algorithms + (such as "strip any leading space characters" + or "return false and abort these steps") + are to be interpreted with the meaning of the key word + ("must", "should", "may", etc) + used in introducing the algorithm.

    +

    Conformance requirements phrased as algorithms or specific steps + can be implemented in any manner, + so long as the end result is equivalent. + In particular, the algorithms defined in this specification + are intended to be easy to understand + and are not intended to be performant. + Implementers are encouraged to optimize.

    +
    + +

    References

    +

    Normative References

    +
    +
    [IEEE-754-2019] +
    IEEE Standard for Floating-Point Arithmetic. 29 August 2008. URL: http://ieeexplore.ieee.org/servlet/opac?punumber=4610933 +
    [RFC2119] +
    S. Bradner. Key words for use in RFCs to Indicate Requirement Levels. March 1997. Best Current Practice. URL: https://datatracker.ietf.org/doc/html/rfc2119 +
    [UNICODE] +
    The Unicode Standard. URL: https://www.unicode.org/versions/latest/ +
    \ No newline at end of file diff --git a/core/bikeshed/katex/dist/README.md b/core/bikeshed/katex/dist/README.md new file mode 100644 index 00000000..de4b9faf --- /dev/null +++ b/core/bikeshed/katex/dist/README.md @@ -0,0 +1,119 @@ +# [KaTeX](https://katex.org/) +[![npm](https://img.shields.io/npm/v/katex.svg)](https://www.npmjs.com/package/katex) +[![semantic-release](https://img.shields.io/badge/%20%20%F0%9F%93%A6%F0%9F%9A%80-semantic--release-e10079.svg)](https://github.com/semantic-release/semantic-release) +[![CI](https://github.com/KaTeX/KaTeX/workflows/CI/badge.svg?branch=master&event=push)](https://github.com/KaTeX/KaTeX/actions?query=workflow%3ACI) +[![codecov](https://codecov.io/gh/KaTeX/KaTeX/branch/master/graph/badge.svg)](https://codecov.io/gh/KaTeX/KaTeX) +[![Discussions](https://img.shields.io/badge/Discussions-join-brightgreen)](https://github.com/KaTeX/KaTeX/discussions) +[![jsDelivr](https://data.jsdelivr.com/v1/package/npm/katex/badge?style=rounded)](https://www.jsdelivr.com/package/npm/katex) +![katex.min.js size](https://img.badgesize.io/https://unpkg.com/katex/dist/katex.min.js?compression=gzip) +[![Gitpod ready-to-code](https://img.shields.io/badge/Gitpod-ready--to--code-blue?logo=gitpod)](https://gitpod.io/#https://github.com/KaTeX/KaTeX) +[![Financial Contributors on Open Collective](https://opencollective.com/katex/all/badge.svg?label=financial+contributors)](https://opencollective.com/katex) + +KaTeX is a fast, easy-to-use JavaScript library for TeX math rendering on the web. + + * **Fast:** KaTeX renders its math synchronously and doesn't need to reflow the page. See how it compares to a competitor in [this speed test](http://www.intmath.com/cg5/katex-mathjax-comparison.php). + * **Print quality:** KaTeX's layout is based on Donald Knuth's TeX, the gold standard for math typesetting. + * **Self contained:** KaTeX has no dependencies and can easily be bundled with your website resources. + * **Server side rendering:** KaTeX produces the same output regardless of browser or environment, so you can pre-render expressions using Node.js and send them as plain HTML. + +KaTeX is compatible with all major browsers, including Chrome, Safari, Firefox, Opera, Edge, and IE 11. + +KaTeX supports much (but not all) of LaTeX and many LaTeX packages. See the [list of supported functions](https://katex.org/docs/supported.html). + +Try out KaTeX [on the demo page](https://katex.org/#demo)! + +## Getting started + +### Starter template + +```html + + + + + + + + + + + + + ... + +``` + +You can also [download KaTeX](https://github.com/KaTeX/KaTeX/releases) and host it yourself. + +For details on how to configure auto-render extension, refer to [the documentation](https://katex.org/docs/autorender.html). + +### API + +Call `katex.render` to render a TeX expression directly into a DOM element. +For example: + +```js +katex.render("c = \\pm\\sqrt{a^2 + b^2}", element, { + throwOnError: false +}); +``` + +Call `katex.renderToString` to generate an HTML string of the rendered math, +e.g., for server-side rendering. For example: + +```js +var html = katex.renderToString("c = \\pm\\sqrt{a^2 + b^2}", { + throwOnError: false +}); +// '...' +``` + +Make sure to include the CSS and font files in both cases. +If you are doing all rendering on the server, there is no need to include the +JavaScript on the client. + +The examples above use the `throwOnError: false` option, which renders invalid +inputs as the TeX source code in red (by default), with the error message as +hover text. For other available options, see the +[API documentation](https://katex.org/docs/api.html), +[options documentation](https://katex.org/docs/options.html), and +[handling errors documentation](https://katex.org/docs/error.html). + +## Demo and Documentation + +Learn more about using KaTeX [on the website](https://katex.org)! + +## Contributors + +### Code Contributors + +This project exists thanks to all the people who contribute code. If you'd like to help, see [our guide to contributing code](CONTRIBUTING.md). +Code contributors + +### Financial Contributors + +Become a financial contributor and help us sustain our community. + +#### Individuals + +Contribute on Open Collective + +#### Organizations + +Support this project with your organization. Your logo will show up here with a link to your website. + +Organization 1 +Organization 2 +Organization 3 +Organization 4 +Organization 5 +Organization 6 +Organization 7 +Organization 8 +Organization 9 +Organization 10 + +## License + +KaTeX is licensed under the [MIT License](http://opensource.org/licenses/MIT). diff --git a/core/bikeshed/katex/dist/contrib/auto-render.js b/core/bikeshed/katex/dist/contrib/auto-render.js new file mode 100644 index 00000000..6980cdd1 --- /dev/null +++ b/core/bikeshed/katex/dist/contrib/auto-render.js @@ -0,0 +1,327 @@ +(function webpackUniversalModuleDefinition(root, factory) { + if(typeof exports === 'object' && typeof module === 'object') + module.exports = factory(require("katex")); + else if(typeof define === 'function' && define.amd) + define(["katex"], factory); + else if(typeof exports === 'object') + exports["renderMathInElement"] = factory(require("katex")); + else + root["renderMathInElement"] = factory(root["katex"]); +})((typeof self !== 'undefined' ? self : this), function(__WEBPACK_EXTERNAL_MODULE__771__) { +return /******/ (function() { // webpackBootstrap +/******/ "use strict"; +/******/ var __webpack_modules__ = ({ + +/***/ 771: +/***/ (function(module) { + +module.exports = __WEBPACK_EXTERNAL_MODULE__771__; + +/***/ }) + +/******/ }); +/************************************************************************/ +/******/ // The module cache +/******/ var __webpack_module_cache__ = {}; +/******/ +/******/ // The require function +/******/ function __webpack_require__(moduleId) { +/******/ // Check if module is in cache +/******/ var cachedModule = __webpack_module_cache__[moduleId]; +/******/ if (cachedModule !== undefined) { +/******/ return cachedModule.exports; +/******/ } +/******/ // Create a new module (and put it into the cache) +/******/ var module = __webpack_module_cache__[moduleId] = { +/******/ // no module.id needed +/******/ // no module.loaded needed +/******/ exports: {} +/******/ }; +/******/ +/******/ // Execute the module function +/******/ __webpack_modules__[moduleId](module, module.exports, __webpack_require__); +/******/ +/******/ // Return the exports of the module +/******/ return module.exports; +/******/ } +/******/ +/************************************************************************/ +/******/ /* webpack/runtime/compat get default export */ +/******/ !function() { +/******/ // getDefaultExport function for compatibility with non-harmony modules +/******/ __webpack_require__.n = function(module) { +/******/ var getter = module && module.__esModule ? +/******/ function() { return module['default']; } : +/******/ function() { return module; }; +/******/ __webpack_require__.d(getter, { a: getter }); +/******/ return getter; +/******/ }; +/******/ }(); +/******/ +/******/ /* webpack/runtime/define property getters */ +/******/ !function() { +/******/ // define getter functions for harmony exports +/******/ __webpack_require__.d = function(exports, definition) { +/******/ for(var key in definition) { +/******/ if(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) { +/******/ Object.defineProperty(exports, key, { enumerable: true, get: definition[key] }); +/******/ } +/******/ } +/******/ }; +/******/ }(); +/******/ +/******/ /* webpack/runtime/hasOwnProperty shorthand */ +/******/ !function() { +/******/ __webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); } +/******/ }(); +/******/ +/************************************************************************/ +var __webpack_exports__ = {}; +// This entry need to be wrapped in an IIFE because it need to be isolated against other modules in the chunk. +!function() { + +// EXPORTS +__webpack_require__.d(__webpack_exports__, { + "default": function() { return /* binding */ auto_render; } +}); + +// EXTERNAL MODULE: external "katex" +var external_katex_ = __webpack_require__(771); +var external_katex_default = /*#__PURE__*/__webpack_require__.n(external_katex_); +;// CONCATENATED MODULE: ./contrib/auto-render/splitAtDelimiters.js +/* eslint no-constant-condition:0 */ +var findEndOfMath = function findEndOfMath(delimiter, text, startIndex) { + // Adapted from + // https://github.com/Khan/perseus/blob/master/src/perseus-markdown.jsx + var index = startIndex; + var braceLevel = 0; + var delimLength = delimiter.length; + + while (index < text.length) { + var character = text[index]; + + if (braceLevel <= 0 && text.slice(index, index + delimLength) === delimiter) { + return index; + } else if (character === "\\") { + index++; + } else if (character === "{") { + braceLevel++; + } else if (character === "}") { + braceLevel--; + } + + index++; + } + + return -1; +}; + +var escapeRegex = function escapeRegex(string) { + return string.replace(/[-/\\^$*+?.()|[\]{}]/g, "\\$&"); +}; + +var amsRegex = /^\\begin{/; + +var splitAtDelimiters = function splitAtDelimiters(text, delimiters) { + var index; + var data = []; + var regexLeft = new RegExp("(" + delimiters.map(function (x) { + return escapeRegex(x.left); + }).join("|") + ")"); + + while (true) { + index = text.search(regexLeft); + + if (index === -1) { + break; + } + + if (index > 0) { + data.push({ + type: "text", + data: text.slice(0, index) + }); + text = text.slice(index); // now text starts with delimiter + } // ... so this always succeeds: + + + var i = delimiters.findIndex(function (delim) { + return text.startsWith(delim.left); + }); + index = findEndOfMath(delimiters[i].right, text, delimiters[i].left.length); + + if (index === -1) { + break; + } + + var rawData = text.slice(0, index + delimiters[i].right.length); + var math = amsRegex.test(rawData) ? rawData : text.slice(delimiters[i].left.length, index); + data.push({ + type: "math", + data: math, + rawData: rawData, + display: delimiters[i].display + }); + text = text.slice(index + delimiters[i].right.length); + } + + if (text !== "") { + data.push({ + type: "text", + data: text + }); + } + + return data; +}; + +/* harmony default export */ var auto_render_splitAtDelimiters = (splitAtDelimiters); +;// CONCATENATED MODULE: ./contrib/auto-render/auto-render.js +/* eslint no-console:0 */ + + +/* Note: optionsCopy is mutated by this method. If it is ever exposed in the + * API, we should copy it before mutating. + */ + +var renderMathInText = function renderMathInText(text, optionsCopy) { + var data = auto_render_splitAtDelimiters(text, optionsCopy.delimiters); + + if (data.length === 1 && data[0].type === 'text') { + // There is no formula in the text. + // Let's return null which means there is no need to replace + // the current text node with a new one. + return null; + } + + var fragment = document.createDocumentFragment(); + + for (var i = 0; i < data.length; i++) { + if (data[i].type === "text") { + fragment.appendChild(document.createTextNode(data[i].data)); + } else { + var span = document.createElement("span"); + var math = data[i].data; // Override any display mode defined in the settings with that + // defined by the text itself + + optionsCopy.displayMode = data[i].display; + + try { + if (optionsCopy.preProcess) { + math = optionsCopy.preProcess(math); + } + + external_katex_default().render(math, span, optionsCopy); + } catch (e) { + if (!(e instanceof (external_katex_default()).ParseError)) { + throw e; + } + + optionsCopy.errorCallback("KaTeX auto-render: Failed to parse `" + data[i].data + "` with ", e); + fragment.appendChild(document.createTextNode(data[i].rawData)); + continue; + } + + fragment.appendChild(span); + } + } + + return fragment; +}; + +var renderElem = function renderElem(elem, optionsCopy) { + for (var i = 0; i < elem.childNodes.length; i++) { + var childNode = elem.childNodes[i]; + + if (childNode.nodeType === 3) { + // Text node + var frag = renderMathInText(childNode.textContent, optionsCopy); + + if (frag) { + i += frag.childNodes.length - 1; + elem.replaceChild(frag, childNode); + } + } else if (childNode.nodeType === 1) { + (function () { + // Element node + var className = ' ' + childNode.className + ' '; + var shouldRender = optionsCopy.ignoredTags.indexOf(childNode.nodeName.toLowerCase()) === -1 && optionsCopy.ignoredClasses.every(function (x) { + return className.indexOf(' ' + x + ' ') === -1; + }); + + if (shouldRender) { + renderElem(childNode, optionsCopy); + } + })(); + } // Otherwise, it's something else, and ignore it. + + } +}; + +var renderMathInElement = function renderMathInElement(elem, options) { + if (!elem) { + throw new Error("No element provided to render"); + } + + var optionsCopy = {}; // Object.assign(optionsCopy, option) + + for (var option in options) { + if (options.hasOwnProperty(option)) { + optionsCopy[option] = options[option]; + } + } // default options + + + optionsCopy.delimiters = optionsCopy.delimiters || [{ + left: "$$", + right: "$$", + display: true + }, { + left: "\\(", + right: "\\)", + display: false + }, // LaTeX uses $…$, but it ruins the display of normal `$` in text: + // {left: "$", right: "$", display: false}, + // $ must come after $$ + // Render AMS environments even if outside $$…$$ delimiters. + { + left: "\\begin{equation}", + right: "\\end{equation}", + display: true + }, { + left: "\\begin{align}", + right: "\\end{align}", + display: true + }, { + left: "\\begin{alignat}", + right: "\\end{alignat}", + display: true + }, { + left: "\\begin{gather}", + right: "\\end{gather}", + display: true + }, { + left: "\\begin{CD}", + right: "\\end{CD}", + display: true + }, { + left: "\\[", + right: "\\]", + display: true + }]; + optionsCopy.ignoredTags = optionsCopy.ignoredTags || ["script", "noscript", "style", "textarea", "pre", "code", "option"]; + optionsCopy.ignoredClasses = optionsCopy.ignoredClasses || []; + optionsCopy.errorCallback = optionsCopy.errorCallback || console.error; // Enable sharing of global macros defined via `\gdef` between different + // math elements within a single call to `renderMathInElement`. + + optionsCopy.macros = optionsCopy.macros || {}; + renderElem(elem, optionsCopy); +}; + +/* harmony default export */ var auto_render = (renderMathInElement); +}(); +__webpack_exports__ = __webpack_exports__["default"]; +/******/ return __webpack_exports__; +/******/ })() +; +}); \ No newline at end of file diff --git a/core/bikeshed/katex/dist/contrib/auto-render.min.js b/core/bikeshed/katex/dist/contrib/auto-render.min.js new file mode 100644 index 00000000..c169ec63 --- /dev/null +++ b/core/bikeshed/katex/dist/contrib/auto-render.min.js @@ -0,0 +1 @@ +!function(e,t){"object"==typeof exports&&"object"==typeof module?module.exports=t(require("katex")):"function"==typeof define&&define.amd?define(["katex"],t):"object"==typeof exports?exports.renderMathInElement=t(require("katex")):e.renderMathInElement=t(e.katex)}("undefined"!=typeof self?self:this,(function(e){return function(){"use strict";var t={771:function(t){t.exports=e}},r={};function n(e){var a=r[e];if(void 0!==a)return a.exports;var i=r[e]={exports:{}};return t[e](i,i.exports,n),i.exports}n.n=function(e){var t=e&&e.__esModule?function(){return e.default}:function(){return e};return n.d(t,{a:t}),t},n.d=function(e,t){for(var r in t)n.o(t,r)&&!n.o(e,r)&&Object.defineProperty(e,r,{enumerable:!0,get:t[r]})},n.o=function(e,t){return Object.prototype.hasOwnProperty.call(e,t)};var a={};return function(){n.d(a,{default:function(){return s}});var e=n(771),t=n.n(e),r=function(e,t,r){for(var n=r,a=0,i=e.length;n0&&(a.push({type:"text",data:e.slice(0,n)}),e=e.slice(n));var l=t.findIndex((function(t){return e.startsWith(t.left)}));if(-1===(n=r(t[l].right,e,t[l].left.length)))break;var d=e.slice(0,n+t[l].right.length),s=i.test(d)?d:e.slice(t[l].left.length,n);a.push({type:"math",data:s,rawData:d,display:t[l].display}),e=e.slice(n+t[l].right.length)}return""!==e&&a.push({type:"text",data:e}),a},l=function(e,r){var n=o(e,r.delimiters);if(1===n.length&&"text"===n[0].type)return null;for(var a=document.createDocumentFragment(),i=0;i escapeRegex(x.left)).join("|") + ")"); + + while (true) { + index = text.search(regexLeft); + + if (index === -1) { + break; + } + + if (index > 0) { + data.push({ + type: "text", + data: text.slice(0, index) + }); + text = text.slice(index); // now text starts with delimiter + } // ... so this always succeeds: + + + var i = delimiters.findIndex(delim => text.startsWith(delim.left)); + index = findEndOfMath(delimiters[i].right, text, delimiters[i].left.length); + + if (index === -1) { + break; + } + + var rawData = text.slice(0, index + delimiters[i].right.length); + var math = amsRegex.test(rawData) ? rawData : text.slice(delimiters[i].left.length, index); + data.push({ + type: "math", + data: math, + rawData, + display: delimiters[i].display + }); + text = text.slice(index + delimiters[i].right.length); + } + + if (text !== "") { + data.push({ + type: "text", + data: text + }); + } + + return data; +}; + +/* eslint no-console:0 */ +/* Note: optionsCopy is mutated by this method. If it is ever exposed in the + * API, we should copy it before mutating. + */ + +var renderMathInText = function renderMathInText(text, optionsCopy) { + var data = splitAtDelimiters(text, optionsCopy.delimiters); + + if (data.length === 1 && data[0].type === 'text') { + // There is no formula in the text. + // Let's return null which means there is no need to replace + // the current text node with a new one. + return null; + } + + var fragment = document.createDocumentFragment(); + + for (var i = 0; i < data.length; i++) { + if (data[i].type === "text") { + fragment.appendChild(document.createTextNode(data[i].data)); + } else { + var span = document.createElement("span"); + var math = data[i].data; // Override any display mode defined in the settings with that + // defined by the text itself + + optionsCopy.displayMode = data[i].display; + + try { + if (optionsCopy.preProcess) { + math = optionsCopy.preProcess(math); + } + + katex.render(math, span, optionsCopy); + } catch (e) { + if (!(e instanceof katex.ParseError)) { + throw e; + } + + optionsCopy.errorCallback("KaTeX auto-render: Failed to parse `" + data[i].data + "` with ", e); + fragment.appendChild(document.createTextNode(data[i].rawData)); + continue; + } + + fragment.appendChild(span); + } + } + + return fragment; +}; + +var renderElem = function renderElem(elem, optionsCopy) { + for (var i = 0; i < elem.childNodes.length; i++) { + var childNode = elem.childNodes[i]; + + if (childNode.nodeType === 3) { + // Text node + var frag = renderMathInText(childNode.textContent, optionsCopy); + + if (frag) { + i += frag.childNodes.length - 1; + elem.replaceChild(frag, childNode); + } + } else if (childNode.nodeType === 1) { + (function () { + // Element node + var className = ' ' + childNode.className + ' '; + var shouldRender = optionsCopy.ignoredTags.indexOf(childNode.nodeName.toLowerCase()) === -1 && optionsCopy.ignoredClasses.every(x => className.indexOf(' ' + x + ' ') === -1); + + if (shouldRender) { + renderElem(childNode, optionsCopy); + } + })(); + } // Otherwise, it's something else, and ignore it. + + } +}; + +var renderMathInElement = function renderMathInElement(elem, options) { + if (!elem) { + throw new Error("No element provided to render"); + } + + var optionsCopy = {}; // Object.assign(optionsCopy, option) + + for (var option in options) { + if (options.hasOwnProperty(option)) { + optionsCopy[option] = options[option]; + } + } // default options + + + optionsCopy.delimiters = optionsCopy.delimiters || [{ + left: "$$", + right: "$$", + display: true + }, { + left: "\\(", + right: "\\)", + display: false + }, // LaTeX uses $…$, but it ruins the display of normal `$` in text: + // {left: "$", right: "$", display: false}, + // $ must come after $$ + // Render AMS environments even if outside $$…$$ delimiters. + { + left: "\\begin{equation}", + right: "\\end{equation}", + display: true + }, { + left: "\\begin{align}", + right: "\\end{align}", + display: true + }, { + left: "\\begin{alignat}", + right: "\\end{alignat}", + display: true + }, { + left: "\\begin{gather}", + right: "\\end{gather}", + display: true + }, { + left: "\\begin{CD}", + right: "\\end{CD}", + display: true + }, { + left: "\\[", + right: "\\]", + display: true + }]; + optionsCopy.ignoredTags = optionsCopy.ignoredTags || ["script", "noscript", "style", "textarea", "pre", "code", "option"]; + optionsCopy.ignoredClasses = optionsCopy.ignoredClasses || []; + optionsCopy.errorCallback = optionsCopy.errorCallback || console.error; // Enable sharing of global macros defined via `\gdef` between different + // math elements within a single call to `renderMathInElement`. + + optionsCopy.macros = optionsCopy.macros || {}; + renderElem(elem, optionsCopy); +}; + +export { renderMathInElement as default }; diff --git a/core/bikeshed/katex/dist/contrib/copy-tex.css b/core/bikeshed/katex/dist/contrib/copy-tex.css new file mode 100644 index 00000000..f9255789 --- /dev/null +++ b/core/bikeshed/katex/dist/contrib/copy-tex.css @@ -0,0 +1,14 @@ +/* Force selection of entire .katex/.katex-display blocks, so that we can + * copy/paste the entire source code. If you omit this CSS, partial + * selections of a formula will work, but will copy the ugly HTML + * representation instead of the LaTeX source code. (Full selections will + * still produce the LaTeX source code.) + */ +.katex, +.katex-display { + -webkit-user-select: all; + -moz-user-select: all; + -ms-user-select: all; + user-select: all; +} + diff --git a/core/bikeshed/katex/dist/contrib/copy-tex.js b/core/bikeshed/katex/dist/contrib/copy-tex.js new file mode 100644 index 00000000..bf54df2f --- /dev/null +++ b/core/bikeshed/katex/dist/contrib/copy-tex.js @@ -0,0 +1,116 @@ +(function webpackUniversalModuleDefinition(root, factory) { + if(typeof exports === 'object' && typeof module === 'object') + module.exports = factory(); + else if(typeof define === 'function' && define.amd) + define([], factory); + else { + var a = factory(); + for(var i in a) (typeof exports === 'object' ? exports : root)[i] = a[i]; + } +})((typeof self !== 'undefined' ? self : this), function() { +return /******/ (function() { // webpackBootstrap +/******/ "use strict"; +var __webpack_exports__ = {}; + +;// CONCATENATED MODULE: ./contrib/copy-tex/katex2tex.js +// Set these to how you want inline and display math to be delimited. +var defaultCopyDelimiters = { + inline: ['$', '$'], + // alternative: ['\(', '\)'] + display: ['$$', '$$'] // alternative: ['\[', '\]'] + +}; // Replace .katex elements with their TeX source ( element). +// Modifies fragment in-place. Useful for writing your own 'copy' handler, +// as in copy-tex.js. + +var katexReplaceWithTex = function katexReplaceWithTex(fragment, copyDelimiters) { + if (copyDelimiters === void 0) { + copyDelimiters = defaultCopyDelimiters; + } + + // Remove .katex-html blocks that are preceded by .katex-mathml blocks + // (which will get replaced below). + var katexHtml = fragment.querySelectorAll('.katex-mathml + .katex-html'); + + for (var i = 0; i < katexHtml.length; i++) { + var element = katexHtml[i]; + + if (element.remove) { + element.remove(null); + } else { + element.parentNode.removeChild(element); + } + } // Replace .katex-mathml elements with their annotation (TeX source) + // descendant, with inline delimiters. + + + var katexMathml = fragment.querySelectorAll('.katex-mathml'); + + for (var _i = 0; _i < katexMathml.length; _i++) { + var _element = katexMathml[_i]; + + var texSource = _element.querySelector('annotation'); + + if (texSource) { + if (_element.replaceWith) { + _element.replaceWith(texSource); + } else { + _element.parentNode.replaceChild(texSource, _element); + } + + texSource.innerHTML = copyDelimiters.inline[0] + texSource.innerHTML + copyDelimiters.inline[1]; + } + } // Switch display math to display delimiters. + + + var displays = fragment.querySelectorAll('.katex-display annotation'); + + for (var _i2 = 0; _i2 < displays.length; _i2++) { + var _element2 = displays[_i2]; + _element2.innerHTML = copyDelimiters.display[0] + _element2.innerHTML.substr(copyDelimiters.inline[0].length, _element2.innerHTML.length - copyDelimiters.inline[0].length - copyDelimiters.inline[1].length) + copyDelimiters.display[1]; + } + + return fragment; +}; +/* harmony default export */ var katex2tex = (katexReplaceWithTex); +;// CONCATENATED MODULE: ./contrib/copy-tex/copy-tex.js + // Global copy handler to modify behavior on .katex elements. + +document.addEventListener('copy', function (event) { + var selection = window.getSelection(); + + if (selection.isCollapsed) { + return; // default action OK if selection is empty + } + + var fragment = selection.getRangeAt(0).cloneContents(); + + if (!fragment.querySelector('.katex-mathml')) { + return; // default action OK if no .katex-mathml elements + } // Preserve usual HTML copy/paste behavior. + + + var html = []; + + for (var i = 0; i < fragment.childNodes.length; i++) { + html.push(fragment.childNodes[i].outerHTML); + } + + event.clipboardData.setData('text/html', html.join('')); // Rewrite plain-text version. + + event.clipboardData.setData('text/plain', katex2tex(fragment).textContent); // Prevent normal copy handling. + + event.preventDefault(); +}); +;// CONCATENATED MODULE: ./contrib/copy-tex/copy-tex.webpack.js +/** + * This is the webpack entry point for KaTeX. As ECMAScript doesn't support + * CSS modules natively, a separate entry point is used. + */ + + +__webpack_exports__ = __webpack_exports__["default"]; +/******/ return __webpack_exports__; +/******/ })() +; +}); \ No newline at end of file diff --git a/core/bikeshed/katex/dist/contrib/copy-tex.min.css b/core/bikeshed/katex/dist/contrib/copy-tex.min.css new file mode 100644 index 00000000..6f97f56c --- /dev/null +++ b/core/bikeshed/katex/dist/contrib/copy-tex.min.css @@ -0,0 +1 @@ +.katex,.katex-display{-webkit-user-select:all;-moz-user-select:all;-ms-user-select:all;user-select:all} diff --git a/core/bikeshed/katex/dist/contrib/copy-tex.min.js b/core/bikeshed/katex/dist/contrib/copy-tex.min.js new file mode 100644 index 00000000..9e9d26ec --- /dev/null +++ b/core/bikeshed/katex/dist/contrib/copy-tex.min.js @@ -0,0 +1 @@ +!function(e,t){if("object"==typeof exports&&"object"==typeof module)module.exports=t();else if("function"==typeof define&&define.amd)define([],t);else{var n=t();for(var l in n)("object"==typeof exports?exports:e)[l]=n[l]}}("undefined"!=typeof self?self:this,(function(){return function(){"use strict";var e={},t={inline:["$","$"],display:["$$","$$"]},n=function(e,n){void 0===n&&(n=t);for(var l=e.querySelectorAll(".katex-mathml + .katex-html"),r=0;r element). +// Modifies fragment in-place. Useful for writing your own 'copy' handler, +// as in copy-tex.js. + +var katexReplaceWithTex = function katexReplaceWithTex(fragment, copyDelimiters) { + if (copyDelimiters === void 0) { + copyDelimiters = defaultCopyDelimiters; + } + + // Remove .katex-html blocks that are preceded by .katex-mathml blocks + // (which will get replaced below). + var katexHtml = fragment.querySelectorAll('.katex-mathml + .katex-html'); + + for (var i = 0; i < katexHtml.length; i++) { + var element = katexHtml[i]; + + if (element.remove) { + element.remove(null); + } else { + element.parentNode.removeChild(element); + } + } // Replace .katex-mathml elements with their annotation (TeX source) + // descendant, with inline delimiters. + + + var katexMathml = fragment.querySelectorAll('.katex-mathml'); + + for (var _i = 0; _i < katexMathml.length; _i++) { + var _element = katexMathml[_i]; + + var texSource = _element.querySelector('annotation'); + + if (texSource) { + if (_element.replaceWith) { + _element.replaceWith(texSource); + } else { + _element.parentNode.replaceChild(texSource, _element); + } + + texSource.innerHTML = copyDelimiters.inline[0] + texSource.innerHTML + copyDelimiters.inline[1]; + } + } // Switch display math to display delimiters. + + + var displays = fragment.querySelectorAll('.katex-display annotation'); + + for (var _i2 = 0; _i2 < displays.length; _i2++) { + var _element2 = displays[_i2]; + _element2.innerHTML = copyDelimiters.display[0] + _element2.innerHTML.substr(copyDelimiters.inline[0].length, _element2.innerHTML.length - copyDelimiters.inline[0].length - copyDelimiters.inline[1].length) + copyDelimiters.display[1]; + } + + return fragment; +}; + +document.addEventListener('copy', function (event) { + var selection = window.getSelection(); + + if (selection.isCollapsed) { + return; // default action OK if selection is empty + } + + var fragment = selection.getRangeAt(0).cloneContents(); + + if (!fragment.querySelector('.katex-mathml')) { + return; // default action OK if no .katex-mathml elements + } // Preserve usual HTML copy/paste behavior. + + + var html = []; + + for (var i = 0; i < fragment.childNodes.length; i++) { + html.push(fragment.childNodes[i].outerHTML); + } + + event.clipboardData.setData('text/html', html.join('')); // Rewrite plain-text version. + + event.clipboardData.setData('text/plain', katexReplaceWithTex(fragment).textContent); // Prevent normal copy handling. + + event.preventDefault(); +}); diff --git a/core/bikeshed/katex/dist/contrib/mathtex-script-type.js b/core/bikeshed/katex/dist/contrib/mathtex-script-type.js new file mode 100644 index 00000000..d82c41d8 --- /dev/null +++ b/core/bikeshed/katex/dist/contrib/mathtex-script-type.js @@ -0,0 +1,112 @@ +(function webpackUniversalModuleDefinition(root, factory) { + if(typeof exports === 'object' && typeof module === 'object') + module.exports = factory(require("katex")); + else if(typeof define === 'function' && define.amd) + define(["katex"], factory); + else { + var a = typeof exports === 'object' ? factory(require("katex")) : factory(root["katex"]); + for(var i in a) (typeof exports === 'object' ? exports : root)[i] = a[i]; + } +})((typeof self !== 'undefined' ? self : this), function(__WEBPACK_EXTERNAL_MODULE__771__) { +return /******/ (function() { // webpackBootstrap +/******/ "use strict"; +/******/ var __webpack_modules__ = ({ + +/***/ 771: +/***/ (function(module) { + +module.exports = __WEBPACK_EXTERNAL_MODULE__771__; + +/***/ }) + +/******/ }); +/************************************************************************/ +/******/ // The module cache +/******/ var __webpack_module_cache__ = {}; +/******/ +/******/ // The require function +/******/ function __webpack_require__(moduleId) { +/******/ // Check if module is in cache +/******/ var cachedModule = __webpack_module_cache__[moduleId]; +/******/ if (cachedModule !== undefined) { +/******/ return cachedModule.exports; +/******/ } +/******/ // Create a new module (and put it into the cache) +/******/ var module = __webpack_module_cache__[moduleId] = { +/******/ // no module.id needed +/******/ // no module.loaded needed +/******/ exports: {} +/******/ }; +/******/ +/******/ // Execute the module function +/******/ __webpack_modules__[moduleId](module, module.exports, __webpack_require__); +/******/ +/******/ // Return the exports of the module +/******/ return module.exports; +/******/ } +/******/ +/************************************************************************/ +/******/ /* webpack/runtime/compat get default export */ +/******/ !function() { +/******/ // getDefaultExport function for compatibility with non-harmony modules +/******/ __webpack_require__.n = function(module) { +/******/ var getter = module && module.__esModule ? +/******/ function() { return module['default']; } : +/******/ function() { return module; }; +/******/ __webpack_require__.d(getter, { a: getter }); +/******/ return getter; +/******/ }; +/******/ }(); +/******/ +/******/ /* webpack/runtime/define property getters */ +/******/ !function() { +/******/ // define getter functions for harmony exports +/******/ __webpack_require__.d = function(exports, definition) { +/******/ for(var key in definition) { +/******/ if(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) { +/******/ Object.defineProperty(exports, key, { enumerable: true, get: definition[key] }); +/******/ } +/******/ } +/******/ }; +/******/ }(); +/******/ +/******/ /* webpack/runtime/hasOwnProperty shorthand */ +/******/ !function() { +/******/ __webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); } +/******/ }(); +/******/ +/************************************************************************/ +var __webpack_exports__ = {}; +// This entry need to be wrapped in an IIFE because it need to be isolated against other modules in the chunk. +!function() { +/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0__ = __webpack_require__(771); +/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0___default = /*#__PURE__*/__webpack_require__.n(katex__WEBPACK_IMPORTED_MODULE_0__); + +var scripts = document.body.getElementsByTagName("script"); +scripts = Array.prototype.slice.call(scripts); +scripts.forEach(function (script) { + if (!script.type || !script.type.match(/math\/tex/i)) { + return -1; + } + + var display = script.type.match(/mode\s*=\s*display(;|\s|\n|$)/) != null; + var katexElement = document.createElement(display ? "div" : "span"); + katexElement.setAttribute("class", display ? "equation" : "inline-equation"); + + try { + katex__WEBPACK_IMPORTED_MODULE_0___default().render(script.text, katexElement, { + displayMode: display + }); + } catch (err) { + //console.error(err); linter doesn't like this + katexElement.textContent = script.text; + } + + script.parentNode.replaceChild(katexElement, script); +}); +}(); +__webpack_exports__ = __webpack_exports__["default"]; +/******/ return __webpack_exports__; +/******/ })() +; +}); \ No newline at end of file diff --git a/core/bikeshed/katex/dist/contrib/mathtex-script-type.min.js b/core/bikeshed/katex/dist/contrib/mathtex-script-type.min.js new file mode 100644 index 00000000..af028303 --- /dev/null +++ b/core/bikeshed/katex/dist/contrib/mathtex-script-type.min.js @@ -0,0 +1 @@ +!function(e,t){if("object"==typeof exports&&"object"==typeof module)module.exports=t(require("katex"));else if("function"==typeof define&&define.amd)define(["katex"],t);else{var r="object"==typeof exports?t(require("katex")):t(e.katex);for(var n in r)("object"==typeof exports?exports:e)[n]=r[n]}}("undefined"!=typeof self?self:this,(function(e){return function(){"use strict";var t={771:function(t){t.exports=e}},r={};function n(e){var o=r[e];if(void 0!==o)return o.exports;var i=r[e]={exports:{}};return t[e](i,i.exports,n),i.exports}n.n=function(e){var t=e&&e.__esModule?function(){return e.default}:function(){return e};return n.d(t,{a:t}),t},n.d=function(e,t){for(var r in t)n.o(t,r)&&!n.o(e,r)&&Object.defineProperty(e,r,{enumerable:!0,get:t[r]})},n.o=function(e,t){return Object.prototype.hasOwnProperty.call(e,t)};var o,i,a,u={};return o=n(771),i=n.n(o),a=document.body.getElementsByTagName("script"),(a=Array.prototype.slice.call(a)).forEach((function(e){if(!e.type||!e.type.match(/math\/tex/i))return-1;var t=null!=e.type.match(/mode\s*=\s*display(;|\s|\n|$)/),r=document.createElement(t?"div":"span");r.setAttribute("class",t?"equation":"inline-equation");try{i().render(e.text,r,{displayMode:t})}catch(t){r.textContent=e.text}e.parentNode.replaceChild(r,e)})),u=u.default}()})); \ No newline at end of file diff --git a/core/bikeshed/katex/dist/contrib/mathtex-script-type.mjs b/core/bikeshed/katex/dist/contrib/mathtex-script-type.mjs new file mode 100644 index 00000000..1083b927 --- /dev/null +++ b/core/bikeshed/katex/dist/contrib/mathtex-script-type.mjs @@ -0,0 +1,24 @@ +import katex from '../katex.mjs'; + +var scripts = document.body.getElementsByTagName("script"); +scripts = Array.prototype.slice.call(scripts); +scripts.forEach(function (script) { + if (!script.type || !script.type.match(/math\/tex/i)) { + return -1; + } + + var display = script.type.match(/mode\s*=\s*display(;|\s|\n|$)/) != null; + var katexElement = document.createElement(display ? "div" : "span"); + katexElement.setAttribute("class", display ? 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The interface is changed so that it can be called from KaTeX, not MathJax. + * 2. \rlap and \llap are replaced with \mathrlap and \mathllap. + * 3. Four lines of code are edited in order to use \raisebox instead of \raise. + * 4. The reaction arrow code is simplified. All reaction arrows are rendered + * using KaTeX extensible arrows instead of building non-extensible arrows. + * 5. \tripledash vertical alignment is slightly adjusted. + * + * This code, as other KaTeX code, is released under the MIT license. + * + * /************************************************************* + * + * MathJax/extensions/TeX/mhchem.js + * + * Implements the \ce command for handling chemical formulas + * from the mhchem LaTeX package. + * + * --------------------------------------------------------------------- + * + * Copyright (c) 2011-2015 The MathJax Consortium + * Copyright (c) 2015-2018 Martin Hensel + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +// +// Coding Style +// - use '' for identifiers that can by minified/uglified +// - use "" for strings that need to stay untouched +// version: "3.3.0" for MathJax and KaTeX +// Add \ce, \pu, and \tripledash to the KaTeX macros. +katex__WEBPACK_IMPORTED_MODULE_0___default().__defineMacro("\\ce", function (context) { + return chemParse(context.consumeArgs(1)[0], "ce"); +}); + +katex__WEBPACK_IMPORTED_MODULE_0___default().__defineMacro("\\pu", function (context) { + return chemParse(context.consumeArgs(1)[0], "pu"); +}); // Needed for \bond for the ~ forms +// Raise by 2.56mu, not 2mu. We're raising a hyphen-minus, U+002D, not +// a mathematical minus, U+2212. So we need that extra 0.56. + + +katex__WEBPACK_IMPORTED_MODULE_0___default().__defineMacro("\\tripledash", "{\\vphantom{-}\\raisebox{2.56mu}{$\\mkern2mu" + "\\tiny\\text{-}\\mkern1mu\\text{-}\\mkern1mu\\text{-}\\mkern2mu$}}"); + + // +// This is the main function for handing the \ce and \pu commands. +// It takes the argument to \ce or \pu and returns the corresponding TeX string. +// + +var chemParse = function chemParse(tokens, stateMachine) { + // Recreate the argument string from KaTeX's array of tokens. + var str = ""; + var expectedLoc = tokens[tokens.length - 1].loc.start; + + for (var i = tokens.length - 1; i >= 0; i--) { + if (tokens[i].loc.start > expectedLoc) { + // context.consumeArgs has eaten a space. + str += " "; + expectedLoc = tokens[i].loc.start; + } + + str += tokens[i].text; + expectedLoc += tokens[i].text.length; + } + + var tex = texify.go(mhchemParser.go(str, stateMachine)); + return tex; +}; // +// Core parser for mhchem syntax (recursive) +// + +/** @type {MhchemParser} */ + + +var mhchemParser = { + // + // Parses mchem \ce syntax + // + // Call like + // go("H2O"); + // + go: function go(input, stateMachine) { + if (!input) { + return []; + } + + if (stateMachine === undefined) { + stateMachine = 'ce'; + } + + var state = '0'; // + // String buffers for parsing: + // + // buffer.a == amount + // buffer.o == element + // buffer.b == left-side superscript + // buffer.p == left-side subscript + // buffer.q == right-side subscript + // buffer.d == right-side superscript + // + // buffer.r == arrow + // buffer.rdt == arrow, script above, type + // buffer.rd == arrow, script above, content + // buffer.rqt == arrow, script below, type + // buffer.rq == arrow, script below, content + // + // buffer.text_ + // buffer.rm + // etc. + // + // buffer.parenthesisLevel == int, starting at 0 + // buffer.sb == bool, space before + // buffer.beginsWithBond == bool + // + // These letters are also used as state names. + // + // Other states: + // 0 == begin of main part (arrow/operator unlikely) + // 1 == next entity + // 2 == next entity (arrow/operator unlikely) + // 3 == next atom + // c == macro + // + + /** @type {Buffer} */ + + var buffer = {}; + buffer['parenthesisLevel'] = 0; + input = input.replace(/\n/g, " "); + input = input.replace(/[\u2212\u2013\u2014\u2010]/g, "-"); + input = input.replace(/[\u2026]/g, "..."); // + // Looks through mhchemParser.transitions, to execute a matching action + // (recursive) + // + + var lastInput; + var watchdog = 10; + /** @type {ParserOutput[]} */ + + var output = []; + + while (true) { + if (lastInput !== input) { + watchdog = 10; + lastInput = input; + } else { + watchdog--; + } // + // Find actions in transition table + // + + + var machine = mhchemParser.stateMachines[stateMachine]; + var t = machine.transitions[state] || machine.transitions['*']; + + iterateTransitions: for (var i = 0; i < t.length; i++) { + var matches = mhchemParser.patterns.match_(t[i].pattern, input); + + if (matches) { + // + // Execute actions + // + var task = t[i].task; + + for (var iA = 0; iA < task.action_.length; iA++) { + var o; // + // Find and execute action + // + + if (machine.actions[task.action_[iA].type_]) { + o = machine.actions[task.action_[iA].type_](buffer, matches.match_, task.action_[iA].option); + } else if (mhchemParser.actions[task.action_[iA].type_]) { + o = mhchemParser.actions[task.action_[iA].type_](buffer, matches.match_, task.action_[iA].option); + } else { + throw ["MhchemBugA", "mhchem bug A. Please report. (" + task.action_[iA].type_ + ")"]; // Trying to use non-existing action + } // + // Add output + // + + + mhchemParser.concatArray(output, o); + } // + // Set next state, + // Shorten input, + // Continue with next character + // (= apply only one transition per position) + // + + + state = task.nextState || state; + + if (input.length > 0) { + if (!task.revisit) { + input = matches.remainder; + } + + if (!task.toContinue) { + break iterateTransitions; + } + } else { + return output; + } + } + } // + // Prevent infinite loop + // + + + if (watchdog <= 0) { + throw ["MhchemBugU", "mhchem bug U. Please report."]; // Unexpected character + } + } + }, + concatArray: function concatArray(a, b) { + if (b) { + if (Array.isArray(b)) { + for (var iB = 0; iB < b.length; iB++) { + a.push(b[iB]); + } + } else { + a.push(b); + } + } + }, + patterns: { + // + // Matching patterns + // either regexps or function that return null or {match_:"a", remainder:"bc"} + // + patterns: { + // property names must not look like integers ("2") for correct property traversal order, later on + 'empty': /^$/, + 'else': /^./, + 'else2': /^./, + 'space': /^\s/, + 'space A': /^\s(?=[A-Z\\$])/, + 'space$': /^\s$/, + 'a-z': /^[a-z]/, + 'x': /^x/, + 'x$': /^x$/, + 'i$': /^i$/, + 'letters': /^(?:[a-zA-Z\u03B1-\u03C9\u0391-\u03A9?@]|(?:\\(?:alpha|beta|gamma|delta|epsilon|zeta|eta|theta|iota|kappa|lambda|mu|nu|xi|omicron|pi|rho|sigma|tau|upsilon|phi|chi|psi|omega|Gamma|Delta|Theta|Lambda|Xi|Pi|Sigma|Upsilon|Phi|Psi|Omega)(?:\s+|\{\}|(?![a-zA-Z]))))+/, + '\\greek': /^\\(?:alpha|beta|gamma|delta|epsilon|zeta|eta|theta|iota|kappa|lambda|mu|nu|xi|omicron|pi|rho|sigma|tau|upsilon|phi|chi|psi|omega|Gamma|Delta|Theta|Lambda|Xi|Pi|Sigma|Upsilon|Phi|Psi|Omega)(?:\s+|\{\}|(?![a-zA-Z]))/, + 'one lowercase latin letter $': /^(?:([a-z])(?:$|[^a-zA-Z]))$/, + '$one lowercase latin letter$ $': /^\$(?:([a-z])(?:$|[^a-zA-Z]))\$$/, + 'one lowercase greek letter $': /^(?:\$?[\u03B1-\u03C9]\$?|\$?\\(?:alpha|beta|gamma|delta|epsilon|zeta|eta|theta|iota|kappa|lambda|mu|nu|xi|omicron|pi|rho|sigma|tau|upsilon|phi|chi|psi|omega)\s*\$?)(?:\s+|\{\}|(?![a-zA-Z]))$/, + 'digits': /^[0-9]+/, + '-9.,9': /^[+\-]?(?:[0-9]+(?:[,.][0-9]+)?|[0-9]*(?:\.[0-9]+))/, + '-9.,9 no missing 0': /^[+\-]?[0-9]+(?:[.,][0-9]+)?/, + '(-)(9.,9)(e)(99)': function e99(input) { + var m = input.match(/^(\+\-|\+\/\-|\+|\-|\\pm\s?)?([0-9]+(?:[,.][0-9]+)?|[0-9]*(?:\.[0-9]+))?(\((?:[0-9]+(?:[,.][0-9]+)?|[0-9]*(?:\.[0-9]+))\))?(?:([eE]|\s*(\*|x|\\times|\u00D7)\s*10\^)([+\-]?[0-9]+|\{[+\-]?[0-9]+\}))?/); + + if (m && m[0]) { + return { + match_: m.splice(1), + remainder: input.substr(m[0].length) + }; + } + + return null; + }, + '(-)(9)^(-9)': function _(input) { + var m = input.match(/^(\+\-|\+\/\-|\+|\-|\\pm\s?)?([0-9]+(?:[,.][0-9]+)?|[0-9]*(?:\.[0-9]+)?)\^([+\-]?[0-9]+|\{[+\-]?[0-9]+\})/); + + if (m && m[0]) { + return { + match_: m.splice(1), + remainder: input.substr(m[0].length) + }; + } + + return null; + }, + 'state of aggregation $': function stateOfAggregation$(input) { + // ... or crystal system + var a = mhchemParser.patterns.findObserveGroups(input, "", /^\([a-z]{1,3}(?=[\),])/, ")", ""); // (aq), (aq,$\infty$), (aq, sat) + + if (a && a.remainder.match(/^($|[\s,;\)\]\}])/)) { + return a; + } // AND end of 'phrase' + + + var m = input.match(/^(?:\((?:\\ca\s?)?\$[amothc]\$\))/); // OR crystal system ($o$) (\ca$c$) + + if (m) { + return { + match_: m[0], + remainder: input.substr(m[0].length) + }; + } + + return null; + }, + '_{(state of aggregation)}$': /^_\{(\([a-z]{1,3}\))\}/, + '{[(': /^(?:\\\{|\[|\()/, + ')]}': /^(?:\)|\]|\\\})/, + ', ': /^[,;]\s*/, + ',': /^[,;]/, + '.': /^[.]/, + '. ': /^([.\u22C5\u00B7\u2022])\s*/, + '...': /^\.\.\.(?=$|[^.])/, + '* ': /^([*])\s*/, + '^{(...)}': function _(input) { + return mhchemParser.patterns.findObserveGroups(input, "^{", "", "", "}"); + }, + '^($...$)': function $$(input) { + return mhchemParser.patterns.findObserveGroups(input, "^", "$", "$", ""); + }, + '^a': /^\^([0-9]+|[^\\_])/, + '^\\x{}{}': function x(input) { + return mhchemParser.patterns.findObserveGroups(input, "^", /^\\[a-zA-Z]+\{/, "}", "", "", "{", "}", "", true); + }, + '^\\x{}': function x(input) { + return mhchemParser.patterns.findObserveGroups(input, "^", /^\\[a-zA-Z]+\{/, "}", ""); + }, + '^\\x': /^\^(\\[a-zA-Z]+)\s*/, + '^(-1)': /^\^(-?\d+)/, + '\'': /^'/, + '_{(...)}': function _(input) { + return mhchemParser.patterns.findObserveGroups(input, "_{", "", "", "}"); + }, + '_($...$)': function _$$(input) { + return mhchemParser.patterns.findObserveGroups(input, "_", "$", "$", ""); + }, + '_9': /^_([+\-]?[0-9]+|[^\\])/, + '_\\x{}{}': function _X(input) { + return mhchemParser.patterns.findObserveGroups(input, "_", /^\\[a-zA-Z]+\{/, "}", "", "", "{", "}", "", true); + }, + '_\\x{}': function _X(input) { + return mhchemParser.patterns.findObserveGroups(input, "_", /^\\[a-zA-Z]+\{/, "}", ""); + }, + '_\\x': /^_(\\[a-zA-Z]+)\s*/, + '^_': /^(?:\^(?=_)|\_(?=\^)|[\^_]$)/, + '{}': /^\{\}/, + '{...}': function _(input) { + return mhchemParser.patterns.findObserveGroups(input, "", "{", "}", ""); + }, + '{(...)}': function _(input) { + return mhchemParser.patterns.findObserveGroups(input, "{", "", "", "}"); + }, + '$...$': function $$(input) { + return mhchemParser.patterns.findObserveGroups(input, "", "$", "$", ""); + }, + '${(...)}$': function $$(input) { + return mhchemParser.patterns.findObserveGroups(input, "${", "", "", "}$"); + }, + '$(...)$': function $$(input) { + return mhchemParser.patterns.findObserveGroups(input, "$", "", "", "$"); + }, + '=<>': /^[=<>]/, + '#': /^[#\u2261]/, + '+': /^\+/, + '-$': /^-(?=[\s_},;\]/]|$|\([a-z]+\))/, + // -space -, -; -] -/ -$ -state-of-aggregation + '-9': /^-(?=[0-9])/, + '- orbital overlap': /^-(?=(?:[spd]|sp)(?:$|[\s,;\)\]\}]))/, + '-': /^-/, + 'pm-operator': /^(?:\\pm|\$\\pm\$|\+-|\+\/-)/, + 'operator': /^(?:\+|(?:[\-=<>]|<<|>>|\\approx|\$\\approx\$)(?=\s|$|-?[0-9]))/, + 'arrowUpDown': /^(?:v|\(v\)|\^|\(\^\))(?=$|[\s,;\)\]\}])/, + '\\bond{(...)}': function bond(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\bond{", "", "", "}"); + }, + '->': /^(?:<->|<-->|->|<-|<=>>|<<=>|<=>|[\u2192\u27F6\u21CC])/, + 'CMT': /^[CMT](?=\[)/, + '[(...)]': function _(input) { + return mhchemParser.patterns.findObserveGroups(input, "[", "", "", "]"); + }, + '1st-level escape': /^(&|\\\\|\\hline)\s*/, + '\\,': /^(?:\\[,\ ;:])/, + // \\x - but output no space before + '\\x{}{}': function x(input) { + return mhchemParser.patterns.findObserveGroups(input, "", /^\\[a-zA-Z]+\{/, "}", "", "", "{", "}", "", true); + }, + '\\x{}': function x(input) { + return mhchemParser.patterns.findObserveGroups(input, "", /^\\[a-zA-Z]+\{/, "}", ""); + }, + '\\ca': /^\\ca(?:\s+|(?![a-zA-Z]))/, + '\\x': /^(?:\\[a-zA-Z]+\s*|\\[_&{}%])/, + 'orbital': /^(?:[0-9]{1,2}[spdfgh]|[0-9]{0,2}sp)(?=$|[^a-zA-Z])/, + // only those with numbers in front, because the others will be formatted correctly anyway + 'others': /^[\/~|]/, + '\\frac{(...)}': function frac(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\frac{", "", "", "}", "{", "", "", "}"); + }, + '\\overset{(...)}': function overset(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\overset{", "", "", "}", "{", "", "", "}"); + }, + "\\underset{(...)}": function underset(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\underset{", "", "", "}", "{", "", "", "}"); + }, + "\\underbrace{(...)}": function underbrace(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\underbrace{", "", "", "}_", "{", "", "", "}"); + }, + '\\color{(...)}0': function color0(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\color{", "", "", "}"); + }, + '\\color{(...)}{(...)}1': function color1(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\color{", "", "", "}", "{", "", "", "}"); + }, + '\\color(...){(...)}2': function color2(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\color", "\\", "", /^(?=\{)/, "{", "", "", "}"); + }, + '\\ce{(...)}': function ce(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\ce{", "", "", "}"); + }, + 'oxidation$': /^(?:[+-][IVX]+|\\pm\s*0|\$\\pm\$\s*0)$/, + 'd-oxidation$': /^(?:[+-]?\s?[IVX]+|\\pm\s*0|\$\\pm\$\s*0)$/, + // 0 could be oxidation or charge + 'roman numeral': /^[IVX]+/, + '1/2$': /^[+\-]?(?:[0-9]+|\$[a-z]\$|[a-z])\/[0-9]+(?:\$[a-z]\$|[a-z])?$/, + 'amount': function amount(input) { + var match; // e.g. 2, 0.5, 1/2, -2, n/2, +; $a$ could be added later in parsing + + match = input.match(/^(?:(?:(?:\([+\-]?[0-9]+\/[0-9]+\)|[+\-]?(?:[0-9]+|\$[a-z]\$|[a-z])\/[0-9]+|[+\-]?[0-9]+[.,][0-9]+|[+\-]?\.[0-9]+|[+\-]?[0-9]+)(?:[a-z](?=\s*[A-Z]))?)|[+\-]?[a-z](?=\s*[A-Z])|\+(?!\s))/); + + if (match) { + return { + match_: match[0], + remainder: input.substr(match[0].length) + }; + } + + var a = mhchemParser.patterns.findObserveGroups(input, "", "$", "$", ""); + + if (a) { + // e.g. $2n-1$, $-$ + match = a.match_.match(/^\$(?:\(?[+\-]?(?:[0-9]*[a-z]?[+\-])?[0-9]*[a-z](?:[+\-][0-9]*[a-z]?)?\)?|\+|-)\$$/); + + if (match) { + return { + match_: match[0], + remainder: input.substr(match[0].length) + }; + } + } + + return null; + }, + 'amount2': function amount2(input) { + return this['amount'](input); + }, + '(KV letters),': /^(?:[A-Z][a-z]{0,2}|i)(?=,)/, + 'formula$': function formula$(input) { + if (input.match(/^\([a-z]+\)$/)) { + return null; + } // state of aggregation = no formula + + + var match = input.match(/^(?:[a-z]|(?:[0-9\ \+\-\,\.\(\)]+[a-z])+[0-9\ \+\-\,\.\(\)]*|(?:[a-z][0-9\ \+\-\,\.\(\)]+)+[a-z]?)$/); + + if (match) { + return { + match_: match[0], + remainder: input.substr(match[0].length) + }; + } + + return null; + }, + 'uprightEntities': /^(?:pH|pOH|pC|pK|iPr|iBu)(?=$|[^a-zA-Z])/, + '/': /^\s*(\/)\s*/, + '//': /^\s*(\/\/)\s*/, + '*': /^\s*[*.]\s*/ + }, + findObserveGroups: function findObserveGroups(input, begExcl, begIncl, endIncl, endExcl, beg2Excl, beg2Incl, end2Incl, end2Excl, combine) { + /** @type {{(input: string, pattern: string | RegExp): string | string[] | null;}} */ + var _match = function _match(input, pattern) { + if (typeof pattern === "string") { + if (input.indexOf(pattern) !== 0) { + return null; + } + + return pattern; + } else { + var match = input.match(pattern); + + if (!match) { + return null; + } + + return match[0]; + } + }; + /** @type {{(input: string, i: number, endChars: string | RegExp): {endMatchBegin: number, endMatchEnd: number} | null;}} */ + + + var _findObserveGroups = function _findObserveGroups(input, i, endChars) { + var braces = 0; + + while (i < input.length) { + var a = input.charAt(i); + + var match = _match(input.substr(i), endChars); + + if (match !== null && braces === 0) { + return { + endMatchBegin: i, + endMatchEnd: i + match.length + }; + } else if (a === "{") { + braces++; + } else if (a === "}") { + if (braces === 0) { + throw ["ExtraCloseMissingOpen", "Extra close brace or missing open brace"]; + } else { + braces--; + } + } + + i++; + } + + if (braces > 0) { + return null; + } + + return null; + }; + + var match = _match(input, begExcl); + + if (match === null) { + return null; + } + + input = input.substr(match.length); + match = _match(input, begIncl); + + if (match === null) { + return null; + } + + var e = _findObserveGroups(input, match.length, endIncl || endExcl); + + if (e === null) { + return null; + } + + var match1 = input.substring(0, endIncl ? e.endMatchEnd : e.endMatchBegin); + + if (!(beg2Excl || beg2Incl)) { + return { + match_: match1, + remainder: input.substr(e.endMatchEnd) + }; + } else { + var group2 = this.findObserveGroups(input.substr(e.endMatchEnd), beg2Excl, beg2Incl, end2Incl, end2Excl); + + if (group2 === null) { + return null; + } + /** @type {string[]} */ + + + var matchRet = [match1, group2.match_]; + return { + match_: combine ? matchRet.join("") : matchRet, + remainder: group2.remainder + }; + } + }, + // + // Matching function + // e.g. match("a", input) will look for the regexp called "a" and see if it matches + // returns null or {match_:"a", remainder:"bc"} + // + match_: function match_(m, input) { + var pattern = mhchemParser.patterns.patterns[m]; + + if (pattern === undefined) { + throw ["MhchemBugP", "mhchem bug P. Please report. (" + m + ")"]; // Trying to use non-existing pattern + } else if (typeof pattern === "function") { + return mhchemParser.patterns.patterns[m](input); // cannot use cached var pattern here, because some pattern functions need this===mhchemParser + } else { + // RegExp + var match = input.match(pattern); + + if (match) { + var mm; + + if (match[2]) { + mm = [match[1], match[2]]; + } else if (match[1]) { + mm = match[1]; + } else { + mm = match[0]; + } + + return { + match_: mm, + remainder: input.substr(match[0].length) + }; + } + + return null; + } + } + }, + // + // Generic state machine actions + // + actions: { + 'a=': function a(buffer, m) { + buffer.a = (buffer.a || "") + m; + }, + 'b=': function b(buffer, m) { + buffer.b = (buffer.b || "") + m; + }, + 'p=': function p(buffer, m) { + buffer.p = (buffer.p || "") + m; + }, + 'o=': function o(buffer, m) { + buffer.o = (buffer.o || "") + m; + }, + 'q=': function q(buffer, m) { + buffer.q = (buffer.q || "") + m; + }, + 'd=': function d(buffer, m) { + buffer.d = (buffer.d || "") + m; + }, + 'rm=': function rm(buffer, m) { + buffer.rm = (buffer.rm || "") + m; + }, + 'text=': function text(buffer, m) { + buffer.text_ = (buffer.text_ || "") + m; + }, + 'insert': function insert(buffer, m, a) { + return { + type_: a + }; + }, + 'insert+p1': function insertP1(buffer, m, a) { + return { + type_: a, + p1: m + }; + }, + 'insert+p1+p2': function insertP1P2(buffer, m, a) { + return { + type_: a, + p1: m[0], + p2: m[1] + }; + }, + 'copy': function copy(buffer, m) { + return m; + }, + 'rm': function rm(buffer, m) { + return { + type_: 'rm', + p1: m || "" + }; + }, + 'text': function text(buffer, m) { + return mhchemParser.go(m, 'text'); + }, + '{text}': function text(buffer, m) { + var ret = ["{"]; + mhchemParser.concatArray(ret, mhchemParser.go(m, 'text')); + ret.push("}"); + return ret; + }, + 'tex-math': function texMath(buffer, m) { + return mhchemParser.go(m, 'tex-math'); + }, + 'tex-math tight': function texMathTight(buffer, m) { + return mhchemParser.go(m, 'tex-math tight'); + }, + 'bond': function bond(buffer, m, k) { + return { + type_: 'bond', + kind_: k || m + }; + }, + 'color0-output': function color0Output(buffer, m) { + return { + type_: 'color0', + color: m[0] + }; + }, + 'ce': function ce(buffer, m) { + return mhchemParser.go(m); + }, + '1/2': function _(buffer, m) { + /** @type {ParserOutput[]} */ + var ret = []; + + if (m.match(/^[+\-]/)) { + ret.push(m.substr(0, 1)); + m = m.substr(1); + } + + var n = m.match(/^([0-9]+|\$[a-z]\$|[a-z])\/([0-9]+)(\$[a-z]\$|[a-z])?$/); + n[1] = n[1].replace(/\$/g, ""); + ret.push({ + type_: 'frac', + p1: n[1], + p2: n[2] + }); + + if (n[3]) { + n[3] = n[3].replace(/\$/g, ""); + ret.push({ + type_: 'tex-math', + p1: n[3] + }); + } + + return ret; + }, + '9,9': function _(buffer, m) { + return mhchemParser.go(m, '9,9'); + } + }, + // + // createTransitions + // convert { 'letter': { 'state': { action_: 'output' } } } to { 'state' => [ { pattern: 'letter', task: { action_: [{type_: 'output'}] } } ] } + // with expansion of 'a|b' to 'a' and 'b' (at 2 places) + // + createTransitions: function createTransitions(o) { + var pattern, state; + /** @type {string[]} */ + + var stateArray; + var i; // + // 1. Collect all states + // + + /** @type {Transitions} */ + + var transitions = {}; + + for (pattern in o) { + for (state in o[pattern]) { + stateArray = state.split("|"); + o[pattern][state].stateArray = stateArray; + + for (i = 0; i < stateArray.length; i++) { + transitions[stateArray[i]] = []; + } + } + } // + // 2. Fill states + // + + + for (pattern in o) { + for (state in o[pattern]) { + stateArray = o[pattern][state].stateArray || []; + + for (i = 0; i < stateArray.length; i++) { + // + // 2a. Normalize actions into array: 'text=' ==> [{type_:'text='}] + // (Note to myself: Resolving the function here would be problematic. It would need .bind (for *this*) and currying (for *option*).) + // + + /** @type {any} */ + var p = o[pattern][state]; + + if (p.action_) { + p.action_ = [].concat(p.action_); + + for (var k = 0; k < p.action_.length; k++) { + if (typeof p.action_[k] === "string") { + p.action_[k] = { + type_: p.action_[k] + }; + } + } + } else { + p.action_ = []; + } // + // 2.b Multi-insert + // + + + var patternArray = pattern.split("|"); + + for (var j = 0; j < patternArray.length; j++) { + if (stateArray[i] === '*') { + // insert into all + for (var t in transitions) { + transitions[t].push({ + pattern: patternArray[j], + task: p + }); + } + } else { + transitions[stateArray[i]].push({ + pattern: patternArray[j], + task: p + }); + } + } + } + } + } + + return transitions; + }, + stateMachines: {} +}; // +// Definition of state machines +// + +mhchemParser.stateMachines = { + // + // \ce state machines + // + //#region ce + 'ce': { + // main parser + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': { + action_: 'output' + } + }, + 'else': { + '0|1|2': { + action_: 'beginsWithBond=false', + revisit: true, + toContinue: true + } + }, + 'oxidation$': { + '0': { + action_: 'oxidation-output' + } + }, + 'CMT': { + 'r': { + action_: 'rdt=', + nextState: 'rt' + }, + 'rd': { + action_: 'rqt=', + nextState: 'rdt' + } + }, + 'arrowUpDown': { + '0|1|2|as': { + action_: ['sb=false', 'output', 'operator'], + nextState: '1' + } + }, + 'uprightEntities': { + '0|1|2': { + action_: ['o=', 'output'], + nextState: '1' + } + }, + 'orbital': { + '0|1|2|3': { + action_: 'o=', + nextState: 'o' + } + }, + '->': { + '0|1|2|3': { + action_: 'r=', + nextState: 'r' + }, + 'a|as': { + action_: ['output', 'r='], + nextState: 'r' + }, + '*': { + action_: ['output', 'r='], + nextState: 'r' + } + }, + '+': { + 'o': { + action_: 'd= kv', + nextState: 'd' + }, + 'd|D': { + action_: 'd=', + nextState: 'd' + }, + 'q': { + action_: 'd=', + nextState: 'qd' + }, + 'qd|qD': { + action_: 'd=', + nextState: 'qd' + }, + 'dq': { + action_: ['output', 'd='], + nextState: 'd' + }, + '3': { + action_: ['sb=false', 'output', 'operator'], + nextState: '0' + } + }, + 'amount': { + '0|2': { + action_: 'a=', + nextState: 'a' + } + }, + 'pm-operator': { + '0|1|2|a|as': { + action_: ['sb=false', 'output', { + type_: 'operator', + option: '\\pm' + }], + nextState: '0' + } + }, + 'operator': { + '0|1|2|a|as': { + action_: ['sb=false', 'output', 'operator'], + nextState: '0' + } + }, + '-$': { + 'o|q': { + action_: ['charge or bond', 'output'], + nextState: 'qd' + }, + 'd': { + action_: 'd=', + nextState: 'd' + }, + 'D': { + action_: ['output', { + type_: 'bond', + option: "-" + }], + nextState: '3' + }, + 'q': { + action_: 'd=', + nextState: 'qd' + }, + 'qd': { + action_: 'd=', + nextState: 'qd' + }, + 'qD|dq': { + action_: ['output', { + type_: 'bond', + option: "-" + }], + nextState: '3' + } + }, + '-9': { + '3|o': { + action_: ['output', { + type_: 'insert', + option: 'hyphen' + }], + nextState: '3' + } + }, + '- orbital overlap': { + 'o': { + action_: ['output', { + type_: 'insert', + option: 'hyphen' + }], + nextState: '2' + }, + 'd': { + action_: ['output', { + type_: 'insert', + option: 'hyphen' + }], + nextState: '2' + } + }, + '-': { + '0|1|2': { + action_: [{ + type_: 'output', + option: 1 + }, 'beginsWithBond=true', { + type_: 'bond', + option: "-" + }], + nextState: '3' + }, + '3': { + action_: { + type_: 'bond', + option: "-" + } + }, + 'a': { + action_: ['output', { + type_: 'insert', + option: 'hyphen' + }], + nextState: '2' + }, + 'as': { + action_: [{ + type_: 'output', + option: 2 + }, { + type_: 'bond', + option: "-" + }], + nextState: '3' + }, + 'b': { + action_: 'b=' + }, + 'o': { + action_: { + type_: '- after o/d', + option: false + }, + nextState: '2' + }, + 'q': { + action_: { + type_: '- after o/d', + option: false + }, + nextState: '2' + }, + 'd|qd|dq': { + action_: { + type_: '- after o/d', + option: true + }, + nextState: '2' + }, + 'D|qD|p': { + action_: ['output', { + type_: 'bond', + option: "-" + }], + nextState: '3' + } + }, + 'amount2': { + '1|3': { + action_: 'a=', + nextState: 'a' + } + }, + 'letters': { + '0|1|2|3|a|as|b|p|bp|o': { + action_: 'o=', + nextState: 'o' + }, + 'q|dq': { + action_: ['output', 'o='], + nextState: 'o' + }, + 'd|D|qd|qD': { + action_: 'o after d', + nextState: 'o' + } + }, + 'digits': { + 'o': { + action_: 'q=', + nextState: 'q' + }, + 'd|D': { + action_: 'q=', + nextState: 'dq' + }, + 'q': { + action_: ['output', 'o='], + nextState: 'o' + }, + 'a': { + action_: 'o=', + nextState: 'o' + } + }, + 'space A': { + 'b|p|bp': {} + }, + 'space': { + 'a': { + nextState: 'as' + }, + '0': { + action_: 'sb=false' + }, + '1|2': { + action_: 'sb=true' + }, + 'r|rt|rd|rdt|rdq': { + action_: 'output', + nextState: '0' + }, + '*': { + action_: ['output', 'sb=true'], + nextState: '1' + } + }, + '1st-level escape': { + '1|2': { + action_: ['output', { + type_: 'insert+p1', + option: '1st-level escape' + }] + }, + '*': { + action_: ['output', { + type_: 'insert+p1', + option: '1st-level escape' + }], + nextState: '0' + } + }, + '[(...)]': { + 'r|rt': { + action_: 'rd=', + nextState: 'rd' + }, + 'rd|rdt': { + action_: 'rq=', + nextState: 'rdq' + } + }, + '...': { + 'o|d|D|dq|qd|qD': { + action_: ['output', { + type_: 'bond', + option: "..." + }], + nextState: '3' + }, + '*': { + action_: [{ + type_: 'output', + option: 1 + }, { + type_: 'insert', + option: 'ellipsis' + }], + nextState: '1' + } + }, + '. |* ': { + '*': { + action_: ['output', { + type_: 'insert', + option: 'addition compound' + }], + nextState: '1' + } + }, + 'state of aggregation $': { + '*': { + action_: ['output', 'state of aggregation'], + nextState: '1' + } + }, + '{[(': { + 'a|as|o': { + action_: ['o=', 'output', 'parenthesisLevel++'], + nextState: '2' + }, + '0|1|2|3': { + action_: ['o=', 'output', 'parenthesisLevel++'], + nextState: '2' + }, + '*': { + action_: ['output', 'o=', 'output', 'parenthesisLevel++'], + nextState: '2' + } + }, + ')]}': { + '0|1|2|3|b|p|bp|o': { + action_: ['o=', 'parenthesisLevel--'], + nextState: 'o' + }, + 'a|as|d|D|q|qd|qD|dq': { + action_: ['output', 'o=', 'parenthesisLevel--'], + nextState: 'o' + } + }, + ', ': { + '*': { + action_: ['output', 'comma'], + nextState: '0' + } + }, + '^_': { + // ^ and _ without a sensible argument + '*': {} + }, + '^{(...)}|^($...$)': { + '0|1|2|as': { + action_: 'b=', + nextState: 'b' + }, + 'p': { + action_: 'b=', + nextState: 'bp' + }, + '3|o': { + action_: 'd= kv', + nextState: 'D' + }, + 'q': { + action_: 'd=', + nextState: 'qD' + }, + 'd|D|qd|qD|dq': { + action_: ['output', 'd='], + nextState: 'D' + } + }, + '^a|^\\x{}{}|^\\x{}|^\\x|\'': { + '0|1|2|as': { + action_: 'b=', + nextState: 'b' + }, + 'p': { + action_: 'b=', + nextState: 'bp' + }, + '3|o': { + action_: 'd= kv', + nextState: 'd' + }, + 'q': { + action_: 'd=', + nextState: 'qd' + }, + 'd|qd|D|qD': { + action_: 'd=' + }, + 'dq': { + action_: ['output', 'd='], + nextState: 'd' + } + }, + '_{(state of aggregation)}$': { + 'd|D|q|qd|qD|dq': { + action_: ['output', 'q='], + nextState: 'q' + } + }, + '_{(...)}|_($...$)|_9|_\\x{}{}|_\\x{}|_\\x': { + '0|1|2|as': { + action_: 'p=', + nextState: 'p' + }, + 'b': { + action_: 'p=', + nextState: 'bp' + }, + '3|o': { + action_: 'q=', + nextState: 'q' + }, + 'd|D': { + action_: 'q=', + nextState: 'dq' + }, + 'q|qd|qD|dq': { + action_: ['output', 'q='], + nextState: 'q' + } + }, + '=<>': { + '0|1|2|3|a|as|o|q|d|D|qd|qD|dq': { + action_: [{ + type_: 'output', + option: 2 + }, 'bond'], + nextState: '3' + } + }, + '#': { + '0|1|2|3|a|as|o': { + action_: [{ + type_: 'output', + option: 2 + }, { + type_: 'bond', + option: "#" + }], + nextState: '3' + } + }, + '{}': { + '*': { + action_: { + type_: 'output', + option: 1 + }, + nextState: '1' + } + }, + '{...}': { + '0|1|2|3|a|as|b|p|bp': { + action_: 'o=', + nextState: 'o' + }, + 'o|d|D|q|qd|qD|dq': { + action_: ['output', 'o='], + nextState: 'o' + } + }, + '$...$': { + 'a': { + action_: 'a=' + }, + // 2$n$ + '0|1|2|3|as|b|p|bp|o': { + action_: 'o=', + nextState: 'o' + }, + // not 'amount' + 'as|o': { + action_: 'o=' + }, + 'q|d|D|qd|qD|dq': { + action_: ['output', 'o='], + nextState: 'o' + } + }, + '\\bond{(...)}': { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'bond'], + nextState: "3" + } + }, + '\\frac{(...)}': { + '*': { + action_: [{ + type_: 'output', + option: 1 + }, 'frac-output'], + nextState: '3' + } + }, + '\\overset{(...)}': { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'overset-output'], + nextState: '3' + } + }, + "\\underset{(...)}": { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'underset-output'], + nextState: '3' + } + }, + "\\underbrace{(...)}": { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'underbrace-output'], + nextState: '3' + } + }, + '\\color{(...)}{(...)}1|\\color(...){(...)}2': { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'color-output'], + nextState: '3' + } + }, + '\\color{(...)}0': { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'color0-output'] + } + }, + '\\ce{(...)}': { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'ce'], + nextState: '3' + } + }, + '\\,': { + '*': { + action_: [{ + type_: 'output', + option: 1 + }, 'copy'], + nextState: '1' + } + }, + '\\x{}{}|\\x{}|\\x': { + '0|1|2|3|a|as|b|p|bp|o|c0': { + action_: ['o=', 'output'], + nextState: '3' + }, + '*': { + action_: ['output', 'o=', 'output'], + nextState: '3' + } + }, + 'others': { + '*': { + action_: [{ + type_: 'output', + option: 1 + }, 'copy'], + nextState: '3' + } + }, + 'else2': { + 'a': { + action_: 'a to o', + nextState: 'o', + revisit: true + }, + 'as': { + action_: ['output', 'sb=true'], + nextState: '1', + revisit: true + }, + 'r|rt|rd|rdt|rdq': { + action_: ['output'], + nextState: '0', + revisit: true + }, + '*': { + action_: ['output', 'copy'], + nextState: '3' + } + } + }), + actions: { + 'o after d': function oAfterD(buffer, m) { + var ret; + + if ((buffer.d || "").match(/^[0-9]+$/)) { + var tmp = buffer.d; + buffer.d = undefined; + ret = this['output'](buffer); + buffer.b = tmp; + } else { + ret = this['output'](buffer); + } + + mhchemParser.actions['o='](buffer, m); + return ret; + }, + 'd= kv': function dKv(buffer, m) { + buffer.d = m; + buffer.dType = 'kv'; + }, + 'charge or bond': function chargeOrBond(buffer, m) { + if (buffer['beginsWithBond']) { + /** @type {ParserOutput[]} */ + var ret = []; + mhchemParser.concatArray(ret, this['output'](buffer)); + mhchemParser.concatArray(ret, mhchemParser.actions['bond'](buffer, m, "-")); + return ret; + } else { + buffer.d = m; + } + }, + '- after o/d': function afterOD(buffer, m, isAfterD) { + var c1 = mhchemParser.patterns.match_('orbital', buffer.o || ""); + var c2 = mhchemParser.patterns.match_('one lowercase greek letter $', buffer.o || ""); + var c3 = mhchemParser.patterns.match_('one lowercase latin letter $', buffer.o || ""); + var c4 = mhchemParser.patterns.match_('$one lowercase latin letter$ $', buffer.o || ""); + var hyphenFollows = m === "-" && (c1 && c1.remainder === "" || c2 || c3 || c4); + + if (hyphenFollows && !buffer.a && !buffer.b && !buffer.p && !buffer.d && !buffer.q && !c1 && c3) { + buffer.o = '$' + buffer.o + '$'; + } + /** @type {ParserOutput[]} */ + + + var ret = []; + + if (hyphenFollows) { + mhchemParser.concatArray(ret, this['output'](buffer)); + ret.push({ + type_: 'hyphen' + }); + } else { + c1 = mhchemParser.patterns.match_('digits', buffer.d || ""); + + if (isAfterD && c1 && c1.remainder === '') { + mhchemParser.concatArray(ret, mhchemParser.actions['d='](buffer, m)); + mhchemParser.concatArray(ret, this['output'](buffer)); + } else { + mhchemParser.concatArray(ret, this['output'](buffer)); + mhchemParser.concatArray(ret, mhchemParser.actions['bond'](buffer, m, "-")); + } + } + + return ret; + }, + 'a to o': function aToO(buffer) { + buffer.o = buffer.a; + buffer.a = undefined; + }, + 'sb=true': function sbTrue(buffer) { + buffer.sb = true; + }, + 'sb=false': function sbFalse(buffer) { + buffer.sb = false; + }, + 'beginsWithBond=true': function beginsWithBondTrue(buffer) { + buffer['beginsWithBond'] = true; + }, + 'beginsWithBond=false': function beginsWithBondFalse(buffer) { + buffer['beginsWithBond'] = false; + }, + 'parenthesisLevel++': function parenthesisLevel(buffer) { + buffer['parenthesisLevel']++; + }, + 'parenthesisLevel--': function parenthesisLevel(buffer) { + buffer['parenthesisLevel']--; + }, + 'state of aggregation': function stateOfAggregation(buffer, m) { + return { + type_: 'state of aggregation', + p1: mhchemParser.go(m, 'o') + }; + }, + 'comma': function comma(buffer, m) { + var a = m.replace(/\s*$/, ''); + var withSpace = a !== m; + + if (withSpace && buffer['parenthesisLevel'] === 0) { + return { + type_: 'comma enumeration L', + p1: a + }; + } else { + return { + type_: 'comma enumeration M', + p1: a + }; + } + }, + 'output': function output(buffer, m, entityFollows) { + // entityFollows: + // undefined = if we have nothing else to output, also ignore the just read space (buffer.sb) + // 1 = an entity follows, never omit the space if there was one just read before (can only apply to state 1) + // 2 = 1 + the entity can have an amount, so output a\, instead of converting it to o (can only apply to states a|as) + + /** @type {ParserOutput | ParserOutput[]} */ + var ret; + + if (!buffer.r) { + ret = []; + + if (!buffer.a && !buffer.b && !buffer.p && !buffer.o && !buffer.q && !buffer.d && !entityFollows) {//ret = []; + } else { + if (buffer.sb) { + ret.push({ + type_: 'entitySkip' + }); + } + + if (!buffer.o && !buffer.q && !buffer.d && !buffer.b && !buffer.p && entityFollows !== 2) { + buffer.o = buffer.a; + buffer.a = undefined; + } else if (!buffer.o && !buffer.q && !buffer.d && (buffer.b || buffer.p)) { + buffer.o = buffer.a; + buffer.d = buffer.b; + buffer.q = buffer.p; + buffer.a = buffer.b = buffer.p = undefined; + } else { + if (buffer.o && buffer.dType === 'kv' && mhchemParser.patterns.match_('d-oxidation$', buffer.d || "")) { + buffer.dType = 'oxidation'; + } else if (buffer.o && buffer.dType === 'kv' && !buffer.q) { + buffer.dType = undefined; + } + } + + ret.push({ + type_: 'chemfive', + a: mhchemParser.go(buffer.a, 'a'), + b: mhchemParser.go(buffer.b, 'bd'), + p: mhchemParser.go(buffer.p, 'pq'), + o: mhchemParser.go(buffer.o, 'o'), + q: mhchemParser.go(buffer.q, 'pq'), + d: mhchemParser.go(buffer.d, buffer.dType === 'oxidation' ? 'oxidation' : 'bd'), + dType: buffer.dType + }); + } + } else { + // r + + /** @type {ParserOutput[]} */ + var rd; + + if (buffer.rdt === 'M') { + rd = mhchemParser.go(buffer.rd, 'tex-math'); + } else if (buffer.rdt === 'T') { + rd = [{ + type_: 'text', + p1: buffer.rd || "" + }]; + } else { + rd = mhchemParser.go(buffer.rd); + } + /** @type {ParserOutput[]} */ + + + var rq; + + if (buffer.rqt === 'M') { + rq = mhchemParser.go(buffer.rq, 'tex-math'); + } else if (buffer.rqt === 'T') { + rq = [{ + type_: 'text', + p1: buffer.rq || "" + }]; + } else { + rq = mhchemParser.go(buffer.rq); + } + + ret = { + type_: 'arrow', + r: buffer.r, + rd: rd, + rq: rq + }; + } + + for (var p in buffer) { + if (p !== 'parenthesisLevel' && p !== 'beginsWithBond') { + delete buffer[p]; + } + } + + return ret; + }, + 'oxidation-output': function oxidationOutput(buffer, m) { + var ret = ["{"]; + mhchemParser.concatArray(ret, mhchemParser.go(m, 'oxidation')); + ret.push("}"); + return ret; + }, + 'frac-output': function fracOutput(buffer, m) { + return { + type_: 'frac-ce', + p1: mhchemParser.go(m[0]), + p2: mhchemParser.go(m[1]) + }; + }, + 'overset-output': function oversetOutput(buffer, m) { + return { + type_: 'overset', + p1: mhchemParser.go(m[0]), + p2: mhchemParser.go(m[1]) + }; + }, + 'underset-output': function undersetOutput(buffer, m) { + return { + type_: 'underset', + p1: mhchemParser.go(m[0]), + p2: mhchemParser.go(m[1]) + }; + }, + 'underbrace-output': function underbraceOutput(buffer, m) { + return { + type_: 'underbrace', + p1: mhchemParser.go(m[0]), + p2: mhchemParser.go(m[1]) + }; + }, + 'color-output': function colorOutput(buffer, m) { + return { + type_: 'color', + color1: m[0], + color2: mhchemParser.go(m[1]) + }; + }, + 'r=': function r(buffer, m) { + buffer.r = m; + }, + 'rdt=': function rdt(buffer, m) { + buffer.rdt = m; + }, + 'rd=': function rd(buffer, m) { + buffer.rd = m; + }, + 'rqt=': function rqt(buffer, m) { + buffer.rqt = m; + }, + 'rq=': function rq(buffer, m) { + buffer.rq = m; + }, + 'operator': function operator(buffer, m, p1) { + return { + type_: 'operator', + kind_: p1 || m + }; + } + } + }, + 'a': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': {} + }, + '1/2$': { + '0': { + action_: '1/2' + } + }, + 'else': { + '0': { + nextState: '1', + revisit: true + } + }, + '$(...)$': { + '*': { + action_: 'tex-math tight', + nextState: '1' + } + }, + ',': { + '*': { + action_: { + type_: 'insert', + option: 'commaDecimal' + } + } + }, + 'else2': { + '*': { + action_: 'copy' + } + } + }), + actions: {} + }, + 'o': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': {} + }, + '1/2$': { + '0': { + action_: '1/2' + } + }, + 'else': { + '0': { + nextState: '1', + revisit: true + } + }, + 'letters': { + '*': { + action_: 'rm' + } + }, + '\\ca': { + '*': { + action_: { + type_: 'insert', + option: 'circa' + } + } + }, + '\\x{}{}|\\x{}|\\x': { + '*': { + action_: 'copy' + } + }, + '${(...)}$|$(...)$': { + '*': { + action_: 'tex-math' + } + }, + '{(...)}': { + '*': { + action_: '{text}' + } + }, + 'else2': { + '*': { + action_: 'copy' + } + } + }), + actions: {} + }, + 'text': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': { + action_: 'output' + } + }, + '{...}': { + '*': { + action_: 'text=' + } + }, + '${(...)}$|$(...)$': { + '*': { + action_: 'tex-math' + } + }, + '\\greek': { + '*': { + action_: ['output', 'rm'] + } + }, + '\\,|\\x{}{}|\\x{}|\\x': { + '*': { + action_: ['output', 'copy'] + } + }, + 'else': { + '*': { + action_: 'text=' + } + } + }), + actions: { + 'output': function output(buffer) { + if (buffer.text_) { + /** @type {ParserOutput} */ + var ret = { + type_: 'text', + p1: buffer.text_ + }; + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + } + } + } + }, + 'pq': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': {} + }, + 'state of aggregation $': { + '*': { + action_: 'state of aggregation' + } + }, + 'i$': { + '0': { + nextState: '!f', + revisit: true + } + }, + '(KV letters),': { + '0': { + action_: 'rm', + nextState: '0' + } + }, + 'formula$': { + '0': { + nextState: 'f', + revisit: true + } + }, + '1/2$': { + '0': { + action_: '1/2' + } + }, + 'else': { + '0': { + nextState: '!f', + revisit: true + } + }, + '${(...)}$|$(...)$': { + '*': { + action_: 'tex-math' + } + }, + '{(...)}': { + '*': { + action_: 'text' + } + }, + 'a-z': { + 'f': { + action_: 'tex-math' + } + }, + 'letters': { + '*': { + action_: 'rm' + } + }, + '-9.,9': { + '*': { + action_: '9,9' + } + }, + ',': { + '*': { + action_: { + type_: 'insert+p1', + option: 'comma enumeration S' + } + } + }, + '\\color{(...)}{(...)}1|\\color(...){(...)}2': { + '*': { + action_: 'color-output' + } + }, + '\\color{(...)}0': { + '*': { + action_: 'color0-output' + } + }, + '\\ce{(...)}': { + '*': { + action_: 'ce' + } + }, + '\\,|\\x{}{}|\\x{}|\\x': { + '*': { + action_: 'copy' + } + }, + 'else2': { + '*': { + action_: 'copy' + } + } + }), + actions: { + 'state of aggregation': function stateOfAggregation(buffer, m) { + return { + type_: 'state of aggregation subscript', + p1: mhchemParser.go(m, 'o') + }; + }, + 'color-output': function colorOutput(buffer, m) { + return { + type_: 'color', + color1: m[0], + color2: mhchemParser.go(m[1], 'pq') + }; + } + } + }, + 'bd': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': {} + }, + 'x$': { + '0': { + nextState: '!f', + revisit: true + } + }, + 'formula$': { + '0': { + nextState: 'f', + revisit: true + } + }, + 'else': { + '0': { + nextState: '!f', + revisit: true + } + }, + '-9.,9 no missing 0': { + '*': { + action_: '9,9' + } + }, + '.': { + '*': { + action_: { + type_: 'insert', + option: 'electron dot' + } + } + }, + 'a-z': { + 'f': { + action_: 'tex-math' + } + }, + 'x': { + '*': { + action_: { + type_: 'insert', + option: 'KV x' + } + } + }, + 'letters': { + '*': { + action_: 'rm' + } + }, + '\'': { + '*': { + action_: { + type_: 'insert', + option: 'prime' + } + } + }, + '${(...)}$|$(...)$': { + '*': { + action_: 'tex-math' + } + }, + '{(...)}': { + '*': { + action_: 'text' + } + }, + '\\color{(...)}{(...)}1|\\color(...){(...)}2': { + '*': { + action_: 'color-output' + } + }, + '\\color{(...)}0': { + '*': { + action_: 'color0-output' + } + }, + '\\ce{(...)}': { + '*': { + action_: 'ce' + } + }, + '\\,|\\x{}{}|\\x{}|\\x': { + '*': { + action_: 'copy' + } + }, + 'else2': { + '*': { + action_: 'copy' + } + } + }), + actions: { + 'color-output': function colorOutput(buffer, m) { + return { + type_: 'color', + color1: m[0], + color2: mhchemParser.go(m[1], 'bd') + }; + } + } + }, + 'oxidation': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': {} + }, + 'roman numeral': { + '*': { + action_: 'roman-numeral' + } + }, + '${(...)}$|$(...)$': { + '*': { + action_: 'tex-math' + } + }, + 'else': { + '*': { + action_: 'copy' + } + } + }), + actions: { + 'roman-numeral': function romanNumeral(buffer, m) { + return { + type_: 'roman numeral', + p1: m || "" + }; + } + } + }, + 'tex-math': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': { + action_: 'output' + } + }, + '\\ce{(...)}': { + '*': { + action_: ['output', 'ce'] + } + }, + '{...}|\\,|\\x{}{}|\\x{}|\\x': { + '*': { + action_: 'o=' + } + }, + 'else': { + '*': { + action_: 'o=' + } + } + }), + actions: { + 'output': function output(buffer) { + if (buffer.o) { + /** @type {ParserOutput} */ + var ret = { + type_: 'tex-math', + p1: buffer.o + }; + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + } + } + } + }, + 'tex-math tight': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': { + action_: 'output' + } + }, + '\\ce{(...)}': { + '*': { + action_: ['output', 'ce'] + } + }, + '{...}|\\,|\\x{}{}|\\x{}|\\x': { + '*': { + action_: 'o=' + } + }, + '-|+': { + '*': { + action_: 'tight operator' + } + }, + 'else': { + '*': { + action_: 'o=' + } + } + }), + actions: { + 'tight operator': function tightOperator(buffer, m) { + buffer.o = (buffer.o || "") + "{" + m + "}"; + }, + 'output': function output(buffer) { + if (buffer.o) { + /** @type {ParserOutput} */ + var ret = { + type_: 'tex-math', + p1: buffer.o + }; + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + } + } + } + }, + '9,9': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': {} + }, + ',': { + '*': { + action_: 'comma' + } + }, + 'else': { + '*': { + action_: 'copy' + } + } + }), + actions: { + 'comma': function comma() { + return { + type_: 'commaDecimal' + }; + } + } + }, + //#endregion + // + // \pu state machines + // + //#region pu + 'pu': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': { + action_: 'output' + } + }, + 'space$': { + '*': { + action_: ['output', 'space'] + } + }, + '{[(|)]}': { + '0|a': { + action_: 'copy' + } + }, + '(-)(9)^(-9)': { + '0': { + action_: 'number^', + nextState: 'a' + } + }, + '(-)(9.,9)(e)(99)': { + '0': { + action_: 'enumber', + nextState: 'a' + } + }, + 'space': { + '0|a': {} + }, + 'pm-operator': { + '0|a': { + action_: { + type_: 'operator', + option: '\\pm' + }, + nextState: '0' + } + }, + 'operator': { + '0|a': { + action_: 'copy', + nextState: '0' + } + }, + '//': { + 'd': { + action_: 'o=', + nextState: '/' + } + }, + '/': { + 'd': { + action_: 'o=', + nextState: '/' + } + }, + '{...}|else': { + '0|d': { + action_: 'd=', + nextState: 'd' + }, + 'a': { + action_: ['space', 'd='], + nextState: 'd' + }, + '/|q': { + action_: 'q=', + nextState: 'q' + } + } + }), + actions: { + 'enumber': function enumber(buffer, m) { + /** @type {ParserOutput[]} */ + var ret = []; + + if (m[0] === "+-" || m[0] === "+/-") { + ret.push("\\pm "); + } else if (m[0]) { + ret.push(m[0]); + } + + if (m[1]) { + mhchemParser.concatArray(ret, mhchemParser.go(m[1], 'pu-9,9')); + + if (m[2]) { + if (m[2].match(/[,.]/)) { + mhchemParser.concatArray(ret, mhchemParser.go(m[2], 'pu-9,9')); + } else { + ret.push(m[2]); + } + } + + m[3] = m[4] || m[3]; + + if (m[3]) { + m[3] = m[3].trim(); + + if (m[3] === "e" || m[3].substr(0, 1) === "*") { + ret.push({ + type_: 'cdot' + }); + } else { + ret.push({ + type_: 'times' + }); + } + } + } + + if (m[3]) { + ret.push("10^{" + m[5] + "}"); + } + + return ret; + }, + 'number^': function number(buffer, m) { + /** @type {ParserOutput[]} */ + var ret = []; + + if (m[0] === "+-" || m[0] === "+/-") { + ret.push("\\pm "); + } else if (m[0]) { + ret.push(m[0]); + } + + mhchemParser.concatArray(ret, mhchemParser.go(m[1], 'pu-9,9')); + ret.push("^{" + m[2] + "}"); + return ret; + }, + 'operator': function operator(buffer, m, p1) { + return { + type_: 'operator', + kind_: p1 || m + }; + }, + 'space': function space() { + return { + type_: 'pu-space-1' + }; + }, + 'output': function output(buffer) { + /** @type {ParserOutput | ParserOutput[]} */ + var ret; + var md = mhchemParser.patterns.match_('{(...)}', buffer.d || ""); + + if (md && md.remainder === '') { + buffer.d = md.match_; + } + + var mq = mhchemParser.patterns.match_('{(...)}', buffer.q || ""); + + if (mq && mq.remainder === '') { + buffer.q = mq.match_; + } + + if (buffer.d) { + buffer.d = buffer.d.replace(/\u00B0C|\^oC|\^{o}C/g, "{}^{\\circ}C"); + buffer.d = buffer.d.replace(/\u00B0F|\^oF|\^{o}F/g, "{}^{\\circ}F"); + } + + if (buffer.q) { + // fraction + buffer.q = buffer.q.replace(/\u00B0C|\^oC|\^{o}C/g, "{}^{\\circ}C"); + buffer.q = buffer.q.replace(/\u00B0F|\^oF|\^{o}F/g, "{}^{\\circ}F"); + var b5 = { + d: mhchemParser.go(buffer.d, 'pu'), + q: mhchemParser.go(buffer.q, 'pu') + }; + + if (buffer.o === '//') { + ret = { + type_: 'pu-frac', + p1: b5.d, + p2: b5.q + }; + } else { + ret = b5.d; + + if (b5.d.length > 1 || b5.q.length > 1) { + ret.push({ + type_: ' / ' + }); + } else { + ret.push({ + type_: '/' + }); + } + + mhchemParser.concatArray(ret, b5.q); + } + } else { + // no fraction + ret = mhchemParser.go(buffer.d, 'pu-2'); + } + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + } + } + }, + 'pu-2': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': { + action_: 'output' + } + }, + '*': { + '*': { + action_: ['output', 'cdot'], + nextState: '0' + } + }, + '\\x': { + '*': { + action_: 'rm=' + } + }, + 'space': { + '*': { + action_: ['output', 'space'], + nextState: '0' + } + }, + '^{(...)}|^(-1)': { + '1': { + action_: '^(-1)' + } + }, + '-9.,9': { + '0': { + action_: 'rm=', + nextState: '0' + }, + '1': { + action_: '^(-1)', + nextState: '0' + } + }, + '{...}|else': { + '*': { + action_: 'rm=', + nextState: '1' + } + } + }), + actions: { + 'cdot': function cdot() { + return { + type_: 'tight cdot' + }; + }, + '^(-1)': function _(buffer, m) { + buffer.rm += "^{" + m + "}"; + }, + 'space': function space() { + return { + type_: 'pu-space-2' + }; + }, + 'output': function output(buffer) { + /** @type {ParserOutput | ParserOutput[]} */ + var ret = []; + + if (buffer.rm) { + var mrm = mhchemParser.patterns.match_('{(...)}', buffer.rm || ""); + + if (mrm && mrm.remainder === '') { + ret = mhchemParser.go(mrm.match_, 'pu'); + } else { + ret = { + type_: 'rm', + p1: buffer.rm + }; + } + } + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + } + } + }, + 'pu-9,9': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '0': { + action_: 'output-0' + }, + 'o': { + action_: 'output-o' + } + }, + ',': { + '0': { + action_: ['output-0', 'comma'], + nextState: 'o' + } + }, + '.': { + '0': { + action_: ['output-0', 'copy'], + nextState: 'o' + } + }, + 'else': { + '*': { + action_: 'text=' + } + } + }), + actions: { + 'comma': function comma() { + return { + type_: 'commaDecimal' + }; + }, + 'output-0': function output0(buffer) { + /** @type {ParserOutput[]} */ + var ret = []; + buffer.text_ = buffer.text_ || ""; + + if (buffer.text_.length > 4) { + var a = buffer.text_.length % 3; + + if (a === 0) { + a = 3; + } + + for (var i = buffer.text_.length - 3; i > 0; i -= 3) { + ret.push(buffer.text_.substr(i, 3)); + ret.push({ + type_: '1000 separator' + }); + } + + ret.push(buffer.text_.substr(0, a)); + ret.reverse(); + } else { + ret.push(buffer.text_); + } + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + }, + 'output-o': function outputO(buffer) { + /** @type {ParserOutput[]} */ + var ret = []; + buffer.text_ = buffer.text_ || ""; + + if (buffer.text_.length > 4) { + var a = buffer.text_.length - 3; + + for (var i = 0; i < a; i += 3) { + ret.push(buffer.text_.substr(i, 3)); + ret.push({ + type_: '1000 separator' + }); + } + + ret.push(buffer.text_.substr(i)); + } else { + ret.push(buffer.text_); + } + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + } + } + } //#endregion + +}; // +// texify: Take MhchemParser output and convert it to TeX +// + +/** @type {Texify} */ + +var texify = { + go: function go(input, isInner) { + // (recursive, max 4 levels) + if (!input) { + return ""; + } + + var res = ""; + var cee = false; + + for (var i = 0; i < input.length; i++) { + var inputi = input[i]; + + if (typeof inputi === "string") { + res += inputi; + } else { + res += texify._go2(inputi); + + if (inputi.type_ === '1st-level escape') { + cee = true; + } + } + } + + if (!isInner && !cee && res) { + res = "{" + res + "}"; + } + + return res; + }, + _goInner: function _goInner(input) { + if (!input) { + return input; + } + + return texify.go(input, true); + }, + _go2: function _go2(buf) { + /** @type {undefined | string} */ + var res; + + switch (buf.type_) { + case 'chemfive': + res = ""; + var b5 = { + a: texify._goInner(buf.a), + b: texify._goInner(buf.b), + p: texify._goInner(buf.p), + o: texify._goInner(buf.o), + q: texify._goInner(buf.q), + d: texify._goInner(buf.d) + }; // + // a + // + + if (b5.a) { + if (b5.a.match(/^[+\-]/)) { + b5.a = "{" + b5.a + "}"; + } + + res += b5.a + "\\,"; + } // + // b and p + // + + + if (b5.b || b5.p) { + res += "{\\vphantom{X}}"; + res += "^{\\hphantom{" + (b5.b || "") + "}}_{\\hphantom{" + (b5.p || "") + "}}"; + res += "{\\vphantom{X}}"; + res += "^{\\smash[t]{\\vphantom{2}}\\mathllap{" + (b5.b || "") + "}}"; + res += "_{\\vphantom{2}\\mathllap{\\smash[t]{" + (b5.p || "") + "}}}"; + } // + // o + // + + + if (b5.o) { + if (b5.o.match(/^[+\-]/)) { + b5.o = "{" + b5.o + "}"; + } + + res += b5.o; + } // + // q and d + // + + + if (buf.dType === 'kv') { + if (b5.d || b5.q) { + res += "{\\vphantom{X}}"; + } + + if (b5.d) { + res += "^{" + b5.d + "}"; + } + + if (b5.q) { + res += "_{\\smash[t]{" + b5.q + "}}"; + } + } else if (buf.dType === 'oxidation') { + if (b5.d) { + res += "{\\vphantom{X}}"; + res += "^{" + b5.d + "}"; + } + + if (b5.q) { + res += "{\\vphantom{X}}"; + res += "_{\\smash[t]{" + b5.q + "}}"; + } + } else { + if (b5.q) { + res += "{\\vphantom{X}}"; + res += "_{\\smash[t]{" + b5.q + "}}"; + } + + if (b5.d) { + res += "{\\vphantom{X}}"; + res += "^{" + b5.d + "}"; + } + } + + break; + + case 'rm': + res = "\\mathrm{" + buf.p1 + "}"; + break; + + case 'text': + if (buf.p1.match(/[\^_]/)) { + buf.p1 = buf.p1.replace(" ", "~").replace("-", "\\text{-}"); + res = "\\mathrm{" + buf.p1 + "}"; + } else { + res = "\\text{" + buf.p1 + "}"; + } + + break; + + case 'roman numeral': + res = "\\mathrm{" + buf.p1 + "}"; + break; + + case 'state of aggregation': + res = "\\mskip2mu " + texify._goInner(buf.p1); + break; + + case 'state of aggregation subscript': + res = "\\mskip1mu " + texify._goInner(buf.p1); + break; + + case 'bond': + res = texify._getBond(buf.kind_); + + if (!res) { + throw ["MhchemErrorBond", "mhchem Error. Unknown bond type (" + buf.kind_ + ")"]; + } + + break; + + case 'frac': + var c = "\\frac{" + buf.p1 + "}{" + buf.p2 + "}"; + res = "\\mathchoice{\\textstyle" + c + "}{" + c + "}{" + c + "}{" + c + "}"; + break; + + case 'pu-frac': + var d = "\\frac{" + texify._goInner(buf.p1) + "}{" + texify._goInner(buf.p2) + "}"; + res = "\\mathchoice{\\textstyle" + d + "}{" + d + "}{" + d + "}{" + d + "}"; + break; + + case 'tex-math': + res = buf.p1 + " "; + break; + + case 'frac-ce': + res = "\\frac{" + texify._goInner(buf.p1) + "}{" + texify._goInner(buf.p2) + "}"; + break; + + case 'overset': + res = "\\overset{" + texify._goInner(buf.p1) + "}{" + texify._goInner(buf.p2) + "}"; + break; + + case 'underset': + res = "\\underset{" + texify._goInner(buf.p1) + "}{" + texify._goInner(buf.p2) + "}"; + break; + + case 'underbrace': + res = "\\underbrace{" + texify._goInner(buf.p1) + "}_{" + texify._goInner(buf.p2) + "}"; + break; + + case 'color': + res = "{\\color{" + buf.color1 + "}{" + texify._goInner(buf.color2) + "}}"; + break; + + case 'color0': + res = "\\color{" + buf.color + "}"; + break; + + case 'arrow': + var b6 = { + rd: texify._goInner(buf.rd), + rq: texify._goInner(buf.rq) + }; + + var arrow = "\\x" + texify._getArrow(buf.r); + + if (b6.rq) { + arrow += "[{" + b6.rq + "}]"; + } + + if (b6.rd) { + arrow += "{" + b6.rd + "}"; + } else { + arrow += "{}"; + } + + res = arrow; + break; + + case 'operator': + res = texify._getOperator(buf.kind_); + break; + + case '1st-level escape': + res = buf.p1 + " "; // &, \\\\, \\hlin + + break; + + case 'space': + res = " "; + break; + + case 'entitySkip': + res = "~"; + break; + + case 'pu-space-1': + res = "~"; + break; + + case 'pu-space-2': + res = "\\mkern3mu "; + break; + + case '1000 separator': + res = "\\mkern2mu "; + break; + + case 'commaDecimal': + res = "{,}"; + break; + + case 'comma enumeration L': + res = "{" + buf.p1 + "}\\mkern6mu "; + break; + + case 'comma enumeration M': + res = "{" + buf.p1 + "}\\mkern3mu "; + break; + + case 'comma enumeration S': + res = "{" + buf.p1 + "}\\mkern1mu "; + break; + + case 'hyphen': + res = "\\text{-}"; + break; + + case 'addition compound': + res = "\\,{\\cdot}\\,"; + break; + + case 'electron dot': + res = "\\mkern1mu \\bullet\\mkern1mu "; + break; + + case 'KV x': + res = "{\\times}"; + break; + + case 'prime': + res = "\\prime "; + break; + + case 'cdot': + res = "\\cdot "; + break; + + case 'tight cdot': + res = "\\mkern1mu{\\cdot}\\mkern1mu "; + break; + + case 'times': + res = "\\times "; + break; + + case 'circa': + res = "{\\sim}"; + break; + + case '^': + res = "uparrow"; + break; + + case 'v': + res = "downarrow"; + break; + + case 'ellipsis': + res = "\\ldots "; + break; + + case '/': + res = "/"; + break; + + case ' / ': + res = "\\,/\\,"; + break; + + default: + assertNever(buf); + throw ["MhchemBugT", "mhchem bug T. Please report."]; + // Missing texify rule or unknown MhchemParser output + } + + assertString(res); + return res; + }, + _getArrow: function _getArrow(a) { + switch (a) { + case "->": + return "rightarrow"; + + case "\u2192": + return "rightarrow"; + + case "\u27F6": + return "rightarrow"; + + case "<-": + return "leftarrow"; + + case "<->": + return "leftrightarrow"; + + case "<-->": + return "rightleftarrows"; + + case "<=>": + return "rightleftharpoons"; + + case "\u21CC": + return "rightleftharpoons"; + + case "<=>>": + return "rightequilibrium"; + + case "<<=>": + return "leftequilibrium"; + + default: + assertNever(a); + throw ["MhchemBugT", "mhchem bug T. Please report."]; + } + }, + _getBond: function _getBond(a) { + switch (a) { + case "-": + return "{-}"; + + case "1": + return "{-}"; + + case "=": + return "{=}"; + + case "2": + return "{=}"; + + case "#": + return "{\\equiv}"; + + case "3": + return "{\\equiv}"; + + case "~": + return "{\\tripledash}"; + + case "~-": + return "{\\mathrlap{\\raisebox{-.1em}{$-$}}\\raisebox{.1em}{$\\tripledash$}}"; + + case "~=": + return "{\\mathrlap{\\raisebox{-.2em}{$-$}}\\mathrlap{\\raisebox{.2em}{$\\tripledash$}}-}"; + + case "~--": + return "{\\mathrlap{\\raisebox{-.2em}{$-$}}\\mathrlap{\\raisebox{.2em}{$\\tripledash$}}-}"; + + case "-~-": + return "{\\mathrlap{\\raisebox{-.2em}{$-$}}\\mathrlap{\\raisebox{.2em}{$-$}}\\tripledash}"; + + case "...": + return "{{\\cdot}{\\cdot}{\\cdot}}"; + + case "....": + return "{{\\cdot}{\\cdot}{\\cdot}{\\cdot}}"; + + case "->": + return "{\\rightarrow}"; + + case "<-": + return "{\\leftarrow}"; + + case "<": + return "{<}"; + + case ">": + return "{>}"; + + default: + assertNever(a); + throw ["MhchemBugT", "mhchem bug T. Please report."]; + } + }, + _getOperator: function _getOperator(a) { + switch (a) { + case "+": + return " {}+{} "; + + case "-": + return " {}-{} "; + + case "=": + return " {}={} "; + + case "<": + return " {}<{} "; + + case ">": + return " {}>{} "; + + case "<<": + return " {}\\ll{} "; + + case ">>": + return " {}\\gg{} "; + + case "\\pm": + return " {}\\pm{} "; + + case "\\approx": + return " {}\\approx{} "; + + case "$\\approx$": + return " {}\\approx{} "; + + case "v": + return " \\downarrow{} "; + + case "(v)": + return " \\downarrow{} "; + + case "^": + return " \\uparrow{} "; + + case "(^)": + return " \\uparrow{} "; + + default: + assertNever(a); + throw ["MhchemBugT", "mhchem bug T. Please report."]; + } + } +}; // +// Helpers for code anaylsis +// Will show type error at calling position +// + +/** @param {number} a */ + +function assertNever(a) {} +/** @param {string} a */ + + +function assertString(a) {} +}(); +__webpack_exports__ = __webpack_exports__["default"]; +/******/ return __webpack_exports__; +/******/ })() +; +}); \ No newline at end of file diff --git a/core/bikeshed/katex/dist/contrib/mhchem.min.js b/core/bikeshed/katex/dist/contrib/mhchem.min.js new file mode 100644 index 00000000..e0c4a5e4 --- /dev/null +++ b/core/bikeshed/katex/dist/contrib/mhchem.min.js @@ -0,0 +1 @@ +!function(t,e){if("object"==typeof exports&&"object"==typeof module)module.exports=e(require("katex"));else if("function"==typeof define&&define.amd)define(["katex"],e);else{var n="object"==typeof exports?e(require("katex")):e(t.katex);for(var o in n)("object"==typeof exports?exports:t)[o]=n[o]}}("undefined"!=typeof self?self:this,(function(t){return function(){"use strict";var e={771:function(e){e.exports=t}},n={};function o(t){var a=n[t];if(void 0!==a)return a.exports;var r=n[t]={exports:{}};return e[t](r,r.exports,o),r.exports}o.n=function(t){var e=t&&t.__esModule?function(){return t.default}:function(){return t};return o.d(e,{a:e}),e},o.d=function(t,e){for(var n in e)o.o(e,n)&&!o.o(t,n)&&Object.defineProperty(t,n,{enumerable:!0,get:e[n]})},o.o=function(t,e){return Object.prototype.hasOwnProperty.call(t,e)};var a={};return function(){var t=o(771),e=o.n(t);e().__defineMacro("\\ce",(function(t){return n(t.consumeArgs(1)[0],"ce")})),e().__defineMacro("\\pu",(function(t){return n(t.consumeArgs(1)[0],"pu")})),e().__defineMacro("\\tripledash","{\\vphantom{-}\\raisebox{2.56mu}{$\\mkern2mu\\tiny\\text{-}\\mkern1mu\\text{-}\\mkern1mu\\text{-}\\mkern2mu$}}");var n=function(t,e){for(var n="",o=t[t.length-1].loc.start,i=t.length-1;i>=0;i--)t[i].loc.start>o&&(n+=" ",o=t[i].loc.start),n+=t[i].text,o+=t[i].text.length;return r.go(a.go(n,e))},a={go:function(t,e){if(!t)return[];void 0===e&&(e="ce");var n,o="0",r={};r.parenthesisLevel=0,t=(t=(t=t.replace(/\n/g," ")).replace(/[\u2212\u2013\u2014\u2010]/g,"-")).replace(/[\u2026]/g,"...");for(var i=10,c=[];;){n!==t?(i=10,n=t):i--;var u=a.stateMachines[e],p=u.transitions[o]||u.transitions["*"];t:for(var s=0;s0))return c;if(d.revisit||(t=_.remainder),!d.toContinue)break t}}if(i<=0)throw["MhchemBugU","mhchem bug U. 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The reaction arrow code is simplified. All reaction arrows are rendered + * using KaTeX extensible arrows instead of building non-extensible arrows. + * 5. \tripledash vertical alignment is slightly adjusted. + * + * This code, as other KaTeX code, is released under the MIT license. + * + * /************************************************************* + * + * MathJax/extensions/TeX/mhchem.js + * + * Implements the \ce command for handling chemical formulas + * from the mhchem LaTeX package. + * + * --------------------------------------------------------------------- + * + * Copyright (c) 2011-2015 The MathJax Consortium + * Copyright (c) 2015-2018 Martin Hensel + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ +// +// Coding Style +// - use '' for identifiers that can by minified/uglified +// - use "" for strings that need to stay untouched +// version: "3.3.0" for MathJax and KaTeX +// Add \ce, \pu, and \tripledash to the KaTeX macros. +katex.__defineMacro("\\ce", function (context) { + return chemParse(context.consumeArgs(1)[0], "ce"); +}); + +katex.__defineMacro("\\pu", function (context) { + return chemParse(context.consumeArgs(1)[0], "pu"); +}); // Needed for \bond for the ~ forms +// Raise by 2.56mu, not 2mu. We're raising a hyphen-minus, U+002D, not +// a mathematical minus, U+2212. So we need that extra 0.56. + + +katex.__defineMacro("\\tripledash", "{\\vphantom{-}\\raisebox{2.56mu}{$\\mkern2mu" + "\\tiny\\text{-}\\mkern1mu\\text{-}\\mkern1mu\\text{-}\\mkern2mu$}}"); +// This is the main function for handing the \ce and \pu commands. +// It takes the argument to \ce or \pu and returns the corresponding TeX string. +// + +var chemParse = function chemParse(tokens, stateMachine) { + // Recreate the argument string from KaTeX's array of tokens. + var str = ""; + var expectedLoc = tokens[tokens.length - 1].loc.start; + + for (var i = tokens.length - 1; i >= 0; i--) { + if (tokens[i].loc.start > expectedLoc) { + // context.consumeArgs has eaten a space. + str += " "; + expectedLoc = tokens[i].loc.start; + } + + str += tokens[i].text; + expectedLoc += tokens[i].text.length; + } + + var tex = texify.go(mhchemParser.go(str, stateMachine)); + return tex; +}; // +// Core parser for mhchem syntax (recursive) +// + +/** @type {MhchemParser} */ + + +var mhchemParser = { + // + // Parses mchem \ce syntax + // + // Call like + // go("H2O"); + // + go: function go(input, stateMachine) { + if (!input) { + return []; + } + + if (stateMachine === undefined) { + stateMachine = 'ce'; + } + + var state = '0'; // + // String buffers for parsing: + // + // buffer.a == amount + // buffer.o == element + // buffer.b == left-side superscript + // buffer.p == left-side subscript + // buffer.q == right-side subscript + // buffer.d == right-side superscript + // + // buffer.r == arrow + // buffer.rdt == arrow, script above, type + // buffer.rd == arrow, script above, content + // buffer.rqt == arrow, script below, type + // buffer.rq == arrow, script below, content + // + // buffer.text_ + // buffer.rm + // etc. + // + // buffer.parenthesisLevel == int, starting at 0 + // buffer.sb == bool, space before + // buffer.beginsWithBond == bool + // + // These letters are also used as state names. + // + // Other states: + // 0 == begin of main part (arrow/operator unlikely) + // 1 == next entity + // 2 == next entity (arrow/operator unlikely) + // 3 == next atom + // c == macro + // + + /** @type {Buffer} */ + + var buffer = {}; + buffer['parenthesisLevel'] = 0; + input = input.replace(/\n/g, " "); + input = input.replace(/[\u2212\u2013\u2014\u2010]/g, "-"); + input = input.replace(/[\u2026]/g, "..."); // + // Looks through mhchemParser.transitions, to execute a matching action + // (recursive) + // + + var lastInput; + var watchdog = 10; + /** @type {ParserOutput[]} */ + + var output = []; + + while (true) { + if (lastInput !== input) { + watchdog = 10; + lastInput = input; + } else { + watchdog--; + } // + // Find actions in transition table + // + + + var machine = mhchemParser.stateMachines[stateMachine]; + var t = machine.transitions[state] || machine.transitions['*']; + + iterateTransitions: for (var i = 0; i < t.length; i++) { + var matches = mhchemParser.patterns.match_(t[i].pattern, input); + + if (matches) { + // + // Execute actions + // + var task = t[i].task; + + for (var iA = 0; iA < task.action_.length; iA++) { + var o; // + // Find and execute action + // + + if (machine.actions[task.action_[iA].type_]) { + o = machine.actions[task.action_[iA].type_](buffer, matches.match_, task.action_[iA].option); + } else if (mhchemParser.actions[task.action_[iA].type_]) { + o = mhchemParser.actions[task.action_[iA].type_](buffer, matches.match_, task.action_[iA].option); + } else { + throw ["MhchemBugA", "mhchem bug A. Please report. (" + task.action_[iA].type_ + ")"]; // Trying to use non-existing action + } // + // Add output + // + + + mhchemParser.concatArray(output, o); + } // + // Set next state, + // Shorten input, + // Continue with next character + // (= apply only one transition per position) + // + + + state = task.nextState || state; + + if (input.length > 0) { + if (!task.revisit) { + input = matches.remainder; + } + + if (!task.toContinue) { + break iterateTransitions; + } + } else { + return output; + } + } + } // + // Prevent infinite loop + // + + + if (watchdog <= 0) { + throw ["MhchemBugU", "mhchem bug U. Please report."]; // Unexpected character + } + } + }, + concatArray: function concatArray(a, b) { + if (b) { + if (Array.isArray(b)) { + for (var iB = 0; iB < b.length; iB++) { + a.push(b[iB]); + } + } else { + a.push(b); + } + } + }, + patterns: { + // + // Matching patterns + // either regexps or function that return null or {match_:"a", remainder:"bc"} + // + patterns: { + // property names must not look like integers ("2") for correct property traversal order, later on + 'empty': /^$/, + 'else': /^./, + 'else2': /^./, + 'space': /^\s/, + 'space A': /^\s(?=[A-Z\\$])/, + 'space$': /^\s$/, + 'a-z': /^[a-z]/, + 'x': /^x/, + 'x$': /^x$/, + 'i$': /^i$/, + 'letters': /^(?:[a-zA-Z\u03B1-\u03C9\u0391-\u03A9?@]|(?:\\(?:alpha|beta|gamma|delta|epsilon|zeta|eta|theta|iota|kappa|lambda|mu|nu|xi|omicron|pi|rho|sigma|tau|upsilon|phi|chi|psi|omega|Gamma|Delta|Theta|Lambda|Xi|Pi|Sigma|Upsilon|Phi|Psi|Omega)(?:\s+|\{\}|(?![a-zA-Z]))))+/, + '\\greek': /^\\(?:alpha|beta|gamma|delta|epsilon|zeta|eta|theta|iota|kappa|lambda|mu|nu|xi|omicron|pi|rho|sigma|tau|upsilon|phi|chi|psi|omega|Gamma|Delta|Theta|Lambda|Xi|Pi|Sigma|Upsilon|Phi|Psi|Omega)(?:\s+|\{\}|(?![a-zA-Z]))/, + 'one lowercase latin letter $': /^(?:([a-z])(?:$|[^a-zA-Z]))$/, + '$one lowercase latin letter$ $': /^\$(?:([a-z])(?:$|[^a-zA-Z]))\$$/, + 'one lowercase greek letter $': /^(?:\$?[\u03B1-\u03C9]\$?|\$?\\(?:alpha|beta|gamma|delta|epsilon|zeta|eta|theta|iota|kappa|lambda|mu|nu|xi|omicron|pi|rho|sigma|tau|upsilon|phi|chi|psi|omega)\s*\$?)(?:\s+|\{\}|(?![a-zA-Z]))$/, + 'digits': /^[0-9]+/, + '-9.,9': /^[+\-]?(?:[0-9]+(?:[,.][0-9]+)?|[0-9]*(?:\.[0-9]+))/, + '-9.,9 no missing 0': /^[+\-]?[0-9]+(?:[.,][0-9]+)?/, + '(-)(9.,9)(e)(99)': function e99(input) { + var m = input.match(/^(\+\-|\+\/\-|\+|\-|\\pm\s?)?([0-9]+(?:[,.][0-9]+)?|[0-9]*(?:\.[0-9]+))?(\((?:[0-9]+(?:[,.][0-9]+)?|[0-9]*(?:\.[0-9]+))\))?(?:([eE]|\s*(\*|x|\\times|\u00D7)\s*10\^)([+\-]?[0-9]+|\{[+\-]?[0-9]+\}))?/); + + if (m && m[0]) { + return { + match_: m.splice(1), + remainder: input.substr(m[0].length) + }; + } + + return null; + }, + '(-)(9)^(-9)': function _(input) { + var m = input.match(/^(\+\-|\+\/\-|\+|\-|\\pm\s?)?([0-9]+(?:[,.][0-9]+)?|[0-9]*(?:\.[0-9]+)?)\^([+\-]?[0-9]+|\{[+\-]?[0-9]+\})/); + + if (m && m[0]) { + return { + match_: m.splice(1), + remainder: input.substr(m[0].length) + }; + } + + return null; + }, + 'state of aggregation $': function stateOfAggregation$(input) { + // ... or crystal system + var a = mhchemParser.patterns.findObserveGroups(input, "", /^\([a-z]{1,3}(?=[\),])/, ")", ""); // (aq), (aq,$\infty$), (aq, sat) + + if (a && a.remainder.match(/^($|[\s,;\)\]\}])/)) { + return a; + } // AND end of 'phrase' + + + var m = input.match(/^(?:\((?:\\ca\s?)?\$[amothc]\$\))/); // OR crystal system ($o$) (\ca$c$) + + if (m) { + return { + match_: m[0], + remainder: input.substr(m[0].length) + }; + } + + return null; + }, + '_{(state of aggregation)}$': /^_\{(\([a-z]{1,3}\))\}/, + '{[(': /^(?:\\\{|\[|\()/, + ')]}': /^(?:\)|\]|\\\})/, + ', ': /^[,;]\s*/, + ',': /^[,;]/, + '.': /^[.]/, + '. ': /^([.\u22C5\u00B7\u2022])\s*/, + '...': /^\.\.\.(?=$|[^.])/, + '* ': /^([*])\s*/, + '^{(...)}': function _(input) { + return mhchemParser.patterns.findObserveGroups(input, "^{", "", "", "}"); + }, + '^($...$)': function $$(input) { + return mhchemParser.patterns.findObserveGroups(input, "^", "$", "$", ""); + }, + '^a': /^\^([0-9]+|[^\\_])/, + '^\\x{}{}': function x(input) { + return mhchemParser.patterns.findObserveGroups(input, "^", /^\\[a-zA-Z]+\{/, "}", "", "", "{", "}", "", true); + }, + '^\\x{}': function x(input) { + return mhchemParser.patterns.findObserveGroups(input, "^", /^\\[a-zA-Z]+\{/, "}", ""); + }, + '^\\x': /^\^(\\[a-zA-Z]+)\s*/, + '^(-1)': /^\^(-?\d+)/, + '\'': /^'/, + '_{(...)}': function _(input) { + return mhchemParser.patterns.findObserveGroups(input, "_{", "", "", "}"); + }, + '_($...$)': function _$$(input) { + return mhchemParser.patterns.findObserveGroups(input, "_", "$", "$", ""); + }, + '_9': /^_([+\-]?[0-9]+|[^\\])/, + '_\\x{}{}': function _X(input) { + return mhchemParser.patterns.findObserveGroups(input, "_", /^\\[a-zA-Z]+\{/, "}", "", "", "{", "}", "", true); + }, + '_\\x{}': function _X(input) { + return mhchemParser.patterns.findObserveGroups(input, "_", /^\\[a-zA-Z]+\{/, "}", ""); + }, + '_\\x': /^_(\\[a-zA-Z]+)\s*/, + '^_': /^(?:\^(?=_)|\_(?=\^)|[\^_]$)/, + '{}': /^\{\}/, + '{...}': function _(input) { + return mhchemParser.patterns.findObserveGroups(input, "", "{", "}", ""); + }, + '{(...)}': function _(input) { + return mhchemParser.patterns.findObserveGroups(input, "{", "", "", "}"); + }, + '$...$': function $$(input) { + return mhchemParser.patterns.findObserveGroups(input, "", "$", "$", ""); + }, + '${(...)}$': function $$(input) { + return mhchemParser.patterns.findObserveGroups(input, "${", "", "", "}$"); + }, + '$(...)$': function $$(input) { + return mhchemParser.patterns.findObserveGroups(input, "$", "", "", "$"); + }, + '=<>': /^[=<>]/, + '#': /^[#\u2261]/, + '+': /^\+/, + '-$': /^-(?=[\s_},;\]/]|$|\([a-z]+\))/, + // -space -, -; -] -/ -$ -state-of-aggregation + '-9': /^-(?=[0-9])/, + '- orbital overlap': /^-(?=(?:[spd]|sp)(?:$|[\s,;\)\]\}]))/, + '-': /^-/, + 'pm-operator': /^(?:\\pm|\$\\pm\$|\+-|\+\/-)/, + 'operator': /^(?:\+|(?:[\-=<>]|<<|>>|\\approx|\$\\approx\$)(?=\s|$|-?[0-9]))/, + 'arrowUpDown': /^(?:v|\(v\)|\^|\(\^\))(?=$|[\s,;\)\]\}])/, + '\\bond{(...)}': function bond(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\bond{", "", "", "}"); + }, + '->': /^(?:<->|<-->|->|<-|<=>>|<<=>|<=>|[\u2192\u27F6\u21CC])/, + 'CMT': /^[CMT](?=\[)/, + '[(...)]': function _(input) { + return mhchemParser.patterns.findObserveGroups(input, "[", "", "", "]"); + }, + '1st-level escape': /^(&|\\\\|\\hline)\s*/, + '\\,': /^(?:\\[,\ ;:])/, + // \\x - but output no space before + '\\x{}{}': function x(input) { + return mhchemParser.patterns.findObserveGroups(input, "", /^\\[a-zA-Z]+\{/, "}", "", "", "{", "}", "", true); + }, + '\\x{}': function x(input) { + return mhchemParser.patterns.findObserveGroups(input, "", /^\\[a-zA-Z]+\{/, "}", ""); + }, + '\\ca': /^\\ca(?:\s+|(?![a-zA-Z]))/, + '\\x': /^(?:\\[a-zA-Z]+\s*|\\[_&{}%])/, + 'orbital': /^(?:[0-9]{1,2}[spdfgh]|[0-9]{0,2}sp)(?=$|[^a-zA-Z])/, + // only those with numbers in front, because the others will be formatted correctly anyway + 'others': /^[\/~|]/, + '\\frac{(...)}': function frac(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\frac{", "", "", "}", "{", "", "", "}"); + }, + '\\overset{(...)}': function overset(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\overset{", "", "", "}", "{", "", "", "}"); + }, + '\\underset{(...)}': function underset(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\underset{", "", "", "}", "{", "", "", "}"); + }, + '\\underbrace{(...)}': function underbrace(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\underbrace{", "", "", "}_", "{", "", "", "}"); + }, + '\\color{(...)}0': function color0(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\color{", "", "", "}"); + }, + '\\color{(...)}{(...)}1': function color1(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\color{", "", "", "}", "{", "", "", "}"); + }, + '\\color(...){(...)}2': function color2(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\color", "\\", "", /^(?=\{)/, "{", "", "", "}"); + }, + '\\ce{(...)}': function ce(input) { + return mhchemParser.patterns.findObserveGroups(input, "\\ce{", "", "", "}"); + }, + 'oxidation$': /^(?:[+-][IVX]+|\\pm\s*0|\$\\pm\$\s*0)$/, + 'd-oxidation$': /^(?:[+-]?\s?[IVX]+|\\pm\s*0|\$\\pm\$\s*0)$/, + // 0 could be oxidation or charge + 'roman numeral': /^[IVX]+/, + '1/2$': /^[+\-]?(?:[0-9]+|\$[a-z]\$|[a-z])\/[0-9]+(?:\$[a-z]\$|[a-z])?$/, + 'amount': function amount(input) { + var match; // e.g. 2, 0.5, 1/2, -2, n/2, +; $a$ could be added later in parsing + + match = input.match(/^(?:(?:(?:\([+\-]?[0-9]+\/[0-9]+\)|[+\-]?(?:[0-9]+|\$[a-z]\$|[a-z])\/[0-9]+|[+\-]?[0-9]+[.,][0-9]+|[+\-]?\.[0-9]+|[+\-]?[0-9]+)(?:[a-z](?=\s*[A-Z]))?)|[+\-]?[a-z](?=\s*[A-Z])|\+(?!\s))/); + + if (match) { + return { + match_: match[0], + remainder: input.substr(match[0].length) + }; + } + + var a = mhchemParser.patterns.findObserveGroups(input, "", "$", "$", ""); + + if (a) { + // e.g. $2n-1$, $-$ + match = a.match_.match(/^\$(?:\(?[+\-]?(?:[0-9]*[a-z]?[+\-])?[0-9]*[a-z](?:[+\-][0-9]*[a-z]?)?\)?|\+|-)\$$/); + + if (match) { + return { + match_: match[0], + remainder: input.substr(match[0].length) + }; + } + } + + return null; + }, + 'amount2': function amount2(input) { + return this['amount'](input); + }, + '(KV letters),': /^(?:[A-Z][a-z]{0,2}|i)(?=,)/, + 'formula$': function formula$(input) { + if (input.match(/^\([a-z]+\)$/)) { + return null; + } // state of aggregation = no formula + + + var match = input.match(/^(?:[a-z]|(?:[0-9\ \+\-\,\.\(\)]+[a-z])+[0-9\ \+\-\,\.\(\)]*|(?:[a-z][0-9\ \+\-\,\.\(\)]+)+[a-z]?)$/); + + if (match) { + return { + match_: match[0], + remainder: input.substr(match[0].length) + }; + } + + return null; + }, + 'uprightEntities': /^(?:pH|pOH|pC|pK|iPr|iBu)(?=$|[^a-zA-Z])/, + '/': /^\s*(\/)\s*/, + '//': /^\s*(\/\/)\s*/, + '*': /^\s*[*.]\s*/ + }, + findObserveGroups: function findObserveGroups(input, begExcl, begIncl, endIncl, endExcl, beg2Excl, beg2Incl, end2Incl, end2Excl, combine) { + /** @type {{(input: string, pattern: string | RegExp): string | string[] | null;}} */ + var _match = function _match(input, pattern) { + if (typeof pattern === "string") { + if (input.indexOf(pattern) !== 0) { + return null; + } + + return pattern; + } else { + var match = input.match(pattern); + + if (!match) { + return null; + } + + return match[0]; + } + }; + /** @type {{(input: string, i: number, endChars: string | RegExp): {endMatchBegin: number, endMatchEnd: number} | null;}} */ + + + var _findObserveGroups = function _findObserveGroups(input, i, endChars) { + var braces = 0; + + while (i < input.length) { + var a = input.charAt(i); + + var match = _match(input.substr(i), endChars); + + if (match !== null && braces === 0) { + return { + endMatchBegin: i, + endMatchEnd: i + match.length + }; + } else if (a === "{") { + braces++; + } else if (a === "}") { + if (braces === 0) { + throw ["ExtraCloseMissingOpen", "Extra close brace or missing open brace"]; + } else { + braces--; + } + } + + i++; + } + + if (braces > 0) { + return null; + } + + return null; + }; + + var match = _match(input, begExcl); + + if (match === null) { + return null; + } + + input = input.substr(match.length); + match = _match(input, begIncl); + + if (match === null) { + return null; + } + + var e = _findObserveGroups(input, match.length, endIncl || endExcl); + + if (e === null) { + return null; + } + + var match1 = input.substring(0, endIncl ? e.endMatchEnd : e.endMatchBegin); + + if (!(beg2Excl || beg2Incl)) { + return { + match_: match1, + remainder: input.substr(e.endMatchEnd) + }; + } else { + var group2 = this.findObserveGroups(input.substr(e.endMatchEnd), beg2Excl, beg2Incl, end2Incl, end2Excl); + + if (group2 === null) { + return null; + } + /** @type {string[]} */ + + + var matchRet = [match1, group2.match_]; + return { + match_: combine ? matchRet.join("") : matchRet, + remainder: group2.remainder + }; + } + }, + // + // Matching function + // e.g. match("a", input) will look for the regexp called "a" and see if it matches + // returns null or {match_:"a", remainder:"bc"} + // + match_: function match_(m, input) { + var pattern = mhchemParser.patterns.patterns[m]; + + if (pattern === undefined) { + throw ["MhchemBugP", "mhchem bug P. Please report. (" + m + ")"]; // Trying to use non-existing pattern + } else if (typeof pattern === "function") { + return mhchemParser.patterns.patterns[m](input); // cannot use cached var pattern here, because some pattern functions need this===mhchemParser + } else { + // RegExp + var match = input.match(pattern); + + if (match) { + var mm; + + if (match[2]) { + mm = [match[1], match[2]]; + } else if (match[1]) { + mm = match[1]; + } else { + mm = match[0]; + } + + return { + match_: mm, + remainder: input.substr(match[0].length) + }; + } + + return null; + } + } + }, + // + // Generic state machine actions + // + actions: { + 'a=': function a(buffer, m) { + buffer.a = (buffer.a || "") + m; + }, + 'b=': function b(buffer, m) { + buffer.b = (buffer.b || "") + m; + }, + 'p=': function p(buffer, m) { + buffer.p = (buffer.p || "") + m; + }, + 'o=': function o(buffer, m) { + buffer.o = (buffer.o || "") + m; + }, + 'q=': function q(buffer, m) { + buffer.q = (buffer.q || "") + m; + }, + 'd=': function d(buffer, m) { + buffer.d = (buffer.d || "") + m; + }, + 'rm=': function rm(buffer, m) { + buffer.rm = (buffer.rm || "") + m; + }, + 'text=': function text(buffer, m) { + buffer.text_ = (buffer.text_ || "") + m; + }, + 'insert': function insert(buffer, m, a) { + return { + type_: a + }; + }, + 'insert+p1': function insertP1(buffer, m, a) { + return { + type_: a, + p1: m + }; + }, + 'insert+p1+p2': function insertP1P2(buffer, m, a) { + return { + type_: a, + p1: m[0], + p2: m[1] + }; + }, + 'copy': function copy(buffer, m) { + return m; + }, + 'rm': function rm(buffer, m) { + return { + type_: 'rm', + p1: m || "" + }; + }, + 'text': function text(buffer, m) { + return mhchemParser.go(m, 'text'); + }, + '{text}': function text(buffer, m) { + var ret = ["{"]; + mhchemParser.concatArray(ret, mhchemParser.go(m, 'text')); + ret.push("}"); + return ret; + }, + 'tex-math': function texMath(buffer, m) { + return mhchemParser.go(m, 'tex-math'); + }, + 'tex-math tight': function texMathTight(buffer, m) { + return mhchemParser.go(m, 'tex-math tight'); + }, + 'bond': function bond(buffer, m, k) { + return { + type_: 'bond', + kind_: k || m + }; + }, + 'color0-output': function color0Output(buffer, m) { + return { + type_: 'color0', + color: m[0] + }; + }, + 'ce': function ce(buffer, m) { + return mhchemParser.go(m); + }, + '1/2': function _(buffer, m) { + /** @type {ParserOutput[]} */ + var ret = []; + + if (m.match(/^[+\-]/)) { + ret.push(m.substr(0, 1)); + m = m.substr(1); + } + + var n = m.match(/^([0-9]+|\$[a-z]\$|[a-z])\/([0-9]+)(\$[a-z]\$|[a-z])?$/); + n[1] = n[1].replace(/\$/g, ""); + ret.push({ + type_: 'frac', + p1: n[1], + p2: n[2] + }); + + if (n[3]) { + n[3] = n[3].replace(/\$/g, ""); + ret.push({ + type_: 'tex-math', + p1: n[3] + }); + } + + return ret; + }, + '9,9': function _(buffer, m) { + return mhchemParser.go(m, '9,9'); + } + }, + // + // createTransitions + // convert { 'letter': { 'state': { action_: 'output' } } } to { 'state' => [ { pattern: 'letter', task: { action_: [{type_: 'output'}] } } ] } + // with expansion of 'a|b' to 'a' and 'b' (at 2 places) + // + createTransitions: function createTransitions(o) { + var pattern, state; + /** @type {string[]} */ + + var stateArray; + var i; // + // 1. Collect all states + // + + /** @type {Transitions} */ + + var transitions = {}; + + for (pattern in o) { + for (state in o[pattern]) { + stateArray = state.split("|"); + o[pattern][state].stateArray = stateArray; + + for (i = 0; i < stateArray.length; i++) { + transitions[stateArray[i]] = []; + } + } + } // + // 2. Fill states + // + + + for (pattern in o) { + for (state in o[pattern]) { + stateArray = o[pattern][state].stateArray || []; + + for (i = 0; i < stateArray.length; i++) { + // + // 2a. Normalize actions into array: 'text=' ==> [{type_:'text='}] + // (Note to myself: Resolving the function here would be problematic. It would need .bind (for *this*) and currying (for *option*).) + // + + /** @type {any} */ + var p = o[pattern][state]; + + if (p.action_) { + p.action_ = [].concat(p.action_); + + for (var k = 0; k < p.action_.length; k++) { + if (typeof p.action_[k] === "string") { + p.action_[k] = { + type_: p.action_[k] + }; + } + } + } else { + p.action_ = []; + } // + // 2.b Multi-insert + // + + + var patternArray = pattern.split("|"); + + for (var j = 0; j < patternArray.length; j++) { + if (stateArray[i] === '*') { + // insert into all + for (var t in transitions) { + transitions[t].push({ + pattern: patternArray[j], + task: p + }); + } + } else { + transitions[stateArray[i]].push({ + pattern: patternArray[j], + task: p + }); + } + } + } + } + } + + return transitions; + }, + stateMachines: {} +}; // +// Definition of state machines +// + +mhchemParser.stateMachines = { + // + // \ce state machines + // + //#region ce + 'ce': { + // main parser + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': { + action_: 'output' + } + }, + 'else': { + '0|1|2': { + action_: 'beginsWithBond=false', + revisit: true, + toContinue: true + } + }, + 'oxidation$': { + '0': { + action_: 'oxidation-output' + } + }, + 'CMT': { + 'r': { + action_: 'rdt=', + nextState: 'rt' + }, + 'rd': { + action_: 'rqt=', + nextState: 'rdt' + } + }, + 'arrowUpDown': { + '0|1|2|as': { + action_: ['sb=false', 'output', 'operator'], + nextState: '1' + } + }, + 'uprightEntities': { + '0|1|2': { + action_: ['o=', 'output'], + nextState: '1' + } + }, + 'orbital': { + '0|1|2|3': { + action_: 'o=', + nextState: 'o' + } + }, + '->': { + '0|1|2|3': { + action_: 'r=', + nextState: 'r' + }, + 'a|as': { + action_: ['output', 'r='], + nextState: 'r' + }, + '*': { + action_: ['output', 'r='], + nextState: 'r' + } + }, + '+': { + 'o': { + action_: 'd= kv', + nextState: 'd' + }, + 'd|D': { + action_: 'd=', + nextState: 'd' + }, + 'q': { + action_: 'd=', + nextState: 'qd' + }, + 'qd|qD': { + action_: 'd=', + nextState: 'qd' + }, + 'dq': { + action_: ['output', 'd='], + nextState: 'd' + }, + '3': { + action_: ['sb=false', 'output', 'operator'], + nextState: '0' + } + }, + 'amount': { + '0|2': { + action_: 'a=', + nextState: 'a' + } + }, + 'pm-operator': { + '0|1|2|a|as': { + action_: ['sb=false', 'output', { + type_: 'operator', + option: '\\pm' + }], + nextState: '0' + } + }, + 'operator': { + '0|1|2|a|as': { + action_: ['sb=false', 'output', 'operator'], + nextState: '0' + } + }, + '-$': { + 'o|q': { + action_: ['charge or bond', 'output'], + nextState: 'qd' + }, + 'd': { + action_: 'd=', + nextState: 'd' + }, + 'D': { + action_: ['output', { + type_: 'bond', + option: "-" + }], + nextState: '3' + }, + 'q': { + action_: 'd=', + nextState: 'qd' + }, + 'qd': { + action_: 'd=', + nextState: 'qd' + }, + 'qD|dq': { + action_: ['output', { + type_: 'bond', + option: "-" + }], + nextState: '3' + } + }, + '-9': { + '3|o': { + action_: ['output', { + type_: 'insert', + option: 'hyphen' + }], + nextState: '3' + } + }, + '- orbital overlap': { + 'o': { + action_: ['output', { + type_: 'insert', + option: 'hyphen' + }], + nextState: '2' + }, + 'd': { + action_: ['output', { + type_: 'insert', + option: 'hyphen' + }], + nextState: '2' + } + }, + '-': { + '0|1|2': { + action_: [{ + type_: 'output', + option: 1 + }, 'beginsWithBond=true', { + type_: 'bond', + option: "-" + }], + nextState: '3' + }, + '3': { + action_: { + type_: 'bond', + option: "-" + } + }, + 'a': { + action_: ['output', { + type_: 'insert', + option: 'hyphen' + }], + nextState: '2' + }, + 'as': { + action_: [{ + type_: 'output', + option: 2 + }, { + type_: 'bond', + option: "-" + }], + nextState: '3' + }, + 'b': { + action_: 'b=' + }, + 'o': { + action_: { + type_: '- after o/d', + option: false + }, + nextState: '2' + }, + 'q': { + action_: { + type_: '- after o/d', + option: false + }, + nextState: '2' + }, + 'd|qd|dq': { + action_: { + type_: '- after o/d', + option: true + }, + nextState: '2' + }, + 'D|qD|p': { + action_: ['output', { + type_: 'bond', + option: "-" + }], + nextState: '3' + } + }, + 'amount2': { + '1|3': { + action_: 'a=', + nextState: 'a' + } + }, + 'letters': { + '0|1|2|3|a|as|b|p|bp|o': { + action_: 'o=', + nextState: 'o' + }, + 'q|dq': { + action_: ['output', 'o='], + nextState: 'o' + }, + 'd|D|qd|qD': { + action_: 'o after d', + nextState: 'o' + } + }, + 'digits': { + 'o': { + action_: 'q=', + nextState: 'q' + }, + 'd|D': { + action_: 'q=', + nextState: 'dq' + }, + 'q': { + action_: ['output', 'o='], + nextState: 'o' + }, + 'a': { + action_: 'o=', + nextState: 'o' + } + }, + 'space A': { + 'b|p|bp': {} + }, + 'space': { + 'a': { + nextState: 'as' + }, + '0': { + action_: 'sb=false' + }, + '1|2': { + action_: 'sb=true' + }, + 'r|rt|rd|rdt|rdq': { + action_: 'output', + nextState: '0' + }, + '*': { + action_: ['output', 'sb=true'], + nextState: '1' + } + }, + '1st-level escape': { + '1|2': { + action_: ['output', { + type_: 'insert+p1', + option: '1st-level escape' + }] + }, + '*': { + action_: ['output', { + type_: 'insert+p1', + option: '1st-level escape' + }], + nextState: '0' + } + }, + '[(...)]': { + 'r|rt': { + action_: 'rd=', + nextState: 'rd' + }, + 'rd|rdt': { + action_: 'rq=', + nextState: 'rdq' + } + }, + '...': { + 'o|d|D|dq|qd|qD': { + action_: ['output', { + type_: 'bond', + option: "..." + }], + nextState: '3' + }, + '*': { + action_: [{ + type_: 'output', + option: 1 + }, { + type_: 'insert', + option: 'ellipsis' + }], + nextState: '1' + } + }, + '. |* ': { + '*': { + action_: ['output', { + type_: 'insert', + option: 'addition compound' + }], + nextState: '1' + } + }, + 'state of aggregation $': { + '*': { + action_: ['output', 'state of aggregation'], + nextState: '1' + } + }, + '{[(': { + 'a|as|o': { + action_: ['o=', 'output', 'parenthesisLevel++'], + nextState: '2' + }, + '0|1|2|3': { + action_: ['o=', 'output', 'parenthesisLevel++'], + nextState: '2' + }, + '*': { + action_: ['output', 'o=', 'output', 'parenthesisLevel++'], + nextState: '2' + } + }, + ')]}': { + '0|1|2|3|b|p|bp|o': { + action_: ['o=', 'parenthesisLevel--'], + nextState: 'o' + }, + 'a|as|d|D|q|qd|qD|dq': { + action_: ['output', 'o=', 'parenthesisLevel--'], + nextState: 'o' + } + }, + ', ': { + '*': { + action_: ['output', 'comma'], + nextState: '0' + } + }, + '^_': { + // ^ and _ without a sensible argument + '*': {} + }, + '^{(...)}|^($...$)': { + '0|1|2|as': { + action_: 'b=', + nextState: 'b' + }, + 'p': { + action_: 'b=', + nextState: 'bp' + }, + '3|o': { + action_: 'd= kv', + nextState: 'D' + }, + 'q': { + action_: 'd=', + nextState: 'qD' + }, + 'd|D|qd|qD|dq': { + action_: ['output', 'd='], + nextState: 'D' + } + }, + '^a|^\\x{}{}|^\\x{}|^\\x|\'': { + '0|1|2|as': { + action_: 'b=', + nextState: 'b' + }, + 'p': { + action_: 'b=', + nextState: 'bp' + }, + '3|o': { + action_: 'd= kv', + nextState: 'd' + }, + 'q': { + action_: 'd=', + nextState: 'qd' + }, + 'd|qd|D|qD': { + action_: 'd=' + }, + 'dq': { + action_: ['output', 'd='], + nextState: 'd' + } + }, + '_{(state of aggregation)}$': { + 'd|D|q|qd|qD|dq': { + action_: ['output', 'q='], + nextState: 'q' + } + }, + '_{(...)}|_($...$)|_9|_\\x{}{}|_\\x{}|_\\x': { + '0|1|2|as': { + action_: 'p=', + nextState: 'p' + }, + 'b': { + action_: 'p=', + nextState: 'bp' + }, + '3|o': { + action_: 'q=', + nextState: 'q' + }, + 'd|D': { + action_: 'q=', + nextState: 'dq' + }, + 'q|qd|qD|dq': { + action_: ['output', 'q='], + nextState: 'q' + } + }, + '=<>': { + '0|1|2|3|a|as|o|q|d|D|qd|qD|dq': { + action_: [{ + type_: 'output', + option: 2 + }, 'bond'], + nextState: '3' + } + }, + '#': { + '0|1|2|3|a|as|o': { + action_: [{ + type_: 'output', + option: 2 + }, { + type_: 'bond', + option: "#" + }], + nextState: '3' + } + }, + '{}': { + '*': { + action_: { + type_: 'output', + option: 1 + }, + nextState: '1' + } + }, + '{...}': { + '0|1|2|3|a|as|b|p|bp': { + action_: 'o=', + nextState: 'o' + }, + 'o|d|D|q|qd|qD|dq': { + action_: ['output', 'o='], + nextState: 'o' + } + }, + '$...$': { + 'a': { + action_: 'a=' + }, + // 2$n$ + '0|1|2|3|as|b|p|bp|o': { + action_: 'o=', + nextState: 'o' + }, + // not 'amount' + 'as|o': { + action_: 'o=' + }, + 'q|d|D|qd|qD|dq': { + action_: ['output', 'o='], + nextState: 'o' + } + }, + '\\bond{(...)}': { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'bond'], + nextState: "3" + } + }, + '\\frac{(...)}': { + '*': { + action_: [{ + type_: 'output', + option: 1 + }, 'frac-output'], + nextState: '3' + } + }, + '\\overset{(...)}': { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'overset-output'], + nextState: '3' + } + }, + '\\underset{(...)}': { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'underset-output'], + nextState: '3' + } + }, + '\\underbrace{(...)}': { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'underbrace-output'], + nextState: '3' + } + }, + '\\color{(...)}{(...)}1|\\color(...){(...)}2': { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'color-output'], + nextState: '3' + } + }, + '\\color{(...)}0': { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'color0-output'] + } + }, + '\\ce{(...)}': { + '*': { + action_: [{ + type_: 'output', + option: 2 + }, 'ce'], + nextState: '3' + } + }, + '\\,': { + '*': { + action_: [{ + type_: 'output', + option: 1 + }, 'copy'], + nextState: '1' + } + }, + '\\x{}{}|\\x{}|\\x': { + '0|1|2|3|a|as|b|p|bp|o|c0': { + action_: ['o=', 'output'], + nextState: '3' + }, + '*': { + action_: ['output', 'o=', 'output'], + nextState: '3' + } + }, + 'others': { + '*': { + action_: [{ + type_: 'output', + option: 1 + }, 'copy'], + nextState: '3' + } + }, + 'else2': { + 'a': { + action_: 'a to o', + nextState: 'o', + revisit: true + }, + 'as': { + action_: ['output', 'sb=true'], + nextState: '1', + revisit: true + }, + 'r|rt|rd|rdt|rdq': { + action_: ['output'], + nextState: '0', + revisit: true + }, + '*': { + action_: ['output', 'copy'], + nextState: '3' + } + } + }), + actions: { + 'o after d': function oAfterD(buffer, m) { + var ret; + + if ((buffer.d || "").match(/^[0-9]+$/)) { + var tmp = buffer.d; + buffer.d = undefined; + ret = this['output'](buffer); + buffer.b = tmp; + } else { + ret = this['output'](buffer); + } + + mhchemParser.actions['o='](buffer, m); + return ret; + }, + 'd= kv': function dKv(buffer, m) { + buffer.d = m; + buffer.dType = 'kv'; + }, + 'charge or bond': function chargeOrBond(buffer, m) { + if (buffer['beginsWithBond']) { + /** @type {ParserOutput[]} */ + var ret = []; + mhchemParser.concatArray(ret, this['output'](buffer)); + mhchemParser.concatArray(ret, mhchemParser.actions['bond'](buffer, m, "-")); + return ret; + } else { + buffer.d = m; + } + }, + '- after o/d': function afterOD(buffer, m, isAfterD) { + var c1 = mhchemParser.patterns.match_('orbital', buffer.o || ""); + var c2 = mhchemParser.patterns.match_('one lowercase greek letter $', buffer.o || ""); + var c3 = mhchemParser.patterns.match_('one lowercase latin letter $', buffer.o || ""); + var c4 = mhchemParser.patterns.match_('$one lowercase latin letter$ $', buffer.o || ""); + var hyphenFollows = m === "-" && (c1 && c1.remainder === "" || c2 || c3 || c4); + + if (hyphenFollows && !buffer.a && !buffer.b && !buffer.p && !buffer.d && !buffer.q && !c1 && c3) { + buffer.o = '$' + buffer.o + '$'; + } + /** @type {ParserOutput[]} */ + + + var ret = []; + + if (hyphenFollows) { + mhchemParser.concatArray(ret, this['output'](buffer)); + ret.push({ + type_: 'hyphen' + }); + } else { + c1 = mhchemParser.patterns.match_('digits', buffer.d || ""); + + if (isAfterD && c1 && c1.remainder === '') { + mhchemParser.concatArray(ret, mhchemParser.actions['d='](buffer, m)); + mhchemParser.concatArray(ret, this['output'](buffer)); + } else { + mhchemParser.concatArray(ret, this['output'](buffer)); + mhchemParser.concatArray(ret, mhchemParser.actions['bond'](buffer, m, "-")); + } + } + + return ret; + }, + 'a to o': function aToO(buffer) { + buffer.o = buffer.a; + buffer.a = undefined; + }, + 'sb=true': function sbTrue(buffer) { + buffer.sb = true; + }, + 'sb=false': function sbFalse(buffer) { + buffer.sb = false; + }, + 'beginsWithBond=true': function beginsWithBondTrue(buffer) { + buffer['beginsWithBond'] = true; + }, + 'beginsWithBond=false': function beginsWithBondFalse(buffer) { + buffer['beginsWithBond'] = false; + }, + 'parenthesisLevel++': function parenthesisLevel(buffer) { + buffer['parenthesisLevel']++; + }, + 'parenthesisLevel--': function parenthesisLevel(buffer) { + buffer['parenthesisLevel']--; + }, + 'state of aggregation': function stateOfAggregation(buffer, m) { + return { + type_: 'state of aggregation', + p1: mhchemParser.go(m, 'o') + }; + }, + 'comma': function comma(buffer, m) { + var a = m.replace(/\s*$/, ''); + var withSpace = a !== m; + + if (withSpace && buffer['parenthesisLevel'] === 0) { + return { + type_: 'comma enumeration L', + p1: a + }; + } else { + return { + type_: 'comma enumeration M', + p1: a + }; + } + }, + 'output': function output(buffer, m, entityFollows) { + // entityFollows: + // undefined = if we have nothing else to output, also ignore the just read space (buffer.sb) + // 1 = an entity follows, never omit the space if there was one just read before (can only apply to state 1) + // 2 = 1 + the entity can have an amount, so output a\, instead of converting it to o (can only apply to states a|as) + + /** @type {ParserOutput | ParserOutput[]} */ + var ret; + + if (!buffer.r) { + ret = []; + + if (!buffer.a && !buffer.b && !buffer.p && !buffer.o && !buffer.q && !buffer.d && !entityFollows) ; else { + if (buffer.sb) { + ret.push({ + type_: 'entitySkip' + }); + } + + if (!buffer.o && !buffer.q && !buffer.d && !buffer.b && !buffer.p && entityFollows !== 2) { + buffer.o = buffer.a; + buffer.a = undefined; + } else if (!buffer.o && !buffer.q && !buffer.d && (buffer.b || buffer.p)) { + buffer.o = buffer.a; + buffer.d = buffer.b; + buffer.q = buffer.p; + buffer.a = buffer.b = buffer.p = undefined; + } else { + if (buffer.o && buffer.dType === 'kv' && mhchemParser.patterns.match_('d-oxidation$', buffer.d || "")) { + buffer.dType = 'oxidation'; + } else if (buffer.o && buffer.dType === 'kv' && !buffer.q) { + buffer.dType = undefined; + } + } + + ret.push({ + type_: 'chemfive', + a: mhchemParser.go(buffer.a, 'a'), + b: mhchemParser.go(buffer.b, 'bd'), + p: mhchemParser.go(buffer.p, 'pq'), + o: mhchemParser.go(buffer.o, 'o'), + q: mhchemParser.go(buffer.q, 'pq'), + d: mhchemParser.go(buffer.d, buffer.dType === 'oxidation' ? 'oxidation' : 'bd'), + dType: buffer.dType + }); + } + } else { + // r + + /** @type {ParserOutput[]} */ + var rd; + + if (buffer.rdt === 'M') { + rd = mhchemParser.go(buffer.rd, 'tex-math'); + } else if (buffer.rdt === 'T') { + rd = [{ + type_: 'text', + p1: buffer.rd || "" + }]; + } else { + rd = mhchemParser.go(buffer.rd); + } + /** @type {ParserOutput[]} */ + + + var rq; + + if (buffer.rqt === 'M') { + rq = mhchemParser.go(buffer.rq, 'tex-math'); + } else if (buffer.rqt === 'T') { + rq = [{ + type_: 'text', + p1: buffer.rq || "" + }]; + } else { + rq = mhchemParser.go(buffer.rq); + } + + ret = { + type_: 'arrow', + r: buffer.r, + rd: rd, + rq: rq + }; + } + + for (var p in buffer) { + if (p !== 'parenthesisLevel' && p !== 'beginsWithBond') { + delete buffer[p]; + } + } + + return ret; + }, + 'oxidation-output': function oxidationOutput(buffer, m) { + var ret = ["{"]; + mhchemParser.concatArray(ret, mhchemParser.go(m, 'oxidation')); + ret.push("}"); + return ret; + }, + 'frac-output': function fracOutput(buffer, m) { + return { + type_: 'frac-ce', + p1: mhchemParser.go(m[0]), + p2: mhchemParser.go(m[1]) + }; + }, + 'overset-output': function oversetOutput(buffer, m) { + return { + type_: 'overset', + p1: mhchemParser.go(m[0]), + p2: mhchemParser.go(m[1]) + }; + }, + 'underset-output': function undersetOutput(buffer, m) { + return { + type_: 'underset', + p1: mhchemParser.go(m[0]), + p2: mhchemParser.go(m[1]) + }; + }, + 'underbrace-output': function underbraceOutput(buffer, m) { + return { + type_: 'underbrace', + p1: mhchemParser.go(m[0]), + p2: mhchemParser.go(m[1]) + }; + }, + 'color-output': function colorOutput(buffer, m) { + return { + type_: 'color', + color1: m[0], + color2: mhchemParser.go(m[1]) + }; + }, + 'r=': function r(buffer, m) { + buffer.r = m; + }, + 'rdt=': function rdt(buffer, m) { + buffer.rdt = m; + }, + 'rd=': function rd(buffer, m) { + buffer.rd = m; + }, + 'rqt=': function rqt(buffer, m) { + buffer.rqt = m; + }, + 'rq=': function rq(buffer, m) { + buffer.rq = m; + }, + 'operator': function operator(buffer, m, p1) { + return { + type_: 'operator', + kind_: p1 || m + }; + } + } + }, + 'a': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': {} + }, + '1/2$': { + '0': { + action_: '1/2' + } + }, + 'else': { + '0': { + nextState: '1', + revisit: true + } + }, + '$(...)$': { + '*': { + action_: 'tex-math tight', + nextState: '1' + } + }, + ',': { + '*': { + action_: { + type_: 'insert', + option: 'commaDecimal' + } + } + }, + 'else2': { + '*': { + action_: 'copy' + } + } + }), + actions: {} + }, + 'o': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': {} + }, + '1/2$': { + '0': { + action_: '1/2' + } + }, + 'else': { + '0': { + nextState: '1', + revisit: true + } + }, + 'letters': { + '*': { + action_: 'rm' + } + }, + '\\ca': { + '*': { + action_: { + type_: 'insert', + option: 'circa' + } + } + }, + '\\x{}{}|\\x{}|\\x': { + '*': { + action_: 'copy' + } + }, + '${(...)}$|$(...)$': { + '*': { + action_: 'tex-math' + } + }, + '{(...)}': { + '*': { + action_: '{text}' + } + }, + 'else2': { + '*': { + action_: 'copy' + } + } + }), + actions: {} + }, + 'text': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': { + action_: 'output' + } + }, + '{...}': { + '*': { + action_: 'text=' + } + }, + '${(...)}$|$(...)$': { + '*': { + action_: 'tex-math' + } + }, + '\\greek': { + '*': { + action_: ['output', 'rm'] + } + }, + '\\,|\\x{}{}|\\x{}|\\x': { + '*': { + action_: ['output', 'copy'] + } + }, + 'else': { + '*': { + action_: 'text=' + } + } + }), + actions: { + 'output': function output(buffer) { + if (buffer.text_) { + /** @type {ParserOutput} */ + var ret = { + type_: 'text', + p1: buffer.text_ + }; + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + } + } + } + }, + 'pq': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': {} + }, + 'state of aggregation $': { + '*': { + action_: 'state of aggregation' + } + }, + 'i$': { + '0': { + nextState: '!f', + revisit: true + } + }, + '(KV letters),': { + '0': { + action_: 'rm', + nextState: '0' + } + }, + 'formula$': { + '0': { + nextState: 'f', + revisit: true + } + }, + '1/2$': { + '0': { + action_: '1/2' + } + }, + 'else': { + '0': { + nextState: '!f', + revisit: true + } + }, + '${(...)}$|$(...)$': { + '*': { + action_: 'tex-math' + } + }, + '{(...)}': { + '*': { + action_: 'text' + } + }, + 'a-z': { + 'f': { + action_: 'tex-math' + } + }, + 'letters': { + '*': { + action_: 'rm' + } + }, + '-9.,9': { + '*': { + action_: '9,9' + } + }, + ',': { + '*': { + action_: { + type_: 'insert+p1', + option: 'comma enumeration S' + } + } + }, + '\\color{(...)}{(...)}1|\\color(...){(...)}2': { + '*': { + action_: 'color-output' + } + }, + '\\color{(...)}0': { + '*': { + action_: 'color0-output' + } + }, + '\\ce{(...)}': { + '*': { + action_: 'ce' + } + }, + '\\,|\\x{}{}|\\x{}|\\x': { + '*': { + action_: 'copy' + } + }, + 'else2': { + '*': { + action_: 'copy' + } + } + }), + actions: { + 'state of aggregation': function stateOfAggregation(buffer, m) { + return { + type_: 'state of aggregation subscript', + p1: mhchemParser.go(m, 'o') + }; + }, + 'color-output': function colorOutput(buffer, m) { + return { + type_: 'color', + color1: m[0], + color2: mhchemParser.go(m[1], 'pq') + }; + } + } + }, + 'bd': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': {} + }, + 'x$': { + '0': { + nextState: '!f', + revisit: true + } + }, + 'formula$': { + '0': { + nextState: 'f', + revisit: true + } + }, + 'else': { + '0': { + nextState: '!f', + revisit: true + } + }, + '-9.,9 no missing 0': { + '*': { + action_: '9,9' + } + }, + '.': { + '*': { + action_: { + type_: 'insert', + option: 'electron dot' + } + } + }, + 'a-z': { + 'f': { + action_: 'tex-math' + } + }, + 'x': { + '*': { + action_: { + type_: 'insert', + option: 'KV x' + } + } + }, + 'letters': { + '*': { + action_: 'rm' + } + }, + '\'': { + '*': { + action_: { + type_: 'insert', + option: 'prime' + } + } + }, + '${(...)}$|$(...)$': { + '*': { + action_: 'tex-math' + } + }, + '{(...)}': { + '*': { + action_: 'text' + } + }, + '\\color{(...)}{(...)}1|\\color(...){(...)}2': { + '*': { + action_: 'color-output' + } + }, + '\\color{(...)}0': { + '*': { + action_: 'color0-output' + } + }, + '\\ce{(...)}': { + '*': { + action_: 'ce' + } + }, + '\\,|\\x{}{}|\\x{}|\\x': { + '*': { + action_: 'copy' + } + }, + 'else2': { + '*': { + action_: 'copy' + } + } + }), + actions: { + 'color-output': function colorOutput(buffer, m) { + return { + type_: 'color', + color1: m[0], + color2: mhchemParser.go(m[1], 'bd') + }; + } + } + }, + 'oxidation': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': {} + }, + 'roman numeral': { + '*': { + action_: 'roman-numeral' + } + }, + '${(...)}$|$(...)$': { + '*': { + action_: 'tex-math' + } + }, + 'else': { + '*': { + action_: 'copy' + } + } + }), + actions: { + 'roman-numeral': function romanNumeral(buffer, m) { + return { + type_: 'roman numeral', + p1: m || "" + }; + } + } + }, + 'tex-math': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': { + action_: 'output' + } + }, + '\\ce{(...)}': { + '*': { + action_: ['output', 'ce'] + } + }, + '{...}|\\,|\\x{}{}|\\x{}|\\x': { + '*': { + action_: 'o=' + } + }, + 'else': { + '*': { + action_: 'o=' + } + } + }), + actions: { + 'output': function output(buffer) { + if (buffer.o) { + /** @type {ParserOutput} */ + var ret = { + type_: 'tex-math', + p1: buffer.o + }; + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + } + } + } + }, + 'tex-math tight': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': { + action_: 'output' + } + }, + '\\ce{(...)}': { + '*': { + action_: ['output', 'ce'] + } + }, + '{...}|\\,|\\x{}{}|\\x{}|\\x': { + '*': { + action_: 'o=' + } + }, + '-|+': { + '*': { + action_: 'tight operator' + } + }, + 'else': { + '*': { + action_: 'o=' + } + } + }), + actions: { + 'tight operator': function tightOperator(buffer, m) { + buffer.o = (buffer.o || "") + "{" + m + "}"; + }, + 'output': function output(buffer) { + if (buffer.o) { + /** @type {ParserOutput} */ + var ret = { + type_: 'tex-math', + p1: buffer.o + }; + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + } + } + } + }, + '9,9': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': {} + }, + ',': { + '*': { + action_: 'comma' + } + }, + 'else': { + '*': { + action_: 'copy' + } + } + }), + actions: { + 'comma': function comma() { + return { + type_: 'commaDecimal' + }; + } + } + }, + //#endregion + // + // \pu state machines + // + //#region pu + 'pu': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': { + action_: 'output' + } + }, + 'space$': { + '*': { + action_: ['output', 'space'] + } + }, + '{[(|)]}': { + '0|a': { + action_: 'copy' + } + }, + '(-)(9)^(-9)': { + '0': { + action_: 'number^', + nextState: 'a' + } + }, + '(-)(9.,9)(e)(99)': { + '0': { + action_: 'enumber', + nextState: 'a' + } + }, + 'space': { + '0|a': {} + }, + 'pm-operator': { + '0|a': { + action_: { + type_: 'operator', + option: '\\pm' + }, + nextState: '0' + } + }, + 'operator': { + '0|a': { + action_: 'copy', + nextState: '0' + } + }, + '//': { + 'd': { + action_: 'o=', + nextState: '/' + } + }, + '/': { + 'd': { + action_: 'o=', + nextState: '/' + } + }, + '{...}|else': { + '0|d': { + action_: 'd=', + nextState: 'd' + }, + 'a': { + action_: ['space', 'd='], + nextState: 'd' + }, + '/|q': { + action_: 'q=', + nextState: 'q' + } + } + }), + actions: { + 'enumber': function enumber(buffer, m) { + /** @type {ParserOutput[]} */ + var ret = []; + + if (m[0] === "+-" || m[0] === "+/-") { + ret.push("\\pm "); + } else if (m[0]) { + ret.push(m[0]); + } + + if (m[1]) { + mhchemParser.concatArray(ret, mhchemParser.go(m[1], 'pu-9,9')); + + if (m[2]) { + if (m[2].match(/[,.]/)) { + mhchemParser.concatArray(ret, mhchemParser.go(m[2], 'pu-9,9')); + } else { + ret.push(m[2]); + } + } + + m[3] = m[4] || m[3]; + + if (m[3]) { + m[3] = m[3].trim(); + + if (m[3] === "e" || m[3].substr(0, 1) === "*") { + ret.push({ + type_: 'cdot' + }); + } else { + ret.push({ + type_: 'times' + }); + } + } + } + + if (m[3]) { + ret.push("10^{" + m[5] + "}"); + } + + return ret; + }, + 'number^': function number(buffer, m) { + /** @type {ParserOutput[]} */ + var ret = []; + + if (m[0] === "+-" || m[0] === "+/-") { + ret.push("\\pm "); + } else if (m[0]) { + ret.push(m[0]); + } + + mhchemParser.concatArray(ret, mhchemParser.go(m[1], 'pu-9,9')); + ret.push("^{" + m[2] + "}"); + return ret; + }, + 'operator': function operator(buffer, m, p1) { + return { + type_: 'operator', + kind_: p1 || m + }; + }, + 'space': function space() { + return { + type_: 'pu-space-1' + }; + }, + 'output': function output(buffer) { + /** @type {ParserOutput | ParserOutput[]} */ + var ret; + var md = mhchemParser.patterns.match_('{(...)}', buffer.d || ""); + + if (md && md.remainder === '') { + buffer.d = md.match_; + } + + var mq = mhchemParser.patterns.match_('{(...)}', buffer.q || ""); + + if (mq && mq.remainder === '') { + buffer.q = mq.match_; + } + + if (buffer.d) { + buffer.d = buffer.d.replace(/\u00B0C|\^oC|\^{o}C/g, "{}^{\\circ}C"); + buffer.d = buffer.d.replace(/\u00B0F|\^oF|\^{o}F/g, "{}^{\\circ}F"); + } + + if (buffer.q) { + // fraction + buffer.q = buffer.q.replace(/\u00B0C|\^oC|\^{o}C/g, "{}^{\\circ}C"); + buffer.q = buffer.q.replace(/\u00B0F|\^oF|\^{o}F/g, "{}^{\\circ}F"); + var b5 = { + d: mhchemParser.go(buffer.d, 'pu'), + q: mhchemParser.go(buffer.q, 'pu') + }; + + if (buffer.o === '//') { + ret = { + type_: 'pu-frac', + p1: b5.d, + p2: b5.q + }; + } else { + ret = b5.d; + + if (b5.d.length > 1 || b5.q.length > 1) { + ret.push({ + type_: ' / ' + }); + } else { + ret.push({ + type_: '/' + }); + } + + mhchemParser.concatArray(ret, b5.q); + } + } else { + // no fraction + ret = mhchemParser.go(buffer.d, 'pu-2'); + } + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + } + } + }, + 'pu-2': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '*': { + action_: 'output' + } + }, + '*': { + '*': { + action_: ['output', 'cdot'], + nextState: '0' + } + }, + '\\x': { + '*': { + action_: 'rm=' + } + }, + 'space': { + '*': { + action_: ['output', 'space'], + nextState: '0' + } + }, + '^{(...)}|^(-1)': { + '1': { + action_: '^(-1)' + } + }, + '-9.,9': { + '0': { + action_: 'rm=', + nextState: '0' + }, + '1': { + action_: '^(-1)', + nextState: '0' + } + }, + '{...}|else': { + '*': { + action_: 'rm=', + nextState: '1' + } + } + }), + actions: { + 'cdot': function cdot() { + return { + type_: 'tight cdot' + }; + }, + '^(-1)': function _(buffer, m) { + buffer.rm += "^{" + m + "}"; + }, + 'space': function space() { + return { + type_: 'pu-space-2' + }; + }, + 'output': function output(buffer) { + /** @type {ParserOutput | ParserOutput[]} */ + var ret = []; + + if (buffer.rm) { + var mrm = mhchemParser.patterns.match_('{(...)}', buffer.rm || ""); + + if (mrm && mrm.remainder === '') { + ret = mhchemParser.go(mrm.match_, 'pu'); + } else { + ret = { + type_: 'rm', + p1: buffer.rm + }; + } + } + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + } + } + }, + 'pu-9,9': { + transitions: mhchemParser.createTransitions({ + 'empty': { + '0': { + action_: 'output-0' + }, + 'o': { + action_: 'output-o' + } + }, + ',': { + '0': { + action_: ['output-0', 'comma'], + nextState: 'o' + } + }, + '.': { + '0': { + action_: ['output-0', 'copy'], + nextState: 'o' + } + }, + 'else': { + '*': { + action_: 'text=' + } + } + }), + actions: { + 'comma': function comma() { + return { + type_: 'commaDecimal' + }; + }, + 'output-0': function output0(buffer) { + /** @type {ParserOutput[]} */ + var ret = []; + buffer.text_ = buffer.text_ || ""; + + if (buffer.text_.length > 4) { + var a = buffer.text_.length % 3; + + if (a === 0) { + a = 3; + } + + for (var i = buffer.text_.length - 3; i > 0; i -= 3) { + ret.push(buffer.text_.substr(i, 3)); + ret.push({ + type_: '1000 separator' + }); + } + + ret.push(buffer.text_.substr(0, a)); + ret.reverse(); + } else { + ret.push(buffer.text_); + } + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + }, + 'output-o': function outputO(buffer) { + /** @type {ParserOutput[]} */ + var ret = []; + buffer.text_ = buffer.text_ || ""; + + if (buffer.text_.length > 4) { + var a = buffer.text_.length - 3; + + for (var i = 0; i < a; i += 3) { + ret.push(buffer.text_.substr(i, 3)); + ret.push({ + type_: '1000 separator' + }); + } + + ret.push(buffer.text_.substr(i)); + } else { + ret.push(buffer.text_); + } + + for (var p in buffer) { + delete buffer[p]; + } + + return ret; + } + } + } //#endregion + +}; // +// texify: Take MhchemParser output and convert it to TeX +// + +/** @type {Texify} */ + +var texify = { + go: function go(input, isInner) { + // (recursive, max 4 levels) + if (!input) { + return ""; + } + + var res = ""; + var cee = false; + + for (var i = 0; i < input.length; i++) { + var inputi = input[i]; + + if (typeof inputi === "string") { + res += inputi; + } else { + res += texify._go2(inputi); + + if (inputi.type_ === '1st-level escape') { + cee = true; + } + } + } + + if (!isInner && !cee && res) { + res = "{" + res + "}"; + } + + return res; + }, + _goInner: function _goInner(input) { + if (!input) { + return input; + } + + return texify.go(input, true); + }, + _go2: function _go2(buf) { + /** @type {undefined | string} */ + var res; + + switch (buf.type_) { + case 'chemfive': + res = ""; + var b5 = { + a: texify._goInner(buf.a), + b: texify._goInner(buf.b), + p: texify._goInner(buf.p), + o: texify._goInner(buf.o), + q: texify._goInner(buf.q), + d: texify._goInner(buf.d) + }; // + // a + // + + if (b5.a) { + if (b5.a.match(/^[+\-]/)) { + b5.a = "{" + b5.a + "}"; + } + + res += b5.a + "\\,"; + } // + // b and p + // + + + if (b5.b || b5.p) { + res += "{\\vphantom{X}}"; + res += "^{\\hphantom{" + (b5.b || "") + "}}_{\\hphantom{" + (b5.p || "") + "}}"; + res += "{\\vphantom{X}}"; + res += "^{\\smash[t]{\\vphantom{2}}\\mathllap{" + (b5.b || "") + "}}"; + res += "_{\\vphantom{2}\\mathllap{\\smash[t]{" + (b5.p || "") + "}}}"; + } // + // o + // + + + if (b5.o) { + if (b5.o.match(/^[+\-]/)) { + b5.o = "{" + b5.o + "}"; + } + + res += b5.o; + } // + // q and d + // + + + if (buf.dType === 'kv') { + if (b5.d || b5.q) { + res += "{\\vphantom{X}}"; + } + + if (b5.d) { + res += "^{" + b5.d + "}"; + } + + if (b5.q) { + res += "_{\\smash[t]{" + b5.q + "}}"; + } + } else if (buf.dType === 'oxidation') { + if (b5.d) { + res += "{\\vphantom{X}}"; + res += "^{" + b5.d + "}"; + } + + if (b5.q) { + res += "{\\vphantom{X}}"; + res += "_{\\smash[t]{" + b5.q + "}}"; + } + } else { + if (b5.q) { + res += "{\\vphantom{X}}"; + res += "_{\\smash[t]{" + b5.q + "}}"; + } + + if (b5.d) { + res += "{\\vphantom{X}}"; + res += "^{" + b5.d + "}"; + } + } + + break; + + case 'rm': + res = "\\mathrm{" + buf.p1 + "}"; + break; + + case 'text': + if (buf.p1.match(/[\^_]/)) { + buf.p1 = buf.p1.replace(" ", "~").replace("-", "\\text{-}"); + res = "\\mathrm{" + buf.p1 + "}"; + } else { + res = "\\text{" + buf.p1 + "}"; + } + + break; + + case 'roman numeral': + res = "\\mathrm{" + buf.p1 + "}"; + break; + + case 'state of aggregation': + res = "\\mskip2mu " + texify._goInner(buf.p1); + break; + + case 'state of aggregation subscript': + res = "\\mskip1mu " + texify._goInner(buf.p1); + break; + + case 'bond': + res = texify._getBond(buf.kind_); + + if (!res) { + throw ["MhchemErrorBond", "mhchem Error. Unknown bond type (" + buf.kind_ + ")"]; + } + + break; + + case 'frac': + var c = "\\frac{" + buf.p1 + "}{" + buf.p2 + "}"; + res = "\\mathchoice{\\textstyle" + c + "}{" + c + "}{" + c + "}{" + c + "}"; + break; + + case 'pu-frac': + var d = "\\frac{" + texify._goInner(buf.p1) + "}{" + texify._goInner(buf.p2) + "}"; + res = "\\mathchoice{\\textstyle" + d + "}{" + d + "}{" + d + "}{" + d + "}"; + break; + + case 'tex-math': + res = buf.p1 + " "; + break; + + case 'frac-ce': + res = "\\frac{" + texify._goInner(buf.p1) + "}{" + texify._goInner(buf.p2) + "}"; + break; + + case 'overset': + res = "\\overset{" + texify._goInner(buf.p1) + "}{" + texify._goInner(buf.p2) + "}"; + break; + + case 'underset': + res = "\\underset{" + texify._goInner(buf.p1) + "}{" + texify._goInner(buf.p2) + "}"; + break; + + case 'underbrace': + res = "\\underbrace{" + texify._goInner(buf.p1) + "}_{" + texify._goInner(buf.p2) + "}"; + break; + + case 'color': + res = "{\\color{" + buf.color1 + "}{" + texify._goInner(buf.color2) + "}}"; + break; + + case 'color0': + res = "\\color{" + buf.color + "}"; + break; + + case 'arrow': + var b6 = { + rd: texify._goInner(buf.rd), + rq: texify._goInner(buf.rq) + }; + + var arrow = "\\x" + texify._getArrow(buf.r); + + if (b6.rq) { + arrow += "[{" + b6.rq + "}]"; + } + + if (b6.rd) { + arrow += "{" + b6.rd + "}"; + } else { + arrow += "{}"; + } + + res = arrow; + break; + + case 'operator': + res = texify._getOperator(buf.kind_); + break; + + case '1st-level escape': + res = buf.p1 + " "; // &, \\\\, \\hlin + + break; + + case 'space': + res = " "; + break; + + case 'entitySkip': + res = "~"; + break; + + case 'pu-space-1': + res = "~"; + break; + + case 'pu-space-2': + res = "\\mkern3mu "; + break; + + case '1000 separator': + res = "\\mkern2mu "; + break; + + case 'commaDecimal': + res = "{,}"; + break; + + case 'comma enumeration L': + res = "{" + buf.p1 + "}\\mkern6mu "; + break; + + case 'comma enumeration M': + res = "{" + buf.p1 + "}\\mkern3mu "; + break; + + case 'comma enumeration S': + res = "{" + buf.p1 + "}\\mkern1mu "; + break; + + case 'hyphen': + res = "\\text{-}"; + break; + + case 'addition compound': + res = "\\,{\\cdot}\\,"; + break; + + case 'electron dot': + res = "\\mkern1mu \\bullet\\mkern1mu "; + break; + + case 'KV x': + res = "{\\times}"; + break; + + case 'prime': + res = "\\prime "; + break; + + case 'cdot': + res = "\\cdot "; + break; + + case 'tight cdot': + res = "\\mkern1mu{\\cdot}\\mkern1mu "; + break; + + case 'times': + res = "\\times "; + break; + + case 'circa': + res = "{\\sim}"; + break; + + case '^': + res = "uparrow"; + break; + + case 'v': + res = "downarrow"; + break; + + case 'ellipsis': + res = "\\ldots "; + break; + + case '/': + res = "/"; + break; + + case ' / ': + res = "\\,/\\,"; + break; + + default: + throw ["MhchemBugT", "mhchem bug T. Please report."]; + // Missing texify rule or unknown MhchemParser output + } + return res; + }, + _getArrow: function _getArrow(a) { + switch (a) { + case "->": + return "rightarrow"; + + case "\u2192": + return "rightarrow"; + + case "\u27F6": + return "rightarrow"; + + case "<-": + return "leftarrow"; + + case "<->": + return "leftrightarrow"; + + case "<-->": + return "rightleftarrows"; + + case "<=>": + return "rightleftharpoons"; + + case "\u21CC": + return "rightleftharpoons"; + + case "<=>>": + return "rightequilibrium"; + + case "<<=>": + return "leftequilibrium"; + + default: + throw ["MhchemBugT", "mhchem bug T. Please report."]; + } + }, + _getBond: function _getBond(a) { + switch (a) { + case "-": + return "{-}"; + + case "1": + return "{-}"; + + case "=": + return "{=}"; + + case "2": + return "{=}"; + + case "#": + return "{\\equiv}"; + + case "3": + return "{\\equiv}"; + + case "~": + return "{\\tripledash}"; + + case "~-": + return "{\\mathrlap{\\raisebox{-.1em}{$-$}}\\raisebox{.1em}{$\\tripledash$}}"; + + case "~=": + return "{\\mathrlap{\\raisebox{-.2em}{$-$}}\\mathrlap{\\raisebox{.2em}{$\\tripledash$}}-}"; + + case "~--": + return "{\\mathrlap{\\raisebox{-.2em}{$-$}}\\mathrlap{\\raisebox{.2em}{$\\tripledash$}}-}"; + + case "-~-": + return "{\\mathrlap{\\raisebox{-.2em}{$-$}}\\mathrlap{\\raisebox{.2em}{$-$}}\\tripledash}"; + + case "...": + return "{{\\cdot}{\\cdot}{\\cdot}}"; + + case "....": + return "{{\\cdot}{\\cdot}{\\cdot}{\\cdot}}"; + + case "->": + return "{\\rightarrow}"; + + case "<-": + return "{\\leftarrow}"; + + case "<": + return "{<}"; + + case ">": + return "{>}"; + + default: + throw ["MhchemBugT", "mhchem bug T. Please report."]; + } + }, + _getOperator: function _getOperator(a) { + switch (a) { + case "+": + return " {}+{} "; + + case "-": + return " {}-{} "; + + case "=": + return " {}={} "; + + case "<": + return " {}<{} "; + + case ">": + return " {}>{} "; + + case "<<": + return " {}\\ll{} "; + + case ">>": + return " {}\\gg{} "; + + case "\\pm": + return " {}\\pm{} "; + + case "\\approx": + return " {}\\approx{} "; + + case "$\\approx$": + return " {}\\approx{} "; + + case "v": + return " \\downarrow{} "; + + case "(v)": + return " \\downarrow{} "; + + case "^": + return " \\uparrow{} "; + + case "(^)": + return " \\uparrow{} "; + + default: + throw ["MhchemBugT", "mhchem bug T. Please report."]; + } + } +}; // diff --git a/core/bikeshed/katex/dist/contrib/render-a11y-string.js b/core/bikeshed/katex/dist/contrib/render-a11y-string.js new file mode 100644 index 00000000..a96caca4 --- /dev/null +++ b/core/bikeshed/katex/dist/contrib/render-a11y-string.js @@ -0,0 +1,875 @@ +(function webpackUniversalModuleDefinition(root, factory) { + if(typeof exports === 'object' && typeof module === 'object') + module.exports = factory(require("katex")); + else if(typeof define === 'function' && define.amd) + define(["katex"], factory); + else { + var a = typeof exports === 'object' ? factory(require("katex")) : factory(root["katex"]); + for(var i in a) (typeof exports === 'object' ? exports : root)[i] = a[i]; + } +})((typeof self !== 'undefined' ? self : this), function(__WEBPACK_EXTERNAL_MODULE__771__) { +return /******/ (function() { // webpackBootstrap +/******/ "use strict"; +/******/ var __webpack_modules__ = ({ + +/***/ 771: +/***/ (function(module) { + +module.exports = __WEBPACK_EXTERNAL_MODULE__771__; + +/***/ }) + +/******/ }); +/************************************************************************/ +/******/ // The module cache +/******/ var __webpack_module_cache__ = {}; +/******/ +/******/ // The require function +/******/ function __webpack_require__(moduleId) { +/******/ // Check if module is in cache +/******/ var cachedModule = __webpack_module_cache__[moduleId]; +/******/ if (cachedModule !== undefined) { +/******/ return cachedModule.exports; +/******/ } +/******/ // Create a new module (and put it into the cache) +/******/ var module = __webpack_module_cache__[moduleId] = { +/******/ // no module.id needed +/******/ // no module.loaded needed +/******/ exports: {} +/******/ }; +/******/ +/******/ // Execute the module function +/******/ __webpack_modules__[moduleId](module, module.exports, __webpack_require__); +/******/ +/******/ // Return the exports of the module +/******/ return module.exports; +/******/ } +/******/ +/************************************************************************/ +/******/ /* webpack/runtime/compat get default export */ +/******/ !function() { +/******/ // getDefaultExport function for compatibility with non-harmony modules +/******/ __webpack_require__.n = function(module) { +/******/ var getter = module && module.__esModule ? +/******/ function() { return module['default']; } : +/******/ function() { return module; }; +/******/ __webpack_require__.d(getter, { a: getter }); +/******/ return getter; +/******/ }; +/******/ }(); +/******/ +/******/ /* webpack/runtime/define property getters */ +/******/ !function() { +/******/ // define getter functions for harmony exports +/******/ __webpack_require__.d = function(exports, definition) { +/******/ for(var key in definition) { +/******/ if(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) { +/******/ Object.defineProperty(exports, key, { enumerable: true, get: definition[key] }); +/******/ } +/******/ } +/******/ }; +/******/ }(); +/******/ +/******/ /* webpack/runtime/hasOwnProperty shorthand */ +/******/ !function() { +/******/ __webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); } +/******/ }(); +/******/ +/************************************************************************/ +var __webpack_exports__ = {}; +// This entry need to be wrapped in an IIFE because it need to be isolated against other modules in the chunk. +!function() { +/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0__ = __webpack_require__(771); +/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0___default = /*#__PURE__*/__webpack_require__.n(katex__WEBPACK_IMPORTED_MODULE_0__); +/** + * renderA11yString returns a readable string. + * + * In some cases the string will have the proper semantic math + * meaning,: + * renderA11yString("\\frac{1}{2}"") + * -> "start fraction, 1, divided by, 2, end fraction" + * + * However, other cases do not: + * renderA11yString("f(x) = x^2") + * -> "f, left parenthesis, x, right parenthesis, equals, x, squared" + * + * The commas in the string aim to increase ease of understanding + * when read by a screenreader. + */ +// NOTE: since we're importing types here these files won't actually be +// included in the build. +// $FlowIgnore: we import the types directly anyways + +var stringMap = { + "(": "left parenthesis", + ")": "right parenthesis", + "[": "open bracket", + "]": "close bracket", + "\\{": "left brace", + "\\}": "right brace", + "\\lvert": "open vertical bar", + "\\rvert": "close vertical bar", + "|": "vertical bar", + "\\uparrow": "up arrow", + "\\Uparrow": "up arrow", + "\\downarrow": "down arrow", + "\\Downarrow": "down arrow", + "\\updownarrow": "up down arrow", + "\\leftarrow": "left arrow", + "\\Leftarrow": "left arrow", + "\\rightarrow": "right arrow", + "\\Rightarrow": "right arrow", + "\\langle": "open angle", + "\\rangle": "close angle", + "\\lfloor": "open floor", + "\\rfloor": "close floor", + "\\int": "integral", + "\\intop": "integral", + "\\lim": "limit", + "\\ln": "natural log", + "\\log": "log", + "\\sin": "sine", + "\\cos": "cosine", + "\\tan": "tangent", + "\\cot": "cotangent", + "\\sum": "sum", + "/": "slash", + ",": "comma", + ".": "point", + "-": "negative", + "+": "plus", + "~": "tilde", + ":": "colon", + "?": "question mark", + "'": "apostrophe", + "\\%": "percent", + " ": "space", + "\\ ": "space", + "\\$": "dollar sign", + "\\angle": "angle", + "\\degree": "degree", + "\\circ": "circle", + "\\vec": "vector", + "\\triangle": "triangle", + "\\pi": "pi", + "\\prime": "prime", + "\\infty": "infinity", + "\\alpha": "alpha", + "\\beta": "beta", + "\\gamma": "gamma", + "\\omega": "omega", + "\\theta": "theta", + "\\sigma": "sigma", + "\\lambda": "lambda", + "\\tau": "tau", + "\\Delta": "delta", + "\\delta": "delta", + "\\mu": "mu", + "\\rho": "rho", + "\\nabla": "del", + "\\ell": "ell", + "\\ldots": "dots", + // TODO: add entries for all accents + "\\hat": "hat", + "\\acute": "acute" +}; +var powerMap = { + "prime": "prime", + "degree": "degrees", + "circle": "degrees", + "2": "squared", + "3": "cubed" +}; +var openMap = { + "|": "open vertical bar", + ".": "" +}; +var closeMap = { + "|": "close vertical bar", + ".": "" +}; +var binMap = { + "+": "plus", + "-": "minus", + "\\pm": "plus minus", + "\\cdot": "dot", + "*": "times", + "/": "divided by", + "\\times": "times", + "\\div": "divided by", + "\\circ": "circle", + "\\bullet": "bullet" +}; +var relMap = { + "=": "equals", + "\\approx": "approximately equals", + "≠": "does not equal", + "\\geq": "is greater than or equal to", + "\\ge": "is greater than or equal to", + "\\leq": "is less than or equal to", + "\\le": "is less than or equal to", + ">": "is greater than", + "<": "is less than", + "\\leftarrow": "left arrow", + "\\Leftarrow": "left arrow", + "\\rightarrow": "right arrow", + "\\Rightarrow": "right arrow", + ":": "colon" +}; +var accentUnderMap = { + "\\underleftarrow": "left arrow", + "\\underrightarrow": "right arrow", + "\\underleftrightarrow": "left-right arrow", + "\\undergroup": "group", + "\\underlinesegment": "line segment", + "\\utilde": "tilde" +}; + +var buildString = function buildString(str, type, a11yStrings) { + if (!str) { + return; + } + + var ret; + + if (type === "open") { + ret = str in openMap ? openMap[str] : stringMap[str] || str; + } else if (type === "close") { + ret = str in closeMap ? closeMap[str] : stringMap[str] || str; + } else if (type === "bin") { + ret = binMap[str] || str; + } else if (type === "rel") { + ret = relMap[str] || str; + } else { + ret = stringMap[str] || str; + } // If the text to add is a number and there is already a string + // in the list and the last string is a number then we should + // combine them into a single number + + + if (/^\d+$/.test(ret) && a11yStrings.length > 0 && // TODO(kevinb): check that the last item in a11yStrings is a string + // I think we might be able to drop the nested arrays, which would make + // this easier to type + // $FlowFixMe + /^\d+$/.test(a11yStrings[a11yStrings.length - 1])) { + a11yStrings[a11yStrings.length - 1] += ret; + } else if (ret) { + a11yStrings.push(ret); + } +}; + +var buildRegion = function buildRegion(a11yStrings, callback) { + var regionStrings = []; + a11yStrings.push(regionStrings); + callback(regionStrings); +}; + +var handleObject = function handleObject(tree, a11yStrings, atomType) { + // Everything else is assumed to be an object... + switch (tree.type) { + case "accent": + { + buildRegion(a11yStrings, function (a11yStrings) { + buildA11yStrings(tree.base, a11yStrings, atomType); + a11yStrings.push("with"); + buildString(tree.label, "normal", a11yStrings); + a11yStrings.push("on top"); + }); + break; + } + + case "accentUnder": + { + buildRegion(a11yStrings, function (a11yStrings) { + buildA11yStrings(tree.base, a11yStrings, atomType); + a11yStrings.push("with"); + buildString(accentUnderMap[tree.label], "normal", a11yStrings); + a11yStrings.push("underneath"); + }); + break; + } + + case "accent-token": + { + // Used internally by accent symbols. + break; + } + + case "atom": + { + var text = tree.text; + + switch (tree.family) { + case "bin": + { + buildString(text, "bin", a11yStrings); + break; + } + + case "close": + { + buildString(text, "close", a11yStrings); + break; + } + // TODO(kevinb): figure out what should be done for inner + + case "inner": + { + buildString(tree.text, "inner", a11yStrings); + break; + } + + case "open": + { + buildString(text, "open", a11yStrings); + break; + } + + case "punct": + { + buildString(text, "punct", a11yStrings); + break; + } + + case "rel": + { + buildString(text, "rel", a11yStrings); + break; + } + + default: + { + tree.family; + throw new Error("\"" + tree.family + "\" is not a valid atom type"); + } + } + + break; + } + + case "color": + { + var color = tree.color.replace(/katex-/, ""); + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start color " + color); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end color " + color); + }); + break; + } + + case "color-token": + { + // Used by \color, \colorbox, and \fcolorbox but not directly rendered. + // It's a leaf node and has no children so just break. + break; + } + + case "delimsizing": + { + if (tree.delim && tree.delim !== ".") { + buildString(tree.delim, "normal", a11yStrings); + } + + break; + } + + case "genfrac": + { + buildRegion(a11yStrings, function (regionStrings) { + // genfrac can have unbalanced delimiters + var leftDelim = tree.leftDelim, + rightDelim = tree.rightDelim; // NOTE: Not sure if this is a safe assumption + // hasBarLine true -> fraction, false -> binomial + + if (tree.hasBarLine) { + regionStrings.push("start fraction"); + leftDelim && buildString(leftDelim, "open", regionStrings); + buildA11yStrings(tree.numer, regionStrings, atomType); + regionStrings.push("divided by"); + buildA11yStrings(tree.denom, regionStrings, atomType); + rightDelim && buildString(rightDelim, "close", regionStrings); + regionStrings.push("end fraction"); + } else { + regionStrings.push("start binomial"); + leftDelim && buildString(leftDelim, "open", regionStrings); + buildA11yStrings(tree.numer, regionStrings, atomType); + regionStrings.push("over"); + buildA11yStrings(tree.denom, regionStrings, atomType); + rightDelim && buildString(rightDelim, "close", regionStrings); + regionStrings.push("end binomial"); + } + }); + break; + } + + case "hbox": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "kern": + { + // No op: we don't attempt to present kerning information + // to the screen reader. + break; + } + + case "leftright": + { + buildRegion(a11yStrings, function (regionStrings) { + buildString(tree.left, "open", regionStrings); + buildA11yStrings(tree.body, regionStrings, atomType); + buildString(tree.right, "close", regionStrings); + }); + break; + } + + case "leftright-right": + { + // TODO: double check that this is a no-op + break; + } + + case "lap": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "mathord": + { + buildString(tree.text, "normal", a11yStrings); + break; + } + + case "op": + { + var body = tree.body, + name = tree.name; + + if (body) { + buildA11yStrings(body, a11yStrings, atomType); + } else if (name) { + buildString(name, "normal", a11yStrings); + } + + break; + } + + case "op-token": + { + // Used internally by operator symbols. + buildString(tree.text, atomType, a11yStrings); + break; + } + + case "ordgroup": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "overline": + { + buildRegion(a11yStrings, function (a11yStrings) { + a11yStrings.push("start overline"); + buildA11yStrings(tree.body, a11yStrings, atomType); + a11yStrings.push("end overline"); + }); + break; + } + + case "phantom": + { + a11yStrings.push("empty space"); + break; + } + + case "raisebox": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "rule": + { + a11yStrings.push("rectangle"); + break; + } + + case "sizing": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "spacing": + { + a11yStrings.push("space"); + break; + } + + case "styling": + { + // We ignore the styling and just pass through the contents + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "sqrt": + { + buildRegion(a11yStrings, function (regionStrings) { + var body = tree.body, + index = tree.index; + + if (index) { + var indexString = flatten(buildA11yStrings(index, [], atomType)).join(","); + + if (indexString === "3") { + regionStrings.push("cube root of"); + buildA11yStrings(body, regionStrings, atomType); + regionStrings.push("end cube root"); + return; + } + + regionStrings.push("root"); + regionStrings.push("start index"); + buildA11yStrings(index, regionStrings, atomType); + regionStrings.push("end index"); + return; + } + + regionStrings.push("square root of"); + buildA11yStrings(body, regionStrings, atomType); + regionStrings.push("end square root"); + }); + break; + } + + case "supsub": + { + var base = tree.base, + sub = tree.sub, + sup = tree.sup; + var isLog = false; + + if (base) { + buildA11yStrings(base, a11yStrings, atomType); + isLog = base.type === "op" && base.name === "\\log"; + } + + if (sub) { + var regionName = isLog ? "base" : "subscript"; + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start " + regionName); + buildA11yStrings(sub, regionStrings, atomType); + regionStrings.push("end " + regionName); + }); + } + + if (sup) { + buildRegion(a11yStrings, function (regionStrings) { + var supString = flatten(buildA11yStrings(sup, [], atomType)).join(","); + + if (supString in powerMap) { + regionStrings.push(powerMap[supString]); + return; + } + + regionStrings.push("start superscript"); + buildA11yStrings(sup, regionStrings, atomType); + regionStrings.push("end superscript"); + }); + } + + break; + } + + case "text": + { + // TODO: handle other fonts + if (tree.font === "\\textbf") { + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start bold text"); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end bold text"); + }); + break; + } + + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start text"); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end text"); + }); + break; + } + + case "textord": + { + buildString(tree.text, atomType, a11yStrings); + break; + } + + case "smash": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "enclose": + { + // TODO: create a map for these. + // TODO: differentiate between a body with a single atom, e.g. + // "cancel a" instead of "start cancel, a, end cancel" + if (/cancel/.test(tree.label)) { + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start cancel"); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end cancel"); + }); + break; + } else if (/box/.test(tree.label)) { + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start box"); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end box"); + }); + break; + } else if (/sout/.test(tree.label)) { + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start strikeout"); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end strikeout"); + }); + break; + } else if (/phase/.test(tree.label)) { + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start phase angle"); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end phase angle"); + }); + break; + } + + throw new Error("KaTeX-a11y: enclose node with " + tree.label + " not supported yet"); + } + + case "vcenter": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "vphantom": + { + throw new Error("KaTeX-a11y: vphantom not implemented yet"); + } + + case "hphantom": + { + throw new Error("KaTeX-a11y: hphantom not implemented yet"); + } + + case "operatorname": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "array": + { + throw new Error("KaTeX-a11y: array not implemented yet"); + } + + case "raw": + { + throw new Error("KaTeX-a11y: raw not implemented yet"); + } + + case "size": + { + // Although there are nodes of type "size" in the parse tree, they have + // no semantic meaning and should be ignored. + break; + } + + case "url": + { + throw new Error("KaTeX-a11y: url not implemented yet"); + } + + case "tag": + { + throw new Error("KaTeX-a11y: tag not implemented yet"); + } + + case "verb": + { + buildString("start verbatim", "normal", a11yStrings); + buildString(tree.body, "normal", a11yStrings); + buildString("end verbatim", "normal", a11yStrings); + break; + } + + case "environment": + { + throw new Error("KaTeX-a11y: environment not implemented yet"); + } + + case "horizBrace": + { + buildString("start " + tree.label.slice(1), "normal", a11yStrings); + buildA11yStrings(tree.base, a11yStrings, atomType); + buildString("end " + tree.label.slice(1), "normal", a11yStrings); + break; + } + + case "infix": + { + // All infix nodes are replace with other nodes. + break; + } + + case "includegraphics": + { + throw new Error("KaTeX-a11y: includegraphics not implemented yet"); + } + + case "font": + { + // TODO: callout the start/end of specific fonts + // TODO: map \BBb{N} to "the naturals" or something like that + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "href": + { + throw new Error("KaTeX-a11y: href not implemented yet"); + } + + case "cr": + { + // This is used by environments. + throw new Error("KaTeX-a11y: cr not implemented yet"); + } + + case "underline": + { + buildRegion(a11yStrings, function (a11yStrings) { + a11yStrings.push("start underline"); + buildA11yStrings(tree.body, a11yStrings, atomType); + a11yStrings.push("end underline"); + }); + break; + } + + case "xArrow": + { + throw new Error("KaTeX-a11y: xArrow not implemented yet"); + } + + case "cdlabel": + { + throw new Error("KaTeX-a11y: cdlabel not implemented yet"); + } + + case "cdlabelparent": + { + throw new Error("KaTeX-a11y: cdlabelparent not implemented yet"); + } + + case "mclass": + { + // \neq and \ne are macros so we let "htmlmathml" render the mathmal + // side of things and extract the text from that. + var _atomType = tree.mclass.slice(1); // $FlowFixMe: drop the leading "m" from the values in mclass + + + buildA11yStrings(tree.body, a11yStrings, _atomType); + break; + } + + case "mathchoice": + { + // TODO: track which which style we're using, e.g. dispaly, text, etc. + // default to text style if even that may not be the correct style + buildA11yStrings(tree.text, a11yStrings, atomType); + break; + } + + case "htmlmathml": + { + buildA11yStrings(tree.mathml, a11yStrings, atomType); + break; + } + + case "middle": + { + buildString(tree.delim, atomType, a11yStrings); + break; + } + + case "internal": + { + // internal nodes are never included in the parse tree + break; + } + + case "html": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + default: + tree.type; + throw new Error("KaTeX a11y un-recognized type: " + tree.type); + } +}; + +var buildA11yStrings = function buildA11yStrings(tree, a11yStrings, atomType) { + if (a11yStrings === void 0) { + a11yStrings = []; + } + + if (tree instanceof Array) { + for (var i = 0; i < tree.length; i++) { + buildA11yStrings(tree[i], a11yStrings, atomType); + } + } else { + handleObject(tree, a11yStrings, atomType); + } + + return a11yStrings; +}; + +var flatten = function flatten(array) { + var result = []; + array.forEach(function (item) { + if (item instanceof Array) { + result = result.concat(flatten(item)); + } else { + result.push(item); + } + }); + return result; +}; + +var renderA11yString = function renderA11yString(text, settings) { + var tree = katex__WEBPACK_IMPORTED_MODULE_0___default().__parse(text, settings); + + var a11yStrings = buildA11yStrings(tree, [], "normal"); + return flatten(a11yStrings).join(", "); +}; + +/* harmony default export */ __webpack_exports__["default"] = (renderA11yString); +}(); +__webpack_exports__ = __webpack_exports__["default"]; +/******/ return __webpack_exports__; +/******/ })() +; +}); \ No newline at end of file diff --git a/core/bikeshed/katex/dist/contrib/render-a11y-string.min.js b/core/bikeshed/katex/dist/contrib/render-a11y-string.min.js new file mode 100644 index 00000000..e7461890 --- /dev/null +++ b/core/bikeshed/katex/dist/contrib/render-a11y-string.min.js @@ -0,0 +1 @@ +!function(e,r){if("object"==typeof exports&&"object"==typeof module)module.exports=r(require("katex"));else if("function"==typeof define&&define.amd)define(["katex"],r);else{var a="object"==typeof exports?r(require("katex")):r(e.katex);for(var t in a)("object"==typeof exports?exports:e)[t]=a[t]}}("undefined"!=typeof self?self:this,(function(e){return function(){"use strict";var r={771:function(r){r.exports=e}},a={};function t(e){var o=a[e];if(void 0!==o)return o.exports;var n=a[e]={exports:{}};return r[e](n,n.exports,t),n.exports}t.n=function(e){var r=e&&e.__esModule?function(){return e.default}:function(){return e};return t.d(r,{a:r}),r},t.d=function(e,r){for(var a in r)t.o(r,a)&&!t.o(e,a)&&Object.defineProperty(e,a,{enumerable:!0,get:r[a]})},t.o=function(e,r){return Object.prototype.hasOwnProperty.call(e,r)};var o,n,s,i,l,c,u,p,d,b,h,m,f,y,w={};return o=t(771),n=t.n(o),s={"(":"left parenthesis",")":"right parenthesis","[":"open bracket","]":"close bracket","\\{":"left brace","\\}":"right brace","\\lvert":"open vertical bar","\\rvert":"close vertical bar","|":"vertical bar","\\uparrow":"up arrow","\\Uparrow":"up arrow","\\downarrow":"down arrow","\\Downarrow":"down arrow","\\updownarrow":"up down arrow","\\leftarrow":"left arrow","\\Leftarrow":"left arrow","\\rightarrow":"right arrow","\\Rightarrow":"right arrow","\\langle":"open angle","\\rangle":"close angle","\\lfloor":"open floor","\\rfloor":"close floor","\\int":"integral","\\intop":"integral","\\lim":"limit","\\ln":"natural 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a=[];e.push(a),r(a)},m=function(e,r,a){switch(e.type){case"accent":h(r,(function(r){f(e.base,r,a),r.push("with"),b(e.label,"normal",r),r.push("on top")}));break;case"accentUnder":h(r,(function(r){f(e.base,r,a),r.push("with"),b(d[e.label],"normal",r),r.push("underneath")}));break;case"accent-token":break;case"atom":var t=e.text;switch(e.family){case"bin":b(t,"bin",r);break;case"close":b(t,"close",r);break;case"inner":b(e.text,"inner",r);break;case"open":b(t,"open",r);break;case"punct":b(t,"punct",r);break;case"rel":b(t,"rel",r);break;default:throw e.family,new Error('"'+e.family+'" is not a valid atom type')}break;case"color":var o=e.color.replace(/katex-/,"");h(r,(function(r){r.push("start color "+o),f(e.body,r,a),r.push("end color "+o)}));break;case"color-token":break;case"delimsizing":e.delim&&"."!==e.delim&&b(e.delim,"normal",r);break;case"genfrac":h(r,(function(r){var t=e.leftDelim,o=e.rightDelim;e.hasBarLine?(r.push("start fraction"),t&&b(t,"open",r),f(e.numer,r,a),r.push("divided 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t=e.body,o=e.index;if(o)return"3"===y(f(o,[],a)).join(",")?(r.push("cube root of"),f(t,r,a),void r.push("end cube root")):(r.push("root"),r.push("start index"),f(o,r,a),void r.push("end index"));r.push("square root of"),f(t,r,a),r.push("end square root")}));break;case"supsub":var l=e.base,c=e.sub,u=e.sup,p=!1;if(l&&(f(l,r,a),p="op"===l.type&&"\\log"===l.name),c){var m=p?"base":"subscript";h(r,(function(e){e.push("start "+m),f(c,e,a),e.push("end "+m)}))}u&&h(r,(function(e){var r=y(f(u,[],a)).join(",");r in i?e.push(i[r]):(e.push("start superscript"),f(u,e,a),e.push("end superscript"))}));break;case"text":if("\\textbf"===e.font){h(r,(function(r){r.push("start bold text"),f(e.body,r,a),r.push("end bold text")}));break}h(r,(function(r){r.push("start text"),f(e.body,r,a),r.push("end text")}));break;case"textord":b(e.text,a,r);break;case"smash":f(e.body,r,a);break;case"enclose":if(/cancel/.test(e.label)){h(r,(function(r){r.push("start cancel"),f(e.body,r,a),r.push("end cancel")}));break}if(/box/.test(e.label)){h(r,(function(r){r.push("start box"),f(e.body,r,a),r.push("end box")}));break}if(/sout/.test(e.label)){h(r,(function(r){r.push("start strikeout"),f(e.body,r,a),r.push("end strikeout")}));break}if(/phase/.test(e.label)){h(r,(function(r){r.push("start phase angle"),f(e.body,r,a),r.push("end phase angle")}));break}throw new Error("KaTeX-a11y: enclose node with "+e.label+" not supported yet");case"vcenter":f(e.body,r,a);break;case"vphantom":throw new Error("KaTeX-a11y: vphantom not implemented yet");case"hphantom":throw new Error("KaTeX-a11y: hphantom not implemented yet");case"operatorname":f(e.body,r,a);break;case"array":throw new Error("KaTeX-a11y: array not implemented yet");case"raw":throw new Error("KaTeX-a11y: raw not implemented yet");case"size":break;case"url":throw new Error("KaTeX-a11y: url not implemented yet");case"tag":throw new Error("KaTeX-a11y: tag not implemented yet");case"verb":b("start verbatim","normal",r),b(e.body,"normal",r),b("end verbatim","normal",r);break;case"environment":throw new Error("KaTeX-a11y: environment not implemented yet");case"horizBrace":b("start "+e.label.slice(1),"normal",r),f(e.base,r,a),b("end "+e.label.slice(1),"normal",r);break;case"infix":break;case"includegraphics":throw new Error("KaTeX-a11y: includegraphics not implemented yet");case"font":f(e.body,r,a);break;case"href":throw new Error("KaTeX-a11y: href not implemented yet");case"cr":throw new Error("KaTeX-a11y: cr not implemented yet");case"underline":h(r,(function(r){r.push("start underline"),f(e.body,r,a),r.push("end underline")}));break;case"xArrow":throw new Error("KaTeX-a11y: xArrow not implemented yet");case"cdlabel":throw new Error("KaTeX-a11y: cdlabel not implemented yet");case"cdlabelparent":throw new Error("KaTeX-a11y: cdlabelparent not implemented yet");case"mclass":var w=e.mclass.slice(1);f(e.body,r,w);break;case"mathchoice":f(e.text,r,a);break;case"htmlmathml":f(e.mathml,r,a);break;case"middle":b(e.delim,a,r);break;case"internal":break;case"html":f(e.body,r,a);break;default:throw e.type,new Error("KaTeX a11y un-recognized type: "+e.type)}},f=function e(r,a,t){if(void 0===a&&(a=[]),r instanceof Array)for(var o=0;o "start fraction, 1, divided by, 2, end fraction" + * + * However, other cases do not: + * renderA11yString("f(x) = x^2") + * -> "f, left parenthesis, x, right parenthesis, equals, x, squared" + * + * The commas in the string aim to increase ease of understanding + * when read by a screenreader. + */ +var stringMap = { + "(": "left parenthesis", + ")": "right parenthesis", + "[": "open bracket", + "]": "close bracket", + "\\{": "left brace", + "\\}": "right brace", + "\\lvert": "open vertical bar", + "\\rvert": "close vertical bar", + "|": "vertical bar", + "\\uparrow": "up arrow", + "\\Uparrow": "up arrow", + "\\downarrow": "down arrow", + "\\Downarrow": "down arrow", + "\\updownarrow": "up down arrow", + "\\leftarrow": "left arrow", + "\\Leftarrow": "left arrow", + "\\rightarrow": "right arrow", + "\\Rightarrow": "right arrow", + "\\langle": "open angle", + "\\rangle": "close angle", + "\\lfloor": "open floor", + "\\rfloor": "close floor", + "\\int": "integral", + "\\intop": "integral", + "\\lim": "limit", + "\\ln": "natural log", + "\\log": "log", + "\\sin": "sine", + "\\cos": "cosine", + "\\tan": "tangent", + "\\cot": "cotangent", + "\\sum": "sum", + "/": "slash", + ",": "comma", + ".": "point", + "-": "negative", + "+": "plus", + "~": "tilde", + ":": "colon", + "?": "question mark", + "'": "apostrophe", + "\\%": "percent", + " ": "space", + "\\ ": "space", + "\\$": "dollar sign", + "\\angle": "angle", + "\\degree": "degree", + "\\circ": "circle", + "\\vec": "vector", + "\\triangle": "triangle", + "\\pi": "pi", + "\\prime": "prime", + "\\infty": "infinity", + "\\alpha": "alpha", + "\\beta": "beta", + "\\gamma": "gamma", + "\\omega": "omega", + "\\theta": "theta", + "\\sigma": "sigma", + "\\lambda": "lambda", + "\\tau": "tau", + "\\Delta": "delta", + "\\delta": "delta", + "\\mu": "mu", + "\\rho": "rho", + "\\nabla": "del", + "\\ell": "ell", + "\\ldots": "dots", + // TODO: add entries for all accents + "\\hat": "hat", + "\\acute": "acute" +}; +var powerMap = { + "prime": "prime", + "degree": "degrees", + "circle": "degrees", + "2": "squared", + "3": "cubed" +}; +var openMap = { + "|": "open vertical bar", + ".": "" +}; +var closeMap = { + "|": "close vertical bar", + ".": "" +}; +var binMap = { + "+": "plus", + "-": "minus", + "\\pm": "plus minus", + "\\cdot": "dot", + "*": "times", + "/": "divided by", + "\\times": "times", + "\\div": "divided by", + "\\circ": "circle", + "\\bullet": "bullet" +}; +var relMap = { + "=": "equals", + "\\approx": "approximately equals", + "≠": "does not equal", + "\\geq": "is greater than or equal to", + "\\ge": "is greater than or equal to", + "\\leq": "is less than or equal to", + "\\le": "is less than or equal to", + ">": "is greater than", + "<": "is less than", + "\\leftarrow": "left arrow", + "\\Leftarrow": "left arrow", + "\\rightarrow": "right arrow", + "\\Rightarrow": "right arrow", + ":": "colon" +}; +var accentUnderMap = { + "\\underleftarrow": "left arrow", + "\\underrightarrow": "right arrow", + "\\underleftrightarrow": "left-right arrow", + "\\undergroup": "group", + "\\underlinesegment": "line segment", + "\\utilde": "tilde" +}; + +var buildString = (str, type, a11yStrings) => { + if (!str) { + return; + } + + var ret; + + if (type === "open") { + ret = str in openMap ? openMap[str] : stringMap[str] || str; + } else if (type === "close") { + ret = str in closeMap ? closeMap[str] : stringMap[str] || str; + } else if (type === "bin") { + ret = binMap[str] || str; + } else if (type === "rel") { + ret = relMap[str] || str; + } else { + ret = stringMap[str] || str; + } // If the text to add is a number and there is already a string + // in the list and the last string is a number then we should + // combine them into a single number + + + if (/^\d+$/.test(ret) && a11yStrings.length > 0 && // TODO(kevinb): check that the last item in a11yStrings is a string + // I think we might be able to drop the nested arrays, which would make + // this easier to type + // $FlowFixMe + /^\d+$/.test(a11yStrings[a11yStrings.length - 1])) { + a11yStrings[a11yStrings.length - 1] += ret; + } else if (ret) { + a11yStrings.push(ret); + } +}; + +var buildRegion = (a11yStrings, callback) => { + var regionStrings = []; + a11yStrings.push(regionStrings); + callback(regionStrings); +}; + +var handleObject = (tree, a11yStrings, atomType) => { + // Everything else is assumed to be an object... + switch (tree.type) { + case "accent": + { + buildRegion(a11yStrings, a11yStrings => { + buildA11yStrings(tree.base, a11yStrings, atomType); + a11yStrings.push("with"); + buildString(tree.label, "normal", a11yStrings); + a11yStrings.push("on top"); + }); + break; + } + + case "accentUnder": + { + buildRegion(a11yStrings, a11yStrings => { + buildA11yStrings(tree.base, a11yStrings, atomType); + a11yStrings.push("with"); + buildString(accentUnderMap[tree.label], "normal", a11yStrings); + a11yStrings.push("underneath"); + }); + break; + } + + case "accent-token": + { + // Used internally by accent symbols. + break; + } + + case "atom": + { + var { + text + } = tree; + + switch (tree.family) { + case "bin": + { + buildString(text, "bin", a11yStrings); + break; + } + + case "close": + { + buildString(text, "close", a11yStrings); + break; + } + // TODO(kevinb): figure out what should be done for inner + + case "inner": + { + buildString(tree.text, "inner", a11yStrings); + break; + } + + case "open": + { + buildString(text, "open", a11yStrings); + break; + } + + case "punct": + { + buildString(text, "punct", a11yStrings); + break; + } + + case "rel": + { + buildString(text, "rel", a11yStrings); + break; + } + + default: + { + tree.family; + throw new Error("\"" + tree.family + "\" is not a valid atom type"); + } + } + + break; + } + + case "color": + { + var color = tree.color.replace(/katex-/, ""); + buildRegion(a11yStrings, regionStrings => { + regionStrings.push("start color " + color); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end color " + color); + }); + break; + } + + case "color-token": + { + // Used by \color, \colorbox, and \fcolorbox but not directly rendered. + // It's a leaf node and has no children so just break. + break; + } + + case "delimsizing": + { + if (tree.delim && tree.delim !== ".") { + buildString(tree.delim, "normal", a11yStrings); + } + + break; + } + + case "genfrac": + { + buildRegion(a11yStrings, regionStrings => { + // genfrac can have unbalanced delimiters + var { + leftDelim, + rightDelim + } = tree; // NOTE: Not sure if this is a safe assumption + // hasBarLine true -> fraction, false -> binomial + + if (tree.hasBarLine) { + regionStrings.push("start fraction"); + leftDelim && buildString(leftDelim, "open", regionStrings); + buildA11yStrings(tree.numer, regionStrings, atomType); + regionStrings.push("divided by"); + buildA11yStrings(tree.denom, regionStrings, atomType); + rightDelim && buildString(rightDelim, "close", regionStrings); + regionStrings.push("end fraction"); + } else { + regionStrings.push("start binomial"); + leftDelim && buildString(leftDelim, "open", regionStrings); + buildA11yStrings(tree.numer, regionStrings, atomType); + regionStrings.push("over"); + buildA11yStrings(tree.denom, regionStrings, atomType); + rightDelim && buildString(rightDelim, "close", regionStrings); + regionStrings.push("end binomial"); + } + }); + break; + } + + case "hbox": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "kern": + { + // No op: we don't attempt to present kerning information + // to the screen reader. + break; + } + + case "leftright": + { + buildRegion(a11yStrings, regionStrings => { + buildString(tree.left, "open", regionStrings); + buildA11yStrings(tree.body, regionStrings, atomType); + buildString(tree.right, "close", regionStrings); + }); + break; + } + + case "leftright-right": + { + // TODO: double check that this is a no-op + break; + } + + case "lap": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "mathord": + { + buildString(tree.text, "normal", a11yStrings); + break; + } + + case "op": + { + var { + body, + name + } = tree; + + if (body) { + buildA11yStrings(body, a11yStrings, atomType); + } else if (name) { + buildString(name, "normal", a11yStrings); + } + + break; + } + + case "op-token": + { + // Used internally by operator symbols. + buildString(tree.text, atomType, a11yStrings); + break; + } + + case "ordgroup": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "overline": + { + buildRegion(a11yStrings, function (a11yStrings) { + a11yStrings.push("start overline"); + buildA11yStrings(tree.body, a11yStrings, atomType); + a11yStrings.push("end overline"); + }); + break; + } + + case "phantom": + { + a11yStrings.push("empty space"); + break; + } + + case "raisebox": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "rule": + { + a11yStrings.push("rectangle"); + break; + } + + case "sizing": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "spacing": + { + a11yStrings.push("space"); + break; + } + + case "styling": + { + // We ignore the styling and just pass through the contents + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "sqrt": + { + buildRegion(a11yStrings, regionStrings => { + var { + body, + index + } = tree; + + if (index) { + var indexString = flatten(buildA11yStrings(index, [], atomType)).join(","); + + if (indexString === "3") { + regionStrings.push("cube root of"); + buildA11yStrings(body, regionStrings, atomType); + regionStrings.push("end cube root"); + return; + } + + regionStrings.push("root"); + regionStrings.push("start index"); + buildA11yStrings(index, regionStrings, atomType); + regionStrings.push("end index"); + return; + } + + regionStrings.push("square root of"); + buildA11yStrings(body, regionStrings, atomType); + regionStrings.push("end square root"); + }); + break; + } + + case "supsub": + { + var { + base, + sub, + sup + } = tree; + var isLog = false; + + if (base) { + buildA11yStrings(base, a11yStrings, atomType); + isLog = base.type === "op" && base.name === "\\log"; + } + + if (sub) { + var regionName = isLog ? "base" : "subscript"; + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start " + regionName); + buildA11yStrings(sub, regionStrings, atomType); + regionStrings.push("end " + regionName); + }); + } + + if (sup) { + buildRegion(a11yStrings, function (regionStrings) { + var supString = flatten(buildA11yStrings(sup, [], atomType)).join(","); + + if (supString in powerMap) { + regionStrings.push(powerMap[supString]); + return; + } + + regionStrings.push("start superscript"); + buildA11yStrings(sup, regionStrings, atomType); + regionStrings.push("end superscript"); + }); + } + + break; + } + + case "text": + { + // TODO: handle other fonts + if (tree.font === "\\textbf") { + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start bold text"); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end bold text"); + }); + break; + } + + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start text"); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end text"); + }); + break; + } + + case "textord": + { + buildString(tree.text, atomType, a11yStrings); + break; + } + + case "smash": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "enclose": + { + // TODO: create a map for these. + // TODO: differentiate between a body with a single atom, e.g. + // "cancel a" instead of "start cancel, a, end cancel" + if (/cancel/.test(tree.label)) { + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start cancel"); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end cancel"); + }); + break; + } else if (/box/.test(tree.label)) { + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start box"); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end box"); + }); + break; + } else if (/sout/.test(tree.label)) { + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start strikeout"); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end strikeout"); + }); + break; + } else if (/phase/.test(tree.label)) { + buildRegion(a11yStrings, function (regionStrings) { + regionStrings.push("start phase angle"); + buildA11yStrings(tree.body, regionStrings, atomType); + regionStrings.push("end phase angle"); + }); + break; + } + + throw new Error("KaTeX-a11y: enclose node with " + tree.label + " not supported yet"); + } + + case "vcenter": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "vphantom": + { + throw new Error("KaTeX-a11y: vphantom not implemented yet"); + } + + case "hphantom": + { + throw new Error("KaTeX-a11y: hphantom not implemented yet"); + } + + case "operatorname": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "array": + { + throw new Error("KaTeX-a11y: array not implemented yet"); + } + + case "raw": + { + throw new Error("KaTeX-a11y: raw not implemented yet"); + } + + case "size": + { + // Although there are nodes of type "size" in the parse tree, they have + // no semantic meaning and should be ignored. + break; + } + + case "url": + { + throw new Error("KaTeX-a11y: url not implemented yet"); + } + + case "tag": + { + throw new Error("KaTeX-a11y: tag not implemented yet"); + } + + case "verb": + { + buildString("start verbatim", "normal", a11yStrings); + buildString(tree.body, "normal", a11yStrings); + buildString("end verbatim", "normal", a11yStrings); + break; + } + + case "environment": + { + throw new Error("KaTeX-a11y: environment not implemented yet"); + } + + case "horizBrace": + { + buildString("start " + tree.label.slice(1), "normal", a11yStrings); + buildA11yStrings(tree.base, a11yStrings, atomType); + buildString("end " + tree.label.slice(1), "normal", a11yStrings); + break; + } + + case "infix": + { + // All infix nodes are replace with other nodes. + break; + } + + case "includegraphics": + { + throw new Error("KaTeX-a11y: includegraphics not implemented yet"); + } + + case "font": + { + // TODO: callout the start/end of specific fonts + // TODO: map \BBb{N} to "the naturals" or something like that + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + case "href": + { + throw new Error("KaTeX-a11y: href not implemented yet"); + } + + case "cr": + { + // This is used by environments. + throw new Error("KaTeX-a11y: cr not implemented yet"); + } + + case "underline": + { + buildRegion(a11yStrings, function (a11yStrings) { + a11yStrings.push("start underline"); + buildA11yStrings(tree.body, a11yStrings, atomType); + a11yStrings.push("end underline"); + }); + break; + } + + case "xArrow": + { + throw new Error("KaTeX-a11y: xArrow not implemented yet"); + } + + case "cdlabel": + { + throw new Error("KaTeX-a11y: cdlabel not implemented yet"); + } + + case "cdlabelparent": + { + throw new Error("KaTeX-a11y: cdlabelparent not implemented yet"); + } + + case "mclass": + { + // \neq and \ne are macros so we let "htmlmathml" render the mathmal + // side of things and extract the text from that. + var _atomType = tree.mclass.slice(1); // $FlowFixMe: drop the leading "m" from the values in mclass + + + buildA11yStrings(tree.body, a11yStrings, _atomType); + break; + } + + case "mathchoice": + { + // TODO: track which which style we're using, e.g. dispaly, text, etc. + // default to text style if even that may not be the correct style + buildA11yStrings(tree.text, a11yStrings, atomType); + break; + } + + case "htmlmathml": + { + buildA11yStrings(tree.mathml, a11yStrings, atomType); + break; + } + + case "middle": + { + buildString(tree.delim, atomType, a11yStrings); + break; + } + + case "internal": + { + // internal nodes are never included in the parse tree + break; + } + + case "html": + { + buildA11yStrings(tree.body, a11yStrings, atomType); + break; + } + + default: + tree.type; + throw new Error("KaTeX a11y un-recognized type: " + tree.type); + } +}; + +var buildA11yStrings = function buildA11yStrings(tree, a11yStrings, atomType) { + if (a11yStrings === void 0) { + a11yStrings = []; + } + + if (tree instanceof Array) { + for (var i = 0; i < tree.length; i++) { + buildA11yStrings(tree[i], a11yStrings, atomType); + } + } else { + handleObject(tree, a11yStrings, atomType); + } + + return a11yStrings; +}; + +var flatten = function flatten(array) { + var result = []; + array.forEach(function (item) { + if (item instanceof Array) { + result = result.concat(flatten(item)); + } else { + result.push(item); + } + }); + return result; +}; + +var renderA11yString = function renderA11yString(text, settings) { + var tree = katex.__parse(text, settings); + + var a11yStrings = buildA11yStrings(tree, [], "normal"); + return flatten(a11yStrings).join(", "); +}; + +export { renderA11yString as default }; diff --git a/core/bikeshed/katex/dist/fonts/KaTeX_AMS-Regular.ttf 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display: block; +} +.katex .mtable .vertical-separator { + display: inline-block; + min-width: 1px; +} +.katex .mtable .arraycolsep { + display: inline-block; +} +.katex .mtable .col-align-c > .vlist-t { + text-align: center; +} +.katex .mtable .col-align-l > .vlist-t { + text-align: left; +} +.katex .mtable .col-align-r > .vlist-t { + text-align: right; +} +.katex .svg-align { + text-align: left; +} +.katex svg { + display: block; + position: absolute; + width: 100%; + height: inherit; + fill: currentColor; + stroke: currentColor; + fill-rule: nonzero; + fill-opacity: 1; + stroke-width: 1; + stroke-linecap: butt; + stroke-linejoin: miter; + stroke-miterlimit: 4; + stroke-dasharray: none; + stroke-dashoffset: 0; + stroke-opacity: 1; +} +.katex svg path { + stroke: none; +} +.katex img { + border-style: none; + min-width: 0; + min-height: 0; + max-width: none; + max-height: none; +} +.katex .stretchy { + width: 100%; + display: block; + position: relative; + overflow: hidden; +} +.katex .stretchy::before, +.katex .stretchy::after { + content: ""; +} +.katex .hide-tail { + width: 100%; + position: relative; + overflow: hidden; +} +.katex .halfarrow-left { + position: absolute; + left: 0; + width: 50.2%; + overflow: hidden; +} +.katex .halfarrow-right { + position: absolute; + right: 0; + width: 50.2%; + overflow: hidden; +} +.katex .brace-left { + position: absolute; + left: 0; + width: 25.1%; + overflow: hidden; +} +.katex .brace-center { + position: absolute; + left: 25%; + width: 50%; + overflow: hidden; +} +.katex .brace-right { + position: absolute; + right: 0; + width: 25.1%; + overflow: hidden; +} +.katex .x-arrow-pad { + padding: 0 0.5em; +} +.katex .cd-arrow-pad { + padding: 0 0.55556em 0 0.27778em; +} +.katex .x-arrow, +.katex .mover, +.katex .munder { + text-align: center; +} +.katex .boxpad { + padding: 0 0.3em 0 0.3em; +} +.katex .fbox, +.katex .fcolorbox { + box-sizing: border-box; + border: 0.04em solid; +} +.katex .cancel-pad { + padding: 0 0.2em 0 0.2em; +} +.katex .cancel-lap { + margin-left: -0.2em; + margin-right: -0.2em; +} +.katex .sout { + border-bottom-style: solid; + border-bottom-width: 0.08em; +} +.katex .angl { + box-sizing: border-box; + border-top: 0.049em solid; + border-right: 0.049em solid; + margin-right: 0.03889em; +} +.katex .anglpad { + padding: 0 0.03889em 0 0.03889em; +} +.katex .eqn-num::before { + counter-increment: katexEqnNo; + content: "(" counter(katexEqnNo) ")"; +} +.katex .mml-eqn-num::before { + counter-increment: mmlEqnNo; + content: "(" counter(mmlEqnNo) ")"; +} +.katex .mtr-glue { + width: 50%; +} +.katex .cd-vert-arrow { + display: inline-block; + position: relative; +} +.katex .cd-label-left { + display: inline-block; + position: absolute; + right: calc(50% + 0.3em); + text-align: left; +} +.katex .cd-label-right { + display: inline-block; + position: absolute; + left: calc(50% + 0.3em); + text-align: right; +} +div > .katex-display { + display: block; + margin: 1em 0; + text-align: center; +} +div > .katex-display > .katex { + display: block; + text-align: center; + white-space: nowrap; +} +div > .katex-display > .katex > .katex-html { + display: block; + position: relative; +} +div > .katex-display > .katex > .katex-html > .tag { + position: absolute; + right: 0; +} +.katex-display.leqno > .katex > .katex-html > .tag { + left: 0; + right: auto; +} +.katex-display.fleqn > .katex { + text-align: left; + padding-left: 2em; +} +body { + counter-reset: katexEqnNo mmlEqnNo; +} +/* Force borders on tables */ +table { + border-collapse: collapse; +} +.docutils th, td { + border: 1px solid; + padding: .4em; +} +.footnote td { + border: 0; +} +.codepre { + white-space: pre; +} diff --git a/core/bikeshed/katex/dist/katex.css.orig b/core/bikeshed/katex/dist/katex.css.orig new file mode 100644 index 00000000..858c48a1 --- /dev/null +++ b/core/bikeshed/katex/dist/katex.css.orig @@ -0,0 +1,1079 @@ +/* stylelint-disable font-family-no-missing-generic-family-keyword */ +@font-face { + font-family: 'KaTeX_AMS'; + src: url(fonts/KaTeX_AMS-Regular.woff2) format('woff2'), url(fonts/KaTeX_AMS-Regular.woff) format('woff'), url(fonts/KaTeX_AMS-Regular.ttf) format('truetype'); + font-weight: normal; + font-style: normal; +} +@font-face { + font-family: 'KaTeX_Caligraphic'; + src: url(fonts/KaTeX_Caligraphic-Bold.woff2) format('woff2'), url(fonts/KaTeX_Caligraphic-Bold.woff) format('woff'), url(fonts/KaTeX_Caligraphic-Bold.ttf) format('truetype'); + font-weight: bold; + font-style: normal; +} +@font-face { + font-family: 'KaTeX_Caligraphic'; + src: url(fonts/KaTeX_Caligraphic-Regular.woff2) format('woff2'), url(fonts/KaTeX_Caligraphic-Regular.woff) format('woff'), url(fonts/KaTeX_Caligraphic-Regular.ttf) format('truetype'); + font-weight: normal; + font-style: normal; +} +@font-face { + font-family: 'KaTeX_Fraktur'; + src: url(fonts/KaTeX_Fraktur-Bold.woff2) format('woff2'), url(fonts/KaTeX_Fraktur-Bold.woff) format('woff'), url(fonts/KaTeX_Fraktur-Bold.ttf) format('truetype'); + font-weight: bold; + font-style: normal; +} +@font-face { + font-family: 'KaTeX_Fraktur'; + src: url(fonts/KaTeX_Fraktur-Regular.woff2) format('woff2'), url(fonts/KaTeX_Fraktur-Regular.woff) format('woff'), url(fonts/KaTeX_Fraktur-Regular.ttf) format('truetype'); + font-weight: normal; + font-style: normal; +} +@font-face { + font-family: 'KaTeX_Main'; + src: url(fonts/KaTeX_Main-Bold.woff2) format('woff2'), url(fonts/KaTeX_Main-Bold.woff) format('woff'), url(fonts/KaTeX_Main-Bold.ttf) format('truetype'); + font-weight: bold; + font-style: normal; +} +@font-face { + font-family: 'KaTeX_Main'; + src: url(fonts/KaTeX_Main-BoldItalic.woff2) format('woff2'), url(fonts/KaTeX_Main-BoldItalic.woff) format('woff'), url(fonts/KaTeX_Main-BoldItalic.ttf) format('truetype'); + font-weight: bold; + font-style: italic; +} +@font-face { + font-family: 'KaTeX_Main'; + src: url(fonts/KaTeX_Main-Italic.woff2) format('woff2'), url(fonts/KaTeX_Main-Italic.woff) format('woff'), url(fonts/KaTeX_Main-Italic.ttf) format('truetype'); + font-weight: normal; + font-style: italic; +} +@font-face { + font-family: 'KaTeX_Main'; + src: url(fonts/KaTeX_Main-Regular.woff2) format('woff2'), url(fonts/KaTeX_Main-Regular.woff) format('woff'), url(fonts/KaTeX_Main-Regular.ttf) format('truetype'); + font-weight: normal; + font-style: normal; +} +@font-face { + font-family: 'KaTeX_Math'; + src: url(fonts/KaTeX_Math-BoldItalic.woff2) format('woff2'), url(fonts/KaTeX_Math-BoldItalic.woff) format('woff'), url(fonts/KaTeX_Math-BoldItalic.ttf) format('truetype'); + font-weight: bold; + font-style: italic; +} +@font-face { + font-family: 'KaTeX_Math'; + src: url(fonts/KaTeX_Math-Italic.woff2) format('woff2'), url(fonts/KaTeX_Math-Italic.woff) format('woff'), url(fonts/KaTeX_Math-Italic.ttf) format('truetype'); + font-weight: normal; + font-style: italic; +} +@font-face { + font-family: 'KaTeX_SansSerif'; + src: url(fonts/KaTeX_SansSerif-Bold.woff2) format('woff2'), url(fonts/KaTeX_SansSerif-Bold.woff) format('woff'), url(fonts/KaTeX_SansSerif-Bold.ttf) format('truetype'); + font-weight: bold; + font-style: normal; +} +@font-face { + font-family: 'KaTeX_SansSerif'; + src: url(fonts/KaTeX_SansSerif-Italic.woff2) format('woff2'), url(fonts/KaTeX_SansSerif-Italic.woff) format('woff'), url(fonts/KaTeX_SansSerif-Italic.ttf) format('truetype'); + font-weight: normal; + font-style: italic; +} +@font-face { + font-family: 'KaTeX_SansSerif'; + src: url(fonts/KaTeX_SansSerif-Regular.woff2) format('woff2'), url(fonts/KaTeX_SansSerif-Regular.woff) format('woff'), url(fonts/KaTeX_SansSerif-Regular.ttf) format('truetype'); + font-weight: normal; + font-style: normal; +} +@font-face { + font-family: 'KaTeX_Script'; + src: url(fonts/KaTeX_Script-Regular.woff2) format('woff2'), url(fonts/KaTeX_Script-Regular.woff) format('woff'), url(fonts/KaTeX_Script-Regular.ttf) format('truetype'); + font-weight: normal; + font-style: normal; +} +@font-face { + font-family: 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normal; +} +@font-face { + font-family: 'KaTeX_Typewriter'; + src: url(fonts/KaTeX_Typewriter-Regular.woff2) format('woff2'), url(fonts/KaTeX_Typewriter-Regular.woff) format('woff'), url(fonts/KaTeX_Typewriter-Regular.ttf) format('truetype'); + font-weight: normal; + font-style: normal; +} +.katex { + font: normal 1.21em KaTeX_Main, Times New Roman, serif; + line-height: 1.2; + text-indent: 0; + text-rendering: auto; +} +.katex * { + -ms-high-contrast-adjust: none !important; + border-color: currentColor; +} +.katex .katex-version::after { + content: "0.13.19"; +} +.katex .katex-mathml { + /* Accessibility hack to only show to screen readers + Found at: http://a11yproject.com/posts/how-to-hide-content/ */ + position: absolute; + clip: rect(1px, 1px, 1px, 1px); + padding: 0; + border: 0; + height: 1px; + width: 1px; + overflow: hidden; +} +.katex .katex-html { + /* \newline is an empty block at top level, between .base elements */ +} +.katex .katex-html > .newline { + display: block; +} 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0.24115756em; +} +.katex .sizing.reset-size11.size3, +.katex .fontsize-ensurer.reset-size11.size3 { + font-size: 0.28135048em; +} +.katex .sizing.reset-size11.size4, +.katex .fontsize-ensurer.reset-size11.size4 { + font-size: 0.32154341em; +} +.katex .sizing.reset-size11.size5, +.katex .fontsize-ensurer.reset-size11.size5 { + font-size: 0.36173633em; +} +.katex .sizing.reset-size11.size6, +.katex .fontsize-ensurer.reset-size11.size6 { + font-size: 0.40192926em; +} +.katex .sizing.reset-size11.size7, +.katex .fontsize-ensurer.reset-size11.size7 { + font-size: 0.48231511em; +} +.katex .sizing.reset-size11.size8, +.katex .fontsize-ensurer.reset-size11.size8 { + font-size: 0.57877814em; +} +.katex .sizing.reset-size11.size9, +.katex .fontsize-ensurer.reset-size11.size9 { + font-size: 0.69453376em; +} +.katex .sizing.reset-size11.size10, +.katex .fontsize-ensurer.reset-size11.size10 { + font-size: 0.83360129em; +} +.katex .sizing.reset-size11.size11, +.katex .fontsize-ensurer.reset-size11.size11 { + font-size: 1em; +} +.katex .delimsizing.size1 { + font-family: KaTeX_Size1; +} +.katex .delimsizing.size2 { + font-family: KaTeX_Size2; +} +.katex .delimsizing.size3 { + font-family: KaTeX_Size3; +} +.katex .delimsizing.size4 { + font-family: KaTeX_Size4; +} +.katex .delimsizing.mult .delim-size1 > span { + font-family: KaTeX_Size1; +} +.katex .delimsizing.mult .delim-size4 > span { + font-family: KaTeX_Size4; +} +.katex .nulldelimiter { + display: inline-block; + width: 0.12em; +} +.katex .delimcenter { + position: relative; +} +.katex .op-symbol { + position: relative; +} +.katex .op-symbol.small-op { + font-family: KaTeX_Size1; +} +.katex .op-symbol.large-op { + font-family: KaTeX_Size2; +} +.katex .op-limits > .vlist-t { + text-align: center; +} +.katex .accent > .vlist-t { + text-align: center; +} +.katex .accent .accent-body { + position: relative; +} +.katex .accent .accent-body:not(.accent-full) { + width: 0; +} +.katex .overlay { + display: block; +} +.katex .mtable .vertical-separator { + display: inline-block; + min-width: 1px; +} +.katex .mtable .arraycolsep { + display: inline-block; +} +.katex .mtable .col-align-c > .vlist-t { + text-align: center; +} +.katex .mtable .col-align-l > .vlist-t { + text-align: left; +} +.katex .mtable .col-align-r > .vlist-t { + text-align: right; +} +.katex .svg-align { + text-align: left; +} +.katex svg { + display: block; + position: absolute; + width: 100%; + height: inherit; + fill: currentColor; + stroke: currentColor; + fill-rule: nonzero; + fill-opacity: 1; + stroke-width: 1; + stroke-linecap: butt; + stroke-linejoin: miter; + stroke-miterlimit: 4; + stroke-dasharray: none; + stroke-dashoffset: 0; + stroke-opacity: 1; +} +.katex svg path { + stroke: none; +} +.katex img { + border-style: none; + min-width: 0; + min-height: 0; + max-width: none; + max-height: none; +} +.katex .stretchy { + width: 100%; + display: block; + position: relative; + overflow: hidden; +} +.katex .stretchy::before, +.katex .stretchy::after { + content: ""; +} +.katex .hide-tail { + width: 100%; + position: relative; + overflow: hidden; +} +.katex .halfarrow-left { + position: absolute; + left: 0; + width: 50.2%; + overflow: hidden; +} +.katex .halfarrow-right { + position: absolute; + right: 0; + width: 50.2%; + overflow: hidden; +} +.katex .brace-left { + position: absolute; + left: 0; + width: 25.1%; + overflow: hidden; +} +.katex .brace-center { + position: absolute; + left: 25%; + width: 50%; + overflow: hidden; +} +.katex .brace-right { + position: absolute; + right: 0; + width: 25.1%; + overflow: hidden; +} +.katex .x-arrow-pad { + padding: 0 0.5em; +} +.katex .cd-arrow-pad { + padding: 0 0.55556em 0 0.27778em; +} +.katex .x-arrow, +.katex .mover, +.katex .munder { + text-align: center; +} +.katex .boxpad { + padding: 0 0.3em 0 0.3em; +} +.katex .fbox, +.katex .fcolorbox { + box-sizing: border-box; + border: 0.04em solid; +} +.katex .cancel-pad { + padding: 0 0.2em 0 0.2em; +} +.katex .cancel-lap { + margin-left: -0.2em; + margin-right: -0.2em; +} +.katex .sout { + border-bottom-style: solid; + border-bottom-width: 0.08em; +} +.katex .angl { + box-sizing: border-box; + border-top: 0.049em solid; + border-right: 0.049em solid; + margin-right: 0.03889em; +} +.katex .anglpad { + padding: 0 0.03889em 0 0.03889em; +} +.katex .eqn-num::before { + counter-increment: katexEqnNo; + content: "(" counter(katexEqnNo) ")"; +} +.katex .mml-eqn-num::before { + counter-increment: mmlEqnNo; + content: "(" counter(mmlEqnNo) ")"; +} +.katex .mtr-glue { + width: 50%; +} +.katex .cd-vert-arrow { + display: inline-block; + position: relative; +} +.katex .cd-label-left { + display: inline-block; + position: absolute; + right: calc(50% + 0.3em); + text-align: left; +} +.katex .cd-label-right { + display: inline-block; + position: absolute; + left: calc(50% + 0.3em); + text-align: right; +} +.katex-display { + display: block; + margin: 1em 0; + text-align: center; +} +.katex-display > .katex { + display: block; + text-align: center; + white-space: nowrap; +} +.katex-display > .katex > .katex-html { + display: block; + position: relative; +} +.katex-display > .katex > .katex-html > .tag { + position: absolute; + right: 0; +} +.katex-display.leqno > .katex > .katex-html > .tag { + left: 0; + right: auto; +} +.katex-display.fleqn > .katex { + text-align: left; + padding-left: 2em; +} +body { + counter-reset: katexEqnNo mmlEqnNo; +} + diff --git a/core/bikeshed/katex/dist/katex.js b/core/bikeshed/katex/dist/katex.js new file mode 100644 index 00000000..30e5b6b7 --- /dev/null +++ b/core/bikeshed/katex/dist/katex.js @@ -0,0 +1,18185 @@ +(function webpackUniversalModuleDefinition(root, factory) { + if(typeof exports === 'object' && typeof module === 'object') + module.exports = factory(); + else if(typeof define === 'function' && define.amd) + define([], factory); + else if(typeof exports === 'object') + exports["katex"] = factory(); + else + root["katex"] = factory(); +})((typeof self !== 'undefined' ? self : this), function() { +return /******/ (function() { // webpackBootstrap +/******/ "use strict"; +/******/ // The require scope +/******/ var __webpack_require__ = {}; +/******/ +/************************************************************************/ +/******/ /* webpack/runtime/define property getters */ +/******/ !function() { +/******/ // define getter functions for harmony exports +/******/ __webpack_require__.d = function(exports, definition) { +/******/ for(var key in definition) { +/******/ if(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) { +/******/ Object.defineProperty(exports, key, { enumerable: true, get: definition[key] }); +/******/ } +/******/ } +/******/ }; +/******/ }(); +/******/ +/******/ /* webpack/runtime/hasOwnProperty shorthand */ +/******/ !function() { +/******/ __webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); } +/******/ }(); +/******/ +/************************************************************************/ +var __webpack_exports__ = {}; + +// EXPORTS +__webpack_require__.d(__webpack_exports__, { + "default": function() { return /* binding */ katex_webpack; } +}); + +;// CONCATENATED MODULE: ./src/ParseError.js + + +/** + * This is the ParseError class, which is the main error thrown by KaTeX + * functions when something has gone wrong. This is used to distinguish internal + * errors from errors in the expression that the user provided. + * + * If possible, a caller should provide a Token or ParseNode with information + * about where in the source string the problem occurred. + */ +var ParseError = // Error position based on passed-in Token or ParseNode. +function ParseError(message, // The error message +token // An object providing position information +) { + this.position = void 0; + var error = "KaTeX parse error: " + message; + var start; + var loc = token && token.loc; + + if (loc && loc.start <= loc.end) { + // If we have the input and a position, make the error a bit fancier + // Get the input + var input = loc.lexer.input; // Prepend some information + + start = loc.start; + var end = loc.end; + + if (start === input.length) { + error += " at end of input: "; + } else { + error += " at position " + (start + 1) + ": "; + } // Underline token in question using combining underscores + + + var underlined = input.slice(start, end).replace(/[^]/g, "$&\u0332"); // Extract some context from the input and add it to the error + + var left; + + if (start > 15) { + left = "…" + input.slice(start - 15, start); + } else { + left = input.slice(0, start); + } + + var right; + + if (end + 15 < input.length) { + right = input.slice(end, end + 15) + "…"; + } else { + right = input.slice(end); + } + + error += left + underlined + right; + } // Some hackery to make ParseError a prototype of Error + // See http://stackoverflow.com/a/8460753 + + + var self = new Error(error); + self.name = "ParseError"; // $FlowFixMe + + self.__proto__ = ParseError.prototype; // $FlowFixMe + + self.position = start; + return self; +}; // $FlowFixMe More hackery + + +ParseError.prototype.__proto__ = Error.prototype; +/* harmony default export */ var src_ParseError = (ParseError); +;// CONCATENATED MODULE: ./src/utils.js +/** + * This file contains a list of utility functions which are useful in other + * files. + */ + +/** + * Return whether an element is contained in a list + */ +var contains = function contains(list, elem) { + return list.indexOf(elem) !== -1; +}; +/** + * Provide a default value if a setting is undefined + * NOTE: Couldn't use `T` as the output type due to facebook/flow#5022. + */ + + +var deflt = function deflt(setting, defaultIfUndefined) { + return setting === undefined ? defaultIfUndefined : setting; +}; // hyphenate and escape adapted from Facebook's React under Apache 2 license + + +var uppercase = /([A-Z])/g; + +var hyphenate = function hyphenate(str) { + return str.replace(uppercase, "-$1").toLowerCase(); +}; + +var ESCAPE_LOOKUP = { + "&": "&", + ">": ">", + "<": "<", + "\"": """, + "'": "'" +}; +var ESCAPE_REGEX = /[&><"']/g; +/** + * Escapes text to prevent scripting attacks. + */ + +function utils_escape(text) { + return String(text).replace(ESCAPE_REGEX, function (match) { + return ESCAPE_LOOKUP[match]; + }); +} +/** + * Sometimes we want to pull out the innermost element of a group. In most + * cases, this will just be the group itself, but when ordgroups and colors have + * a single element, we want to pull that out. + */ + + +var getBaseElem = function getBaseElem(group) { + if (group.type === "ordgroup") { + if (group.body.length === 1) { + return getBaseElem(group.body[0]); + } else { + return group; + } + } else if (group.type === "color") { + if (group.body.length === 1) { + return getBaseElem(group.body[0]); + } else { + return group; + } + } else if (group.type === "font") { + return getBaseElem(group.body); + } else { + return group; + } +}; +/** + * TeXbook algorithms often reference "character boxes", which are simply groups + * with a single character in them. To decide if something is a character box, + * we find its innermost group, and see if it is a single character. + */ + + +var isCharacterBox = function isCharacterBox(group) { + var baseElem = getBaseElem(group); // These are all they types of groups which hold single characters + + return baseElem.type === "mathord" || baseElem.type === "textord" || baseElem.type === "atom"; +}; + +var assert = function assert(value) { + if (!value) { + throw new Error('Expected non-null, but got ' + String(value)); + } + + return value; +}; +/** + * Return the protocol of a URL, or "_relative" if the URL does not specify a + * protocol (and thus is relative). + */ + +var protocolFromUrl = function protocolFromUrl(url) { + var protocol = /^\s*([^\\/#]*?)(?::|�*58|�*3a)/i.exec(url); + return protocol != null ? protocol[1] : "_relative"; +}; +/* harmony default export */ var utils = ({ + contains: contains, + deflt: deflt, + escape: utils_escape, + hyphenate: hyphenate, + getBaseElem: getBaseElem, + isCharacterBox: isCharacterBox, + protocolFromUrl: protocolFromUrl +}); +;// CONCATENATED MODULE: ./src/Settings.js +/* eslint no-console:0 */ + +/** + * This is a module for storing settings passed into KaTeX. It correctly handles + * default settings. + */ + + + + +/** + * The main Settings object + * + * The current options stored are: + * - displayMode: Whether the expression should be typeset as inline math + * (false, the default), meaning that the math starts in + * \textstyle and is placed in an inline-block); or as display + * math (true), meaning that the math starts in \displaystyle + * and is placed in a block with vertical margin. + */ +var Settings = /*#__PURE__*/function () { + function Settings(options) { + this.displayMode = void 0; + this.output = void 0; + this.leqno = void 0; + this.fleqn = void 0; + this.throwOnError = void 0; + this.errorColor = void 0; + this.macros = void 0; + this.minRuleThickness = void 0; + this.colorIsTextColor = void 0; + this.strict = void 0; + this.trust = void 0; + this.maxSize = void 0; + this.maxExpand = void 0; + this.globalGroup = void 0; + // allow null options + options = options || {}; + this.displayMode = utils.deflt(options.displayMode, false); + this.output = utils.deflt(options.output, "htmlAndMathml"); + this.leqno = utils.deflt(options.leqno, false); + this.fleqn = utils.deflt(options.fleqn, false); + this.throwOnError = utils.deflt(options.throwOnError, true); + this.errorColor = utils.deflt(options.errorColor, "#cc0000"); + this.macros = options.macros || {}; + this.minRuleThickness = Math.max(0, utils.deflt(options.minRuleThickness, 0)); + this.colorIsTextColor = utils.deflt(options.colorIsTextColor, false); + this.strict = utils.deflt(options.strict, "warn"); + this.trust = utils.deflt(options.trust, false); + this.maxSize = Math.max(0, utils.deflt(options.maxSize, Infinity)); + this.maxExpand = Math.max(0, utils.deflt(options.maxExpand, 1000)); + this.globalGroup = utils.deflt(options.globalGroup, false); + } + /** + * Report nonstrict (non-LaTeX-compatible) input. + * Can safely not be called if `this.strict` is false in JavaScript. + */ + + + var _proto = Settings.prototype; + + _proto.reportNonstrict = function reportNonstrict(errorCode, errorMsg, token) { + var strict = this.strict; + + if (typeof strict === "function") { + // Allow return value of strict function to be boolean or string + // (or null/undefined, meaning no further processing). + strict = strict(errorCode, errorMsg, token); + } + + if (!strict || strict === "ignore") { + return; + } else if (strict === true || strict === "error") { + throw new src_ParseError("LaTeX-incompatible input and strict mode is set to 'error': " + (errorMsg + " [" + errorCode + "]"), token); + } else if (strict === "warn") { + typeof console !== "undefined" && console.warn("LaTeX-incompatible input and strict mode is set to 'warn': " + (errorMsg + " [" + errorCode + "]")); + } else { + // won't happen in type-safe code + typeof console !== "undefined" && console.warn("LaTeX-incompatible input and strict mode is set to " + ("unrecognized '" + strict + "': " + errorMsg + " [" + errorCode + "]")); + } + } + /** + * Check whether to apply strict (LaTeX-adhering) behavior for unusual + * input (like `\\`). Unlike `nonstrict`, will not throw an error; + * instead, "error" translates to a return value of `true`, while "ignore" + * translates to a return value of `false`. May still print a warning: + * "warn" prints a warning and returns `false`. + * This is for the second category of `errorCode`s listed in the README. + */ + ; + + _proto.useStrictBehavior = function useStrictBehavior(errorCode, errorMsg, token) { + var strict = this.strict; + + if (typeof strict === "function") { + // Allow return value of strict function to be boolean or string + // (or null/undefined, meaning no further processing). + // But catch any exceptions thrown by function, treating them + // like "error". + try { + strict = strict(errorCode, errorMsg, token); + } catch (error) { + strict = "error"; + } + } + + if (!strict || strict === "ignore") { + return false; + } else if (strict === true || strict === "error") { + return true; + } else if (strict === "warn") { + typeof console !== "undefined" && console.warn("LaTeX-incompatible input and strict mode is set to 'warn': " + (errorMsg + " [" + errorCode + "]")); + return false; + } else { + // won't happen in type-safe code + typeof console !== "undefined" && console.warn("LaTeX-incompatible input and strict mode is set to " + ("unrecognized '" + strict + "': " + errorMsg + " [" + errorCode + "]")); + return false; + } + } + /** + * Check whether to test potentially dangerous input, and return + * `true` (trusted) or `false` (untrusted). The sole argument `context` + * should be an object with `command` field specifying the relevant LaTeX + * command (as a string starting with `\`), and any other arguments, etc. + * If `context` has a `url` field, a `protocol` field will automatically + * get added by this function (changing the specified object). + */ + ; + + _proto.isTrusted = function isTrusted(context) { + if (context.url && !context.protocol) { + context.protocol = utils.protocolFromUrl(context.url); + } + + var trust = typeof this.trust === "function" ? this.trust(context) : this.trust; + return Boolean(trust); + }; + + return Settings; +}(); + + +;// CONCATENATED MODULE: ./src/Style.js +/** + * This file contains information and classes for the various kinds of styles + * used in TeX. It provides a generic `Style` class, which holds information + * about a specific style. It then provides instances of all the different kinds + * of styles possible, and provides functions to move between them and get + * information about them. + */ + +/** + * The main style class. Contains a unique id for the style, a size (which is + * the same for cramped and uncramped version of a style), and a cramped flag. + */ +var Style = /*#__PURE__*/function () { + function Style(id, size, cramped) { + this.id = void 0; + this.size = void 0; + this.cramped = void 0; + this.id = id; + this.size = size; + this.cramped = cramped; + } + /** + * Get the style of a superscript given a base in the current style. + */ + + + var _proto = Style.prototype; + + _proto.sup = function sup() { + return styles[_sup[this.id]]; + } + /** + * Get the style of a subscript given a base in the current style. + */ + ; + + _proto.sub = function sub() { + return styles[_sub[this.id]]; + } + /** + * Get the style of a fraction numerator given the fraction in the current + * style. + */ + ; + + _proto.fracNum = function fracNum() { + return styles[_fracNum[this.id]]; + } + /** + * Get the style of a fraction denominator given the fraction in the current + * style. + */ + ; + + _proto.fracDen = function fracDen() { + return styles[_fracDen[this.id]]; + } + /** + * Get the cramped version of a style (in particular, cramping a cramped style + * doesn't change the style). + */ + ; + + _proto.cramp = function cramp() { + return styles[_cramp[this.id]]; + } + /** + * Get a text or display version of this style. + */ + ; + + _proto.text = function text() { + return styles[_text[this.id]]; + } + /** + * Return true if this style is tightly spaced (scriptstyle/scriptscriptstyle) + */ + ; + + _proto.isTight = function isTight() { + return this.size >= 2; + }; + + return Style; +}(); // Export an interface for type checking, but don't expose the implementation. +// This way, no more styles can be generated. + + +// IDs of the different styles +var D = 0; +var Dc = 1; +var T = 2; +var Tc = 3; +var S = 4; +var Sc = 5; +var SS = 6; +var SSc = 7; // Instances of the different styles + +var styles = [new Style(D, 0, false), new Style(Dc, 0, true), new Style(T, 1, false), new Style(Tc, 1, true), new Style(S, 2, false), new Style(Sc, 2, true), new Style(SS, 3, false), new Style(SSc, 3, true)]; // Lookup tables for switching from one style to another + +var _sup = [S, Sc, S, Sc, SS, SSc, SS, SSc]; +var _sub = [Sc, Sc, Sc, Sc, SSc, SSc, SSc, SSc]; +var _fracNum = [T, Tc, S, Sc, SS, SSc, SS, SSc]; +var _fracDen = [Tc, Tc, Sc, Sc, SSc, SSc, SSc, SSc]; +var _cramp = [Dc, Dc, Tc, Tc, Sc, Sc, SSc, SSc]; +var _text = [D, Dc, T, Tc, T, Tc, T, Tc]; // We only export some of the styles. + +/* harmony default export */ var src_Style = ({ + DISPLAY: styles[D], + TEXT: styles[T], + SCRIPT: styles[S], + SCRIPTSCRIPT: styles[SS] +}); +;// CONCATENATED MODULE: ./src/unicodeScripts.js +/* + * This file defines the Unicode scripts and script families that we + * support. To add new scripts or families, just add a new entry to the + * scriptData array below. Adding scripts to the scriptData array allows + * characters from that script to appear in \text{} environments. + */ + +/** + * Each script or script family has a name and an array of blocks. + * Each block is an array of two numbers which specify the start and + * end points (inclusive) of a block of Unicode codepoints. + */ + +/** + * Unicode block data for the families of scripts we support in \text{}. + * Scripts only need to appear here if they do not have font metrics. + */ +var scriptData = [{ + // Latin characters beyond the Latin-1 characters we have metrics for. + // Needed for Czech, Hungarian and Turkish text, for example. + name: 'latin', + blocks: [[0x0100, 0x024f], // Latin Extended-A and Latin Extended-B + [0x0300, 0x036f] // Combining Diacritical marks + ] +}, { + // The Cyrillic script used by Russian and related languages. + // A Cyrillic subset used to be supported as explicitly defined + // symbols in symbols.js + name: 'cyrillic', + blocks: [[0x0400, 0x04ff]] +}, { + // Armenian + name: 'armenian', + blocks: [[0x0530, 0x058F]] +}, { + // The Brahmic scripts of South and Southeast Asia + // Devanagari (0900–097F) + // Bengali (0980–09FF) + // Gurmukhi (0A00–0A7F) + // Gujarati (0A80–0AFF) + // Oriya (0B00–0B7F) + // Tamil (0B80–0BFF) + // Telugu (0C00–0C7F) + // Kannada (0C80–0CFF) + // Malayalam (0D00–0D7F) + // Sinhala (0D80–0DFF) + // Thai (0E00–0E7F) + // Lao (0E80–0EFF) + // Tibetan (0F00–0FFF) + // Myanmar (1000–109F) + name: 'brahmic', + blocks: [[0x0900, 0x109F]] +}, { + name: 'georgian', + blocks: [[0x10A0, 0x10ff]] +}, { + // Chinese and Japanese. + // The "k" in cjk is for Korean, but we've separated Korean out + name: "cjk", + blocks: [[0x3000, 0x30FF], // CJK symbols and punctuation, Hiragana, Katakana + [0x4E00, 0x9FAF], // CJK ideograms + [0xFF00, 0xFF60] // Fullwidth punctuation + // TODO: add halfwidth Katakana and Romanji glyphs + ] +}, { + // Korean + name: 'hangul', + blocks: [[0xAC00, 0xD7AF]] +}]; +/** + * Given a codepoint, return the name of the script or script family + * it is from, or null if it is not part of a known block + */ + +function scriptFromCodepoint(codepoint) { + for (var i = 0; i < scriptData.length; i++) { + var script = scriptData[i]; + + for (var _i = 0; _i < script.blocks.length; _i++) { + var block = script.blocks[_i]; + + if (codepoint >= block[0] && codepoint <= block[1]) { + return script.name; + } + } + } + + return null; +} +/** + * A flattened version of all the supported blocks in a single array. + * This is an optimization to make supportedCodepoint() fast. + */ + +var allBlocks = []; +scriptData.forEach(function (s) { + return s.blocks.forEach(function (b) { + return allBlocks.push.apply(allBlocks, b); + }); +}); +/** + * Given a codepoint, return true if it falls within one of the + * scripts or script families defined above and false otherwise. + * + * Micro benchmarks shows that this is faster than + * /[\u3000-\u30FF\u4E00-\u9FAF\uFF00-\uFF60\uAC00-\uD7AF\u0900-\u109F]/.test() + * in Firefox, Chrome and Node. + */ + +function supportedCodepoint(codepoint) { + for (var i = 0; i < allBlocks.length; i += 2) { + if (codepoint >= allBlocks[i] && codepoint <= allBlocks[i + 1]) { + return true; + } + } + + return false; +} +;// CONCATENATED MODULE: ./src/svgGeometry.js +/** + * This file provides support to domTree.js and delimiter.js. + * It's a storehouse of path geometry for SVG images. + */ +// In all paths below, the viewBox-to-em scale is 1000:1. +var hLinePad = 80; // padding above a sqrt viniculum. Prevents image cropping. +// The viniculum of a \sqrt can be made thicker by a KaTeX rendering option. +// Think of variable extraViniculum as two detours in the SVG path. +// The detour begins at the lower left of the area labeled extraViniculum below. +// The detour proceeds one extraViniculum distance up and slightly to the right, +// displacing the radiused corner between surd and viniculum. The radius is +// traversed as usual, then the detour resumes. It goes right, to the end of +// the very long viniculumn, then down one extraViniculum distance, +// after which it resumes regular path geometry for the radical. + +/* viniculum + / + /▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒←extraViniculum + / █████████████████████←0.04em (40 unit) std viniculum thickness + / / + / / + / /\ + / / surd +*/ + +var sqrtMain = function sqrtMain(extraViniculum, hLinePad) { + // sqrtMain path geometry is from glyph U221A in the font KaTeX Main + return "M95," + (622 + extraViniculum + hLinePad) + "\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl" + extraViniculum / 2.075 + " -" + extraViniculum + "\nc5.3,-9.3,12,-14,20,-14\nH400000v" + (40 + extraViniculum) + "H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM" + (834 + extraViniculum) + " " + hLinePad + "h400000v" + (40 + extraViniculum) + "h-400000z"; +}; + +var sqrtSize1 = function sqrtSize1(extraViniculum, hLinePad) { + // size1 is from glyph U221A in the font KaTeX_Size1-Regular + return "M263," + (601 + extraViniculum + hLinePad) + "c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl" + extraViniculum / 2.084 + " -" + extraViniculum + "\nc4.7,-7.3,11,-11,19,-11\nH40000v" + (40 + extraViniculum) + "H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM" + (1001 + extraViniculum) + " " + hLinePad + "h400000v" + (40 + extraViniculum) + "h-400000z"; +}; + +var sqrtSize2 = function sqrtSize2(extraViniculum, hLinePad) { + // size2 is from glyph U221A in the font KaTeX_Size2-Regular + return "M983 " + (10 + extraViniculum + hLinePad) + "\nl" + extraViniculum / 3.13 + " -" + extraViniculum + "\nc4,-6.7,10,-10,18,-10 H400000v" + (40 + extraViniculum) + "\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM" + (1001 + extraViniculum) + " " + hLinePad + "h400000v" + (40 + extraViniculum) + "h-400000z"; +}; + +var sqrtSize3 = function sqrtSize3(extraViniculum, hLinePad) { + // size3 is from glyph U221A in the font KaTeX_Size3-Regular + return "M424," + (2398 + extraViniculum + hLinePad) + "\nc-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514\nc0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20\ns-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121\ns209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081\nl" + extraViniculum / 4.223 + " -" + extraViniculum + "c4,-6.7,10,-10,18,-10 H400000\nv" + (40 + extraViniculum) + "H1014.6\ns-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185\nc-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2z M" + (1001 + extraViniculum) + " " + hLinePad + "\nh400000v" + (40 + extraViniculum) + "h-400000z"; +}; + +var sqrtSize4 = function sqrtSize4(extraViniculum, hLinePad) { + // size4 is from glyph U221A in the font KaTeX_Size4-Regular + return "M473," + (2713 + extraViniculum + hLinePad) + "\nc339.3,-1799.3,509.3,-2700,510,-2702 l" + extraViniculum / 5.298 + " -" + extraViniculum + "\nc3.3,-7.3,9.3,-11,18,-11 H400000v" + (40 + extraViniculum) + "H1017.7\ns-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200\nc0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26\ns76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,\n606zM" + (1001 + extraViniculum) + " " + hLinePad + "h400000v" + (40 + extraViniculum) + "H1017.7z"; +}; + +var phasePath = function phasePath(y) { + var x = y / 2; // x coordinate at top of angle + + return "M400000 " + y + " H0 L" + x + " 0 l65 45 L145 " + (y - 80) + " H400000z"; +}; + +var sqrtTall = function sqrtTall(extraViniculum, hLinePad, viewBoxHeight) { + // sqrtTall is from glyph U23B7 in the font KaTeX_Size4-Regular + // One path edge has a variable length. It runs vertically from the viniculumn + // to a point near (14 units) the bottom of the surd. The viniculum + // is normally 40 units thick. So the length of the line in question is: + var vertSegment = viewBoxHeight - 54 - hLinePad - extraViniculum; + return "M702 " + (extraViniculum + hLinePad) + "H400000" + (40 + extraViniculum) + "\nH742v" + vertSegment + "l-4 4-4 4c-.667.7 -2 1.5-4 2.5s-4.167 1.833-6.5 2.5-5.5 1-9.5 1\nh-12l-28-84c-16.667-52-96.667 -294.333-240-727l-212 -643 -85 170\nc-4-3.333-8.333-7.667-13 -13l-13-13l77-155 77-156c66 199.333 139 419.667\n219 661 l218 661zM702 " + hLinePad + "H400000v" + (40 + extraViniculum) + "H742z"; +}; + +var sqrtPath = function sqrtPath(size, extraViniculum, viewBoxHeight) { + extraViniculum = 1000 * extraViniculum; // Convert from document ems to viewBox. + + var path = ""; + + switch (size) { + case "sqrtMain": + path = sqrtMain(extraViniculum, hLinePad); + break; + + case "sqrtSize1": + path = sqrtSize1(extraViniculum, hLinePad); + break; + + case "sqrtSize2": + path = sqrtSize2(extraViniculum, hLinePad); + break; + + case "sqrtSize3": + path = sqrtSize3(extraViniculum, hLinePad); + break; + + case "sqrtSize4": + path = sqrtSize4(extraViniculum, hLinePad); + break; + + case "sqrtTall": + path = sqrtTall(extraViniculum, hLinePad, viewBoxHeight); + } + + return path; +}; +var innerPath = function innerPath(name, height) { + // The inner part of stretchy tall delimiters + switch (name) { + case "\u239C": + return "M291 0 H417 V" + height + " H291z M291 0 H417 V" + height + " H291z"; + + case "\u2223": + return "M145 0 H188 V" + height + " H145z M145 0 H188 V" + height + " H145z"; + + case "\u2225": + return "M145 0 H188 V" + height + " H145z M145 0 H188 V" + height + " H145z" + ("M367 0 H410 V" + height + " H367z M367 0 H410 V" + height + " H367z"); + + case "\u239F": + return "M457 0 H583 V" + height + " H457z M457 0 H583 V" + height + " H457z"; + + case "\u23A2": + return "M319 0 H403 V" + height + " H319z M319 0 H403 V" + height + " H319z"; + + case "\u23A5": + return "M263 0 H347 V" + height + " H263z M263 0 H347 V" + height + " H263z"; + + case "\u23AA": + return "M384 0 H504 V" + height + " H384z M384 0 H504 V" + height + " H384z"; + + case "\u23D0": + return "M312 0 H355 V" + height + " H312z M312 0 H355 V" + height + " H312z"; + + case "\u2016": + return "M257 0 H300 V" + height + " H257z M257 0 H300 V" + height + " H257z" + ("M478 0 H521 V" + height + " H478z M478 0 H521 V" + height + " H478z"); + + default: + return ""; + } +}; +var path = { + // The doubleleftarrow geometry is from glyph U+21D0 in the font KaTeX Main + doubleleftarrow: "M262 157\nl10-10c34-36 62.7-77 86-123 3.3-8 5-13.3 5-16 0-5.3-6.7-8-20-8-7.3\n 0-12.2.5-14.5 1.5-2.3 1-4.8 4.5-7.5 10.5-49.3 97.3-121.7 169.3-217 216-28\n 14-57.3 25-88 33-6.7 2-11 3.8-13 5.5-2 1.7-3 4.2-3 7.5s1 5.8 3 7.5\nc2 1.7 6.3 3.5 13 5.5 68 17.3 128.2 47.8 180.5 91.5 52.3 43.7 93.8 96.2 124.5\n 157.5 9.3 8 15.3 12.3 18 13h6c12-.7 18-4 18-10 0-2-1.7-7-5-15-23.3-46-52-87\n-86-123l-10-10h399738v-40H218c328 0 0 0 0 0l-10-8c-26.7-20-65.7-43-117-69 2.7\n-2 6-3.7 10-5 36.7-16 72.3-37.3 107-64l10-8h399782v-40z\nm8 0v40h399730v-40zm0 194v40h399730v-40z", + // doublerightarrow is from glyph U+21D2 in font KaTeX Main + doublerightarrow: "M399738 392l\n-10 10c-34 36-62.7 77-86 123-3.3 8-5 13.3-5 16 0 5.3 6.7 8 20 8 7.3 0 12.2-.5\n 14.5-1.5 2.3-1 4.8-4.5 7.5-10.5 49.3-97.3 121.7-169.3 217-216 28-14 57.3-25 88\n-33 6.7-2 11-3.8 13-5.5 2-1.7 3-4.2 3-7.5s-1-5.8-3-7.5c-2-1.7-6.3-3.5-13-5.5-68\n-17.3-128.2-47.8-180.5-91.5-52.3-43.7-93.8-96.2-124.5-157.5-9.3-8-15.3-12.3-18\n-13h-6c-12 .7-18 4-18 10 0 2 1.7 7 5 15 23.3 46 52 87 86 123l10 10H0v40h399782\nc-328 0 0 0 0 0l10 8c26.7 20 65.7 43 117 69-2.7 2-6 3.7-10 5-36.7 16-72.3 37.3\n-107 64l-10 8H0v40zM0 157v40h399730v-40zm0 194v40h399730v-40z", + // leftarrow is from glyph U+2190 in font KaTeX Main + leftarrow: "M400000 241H110l3-3c68.7-52.7 113.7-120\n 135-202 4-14.7 6-23 6-25 0-7.3-7-11-21-11-8 0-13.2.8-15.5 2.5-2.3 1.7-4.2 5.8\n-5.5 12.5-1.3 4.7-2.7 10.3-4 17-12 48.7-34.8 92-68.5 130S65.3 228.3 18 247\nc-10 4-16 7.7-18 11 0 8.7 6 14.3 18 17 47.3 18.7 87.8 47 121.5 85S196 441.3 208\n 490c.7 2 1.3 5 2 9s1.2 6.7 1.5 8c.3 1.3 1 3.3 2 6s2.2 4.5 3.5 5.5c1.3 1 3.3\n 1.8 6 2.5s6 1 10 1c14 0 21-3.7 21-11 0-2-2-10.3-6-25-20-79.3-65-146.7-135-202\n l-3-3h399890zM100 241v40h399900v-40z", + // overbrace is from glyphs U+23A9/23A8/23A7 in font KaTeX_Size4-Regular + leftbrace: "M6 548l-6-6v-35l6-11c56-104 135.3-181.3 238-232 57.3-28.7 117\n-45 179-50h399577v120H403c-43.3 7-81 15-113 26-100.7 33-179.7 91-237 174-2.7\n 5-6 9-10 13-.7 1-7.3 1-20 1H6z", + leftbraceunder: "M0 6l6-6h17c12.688 0 19.313.3 20 1 4 4 7.313 8.3 10 13\n 35.313 51.3 80.813 93.8 136.5 127.5 55.688 33.7 117.188 55.8 184.5 66.5.688\n 0 2 .3 4 1 18.688 2.7 76 4.3 172 5h399450v120H429l-6-1c-124.688-8-235-61.7\n-331-161C60.687 138.7 32.312 99.3 7 54L0 41V6z", + // overgroup is from the MnSymbol package (public domain) + leftgroup: "M400000 80\nH435C64 80 168.3 229.4 21 260c-5.9 1.2-18 0-18 0-2 0-3-1-3-3v-38C76 61 257 0\n 435 0h399565z", + leftgroupunder: "M400000 262\nH435C64 262 168.3 112.6 21 82c-5.9-1.2-18 0-18 0-2 0-3 1-3 3v38c76 158 257 219\n 435 219h399565z", + // Harpoons are from glyph U+21BD in font KaTeX Main + leftharpoon: "M0 267c.7 5.3 3 10 7 14h399993v-40H93c3.3\n-3.3 10.2-9.5 20.5-18.5s17.8-15.8 22.5-20.5c50.7-52 88-110.3 112-175 4-11.3 5\n-18.3 3-21-1.3-4-7.3-6-18-6-8 0-13 .7-15 2s-4.7 6.7-8 16c-42 98.7-107.3 174.7\n-196 228-6.7 4.7-10.7 8-12 10-1.3 2-2 5.7-2 11zm100-26v40h399900v-40z", + leftharpoonplus: "M0 267c.7 5.3 3 10 7 14h399993v-40H93c3.3-3.3 10.2-9.5\n 20.5-18.5s17.8-15.8 22.5-20.5c50.7-52 88-110.3 112-175 4-11.3 5-18.3 3-21-1.3\n-4-7.3-6-18-6-8 0-13 .7-15 2s-4.7 6.7-8 16c-42 98.7-107.3 174.7-196 228-6.7 4.7\n-10.7 8-12 10-1.3 2-2 5.7-2 11zm100-26v40h399900v-40zM0 435v40h400000v-40z\nm0 0v40h400000v-40z", + leftharpoondown: "M7 241c-4 4-6.333 8.667-7 14 0 5.333.667 9 2 11s5.333\n 5.333 12 10c90.667 54 156 130 196 228 3.333 10.667 6.333 16.333 9 17 2 .667 5\n 1 9 1h5c10.667 0 16.667-2 18-6 2-2.667 1-9.667-3-21-32-87.333-82.667-157.667\n-152-211l-3-3h399907v-40zM93 281 H400000 v-40L7 241z", + leftharpoondownplus: "M7 435c-4 4-6.3 8.7-7 14 0 5.3.7 9 2 11s5.3 5.3 12\n 10c90.7 54 156 130 196 228 3.3 10.7 6.3 16.3 9 17 2 .7 5 1 9 1h5c10.7 0 16.7\n-2 18-6 2-2.7 1-9.7-3-21-32-87.3-82.7-157.7-152-211l-3-3h399907v-40H7zm93 0\nv40h399900v-40zM0 241v40h399900v-40zm0 0v40h399900v-40z", + // hook is from glyph U+21A9 in font KaTeX Main + lefthook: "M400000 281 H103s-33-11.2-61-33.5S0 197.3 0 164s14.2-61.2 42.5\n-83.5C70.8 58.2 104 47 142 47 c16.7 0 25 6.7 25 20 0 12-8.7 18.7-26 20-40 3.3\n-68.7 15.7-86 37-10 12-15 25.3-15 40 0 22.7 9.8 40.7 29.5 54 19.7 13.3 43.5 21\n 71.5 23h399859zM103 281v-40h399897v40z", + leftlinesegment: "M40 281 V428 H0 V94 H40 V241 H400000 v40z\nM40 281 V428 H0 V94 H40 V241 H400000 v40z", + leftmapsto: "M40 281 V448H0V74H40V241H400000v40z\nM40 281 V448H0V74H40V241H400000v40z", + // tofrom is from glyph U+21C4 in font KaTeX AMS Regular + leftToFrom: "M0 147h400000v40H0zm0 214c68 40 115.7 95.7 143 167h22c15.3 0 23\n-.3 23-1 0-1.3-5.3-13.7-16-37-18-35.3-41.3-69-70-101l-7-8h399905v-40H95l7-8\nc28.7-32 52-65.7 70-101 10.7-23.3 16-35.7 16-37 0-.7-7.7-1-23-1h-22C115.7 265.3\n 68 321 0 361zm0-174v-40h399900v40zm100 154v40h399900v-40z", + longequal: "M0 50 h400000 v40H0z m0 194h40000v40H0z\nM0 50 h400000 v40H0z m0 194h40000v40H0z", + midbrace: "M200428 334\nc-100.7-8.3-195.3-44-280-108-55.3-42-101.7-93-139-153l-9-14c-2.7 4-5.7 8.7-9 14\n-53.3 86.7-123.7 153-211 199-66.7 36-137.3 56.3-212 62H0V214h199568c178.3-11.7\n 311.7-78.3 403-201 6-8 9.7-12 11-12 .7-.7 6.7-1 18-1s17.3.3 18 1c1.3 0 5 4 11\n 12 44.7 59.3 101.3 106.3 170 141s145.3 54.3 229 60h199572v120z", + midbraceunder: "M199572 214\nc100.7 8.3 195.3 44 280 108 55.3 42 101.7 93 139 153l9 14c2.7-4 5.7-8.7 9-14\n 53.3-86.7 123.7-153 211-199 66.7-36 137.3-56.3 212-62h199568v120H200432c-178.3\n 11.7-311.7 78.3-403 201-6 8-9.7 12-11 12-.7.7-6.7 1-18 1s-17.3-.3-18-1c-1.3 0\n-5-4-11-12-44.7-59.3-101.3-106.3-170-141s-145.3-54.3-229-60H0V214z", + oiintSize1: "M512.6 71.6c272.6 0 320.3 106.8 320.3 178.2 0 70.8-47.7 177.6\n-320.3 177.6S193.1 320.6 193.1 249.8c0-71.4 46.9-178.2 319.5-178.2z\nm368.1 178.2c0-86.4-60.9-215.4-368.1-215.4-306.4 0-367.3 129-367.3 215.4 0 85.8\n60.9 214.8 367.3 214.8 307.2 0 368.1-129 368.1-214.8z", + oiintSize2: "M757.8 100.1c384.7 0 451.1 137.6 451.1 230 0 91.3-66.4 228.8\n-451.1 228.8-386.3 0-452.7-137.5-452.7-228.8 0-92.4 66.4-230 452.7-230z\nm502.4 230c0-111.2-82.4-277.2-502.4-277.2s-504 166-504 277.2\nc0 110 84 276 504 276s502.4-166 502.4-276z", + oiiintSize1: "M681.4 71.6c408.9 0 480.5 106.8 480.5 178.2 0 70.8-71.6 177.6\n-480.5 177.6S202.1 320.6 202.1 249.8c0-71.4 70.5-178.2 479.3-178.2z\nm525.8 178.2c0-86.4-86.8-215.4-525.7-215.4-437.9 0-524.7 129-524.7 215.4 0\n85.8 86.8 214.8 524.7 214.8 438.9 0 525.7-129 525.7-214.8z", + oiiintSize2: "M1021.2 53c603.6 0 707.8 165.8 707.8 277.2 0 110-104.2 275.8\n-707.8 275.8-606 0-710.2-165.8-710.2-275.8C311 218.8 415.2 53 1021.2 53z\nm770.4 277.1c0-131.2-126.4-327.6-770.5-327.6S248.4 198.9 248.4 330.1\nc0 130 128.8 326.4 772.7 326.4s770.5-196.4 770.5-326.4z", + rightarrow: "M0 241v40h399891c-47.3 35.3-84 78-110 128\n-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20\n 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7\n 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85\n-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n 151.7 139 205zm0 0v40h399900v-40z", + rightbrace: "M400000 542l\n-6 6h-17c-12.7 0-19.3-.3-20-1-4-4-7.3-8.3-10-13-35.3-51.3-80.8-93.8-136.5-127.5\ns-117.2-55.8-184.5-66.5c-.7 0-2-.3-4-1-18.7-2.7-76-4.3-172-5H0V214h399571l6 1\nc124.7 8 235 61.7 331 161 31.3 33.3 59.7 72.7 85 118l7 13v35z", + rightbraceunder: "M399994 0l6 6v35l-6 11c-56 104-135.3 181.3-238 232-57.3\n 28.7-117 45-179 50H-300V214h399897c43.3-7 81-15 113-26 100.7-33 179.7-91 237\n-174 2.7-5 6-9 10-13 .7-1 7.3-1 20-1h17z", + rightgroup: "M0 80h399565c371 0 266.7 149.4 414 180 5.9 1.2 18 0 18 0 2 0\n 3-1 3-3v-38c-76-158-257-219-435-219H0z", + rightgroupunder: "M0 262h399565c371 0 266.7-149.4 414-180 5.9-1.2 18 0 18\n 0 2 0 3 1 3 3v38c-76 158-257 219-435 219H0z", + rightharpoon: "M0 241v40h399993c4.7-4.7 7-9.3 7-14 0-9.3\n-3.7-15.3-11-18-92.7-56.7-159-133.7-199-231-3.3-9.3-6-14.7-8-16-2-1.3-7-2-15-2\n-10.7 0-16.7 2-18 6-2 2.7-1 9.7 3 21 15.3 42 36.7 81.8 64 119.5 27.3 37.7 58\n 69.2 92 94.5zm0 0v40h399900v-40z", + rightharpoonplus: "M0 241v40h399993c4.7-4.7 7-9.3 7-14 0-9.3-3.7-15.3-11\n-18-92.7-56.7-159-133.7-199-231-3.3-9.3-6-14.7-8-16-2-1.3-7-2-15-2-10.7 0-16.7\n 2-18 6-2 2.7-1 9.7 3 21 15.3 42 36.7 81.8 64 119.5 27.3 37.7 58 69.2 92 94.5z\nm0 0v40h399900v-40z m100 194v40h399900v-40zm0 0v40h399900v-40z", + rightharpoondown: "M399747 511c0 7.3 6.7 11 20 11 8 0 13-.8 15-2.5s4.7-6.8\n 8-15.5c40-94 99.3-166.3 178-217 13.3-8 20.3-12.3 21-13 5.3-3.3 8.5-5.8 9.5\n-7.5 1-1.7 1.5-5.2 1.5-10.5s-2.3-10.3-7-15H0v40h399908c-34 25.3-64.7 57-92 95\n-27.3 38-48.7 77.7-64 119-3.3 8.7-5 14-5 16zM0 241v40h399900v-40z", + rightharpoondownplus: "M399747 705c0 7.3 6.7 11 20 11 8 0 13-.8\n 15-2.5s4.7-6.8 8-15.5c40-94 99.3-166.3 178-217 13.3-8 20.3-12.3 21-13 5.3-3.3\n 8.5-5.8 9.5-7.5 1-1.7 1.5-5.2 1.5-10.5s-2.3-10.3-7-15H0v40h399908c-34 25.3\n-64.7 57-92 95-27.3 38-48.7 77.7-64 119-3.3 8.7-5 14-5 16zM0 435v40h399900v-40z\nm0-194v40h400000v-40zm0 0v40h400000v-40z", + righthook: "M399859 241c-764 0 0 0 0 0 40-3.3 68.7-15.7 86-37 10-12 15-25.3\n 15-40 0-22.7-9.8-40.7-29.5-54-19.7-13.3-43.5-21-71.5-23-17.3-1.3-26-8-26-20 0\n-13.3 8.7-20 26-20 38 0 71 11.2 99 33.5 0 0 7 5.6 21 16.7 14 11.2 21 33.5 21\n 66.8s-14 61.2-42 83.5c-28 22.3-61 33.5-99 33.5L0 241z M0 281v-40h399859v40z", + rightlinesegment: "M399960 241 V94 h40 V428 h-40 V281 H0 v-40z\nM399960 241 V94 h40 V428 h-40 V281 H0 v-40z", + rightToFrom: "M400000 167c-70.7-42-118-97.7-142-167h-23c-15.3 0-23 .3-23\n 1 0 1.3 5.3 13.7 16 37 18 35.3 41.3 69 70 101l7 8H0v40h399905l-7 8c-28.7 32\n-52 65.7-70 101-10.7 23.3-16 35.7-16 37 0 .7 7.7 1 23 1h23c24-69.3 71.3-125 142\n-167z M100 147v40h399900v-40zM0 341v40h399900v-40z", + // twoheadleftarrow is from glyph U+219E in font KaTeX AMS Regular + twoheadleftarrow: "M0 167c68 40\n 115.7 95.7 143 167h22c15.3 0 23-.3 23-1 0-1.3-5.3-13.7-16-37-18-35.3-41.3-69\n-70-101l-7-8h125l9 7c50.7 39.3 85 86 103 140h46c0-4.7-6.3-18.7-19-42-18-35.3\n-40-67.3-66-96l-9-9h399716v-40H284l9-9c26-28.7 48-60.7 66-96 12.7-23.333 19\n-37.333 19-42h-46c-18 54-52.3 100.7-103 140l-9 7H95l7-8c28.7-32 52-65.7 70-101\n 10.7-23.333 16-35.7 16-37 0-.7-7.7-1-23-1h-22C115.7 71.3 68 127 0 167z", + twoheadrightarrow: "M400000 167\nc-68-40-115.7-95.7-143-167h-22c-15.3 0-23 .3-23 1 0 1.3 5.3 13.7 16 37 18 35.3\n 41.3 69 70 101l7 8h-125l-9-7c-50.7-39.3-85-86-103-140h-46c0 4.7 6.3 18.7 19 42\n 18 35.3 40 67.3 66 96l9 9H0v40h399716l-9 9c-26 28.7-48 60.7-66 96-12.7 23.333\n-19 37.333-19 42h46c18-54 52.3-100.7 103-140l9-7h125l-7 8c-28.7 32-52 65.7-70\n 101-10.7 23.333-16 35.7-16 37 0 .7 7.7 1 23 1h22c27.3-71.3 75-127 143-167z", + // tilde1 is a modified version of a glyph from the MnSymbol package + tilde1: "M200 55.538c-77 0-168 73.953-177 73.953-3 0-7\n-2.175-9-5.437L2 97c-1-2-2-4-2-6 0-4 2-7 5-9l20-12C116 12 171 0 207 0c86 0\n 114 68 191 68 78 0 168-68 177-68 4 0 7 2 9 5l12 19c1 2.175 2 4.35 2 6.525 0\n 4.35-2 7.613-5 9.788l-19 13.05c-92 63.077-116.937 75.308-183 76.128\n-68.267.847-113-73.952-191-73.952z", + // ditto tilde2, tilde3, & tilde4 + tilde2: "M344 55.266c-142 0-300.638 81.316-311.5 86.418\n-8.01 3.762-22.5 10.91-23.5 5.562L1 120c-1-2-1-3-1-4 0-5 3-9 8-10l18.4-9C160.9\n 31.9 283 0 358 0c148 0 188 122 331 122s314-97 326-97c4 0 8 2 10 7l7 21.114\nc1 2.14 1 3.21 1 4.28 0 5.347-3 9.626-7 10.696l-22.3 12.622C852.6 158.372 751\n 181.476 676 181.476c-149 0-189-126.21-332-126.21z", + tilde3: "M786 59C457 59 32 175.242 13 175.242c-6 0-10-3.457\n-11-10.37L.15 138c-1-7 3-12 10-13l19.2-6.4C378.4 40.7 634.3 0 804.3 0c337 0\n 411.8 157 746.8 157 328 0 754-112 773-112 5 0 10 3 11 9l1 14.075c1 8.066-.697\n 16.595-6.697 17.492l-21.052 7.31c-367.9 98.146-609.15 122.696-778.15 122.696\n -338 0-409-156.573-744-156.573z", + tilde4: "M786 58C457 58 32 177.487 13 177.487c-6 0-10-3.345\n-11-10.035L.15 143c-1-7 3-12 10-13l22-6.7C381.2 35 637.15 0 807.15 0c337 0 409\n 177 744 177 328 0 754-127 773-127 5 0 10 3 11 9l1 14.794c1 7.805-3 13.38-9\n 14.495l-20.7 5.574c-366.85 99.79-607.3 139.372-776.3 139.372-338 0-409\n -175.236-744-175.236z", + // vec is from glyph U+20D7 in font KaTeX Main + vec: "M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z", + // widehat1 is a modified version of a glyph from the MnSymbol package + widehat1: "M529 0h5l519 115c5 1 9 5 9 10 0 1-1 2-1 3l-4 22\nc-1 5-5 9-11 9h-2L532 67 19 159h-2c-5 0-9-4-11-9l-5-22c-1-6 2-12 8-13z", + // ditto widehat2, widehat3, & widehat4 + widehat2: "M1181 0h2l1171 176c6 0 10 5 10 11l-2 23c-1 6-5 10\n-11 10h-1L1182 67 15 220h-1c-6 0-10-4-11-10l-2-23c-1-6 4-11 10-11z", + widehat3: "M1181 0h2l1171 236c6 0 10 5 10 11l-2 23c-1 6-5 10\n-11 10h-1L1182 67 15 280h-1c-6 0-10-4-11-10l-2-23c-1-6 4-11 10-11z", + widehat4: "M1181 0h2l1171 296c6 0 10 5 10 11l-2 23c-1 6-5 10\n-11 10h-1L1182 67 15 340h-1c-6 0-10-4-11-10l-2-23c-1-6 4-11 10-11z", + // widecheck paths are all inverted versions of widehat + widecheck1: "M529,159h5l519,-115c5,-1,9,-5,9,-10c0,-1,-1,-2,-1,-3l-4,-22c-1,\n-5,-5,-9,-11,-9h-2l-512,92l-513,-92h-2c-5,0,-9,4,-11,9l-5,22c-1,6,2,12,8,13z", + widecheck2: "M1181,220h2l1171,-176c6,0,10,-5,10,-11l-2,-23c-1,-6,-5,-10,\n-11,-10h-1l-1168,153l-1167,-153h-1c-6,0,-10,4,-11,10l-2,23c-1,6,4,11,10,11z", + widecheck3: "M1181,280h2l1171,-236c6,0,10,-5,10,-11l-2,-23c-1,-6,-5,-10,\n-11,-10h-1l-1168,213l-1167,-213h-1c-6,0,-10,4,-11,10l-2,23c-1,6,4,11,10,11z", + widecheck4: "M1181,340h2l1171,-296c6,0,10,-5,10,-11l-2,-23c-1,-6,-5,-10,\n-11,-10h-1l-1168,273l-1167,-273h-1c-6,0,-10,4,-11,10l-2,23c-1,6,4,11,10,11z", + // The next ten paths support reaction arrows from the mhchem package. + // Arrows for \ce{<-->} are offset from xAxis by 0.22ex, per mhchem in LaTeX + // baraboveleftarrow is mostly from from glyph U+2190 in font KaTeX Main + baraboveleftarrow: "M400000 620h-399890l3 -3c68.7 -52.7 113.7 -120 135 -202\nc4 -14.7 6 -23 6 -25c0 -7.3 -7 -11 -21 -11c-8 0 -13.2 0.8 -15.5 2.5\nc-2.3 1.7 -4.2 5.8 -5.5 12.5c-1.3 4.7 -2.7 10.3 -4 17c-12 48.7 -34.8 92 -68.5 130\ns-74.2 66.3 -121.5 85c-10 4 -16 7.7 -18 11c0 8.7 6 14.3 18 17c47.3 18.7 87.8 47\n121.5 85s56.5 81.3 68.5 130c0.7 2 1.3 5 2 9s1.2 6.7 1.5 8c0.3 1.3 1 3.3 2 6\ns2.2 4.5 3.5 5.5c1.3 1 3.3 1.8 6 2.5s6 1 10 1c14 0 21 -3.7 21 -11\nc0 -2 -2 -10.3 -6 -25c-20 -79.3 -65 -146.7 -135 -202l-3 -3h399890z\nM100 620v40h399900v-40z M0 241v40h399900v-40zM0 241v40h399900v-40z", + // rightarrowabovebar is mostly from glyph U+2192, KaTeX Main + rightarrowabovebar: "M0 241v40h399891c-47.3 35.3-84 78-110 128-16.7 32\n-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0\n13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39\n-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5\n-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n151.7 139 205zm96 379h399894v40H0zm0 0h399904v40H0z", + // The short left harpoon has 0.5em (i.e. 500 units) kern on the left end. + // Ref from mhchem.sty: \rlap{\raisebox{-.22ex}{$\kern0.5em + baraboveshortleftharpoon: "M507,435c-4,4,-6.3,8.7,-7,14c0,5.3,0.7,9,2,11\nc1.3,2,5.3,5.3,12,10c90.7,54,156,130,196,228c3.3,10.7,6.3,16.3,9,17\nc2,0.7,5,1,9,1c0,0,5,0,5,0c10.7,0,16.7,-2,18,-6c2,-2.7,1,-9.7,-3,-21\nc-32,-87.3,-82.7,-157.7,-152,-211c0,0,-3,-3,-3,-3l399351,0l0,-40\nc-398570,0,-399437,0,-399437,0z M593 435 v40 H399500 v-40z\nM0 281 v-40 H399908 v40z M0 281 v-40 H399908 v40z", + rightharpoonaboveshortbar: "M0,241 l0,40c399126,0,399993,0,399993,0\nc4.7,-4.7,7,-9.3,7,-14c0,-9.3,-3.7,-15.3,-11,-18c-92.7,-56.7,-159,-133.7,-199,\n-231c-3.3,-9.3,-6,-14.7,-8,-16c-2,-1.3,-7,-2,-15,-2c-10.7,0,-16.7,2,-18,6\nc-2,2.7,-1,9.7,3,21c15.3,42,36.7,81.8,64,119.5c27.3,37.7,58,69.2,92,94.5z\nM0 241 v40 H399908 v-40z M0 475 v-40 H399500 v40z M0 475 v-40 H399500 v40z", + shortbaraboveleftharpoon: "M7,435c-4,4,-6.3,8.7,-7,14c0,5.3,0.7,9,2,11\nc1.3,2,5.3,5.3,12,10c90.7,54,156,130,196,228c3.3,10.7,6.3,16.3,9,17c2,0.7,5,1,9,\n1c0,0,5,0,5,0c10.7,0,16.7,-2,18,-6c2,-2.7,1,-9.7,-3,-21c-32,-87.3,-82.7,-157.7,\n-152,-211c0,0,-3,-3,-3,-3l399907,0l0,-40c-399126,0,-399993,0,-399993,0z\nM93 435 v40 H400000 v-40z M500 241 v40 H400000 v-40z M500 241 v40 H400000 v-40z", + shortrightharpoonabovebar: "M53,241l0,40c398570,0,399437,0,399437,0\nc4.7,-4.7,7,-9.3,7,-14c0,-9.3,-3.7,-15.3,-11,-18c-92.7,-56.7,-159,-133.7,-199,\n-231c-3.3,-9.3,-6,-14.7,-8,-16c-2,-1.3,-7,-2,-15,-2c-10.7,0,-16.7,2,-18,6\nc-2,2.7,-1,9.7,3,21c15.3,42,36.7,81.8,64,119.5c27.3,37.7,58,69.2,92,94.5z\nM500 241 v40 H399408 v-40z M500 435 v40 H400000 v-40z" +}; +;// CONCATENATED MODULE: ./src/tree.js + + +/** + * This node represents a document fragment, which contains elements, but when + * placed into the DOM doesn't have any representation itself. It only contains + * children and doesn't have any DOM node properties. + */ +var DocumentFragment = /*#__PURE__*/function () { + // HtmlDomNode + // Never used; needed for satisfying interface. + function DocumentFragment(children) { + this.children = void 0; + this.classes = void 0; + this.height = void 0; + this.depth = void 0; + this.maxFontSize = void 0; + this.style = void 0; + this.children = children; + this.classes = []; + this.height = 0; + this.depth = 0; + this.maxFontSize = 0; + this.style = {}; + } + + var _proto = DocumentFragment.prototype; + + _proto.hasClass = function hasClass(className) { + return utils.contains(this.classes, className); + } + /** Convert the fragment into a node. */ + ; + + _proto.toNode = function toNode() { + var frag = document.createDocumentFragment(); + + for (var i = 0; i < this.children.length; i++) { + frag.appendChild(this.children[i].toNode()); + } + + return frag; + } + /** Convert the fragment into HTML markup. */ + ; + + _proto.toMarkup = function toMarkup() { + var markup = ""; // Simply concatenate the markup for the children together. + + for (var i = 0; i < this.children.length; i++) { + markup += this.children[i].toMarkup(); + } + + return markup; + } + /** + * Converts the math node into a string, similar to innerText. Applies to + * MathDomNode's only. + */ + ; + + _proto.toText = function toText() { + // To avoid this, we would subclass documentFragment separately for + // MathML, but polyfills for subclassing is expensive per PR 1469. + // $FlowFixMe: Only works for ChildType = MathDomNode. + var toText = function toText(child) { + return child.toText(); + }; + + return this.children.map(toText).join(""); + }; + + return DocumentFragment; +}(); +;// CONCATENATED MODULE: ./src/domTree.js +/** + * These objects store the data about the DOM nodes we create, as well as some + * extra data. They can then be transformed into real DOM nodes with the + * `toNode` function or HTML markup using `toMarkup`. They are useful for both + * storing extra properties on the nodes, as well as providing a way to easily + * work with the DOM. + * + * Similar functions for working with MathML nodes exist in mathMLTree.js. + * + * TODO: refactor `span` and `anchor` into common superclass when + * target environments support class inheritance + */ + + + + + +/** + * Create an HTML className based on a list of classes. In addition to joining + * with spaces, we also remove empty classes. + */ +var createClass = function createClass(classes) { + return classes.filter(function (cls) { + return cls; + }).join(" "); +}; + +var initNode = function initNode(classes, options, style) { + this.classes = classes || []; + this.attributes = {}; + this.height = 0; + this.depth = 0; + this.maxFontSize = 0; + this.style = style || {}; + + if (options) { + if (options.style.isTight()) { + this.classes.push("mtight"); + } + + var color = options.getColor(); + + if (color) { + this.style.color = color; + } + } +}; +/** + * Convert into an HTML node + */ + + +var _toNode = function toNode(tagName) { + var node = document.createElement(tagName); // Apply the class + + node.className = createClass(this.classes); // Apply inline styles + + for (var style in this.style) { + if (this.style.hasOwnProperty(style)) { + // $FlowFixMe Flow doesn't seem to understand span.style's type. + node.style[style] = this.style[style]; + } + } // Apply attributes + + + for (var attr in this.attributes) { + if (this.attributes.hasOwnProperty(attr)) { + node.setAttribute(attr, this.attributes[attr]); + } + } // Append the children, also as HTML nodes + + + for (var i = 0; i < this.children.length; i++) { + node.appendChild(this.children[i].toNode()); + } + + return node; +}; +/** + * Convert into an HTML markup string + */ + + +var _toMarkup = function toMarkup(tagName) { + var markup = "<" + tagName; // Add the class + + if (this.classes.length) { + markup += " class=\"" + utils.escape(createClass(this.classes)) + "\""; + } + + var styles = ""; // Add the styles, after hyphenation + + for (var style in this.style) { + if (this.style.hasOwnProperty(style)) { + styles += utils.hyphenate(style) + ":" + this.style[style] + ";"; + } + } + + if (styles) { + markup += " style=\"" + utils.escape(styles) + "\""; + } // Add the attributes + + + for (var attr in this.attributes) { + if (this.attributes.hasOwnProperty(attr)) { + markup += " " + attr + "=\"" + utils.escape(this.attributes[attr]) + "\""; + } + } + + markup += ">"; // Add the markup of the children, also as markup + + for (var i = 0; i < this.children.length; i++) { + markup += this.children[i].toMarkup(); + } + + markup += ""; + return markup; +}; // Making the type below exact with all optional fields doesn't work due to +// - https://github.com/facebook/flow/issues/4582 +// - https://github.com/facebook/flow/issues/5688 +// However, since *all* fields are optional, $Shape<> works as suggested in 5688 +// above. +// This type does not include all CSS properties. Additional properties should +// be added as needed. + + +/** + * This node represents a span node, with a className, a list of children, and + * an inline style. It also contains information about its height, depth, and + * maxFontSize. + * + * Represents two types with different uses: SvgSpan to wrap an SVG and DomSpan + * otherwise. This typesafety is important when HTML builders access a span's + * children. + */ +var Span = /*#__PURE__*/function () { + function Span(classes, children, options, style) { + this.children = void 0; + this.attributes = void 0; + this.classes = void 0; + this.height = void 0; + this.depth = void 0; + this.width = void 0; + this.maxFontSize = void 0; + this.style = void 0; + initNode.call(this, classes, options, style); + this.children = children || []; + } + /** + * Sets an arbitrary attribute on the span. Warning: use this wisely. Not + * all browsers support attributes the same, and having too many custom + * attributes is probably bad. + */ + + + var _proto = Span.prototype; + + _proto.setAttribute = function setAttribute(attribute, value) { + this.attributes[attribute] = value; + }; + + _proto.hasClass = function hasClass(className) { + return utils.contains(this.classes, className); + }; + + _proto.toNode = function toNode() { + return _toNode.call(this, "span"); + }; + + _proto.toMarkup = function toMarkup() { + return _toMarkup.call(this, "span"); + }; + + return Span; +}(); +/** + * This node represents an anchor () element with a hyperlink. See `span` + * for further details. + */ + +var Anchor = /*#__PURE__*/function () { + function Anchor(href, classes, children, options) { + this.children = void 0; + this.attributes = void 0; + this.classes = void 0; + this.height = void 0; + this.depth = void 0; + this.maxFontSize = void 0; + this.style = void 0; + initNode.call(this, classes, options); + this.children = children || []; + this.setAttribute('href', href); + } + + var _proto2 = Anchor.prototype; + + _proto2.setAttribute = function setAttribute(attribute, value) { + this.attributes[attribute] = value; + }; + + _proto2.hasClass = function hasClass(className) { + return utils.contains(this.classes, className); + }; + + _proto2.toNode = function toNode() { + return _toNode.call(this, "a"); + }; + + _proto2.toMarkup = function toMarkup() { + return _toMarkup.call(this, "a"); + }; + + return Anchor; +}(); +/** + * This node represents an image embed () element. + */ + +var Img = /*#__PURE__*/function () { + function Img(src, alt, style) { + this.src = void 0; + this.alt = void 0; + this.classes = void 0; + this.height = void 0; + this.depth = void 0; + this.maxFontSize = void 0; + this.style = void 0; + this.alt = alt; + this.src = src; + this.classes = ["mord"]; + this.style = style; + } + + var _proto3 = Img.prototype; + + _proto3.hasClass = function hasClass(className) { + return utils.contains(this.classes, className); + }; + + _proto3.toNode = function toNode() { + var node = document.createElement("img"); + node.src = this.src; + node.alt = this.alt; + node.className = "mord"; // Apply inline styles + + for (var style in this.style) { + if (this.style.hasOwnProperty(style)) { + // $FlowFixMe + node.style[style] = this.style[style]; + } + } + + return node; + }; + + _proto3.toMarkup = function toMarkup() { + var markup = "" + this.alt + " 0) { + span = document.createElement("span"); + span.style.marginRight = this.italic + "em"; + } + + if (this.classes.length > 0) { + span = span || document.createElement("span"); + span.className = createClass(this.classes); + } + + for (var style in this.style) { + if (this.style.hasOwnProperty(style)) { + span = span || document.createElement("span"); // $FlowFixMe Flow doesn't seem to understand span.style's type. + + span.style[style] = this.style[style]; + } + } + + if (span) { + span.appendChild(node); + return span; + } else { + return node; + } + } + /** + * Creates markup for a symbol node. + */ + ; + + _proto4.toMarkup = function toMarkup() { + // TODO(alpert): More duplication than I'd like from + // span.prototype.toMarkup and symbolNode.prototype.toNode... + var needsSpan = false; + var markup = " 0) { + styles += "margin-right:" + this.italic + "em;"; + } + + for (var style in this.style) { + if (this.style.hasOwnProperty(style)) { + styles += utils.hyphenate(style) + ":" + this.style[style] + ";"; + } + } + + if (styles) { + needsSpan = true; + markup += " style=\"" + utils.escape(styles) + "\""; + } + + var escaped = utils.escape(this.text); + + if (needsSpan) { + markup += ">"; + markup += escaped; + markup += ""; + return markup; + } else { + return escaped; + } + }; + + return SymbolNode; +}(); +/** + * SVG nodes are used to render stretchy wide elements. + */ + +var SvgNode = /*#__PURE__*/function () { + function SvgNode(children, attributes) { + this.children = void 0; + this.attributes = void 0; + this.children = children || []; + this.attributes = attributes || {}; + } + + var _proto5 = SvgNode.prototype; + + _proto5.toNode = function toNode() { + var svgNS = "http://www.w3.org/2000/svg"; + var node = document.createElementNS(svgNS, "svg"); // Apply attributes + + for (var attr in this.attributes) { + if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) { + node.setAttribute(attr, this.attributes[attr]); + } + } + + for (var i = 0; i < this.children.length; i++) { + node.appendChild(this.children[i].toNode()); + } + + return node; + }; + + _proto5.toMarkup = function toMarkup() { + var markup = ""; + } else { + return ""; + } + }; + + return PathNode; +}(); +var LineNode = /*#__PURE__*/function () { + function LineNode(attributes) { + this.attributes = void 0; + this.attributes = attributes || {}; + } + + var _proto7 = LineNode.prototype; + + _proto7.toNode = function toNode() { + var svgNS = "http://www.w3.org/2000/svg"; + var node = document.createElementNS(svgNS, "line"); // Apply attributes + + for (var attr in this.attributes) { + if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) { + node.setAttribute(attr, this.attributes[attr]); + } + } + + return node; + }; + + _proto7.toMarkup = function toMarkup() { + var markup = " but got " + String(group) + "."); + } +} +;// CONCATENATED MODULE: ./src/fontMetricsData.js +// This file is GENERATED by buildMetrics.sh. DO NOT MODIFY. +/* harmony default export */ var fontMetricsData = ({ + "AMS-Regular": { + "32": [0, 0, 0, 0, 0.25], + "65": [0, 0.68889, 0, 0, 0.72222], + "66": [0, 0.68889, 0, 0, 0.66667], + "67": [0, 0.68889, 0, 0, 0.72222], + "68": [0, 0.68889, 0, 0, 0.72222], + "69": [0, 0.68889, 0, 0, 0.66667], + "70": [0, 0.68889, 0, 0, 0.61111], + "71": [0, 0.68889, 0, 0, 0.77778], + "72": [0, 0.68889, 0, 0, 0.77778], + "73": [0, 0.68889, 0, 0, 0.38889], + "74": [0.16667, 0.68889, 0, 0, 0.5], + "75": [0, 0.68889, 0, 0, 0.77778], + "76": [0, 0.68889, 0, 0, 0.66667], + "77": [0, 0.68889, 0, 0, 0.94445], + "78": [0, 0.68889, 0, 0, 0.72222], + "79": [0.16667, 0.68889, 0, 0, 0.77778], + "80": [0, 0.68889, 0, 0, 0.61111], + "81": [0.16667, 0.68889, 0, 0, 0.77778], + "82": [0, 0.68889, 0, 0, 0.72222], + "83": [0, 0.68889, 0, 0, 0.55556], + "84": [0, 0.68889, 0, 0, 0.66667], + "85": [0, 0.68889, 0, 0, 0.72222], + "86": [0, 0.68889, 0, 0, 0.72222], + "87": [0, 0.68889, 0, 0, 1.0], + "88": [0, 0.68889, 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[0, 0.12, 0, 0, 0.45], + "57683": [0, 0.12, 0, 0, 0.45] + }, + "Typewriter-Regular": { + "32": [0, 0, 0, 0, 0.525], + "33": [0, 0.61111, 0, 0, 0.525], + "34": [0, 0.61111, 0, 0, 0.525], + "35": [0, 0.61111, 0, 0, 0.525], + "36": [0.08333, 0.69444, 0, 0, 0.525], + "37": [0.08333, 0.69444, 0, 0, 0.525], + "38": [0, 0.61111, 0, 0, 0.525], + "39": [0, 0.61111, 0, 0, 0.525], + "40": [0.08333, 0.69444, 0, 0, 0.525], + "41": [0.08333, 0.69444, 0, 0, 0.525], + "42": [0, 0.52083, 0, 0, 0.525], + "43": [-0.08056, 0.53055, 0, 0, 0.525], + "44": [0.13889, 0.125, 0, 0, 0.525], + "45": [-0.08056, 0.53055, 0, 0, 0.525], + "46": [0, 0.125, 0, 0, 0.525], + "47": [0.08333, 0.69444, 0, 0, 0.525], + "48": [0, 0.61111, 0, 0, 0.525], + "49": [0, 0.61111, 0, 0, 0.525], + "50": [0, 0.61111, 0, 0, 0.525], + "51": [0, 0.61111, 0, 0, 0.525], + "52": [0, 0.61111, 0, 0, 0.525], + "53": [0, 0.61111, 0, 0, 0.525], + "54": [0, 0.61111, 0, 0, 0.525], + "55": [0, 0.61111, 0, 0, 0.525], + "56": [0, 0.61111, 0, 0, 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0, 0.525], + "112": [0.22222, 0.43056, 0, 0, 0.525], + "113": [0.22222, 0.43056, 0, 0, 0.525], + "114": [0, 0.43056, 0, 0, 0.525], + "115": [0, 0.43056, 0, 0, 0.525], + "116": [0, 0.55358, 0, 0, 0.525], + "117": [0, 0.43056, 0, 0, 0.525], + "118": [0, 0.43056, 0, 0, 0.525], + "119": [0, 0.43056, 0, 0, 0.525], + "120": [0, 0.43056, 0, 0, 0.525], + "121": [0.22222, 0.43056, 0, 0, 0.525], + "122": [0, 0.43056, 0, 0, 0.525], + "123": [0.08333, 0.69444, 0, 0, 0.525], + "124": [0.08333, 0.69444, 0, 0, 0.525], + "125": [0.08333, 0.69444, 0, 0, 0.525], + "126": [0, 0.61111, 0, 0, 0.525], + "127": [0, 0.61111, 0, 0, 0.525], + "160": [0, 0, 0, 0, 0.525], + "176": [0, 0.61111, 0, 0, 0.525], + "184": [0.19445, 0, 0, 0, 0.525], + "305": [0, 0.43056, 0, 0, 0.525], + "567": [0.22222, 0.43056, 0, 0, 0.525], + "711": [0, 0.56597, 0, 0, 0.525], + "713": [0, 0.56555, 0, 0, 0.525], + "714": [0, 0.61111, 0, 0, 0.525], + "715": [0, 0.61111, 0, 0, 0.525], + "728": [0, 0.61111, 0, 0, 0.525], + "730": [0, 0.61111, 0, 0, 0.525], + "770": [0, 0.61111, 0, 0, 0.525], + "771": [0, 0.61111, 0, 0, 0.525], + "776": [0, 0.61111, 0, 0, 0.525], + "915": [0, 0.61111, 0, 0, 0.525], + "916": [0, 0.61111, 0, 0, 0.525], + "920": [0, 0.61111, 0, 0, 0.525], + "923": [0, 0.61111, 0, 0, 0.525], + "926": [0, 0.61111, 0, 0, 0.525], + "928": [0, 0.61111, 0, 0, 0.525], + "931": [0, 0.61111, 0, 0, 0.525], + "933": [0, 0.61111, 0, 0, 0.525], + "934": [0, 0.61111, 0, 0, 0.525], + "936": [0, 0.61111, 0, 0, 0.525], + "937": [0, 0.61111, 0, 0, 0.525], + "8216": [0, 0.61111, 0, 0, 0.525], + "8217": [0, 0.61111, 0, 0, 0.525], + "8242": [0, 0.61111, 0, 0, 0.525], + "9251": [0.11111, 0.21944, 0, 0, 0.525] + } +}); +;// CONCATENATED MODULE: ./src/fontMetrics.js + + +/** + * This file contains metrics regarding fonts and individual symbols. The sigma + * and xi variables, as well as the metricMap map contain data extracted from + * TeX, TeX font metrics, and the TTF files. These data are then exposed via the + * `metrics` variable and the getCharacterMetrics function. + */ +// In TeX, there are actually three sets of dimensions, one for each of +// textstyle (size index 5 and higher: >=9pt), scriptstyle (size index 3 and 4: +// 7-8pt), and scriptscriptstyle (size index 1 and 2: 5-6pt). These are +// provided in the the arrays below, in that order. +// +// The font metrics are stored in fonts cmsy10, cmsy7, and cmsy5 respsectively. +// This was determined by running the following script: +// +// latex -interaction=nonstopmode \ +// '\documentclass{article}\usepackage{amsmath}\begin{document}' \ +// '$a$ \expandafter\show\the\textfont2' \ +// '\expandafter\show\the\scriptfont2' \ +// '\expandafter\show\the\scriptscriptfont2' \ +// '\stop' +// +// The metrics themselves were retreived using the following commands: +// +// tftopl cmsy10 +// tftopl cmsy7 +// tftopl cmsy5 +// +// The output of each of these commands is quite lengthy. The only part we +// care about is the FONTDIMEN section. Each value is measured in EMs. +var sigmasAndXis = { + slant: [0.250, 0.250, 0.250], + // sigma1 + space: [0.000, 0.000, 0.000], + // sigma2 + stretch: [0.000, 0.000, 0.000], + // sigma3 + shrink: [0.000, 0.000, 0.000], + // sigma4 + xHeight: [0.431, 0.431, 0.431], + // sigma5 + quad: [1.000, 1.171, 1.472], + // sigma6 + extraSpace: [0.000, 0.000, 0.000], + // sigma7 + num1: [0.677, 0.732, 0.925], + // sigma8 + num2: [0.394, 0.384, 0.387], + // sigma9 + num3: [0.444, 0.471, 0.504], + // sigma10 + denom1: [0.686, 0.752, 1.025], + // sigma11 + denom2: [0.345, 0.344, 0.532], + // sigma12 + sup1: [0.413, 0.503, 0.504], + // sigma13 + sup2: [0.363, 0.431, 0.404], + // sigma14 + sup3: [0.289, 0.286, 0.294], + // sigma15 + sub1: [0.150, 0.143, 0.200], + // sigma16 + sub2: [0.247, 0.286, 0.400], + // sigma17 + supDrop: [0.386, 0.353, 0.494], + // sigma18 + subDrop: [0.050, 0.071, 0.100], + // sigma19 + delim1: [2.390, 1.700, 1.980], + // sigma20 + delim2: [1.010, 1.157, 1.420], + // sigma21 + axisHeight: [0.250, 0.250, 0.250], + // sigma22 + // These font metrics are extracted from TeX by using tftopl on cmex10.tfm; + // they correspond to the font parameters of the extension fonts (family 3). + // See the TeXbook, page 441. In AMSTeX, the extension fonts scale; to + // match cmex7, we'd use cmex7.tfm values for script and scriptscript + // values. + defaultRuleThickness: [0.04, 0.049, 0.049], + // xi8; cmex7: 0.049 + bigOpSpacing1: [0.111, 0.111, 0.111], + // xi9 + bigOpSpacing2: [0.166, 0.166, 0.166], + // xi10 + bigOpSpacing3: [0.2, 0.2, 0.2], + // xi11 + bigOpSpacing4: [0.6, 0.611, 0.611], + // xi12; cmex7: 0.611 + bigOpSpacing5: [0.1, 0.143, 0.143], + // xi13; cmex7: 0.143 + // The \sqrt rule width is taken from the height of the surd character. + // Since we use the same font at all sizes, this thickness doesn't scale. + sqrtRuleThickness: [0.04, 0.04, 0.04], + // This value determines how large a pt is, for metrics which are defined + // in terms of pts. + // This value is also used in katex.less; if you change it make sure the + // values match. + ptPerEm: [10.0, 10.0, 10.0], + // The space between adjacent `|` columns in an array definition. From + // `\showthe\doublerulesep` in LaTeX. Equals 2.0 / ptPerEm. + doubleRuleSep: [0.2, 0.2, 0.2], + // The width of separator lines in {array} environments. From + // `\showthe\arrayrulewidth` in LaTeX. Equals 0.4 / ptPerEm. + arrayRuleWidth: [0.04, 0.04, 0.04], + // Two values from LaTeX source2e: + fboxsep: [0.3, 0.3, 0.3], + // 3 pt / ptPerEm + fboxrule: [0.04, 0.04, 0.04] // 0.4 pt / ptPerEm + +}; // This map contains a mapping from font name and character code to character +// metrics, including height, depth, italic correction, and skew (kern from the +// character to the corresponding \skewchar) +// This map is generated via `make metrics`. It should not be changed manually. + + // These are very rough approximations. We default to Times New Roman which +// should have Latin-1 and Cyrillic characters, but may not depending on the +// operating system. The metrics do not account for extra height from the +// accents. In the case of Cyrillic characters which have both ascenders and +// descenders we prefer approximations with ascenders, primarily to prevent +// the fraction bar or root line from intersecting the glyph. +// TODO(kevinb) allow union of multiple glyph metrics for better accuracy. + +var extraCharacterMap = { + // Latin-1 + 'Å': 'A', + 'Ð': 'D', + 'Þ': 'o', + 'å': 'a', + 'ð': 'd', + 'þ': 'o', + // Cyrillic + 'А': 'A', + 'Б': 'B', + 'В': 'B', + 'Г': 'F', + 'Д': 'A', + 'Е': 'E', + 'Ж': 'K', + 'З': '3', + 'И': 'N', + 'Й': 'N', + 'К': 'K', + 'Л': 'N', + 'М': 'M', + 'Н': 'H', + 'О': 'O', + 'П': 'N', + 'Р': 'P', + 'С': 'C', + 'Т': 'T', + 'У': 'y', + 'Ф': 'O', + 'Х': 'X', + 'Ц': 'U', + 'Ч': 'h', + 'Ш': 'W', + 'Щ': 'W', + 'Ъ': 'B', + 'Ы': 'X', + 'Ь': 'B', + 'Э': '3', + 'Ю': 'X', + 'Я': 'R', + 'а': 'a', + 'б': 'b', + 'в': 'a', + 'г': 'r', + 'д': 'y', + 'е': 'e', + 'ж': 'm', + 'з': 'e', + 'и': 'n', + 'й': 'n', + 'к': 'n', + 'л': 'n', + 'м': 'm', + 'н': 'n', + 'о': 'o', + 'п': 'n', + 'р': 'p', + 'с': 'c', + 'т': 'o', + 'у': 'y', + 'ф': 'b', + 'х': 'x', + 'ц': 'n', + 'ч': 'n', + 'ш': 'w', + 'щ': 'w', + 'ъ': 'a', + 'ы': 'm', + 'ь': 'a', + 'э': 'e', + 'ю': 'm', + 'я': 'r' +}; + +/** + * This function adds new font metrics to default metricMap + * It can also override existing metrics + */ +function setFontMetrics(fontName, metrics) { + fontMetricsData[fontName] = metrics; +} +/** + * This function is a convenience function for looking up information in the + * metricMap table. It takes a character as a string, and a font. + * + * Note: the `width` property may be undefined if fontMetricsData.js wasn't + * built using `Make extended_metrics`. + */ + +function getCharacterMetrics(character, font, mode) { + if (!fontMetricsData[font]) { + throw new Error("Font metrics not found for font: " + font + "."); + } + + var ch = character.charCodeAt(0); + var metrics = fontMetricsData[font][ch]; + + if (!metrics && character[0] in extraCharacterMap) { + ch = extraCharacterMap[character[0]].charCodeAt(0); + metrics = fontMetricsData[font][ch]; + } + + if (!metrics && mode === 'text') { + // We don't typically have font metrics for Asian scripts. + // But since we support them in text mode, we need to return + // some sort of metrics. + // So if the character is in a script we support but we + // don't have metrics for it, just use the metrics for + // the Latin capital letter M. This is close enough because + // we (currently) only care about the height of the glpyh + // not its width. + if (supportedCodepoint(ch)) { + metrics = fontMetricsData[font][77]; // 77 is the charcode for 'M' + } + } + + if (metrics) { + return { + depth: metrics[0], + height: metrics[1], + italic: metrics[2], + skew: metrics[3], + width: metrics[4] + }; + } +} +var fontMetricsBySizeIndex = {}; +/** + * Get the font metrics for a given size. + */ + +function getGlobalMetrics(size) { + var sizeIndex; + + if (size >= 5) { + sizeIndex = 0; + } else if (size >= 3) { + sizeIndex = 1; + } else { + sizeIndex = 2; + } + + if (!fontMetricsBySizeIndex[sizeIndex]) { + var metrics = fontMetricsBySizeIndex[sizeIndex] = { + cssEmPerMu: sigmasAndXis.quad[sizeIndex] / 18 + }; + + for (var key in sigmasAndXis) { + if (sigmasAndXis.hasOwnProperty(key)) { + metrics[key] = sigmasAndXis[key][sizeIndex]; + } + } + } + + return fontMetricsBySizeIndex[sizeIndex]; +} +;// CONCATENATED MODULE: ./src/symbols.js +/** + * This file holds a list of all no-argument functions and single-character + * symbols (like 'a' or ';'). + * + * For each of the symbols, there are three properties they can have: + * - font (required): the font to be used for this symbol. Either "main" (the + normal font), or "ams" (the ams fonts). + * - group (required): the ParseNode group type the symbol should have (i.e. + "textord", "mathord", etc). + See https://github.com/KaTeX/KaTeX/wiki/Examining-TeX#group-types + * - replace: the character that this symbol or function should be + * replaced with (i.e. "\phi" has a replace value of "\u03d5", the phi + * character in the main font). + * + * The outermost map in the table indicates what mode the symbols should be + * accepted in (e.g. "math" or "text"). + */ +// Some of these have a "-token" suffix since these are also used as `ParseNode` +// types for raw text tokens, and we want to avoid conflicts with higher-level +// `ParseNode` types. These `ParseNode`s are constructed within `Parser` by +// looking up the `symbols` map. +var ATOMS = { + "bin": 1, + "close": 1, + "inner": 1, + "open": 1, + "punct": 1, + "rel": 1 +}; +var NON_ATOMS = { + "accent-token": 1, + "mathord": 1, + "op-token": 1, + "spacing": 1, + "textord": 1 +}; +var symbols = { + "math": {}, + "text": {} +}; +/* harmony default export */ var src_symbols = (symbols); +/** `acceptUnicodeChar = true` is only applicable if `replace` is set. */ + +function defineSymbol(mode, font, group, replace, name, acceptUnicodeChar) { + symbols[mode][name] = { + font: font, + group: group, + replace: replace + }; + + if (acceptUnicodeChar && replace) { + symbols[mode][replace] = symbols[mode][name]; + } +} // Some abbreviations for commonly used strings. +// This helps minify the code, and also spotting typos using jshint. +// modes: + +var math = "math"; +var symbols_text = "text"; // fonts: + +var main = "main"; +var ams = "ams"; // groups: + +var accent = "accent-token"; +var bin = "bin"; +var symbols_close = "close"; +var inner = "inner"; +var mathord = "mathord"; +var op = "op-token"; +var symbols_open = "open"; +var punct = "punct"; +var rel = "rel"; +var spacing = "spacing"; +var textord = "textord"; // Now comes the symbol table +// Relation Symbols + +defineSymbol(math, main, rel, "\u2261", "\\equiv", true); +defineSymbol(math, main, rel, "\u227A", "\\prec", true); +defineSymbol(math, main, rel, "\u227B", "\\succ", true); +defineSymbol(math, main, rel, "\u223C", "\\sim", true); +defineSymbol(math, main, rel, "\u22A5", "\\perp"); +defineSymbol(math, main, rel, "\u2AAF", "\\preceq", true); +defineSymbol(math, main, rel, "\u2AB0", "\\succeq", true); +defineSymbol(math, main, rel, "\u2243", "\\simeq", true); +defineSymbol(math, main, rel, "\u2223", "\\mid", true); +defineSymbol(math, main, rel, "\u226A", "\\ll", true); +defineSymbol(math, main, rel, "\u226B", "\\gg", true); +defineSymbol(math, main, rel, "\u224D", "\\asymp", true); +defineSymbol(math, main, rel, "\u2225", "\\parallel"); +defineSymbol(math, main, rel, "\u22C8", "\\bowtie", true); +defineSymbol(math, main, rel, "\u2323", "\\smile", true); +defineSymbol(math, main, rel, "\u2291", "\\sqsubseteq", true); +defineSymbol(math, main, rel, "\u2292", "\\sqsupseteq", true); +defineSymbol(math, main, rel, "\u2250", "\\doteq", true); +defineSymbol(math, main, rel, "\u2322", "\\frown", true); +defineSymbol(math, main, rel, "\u220B", "\\ni", true); +defineSymbol(math, main, rel, "\u221D", "\\propto", true); +defineSymbol(math, main, rel, "\u22A2", "\\vdash", true); +defineSymbol(math, main, rel, "\u22A3", "\\dashv", true); +defineSymbol(math, main, rel, "\u220B", "\\owns"); // Punctuation + +defineSymbol(math, main, punct, ".", "\\ldotp"); +defineSymbol(math, main, punct, "\u22C5", "\\cdotp"); // Misc Symbols + +defineSymbol(math, main, textord, "#", "\\#"); +defineSymbol(symbols_text, main, textord, "#", "\\#"); +defineSymbol(math, main, textord, "&", "\\&"); +defineSymbol(symbols_text, main, textord, "&", "\\&"); +defineSymbol(math, main, textord, "\u2135", "\\aleph", true); +defineSymbol(math, main, textord, "\u2200", "\\forall", true); +defineSymbol(math, main, textord, "\u210F", "\\hbar", true); +defineSymbol(math, main, textord, "\u2203", "\\exists", true); +defineSymbol(math, main, textord, "\u2207", "\\nabla", true); +defineSymbol(math, main, textord, "\u266D", "\\flat", true); +defineSymbol(math, main, textord, "\u2113", "\\ell", true); +defineSymbol(math, main, textord, "\u266E", "\\natural", true); +defineSymbol(math, main, textord, "\u2663", "\\clubsuit", true); +defineSymbol(math, main, textord, "\u2118", "\\wp", true); +defineSymbol(math, main, textord, "\u266F", "\\sharp", true); +defineSymbol(math, main, textord, "\u2662", "\\diamondsuit", true); +defineSymbol(math, main, textord, "\u211C", "\\Re", true); +defineSymbol(math, main, textord, "\u2661", "\\heartsuit", true); +defineSymbol(math, main, textord, "\u2111", "\\Im", true); +defineSymbol(math, main, textord, "\u2660", "\\spadesuit", true); +defineSymbol(math, main, textord, "\xA7", "\\S", true); +defineSymbol(symbols_text, main, textord, "\xA7", "\\S"); +defineSymbol(math, main, textord, "\xB6", "\\P", true); +defineSymbol(symbols_text, main, textord, "\xB6", "\\P"); // Math and Text + +defineSymbol(math, main, textord, "\u2020", "\\dag"); +defineSymbol(symbols_text, main, textord, "\u2020", "\\dag"); +defineSymbol(symbols_text, main, textord, "\u2020", "\\textdagger"); +defineSymbol(math, main, textord, "\u2021", "\\ddag"); +defineSymbol(symbols_text, main, textord, "\u2021", "\\ddag"); +defineSymbol(symbols_text, main, textord, "\u2021", "\\textdaggerdbl"); // Large Delimiters + +defineSymbol(math, main, symbols_close, "\u23B1", "\\rmoustache", true); +defineSymbol(math, main, symbols_open, "\u23B0", "\\lmoustache", true); +defineSymbol(math, main, symbols_close, "\u27EF", "\\rgroup", true); +defineSymbol(math, main, symbols_open, "\u27EE", "\\lgroup", true); // Binary Operators + +defineSymbol(math, main, bin, "\u2213", "\\mp", true); +defineSymbol(math, main, bin, "\u2296", "\\ominus", true); +defineSymbol(math, main, bin, "\u228E", "\\uplus", true); +defineSymbol(math, main, bin, "\u2293", "\\sqcap", true); +defineSymbol(math, main, bin, "\u2217", "\\ast"); +defineSymbol(math, main, bin, "\u2294", "\\sqcup", true); +defineSymbol(math, main, bin, "\u25EF", "\\bigcirc", true); +defineSymbol(math, main, bin, "\u2219", "\\bullet"); +defineSymbol(math, main, bin, "\u2021", "\\ddagger"); +defineSymbol(math, main, bin, "\u2240", "\\wr", true); +defineSymbol(math, main, bin, "\u2A3F", "\\amalg"); +defineSymbol(math, main, bin, "&", "\\And"); // from amsmath +// Arrow Symbols + +defineSymbol(math, main, rel, "\u27F5", "\\longleftarrow", true); +defineSymbol(math, main, rel, "\u21D0", "\\Leftarrow", true); +defineSymbol(math, main, rel, "\u27F8", "\\Longleftarrow", true); +defineSymbol(math, main, rel, "\u27F6", "\\longrightarrow", true); +defineSymbol(math, main, rel, "\u21D2", "\\Rightarrow", true); +defineSymbol(math, main, rel, "\u27F9", "\\Longrightarrow", true); +defineSymbol(math, main, rel, "\u2194", "\\leftrightarrow", true); +defineSymbol(math, main, rel, "\u27F7", "\\longleftrightarrow", true); +defineSymbol(math, main, rel, "\u21D4", "\\Leftrightarrow", true); +defineSymbol(math, main, rel, "\u27FA", "\\Longleftrightarrow", true); +defineSymbol(math, main, rel, "\u21A6", "\\mapsto", true); +defineSymbol(math, main, rel, "\u27FC", "\\longmapsto", true); +defineSymbol(math, main, rel, "\u2197", "\\nearrow", true); +defineSymbol(math, main, rel, "\u21A9", "\\hookleftarrow", true); +defineSymbol(math, main, rel, "\u21AA", "\\hookrightarrow", true); +defineSymbol(math, main, rel, "\u2198", "\\searrow", true); +defineSymbol(math, main, rel, "\u21BC", "\\leftharpoonup", true); +defineSymbol(math, main, rel, "\u21C0", "\\rightharpoonup", true); +defineSymbol(math, main, rel, "\u2199", "\\swarrow", true); +defineSymbol(math, main, rel, "\u21BD", "\\leftharpoondown", true); +defineSymbol(math, main, rel, "\u21C1", "\\rightharpoondown", true); +defineSymbol(math, main, rel, "\u2196", "\\nwarrow", true); +defineSymbol(math, main, rel, "\u21CC", "\\rightleftharpoons", true); // AMS Negated Binary Relations + +defineSymbol(math, ams, rel, "\u226E", "\\nless", true); // Symbol names preceeded by "@" each have a corresponding macro. + +defineSymbol(math, ams, rel, "\uE010", "\\@nleqslant"); +defineSymbol(math, ams, rel, "\uE011", "\\@nleqq"); +defineSymbol(math, ams, rel, "\u2A87", "\\lneq", true); +defineSymbol(math, ams, rel, "\u2268", "\\lneqq", true); +defineSymbol(math, ams, rel, "\uE00C", "\\@lvertneqq"); +defineSymbol(math, ams, rel, "\u22E6", "\\lnsim", true); +defineSymbol(math, ams, rel, "\u2A89", "\\lnapprox", true); +defineSymbol(math, ams, rel, "\u2280", "\\nprec", true); // unicode-math maps \u22e0 to \npreccurlyeq. We'll use the AMS synonym. + +defineSymbol(math, ams, rel, "\u22E0", "\\npreceq", true); +defineSymbol(math, ams, rel, "\u22E8", "\\precnsim", true); +defineSymbol(math, ams, rel, "\u2AB9", "\\precnapprox", true); +defineSymbol(math, ams, rel, "\u2241", "\\nsim", true); +defineSymbol(math, ams, rel, "\uE006", "\\@nshortmid"); +defineSymbol(math, ams, rel, "\u2224", "\\nmid", true); +defineSymbol(math, ams, rel, "\u22AC", "\\nvdash", true); +defineSymbol(math, ams, rel, "\u22AD", "\\nvDash", true); +defineSymbol(math, ams, rel, "\u22EA", "\\ntriangleleft"); +defineSymbol(math, ams, rel, "\u22EC", "\\ntrianglelefteq", true); +defineSymbol(math, ams, rel, "\u228A", "\\subsetneq", true); +defineSymbol(math, ams, rel, "\uE01A", "\\@varsubsetneq"); +defineSymbol(math, ams, rel, "\u2ACB", "\\subsetneqq", true); +defineSymbol(math, ams, rel, "\uE017", "\\@varsubsetneqq"); +defineSymbol(math, ams, rel, "\u226F", "\\ngtr", true); +defineSymbol(math, ams, rel, "\uE00F", "\\@ngeqslant"); +defineSymbol(math, ams, rel, "\uE00E", "\\@ngeqq"); +defineSymbol(math, ams, rel, "\u2A88", "\\gneq", true); +defineSymbol(math, ams, rel, "\u2269", "\\gneqq", true); +defineSymbol(math, ams, rel, "\uE00D", "\\@gvertneqq"); +defineSymbol(math, ams, rel, "\u22E7", "\\gnsim", true); +defineSymbol(math, ams, rel, "\u2A8A", "\\gnapprox", true); +defineSymbol(math, ams, rel, "\u2281", "\\nsucc", true); // unicode-math maps \u22e1 to \nsucccurlyeq. We'll use the AMS synonym. + +defineSymbol(math, ams, rel, "\u22E1", "\\nsucceq", true); +defineSymbol(math, ams, rel, "\u22E9", "\\succnsim", true); +defineSymbol(math, ams, rel, "\u2ABA", "\\succnapprox", true); // unicode-math maps \u2246 to \simneqq. We'll use the AMS synonym. + +defineSymbol(math, ams, rel, "\u2246", "\\ncong", true); +defineSymbol(math, ams, rel, "\uE007", "\\@nshortparallel"); +defineSymbol(math, ams, rel, "\u2226", "\\nparallel", true); +defineSymbol(math, ams, rel, "\u22AF", "\\nVDash", true); +defineSymbol(math, ams, rel, "\u22EB", "\\ntriangleright"); +defineSymbol(math, ams, rel, "\u22ED", "\\ntrianglerighteq", true); +defineSymbol(math, ams, rel, "\uE018", "\\@nsupseteqq"); +defineSymbol(math, ams, rel, "\u228B", "\\supsetneq", true); +defineSymbol(math, ams, rel, "\uE01B", "\\@varsupsetneq"); +defineSymbol(math, ams, rel, "\u2ACC", "\\supsetneqq", true); +defineSymbol(math, ams, rel, "\uE019", "\\@varsupsetneqq"); +defineSymbol(math, ams, rel, "\u22AE", "\\nVdash", true); +defineSymbol(math, ams, rel, "\u2AB5", "\\precneqq", true); +defineSymbol(math, ams, rel, "\u2AB6", "\\succneqq", true); +defineSymbol(math, ams, rel, "\uE016", "\\@nsubseteqq"); +defineSymbol(math, ams, bin, "\u22B4", "\\unlhd"); +defineSymbol(math, ams, bin, "\u22B5", "\\unrhd"); // AMS Negated Arrows + +defineSymbol(math, ams, rel, "\u219A", "\\nleftarrow", true); +defineSymbol(math, ams, rel, "\u219B", "\\nrightarrow", true); +defineSymbol(math, ams, rel, "\u21CD", "\\nLeftarrow", true); +defineSymbol(math, ams, rel, "\u21CF", "\\nRightarrow", true); +defineSymbol(math, ams, rel, "\u21AE", "\\nleftrightarrow", true); +defineSymbol(math, ams, rel, "\u21CE", "\\nLeftrightarrow", true); // AMS Misc + +defineSymbol(math, ams, rel, "\u25B3", "\\vartriangle"); +defineSymbol(math, ams, textord, "\u210F", "\\hslash"); +defineSymbol(math, ams, textord, "\u25BD", "\\triangledown"); +defineSymbol(math, ams, textord, "\u25CA", "\\lozenge"); +defineSymbol(math, ams, textord, "\u24C8", "\\circledS"); +defineSymbol(math, ams, textord, "\xAE", "\\circledR"); +defineSymbol(symbols_text, ams, textord, "\xAE", "\\circledR"); +defineSymbol(math, ams, textord, "\u2221", "\\measuredangle", true); +defineSymbol(math, ams, textord, "\u2204", "\\nexists"); +defineSymbol(math, ams, textord, "\u2127", "\\mho"); +defineSymbol(math, ams, textord, "\u2132", "\\Finv", true); +defineSymbol(math, ams, textord, "\u2141", "\\Game", true); +defineSymbol(math, ams, textord, "\u2035", "\\backprime"); +defineSymbol(math, ams, textord, "\u25B2", "\\blacktriangle"); +defineSymbol(math, ams, textord, "\u25BC", "\\blacktriangledown"); +defineSymbol(math, ams, textord, "\u25A0", "\\blacksquare"); +defineSymbol(math, ams, textord, "\u29EB", "\\blacklozenge"); +defineSymbol(math, ams, textord, "\u2605", "\\bigstar"); +defineSymbol(math, ams, textord, "\u2222", "\\sphericalangle", true); +defineSymbol(math, ams, textord, "\u2201", "\\complement", true); // unicode-math maps U+F0 to \matheth. We map to AMS function \eth + +defineSymbol(math, ams, textord, "\xF0", "\\eth", true); +defineSymbol(symbols_text, main, textord, "\xF0", "\xF0"); +defineSymbol(math, ams, textord, "\u2571", "\\diagup"); +defineSymbol(math, ams, textord, "\u2572", "\\diagdown"); +defineSymbol(math, ams, textord, "\u25A1", "\\square"); +defineSymbol(math, ams, textord, "\u25A1", "\\Box"); +defineSymbol(math, ams, textord, "\u25CA", "\\Diamond"); // unicode-math maps U+A5 to \mathyen. We map to AMS function \yen + +defineSymbol(math, ams, textord, "\xA5", "\\yen", true); +defineSymbol(symbols_text, ams, textord, "\xA5", "\\yen", true); +defineSymbol(math, ams, textord, "\u2713", "\\checkmark", true); +defineSymbol(symbols_text, ams, textord, "\u2713", "\\checkmark"); // AMS Hebrew + +defineSymbol(math, ams, textord, "\u2136", "\\beth", true); +defineSymbol(math, ams, textord, "\u2138", "\\daleth", true); +defineSymbol(math, ams, textord, "\u2137", "\\gimel", true); // AMS Greek + +defineSymbol(math, ams, textord, "\u03DD", "\\digamma", true); +defineSymbol(math, ams, textord, "\u03F0", "\\varkappa"); // AMS Delimiters + +defineSymbol(math, ams, symbols_open, "\u250C", "\\@ulcorner", true); +defineSymbol(math, ams, symbols_close, "\u2510", "\\@urcorner", true); +defineSymbol(math, ams, symbols_open, "\u2514", "\\@llcorner", true); +defineSymbol(math, ams, symbols_close, "\u2518", "\\@lrcorner", true); // AMS Binary Relations + +defineSymbol(math, ams, rel, "\u2266", "\\leqq", true); +defineSymbol(math, ams, rel, "\u2A7D", "\\leqslant", true); +defineSymbol(math, ams, rel, "\u2A95", "\\eqslantless", true); +defineSymbol(math, ams, rel, "\u2272", "\\lesssim", true); +defineSymbol(math, ams, rel, "\u2A85", "\\lessapprox", true); +defineSymbol(math, ams, rel, "\u224A", "\\approxeq", true); +defineSymbol(math, ams, bin, "\u22D6", "\\lessdot"); +defineSymbol(math, ams, rel, "\u22D8", "\\lll", true); +defineSymbol(math, ams, rel, "\u2276", "\\lessgtr", true); +defineSymbol(math, ams, rel, "\u22DA", "\\lesseqgtr", true); +defineSymbol(math, ams, rel, "\u2A8B", "\\lesseqqgtr", true); +defineSymbol(math, ams, rel, "\u2251", "\\doteqdot"); +defineSymbol(math, ams, rel, "\u2253", "\\risingdotseq", true); +defineSymbol(math, ams, rel, "\u2252", "\\fallingdotseq", true); +defineSymbol(math, ams, rel, "\u223D", "\\backsim", true); +defineSymbol(math, ams, rel, "\u22CD", "\\backsimeq", true); +defineSymbol(math, ams, rel, "\u2AC5", "\\subseteqq", true); +defineSymbol(math, ams, rel, "\u22D0", "\\Subset", true); +defineSymbol(math, ams, rel, "\u228F", "\\sqsubset", true); +defineSymbol(math, ams, rel, "\u227C", "\\preccurlyeq", true); +defineSymbol(math, ams, rel, "\u22DE", "\\curlyeqprec", true); +defineSymbol(math, ams, rel, "\u227E", "\\precsim", true); +defineSymbol(math, ams, rel, "\u2AB7", "\\precapprox", true); +defineSymbol(math, ams, rel, "\u22B2", "\\vartriangleleft"); +defineSymbol(math, ams, rel, "\u22B4", "\\trianglelefteq"); +defineSymbol(math, ams, rel, "\u22A8", "\\vDash", true); +defineSymbol(math, ams, rel, "\u22AA", "\\Vvdash", true); +defineSymbol(math, ams, rel, "\u2323", "\\smallsmile"); +defineSymbol(math, ams, rel, "\u2322", "\\smallfrown"); +defineSymbol(math, ams, rel, "\u224F", "\\bumpeq", true); +defineSymbol(math, ams, rel, "\u224E", "\\Bumpeq", true); +defineSymbol(math, ams, rel, "\u2267", "\\geqq", true); +defineSymbol(math, ams, rel, "\u2A7E", "\\geqslant", true); +defineSymbol(math, ams, rel, "\u2A96", "\\eqslantgtr", true); +defineSymbol(math, ams, rel, "\u2273", "\\gtrsim", true); +defineSymbol(math, ams, rel, "\u2A86", "\\gtrapprox", true); +defineSymbol(math, ams, bin, "\u22D7", "\\gtrdot"); +defineSymbol(math, ams, rel, "\u22D9", "\\ggg", true); +defineSymbol(math, ams, rel, "\u2277", "\\gtrless", true); +defineSymbol(math, ams, rel, "\u22DB", "\\gtreqless", true); +defineSymbol(math, ams, rel, "\u2A8C", "\\gtreqqless", true); +defineSymbol(math, ams, rel, "\u2256", "\\eqcirc", true); +defineSymbol(math, ams, rel, "\u2257", "\\circeq", true); +defineSymbol(math, ams, rel, "\u225C", "\\triangleq", true); +defineSymbol(math, ams, rel, "\u223C", "\\thicksim"); +defineSymbol(math, ams, rel, "\u2248", "\\thickapprox"); +defineSymbol(math, ams, rel, "\u2AC6", "\\supseteqq", true); +defineSymbol(math, ams, rel, "\u22D1", "\\Supset", true); +defineSymbol(math, ams, rel, "\u2290", "\\sqsupset", true); +defineSymbol(math, ams, rel, "\u227D", "\\succcurlyeq", true); +defineSymbol(math, ams, rel, "\u22DF", "\\curlyeqsucc", true); +defineSymbol(math, ams, rel, "\u227F", "\\succsim", true); +defineSymbol(math, ams, rel, "\u2AB8", "\\succapprox", true); +defineSymbol(math, ams, rel, "\u22B3", "\\vartriangleright"); +defineSymbol(math, ams, rel, "\u22B5", "\\trianglerighteq"); +defineSymbol(math, ams, rel, "\u22A9", "\\Vdash", true); +defineSymbol(math, ams, rel, "\u2223", "\\shortmid"); +defineSymbol(math, ams, rel, "\u2225", "\\shortparallel"); +defineSymbol(math, ams, rel, "\u226C", "\\between", true); +defineSymbol(math, ams, rel, "\u22D4", "\\pitchfork", true); +defineSymbol(math, ams, rel, "\u221D", "\\varpropto"); +defineSymbol(math, ams, rel, "\u25C0", "\\blacktriangleleft"); // unicode-math says that \therefore is a mathord atom. +// We kept the amssymb atom type, which is rel. + +defineSymbol(math, ams, rel, "\u2234", "\\therefore", true); +defineSymbol(math, ams, rel, "\u220D", "\\backepsilon"); +defineSymbol(math, ams, rel, "\u25B6", "\\blacktriangleright"); // unicode-math says that \because is a mathord atom. +// We kept the amssymb atom type, which is rel. + +defineSymbol(math, ams, rel, "\u2235", "\\because", true); +defineSymbol(math, ams, rel, "\u22D8", "\\llless"); +defineSymbol(math, ams, rel, "\u22D9", "\\gggtr"); +defineSymbol(math, ams, bin, "\u22B2", "\\lhd"); +defineSymbol(math, ams, bin, "\u22B3", "\\rhd"); +defineSymbol(math, ams, rel, "\u2242", "\\eqsim", true); +defineSymbol(math, main, rel, "\u22C8", "\\Join"); +defineSymbol(math, ams, rel, "\u2251", "\\Doteq", true); // AMS Binary Operators + +defineSymbol(math, ams, bin, "\u2214", "\\dotplus", true); +defineSymbol(math, ams, bin, "\u2216", "\\smallsetminus"); +defineSymbol(math, ams, bin, "\u22D2", "\\Cap", true); +defineSymbol(math, ams, bin, "\u22D3", "\\Cup", true); +defineSymbol(math, ams, bin, "\u2A5E", "\\doublebarwedge", true); +defineSymbol(math, ams, bin, "\u229F", "\\boxminus", true); +defineSymbol(math, ams, bin, "\u229E", "\\boxplus", true); +defineSymbol(math, ams, bin, "\u22C7", "\\divideontimes", true); +defineSymbol(math, ams, bin, "\u22C9", "\\ltimes", true); +defineSymbol(math, ams, bin, "\u22CA", "\\rtimes", true); +defineSymbol(math, ams, bin, "\u22CB", "\\leftthreetimes", true); +defineSymbol(math, ams, bin, "\u22CC", "\\rightthreetimes", true); +defineSymbol(math, ams, bin, "\u22CF", "\\curlywedge", true); +defineSymbol(math, ams, bin, "\u22CE", "\\curlyvee", true); +defineSymbol(math, ams, bin, "\u229D", "\\circleddash", true); +defineSymbol(math, ams, bin, "\u229B", "\\circledast", true); +defineSymbol(math, ams, bin, "\u22C5", "\\centerdot"); +defineSymbol(math, ams, bin, "\u22BA", "\\intercal", true); +defineSymbol(math, ams, bin, "\u22D2", "\\doublecap"); +defineSymbol(math, ams, bin, "\u22D3", "\\doublecup"); +defineSymbol(math, ams, bin, "\u22A0", "\\boxtimes", true); // AMS Arrows +// Note: unicode-math maps \u21e2 to their own function \rightdasharrow. +// We'll map it to AMS function \dashrightarrow. It produces the same atom. + +defineSymbol(math, ams, rel, "\u21E2", "\\dashrightarrow", true); // unicode-math maps \u21e0 to \leftdasharrow. We'll use the AMS synonym. + +defineSymbol(math, ams, rel, "\u21E0", "\\dashleftarrow", true); +defineSymbol(math, ams, rel, "\u21C7", "\\leftleftarrows", true); +defineSymbol(math, ams, rel, "\u21C6", "\\leftrightarrows", true); +defineSymbol(math, ams, rel, "\u21DA", "\\Lleftarrow", true); +defineSymbol(math, ams, rel, "\u219E", "\\twoheadleftarrow", true); +defineSymbol(math, ams, rel, "\u21A2", "\\leftarrowtail", true); +defineSymbol(math, ams, rel, "\u21AB", "\\looparrowleft", true); +defineSymbol(math, ams, rel, "\u21CB", "\\leftrightharpoons", true); +defineSymbol(math, ams, rel, "\u21B6", "\\curvearrowleft", true); // unicode-math maps \u21ba to \acwopencirclearrow. We'll use the AMS synonym. + +defineSymbol(math, ams, rel, "\u21BA", "\\circlearrowleft", true); +defineSymbol(math, ams, rel, "\u21B0", "\\Lsh", true); +defineSymbol(math, ams, rel, "\u21C8", "\\upuparrows", true); +defineSymbol(math, ams, rel, "\u21BF", "\\upharpoonleft", true); +defineSymbol(math, ams, rel, "\u21C3", "\\downharpoonleft", true); +defineSymbol(math, main, rel, "\u22B6", "\\origof", true); // not in font + +defineSymbol(math, main, rel, "\u22B7", "\\imageof", true); // not in font + +defineSymbol(math, ams, rel, "\u22B8", "\\multimap", true); +defineSymbol(math, ams, rel, "\u21AD", "\\leftrightsquigarrow", true); +defineSymbol(math, ams, rel, "\u21C9", "\\rightrightarrows", true); +defineSymbol(math, ams, rel, "\u21C4", "\\rightleftarrows", true); +defineSymbol(math, ams, rel, "\u21A0", "\\twoheadrightarrow", true); +defineSymbol(math, ams, rel, "\u21A3", "\\rightarrowtail", true); +defineSymbol(math, ams, rel, "\u21AC", "\\looparrowright", true); +defineSymbol(math, ams, rel, "\u21B7", "\\curvearrowright", true); // unicode-math maps \u21bb to \cwopencirclearrow. We'll use the AMS synonym. + +defineSymbol(math, ams, rel, "\u21BB", "\\circlearrowright", true); +defineSymbol(math, ams, rel, "\u21B1", "\\Rsh", true); +defineSymbol(math, ams, rel, "\u21CA", "\\downdownarrows", true); +defineSymbol(math, ams, rel, "\u21BE", "\\upharpoonright", true); +defineSymbol(math, ams, rel, "\u21C2", "\\downharpoonright", true); +defineSymbol(math, ams, rel, "\u21DD", "\\rightsquigarrow", true); +defineSymbol(math, ams, rel, "\u21DD", "\\leadsto"); +defineSymbol(math, ams, rel, "\u21DB", "\\Rrightarrow", true); +defineSymbol(math, ams, rel, "\u21BE", "\\restriction"); +defineSymbol(math, main, textord, "\u2018", "`"); +defineSymbol(math, main, textord, "$", "\\$"); +defineSymbol(symbols_text, main, textord, "$", "\\$"); +defineSymbol(symbols_text, main, textord, "$", "\\textdollar"); +defineSymbol(math, main, textord, "%", "\\%"); +defineSymbol(symbols_text, main, textord, "%", "\\%"); +defineSymbol(math, main, textord, "_", "\\_"); +defineSymbol(symbols_text, main, textord, "_", "\\_"); +defineSymbol(symbols_text, main, textord, "_", "\\textunderscore"); +defineSymbol(math, main, textord, "\u2220", "\\angle", true); +defineSymbol(math, main, textord, "\u221E", "\\infty", true); +defineSymbol(math, main, textord, "\u2032", "\\prime"); +defineSymbol(math, main, textord, "\u25B3", "\\triangle"); +defineSymbol(math, main, textord, "\u0393", "\\Gamma", true); +defineSymbol(math, main, textord, "\u0394", "\\Delta", true); +defineSymbol(math, main, textord, "\u0398", "\\Theta", true); +defineSymbol(math, main, textord, "\u039B", "\\Lambda", true); +defineSymbol(math, main, textord, "\u039E", "\\Xi", true); +defineSymbol(math, main, textord, "\u03A0", "\\Pi", true); +defineSymbol(math, main, textord, "\u03A3", "\\Sigma", true); +defineSymbol(math, main, textord, "\u03A5", "\\Upsilon", true); +defineSymbol(math, main, textord, "\u03A6", "\\Phi", true); +defineSymbol(math, main, textord, "\u03A8", "\\Psi", true); +defineSymbol(math, main, textord, "\u03A9", "\\Omega", true); +defineSymbol(math, main, textord, "A", "\u0391"); +defineSymbol(math, main, textord, "B", "\u0392"); +defineSymbol(math, main, textord, "E", "\u0395"); +defineSymbol(math, main, textord, "Z", "\u0396"); +defineSymbol(math, main, textord, "H", "\u0397"); +defineSymbol(math, main, textord, "I", "\u0399"); +defineSymbol(math, main, textord, "K", "\u039A"); +defineSymbol(math, main, textord, "M", "\u039C"); +defineSymbol(math, main, textord, "N", "\u039D"); +defineSymbol(math, main, textord, "O", "\u039F"); +defineSymbol(math, main, textord, "P", "\u03A1"); +defineSymbol(math, main, textord, "T", "\u03A4"); +defineSymbol(math, main, textord, "X", "\u03A7"); +defineSymbol(math, main, textord, "\xAC", "\\neg", true); +defineSymbol(math, main, textord, "\xAC", "\\lnot"); +defineSymbol(math, main, textord, "\u22A4", "\\top"); +defineSymbol(math, main, textord, "\u22A5", "\\bot"); +defineSymbol(math, main, textord, "\u2205", "\\emptyset"); +defineSymbol(math, ams, textord, "\u2205", "\\varnothing"); +defineSymbol(math, main, mathord, "\u03B1", "\\alpha", true); +defineSymbol(math, main, mathord, "\u03B2", "\\beta", true); +defineSymbol(math, main, mathord, "\u03B3", "\\gamma", true); +defineSymbol(math, main, mathord, "\u03B4", "\\delta", true); +defineSymbol(math, main, mathord, "\u03F5", "\\epsilon", true); +defineSymbol(math, main, mathord, "\u03B6", "\\zeta", true); +defineSymbol(math, main, mathord, "\u03B7", "\\eta", true); +defineSymbol(math, main, mathord, "\u03B8", "\\theta", true); +defineSymbol(math, main, mathord, "\u03B9", "\\iota", true); +defineSymbol(math, main, mathord, "\u03BA", "\\kappa", true); +defineSymbol(math, main, mathord, "\u03BB", "\\lambda", true); +defineSymbol(math, main, mathord, "\u03BC", "\\mu", true); +defineSymbol(math, main, mathord, "\u03BD", "\\nu", true); +defineSymbol(math, main, mathord, "\u03BE", "\\xi", true); +defineSymbol(math, main, mathord, "\u03BF", "\\omicron", true); +defineSymbol(math, main, mathord, "\u03C0", "\\pi", true); +defineSymbol(math, main, mathord, "\u03C1", "\\rho", true); +defineSymbol(math, main, mathord, "\u03C3", "\\sigma", true); +defineSymbol(math, main, mathord, "\u03C4", "\\tau", true); +defineSymbol(math, main, mathord, "\u03C5", "\\upsilon", true); +defineSymbol(math, main, mathord, "\u03D5", "\\phi", true); +defineSymbol(math, main, mathord, "\u03C7", "\\chi", true); +defineSymbol(math, main, mathord, "\u03C8", "\\psi", true); +defineSymbol(math, main, mathord, "\u03C9", "\\omega", true); +defineSymbol(math, main, mathord, "\u03B5", "\\varepsilon", true); +defineSymbol(math, main, mathord, "\u03D1", "\\vartheta", true); +defineSymbol(math, main, mathord, "\u03D6", "\\varpi", true); +defineSymbol(math, main, mathord, "\u03F1", "\\varrho", true); +defineSymbol(math, main, mathord, "\u03C2", "\\varsigma", true); +defineSymbol(math, main, mathord, "\u03C6", "\\varphi", true); +defineSymbol(math, main, bin, "\u2217", "*", true); +defineSymbol(math, main, bin, "+", "+"); +defineSymbol(math, main, bin, "\u2212", "-", true); +defineSymbol(math, main, bin, "\u22C5", "\\cdot", true); +defineSymbol(math, main, bin, "\u2218", "\\circ"); +defineSymbol(math, main, bin, "\xF7", "\\div", true); +defineSymbol(math, main, bin, "\xB1", "\\pm", true); +defineSymbol(math, main, bin, "\xD7", "\\times", true); +defineSymbol(math, main, bin, "\u2229", "\\cap", true); +defineSymbol(math, main, bin, "\u222A", "\\cup", true); +defineSymbol(math, main, bin, "\u2216", "\\setminus"); +defineSymbol(math, main, bin, "\u2227", "\\land"); +defineSymbol(math, main, bin, "\u2228", "\\lor"); +defineSymbol(math, main, bin, "\u2227", "\\wedge", true); +defineSymbol(math, main, bin, "\u2228", "\\vee", true); +defineSymbol(math, main, textord, "\u221A", "\\surd"); +defineSymbol(math, main, symbols_open, "\u27E8", "\\langle", true); +defineSymbol(math, main, symbols_open, "\u2223", "\\lvert"); +defineSymbol(math, main, symbols_open, "\u2225", "\\lVert"); +defineSymbol(math, main, symbols_close, "?", "?"); +defineSymbol(math, main, symbols_close, "!", "!"); +defineSymbol(math, main, symbols_close, "\u27E9", "\\rangle", true); +defineSymbol(math, main, symbols_close, "\u2223", "\\rvert"); +defineSymbol(math, main, symbols_close, "\u2225", "\\rVert"); +defineSymbol(math, main, rel, "=", "="); +defineSymbol(math, main, rel, ":", ":"); +defineSymbol(math, main, rel, "\u2248", "\\approx", true); +defineSymbol(math, main, rel, "\u2245", "\\cong", true); +defineSymbol(math, main, rel, "\u2265", "\\ge"); +defineSymbol(math, main, rel, "\u2265", "\\geq", true); +defineSymbol(math, main, rel, "\u2190", "\\gets"); +defineSymbol(math, main, rel, ">", "\\gt", true); +defineSymbol(math, main, rel, "\u2208", "\\in", true); +defineSymbol(math, main, rel, "\uE020", "\\@not"); +defineSymbol(math, main, rel, "\u2282", "\\subset", true); +defineSymbol(math, main, rel, "\u2283", "\\supset", true); +defineSymbol(math, main, rel, "\u2286", "\\subseteq", true); +defineSymbol(math, main, rel, "\u2287", "\\supseteq", true); +defineSymbol(math, ams, rel, "\u2288", "\\nsubseteq", true); +defineSymbol(math, ams, rel, "\u2289", "\\nsupseteq", true); +defineSymbol(math, main, rel, "\u22A8", "\\models"); +defineSymbol(math, main, rel, "\u2190", "\\leftarrow", true); +defineSymbol(math, main, rel, "\u2264", "\\le"); +defineSymbol(math, main, rel, "\u2264", "\\leq", true); +defineSymbol(math, main, rel, "<", "\\lt", true); +defineSymbol(math, main, rel, "\u2192", "\\rightarrow", true); +defineSymbol(math, main, rel, "\u2192", "\\to"); +defineSymbol(math, ams, rel, "\u2271", "\\ngeq", true); +defineSymbol(math, ams, rel, "\u2270", "\\nleq", true); +defineSymbol(math, main, spacing, "\xA0", "\\ "); +defineSymbol(math, main, spacing, "\xA0", "\\space"); // Ref: LaTeX Source 2e: \DeclareRobustCommand{\nobreakspace}{% + +defineSymbol(math, main, spacing, "\xA0", "\\nobreakspace"); +defineSymbol(symbols_text, main, spacing, "\xA0", "\\ "); +defineSymbol(symbols_text, main, spacing, "\xA0", " "); +defineSymbol(symbols_text, main, spacing, "\xA0", "\\space"); +defineSymbol(symbols_text, main, spacing, "\xA0", "\\nobreakspace"); +defineSymbol(math, main, spacing, null, "\\nobreak"); +defineSymbol(math, main, spacing, null, "\\allowbreak"); +defineSymbol(math, main, punct, ",", ","); +defineSymbol(math, main, punct, ";", ";"); +defineSymbol(math, ams, bin, "\u22BC", "\\barwedge", true); +defineSymbol(math, ams, bin, "\u22BB", "\\veebar", true); +defineSymbol(math, main, bin, "\u2299", "\\odot", true); +defineSymbol(math, main, bin, "\u2295", "\\oplus", true); +defineSymbol(math, main, bin, "\u2297", "\\otimes", true); +defineSymbol(math, main, textord, "\u2202", "\\partial", true); +defineSymbol(math, main, bin, "\u2298", "\\oslash", true); +defineSymbol(math, ams, bin, "\u229A", "\\circledcirc", true); +defineSymbol(math, ams, bin, "\u22A1", "\\boxdot", true); +defineSymbol(math, main, bin, "\u25B3", "\\bigtriangleup"); +defineSymbol(math, main, bin, "\u25BD", "\\bigtriangledown"); +defineSymbol(math, main, bin, "\u2020", "\\dagger"); +defineSymbol(math, main, bin, "\u22C4", "\\diamond"); +defineSymbol(math, main, bin, "\u22C6", "\\star"); +defineSymbol(math, main, bin, "\u25C3", "\\triangleleft"); +defineSymbol(math, main, bin, "\u25B9", "\\triangleright"); +defineSymbol(math, main, symbols_open, "{", "\\{"); +defineSymbol(symbols_text, main, textord, "{", "\\{"); +defineSymbol(symbols_text, main, textord, "{", "\\textbraceleft"); +defineSymbol(math, main, symbols_close, "}", "\\}"); +defineSymbol(symbols_text, main, textord, "}", "\\}"); +defineSymbol(symbols_text, main, textord, "}", "\\textbraceright"); +defineSymbol(math, main, symbols_open, "{", "\\lbrace"); +defineSymbol(math, main, symbols_close, "}", "\\rbrace"); +defineSymbol(math, main, symbols_open, "[", "\\lbrack", true); +defineSymbol(symbols_text, main, textord, "[", "\\lbrack", true); +defineSymbol(math, main, symbols_close, "]", "\\rbrack", true); +defineSymbol(symbols_text, main, textord, "]", "\\rbrack", true); +defineSymbol(math, main, symbols_open, "(", "\\lparen", true); +defineSymbol(math, main, symbols_close, ")", "\\rparen", true); +defineSymbol(symbols_text, main, textord, "<", "\\textless", true); // in T1 fontenc + +defineSymbol(symbols_text, main, textord, ">", "\\textgreater", true); // in T1 fontenc + +defineSymbol(math, main, symbols_open, "\u230A", "\\lfloor", true); +defineSymbol(math, main, symbols_close, "\u230B", "\\rfloor", true); +defineSymbol(math, main, symbols_open, "\u2308", "\\lceil", true); +defineSymbol(math, main, symbols_close, "\u2309", "\\rceil", true); +defineSymbol(math, main, textord, "\\", "\\backslash"); +defineSymbol(math, main, textord, "\u2223", "|"); +defineSymbol(math, main, textord, "\u2223", "\\vert"); +defineSymbol(symbols_text, main, textord, "|", "\\textbar", true); // in T1 fontenc + +defineSymbol(math, main, textord, "\u2225", "\\|"); +defineSymbol(math, main, textord, "\u2225", "\\Vert"); +defineSymbol(symbols_text, main, textord, "\u2225", "\\textbardbl"); +defineSymbol(symbols_text, main, textord, "~", "\\textasciitilde"); +defineSymbol(symbols_text, main, textord, "\\", "\\textbackslash"); +defineSymbol(symbols_text, main, textord, "^", "\\textasciicircum"); +defineSymbol(math, main, rel, "\u2191", "\\uparrow", true); +defineSymbol(math, main, rel, "\u21D1", "\\Uparrow", true); +defineSymbol(math, main, rel, "\u2193", "\\downarrow", true); +defineSymbol(math, main, rel, "\u21D3", "\\Downarrow", true); +defineSymbol(math, main, rel, "\u2195", "\\updownarrow", true); +defineSymbol(math, main, rel, "\u21D5", "\\Updownarrow", true); +defineSymbol(math, main, op, "\u2210", "\\coprod"); +defineSymbol(math, main, op, "\u22C1", "\\bigvee"); +defineSymbol(math, main, op, "\u22C0", "\\bigwedge"); +defineSymbol(math, main, op, "\u2A04", "\\biguplus"); +defineSymbol(math, main, op, "\u22C2", "\\bigcap"); +defineSymbol(math, main, op, "\u22C3", "\\bigcup"); +defineSymbol(math, main, op, "\u222B", "\\int"); +defineSymbol(math, main, op, "\u222B", "\\intop"); +defineSymbol(math, main, op, "\u222C", "\\iint"); +defineSymbol(math, main, op, "\u222D", "\\iiint"); +defineSymbol(math, main, op, "\u220F", "\\prod"); +defineSymbol(math, main, op, "\u2211", "\\sum"); +defineSymbol(math, main, op, "\u2A02", "\\bigotimes"); +defineSymbol(math, main, op, "\u2A01", "\\bigoplus"); +defineSymbol(math, main, op, "\u2A00", "\\bigodot"); +defineSymbol(math, main, op, "\u222E", "\\oint"); +defineSymbol(math, main, op, "\u222F", "\\oiint"); +defineSymbol(math, main, op, "\u2230", "\\oiiint"); +defineSymbol(math, main, op, "\u2A06", "\\bigsqcup"); +defineSymbol(math, main, op, "\u222B", "\\smallint"); +defineSymbol(symbols_text, main, inner, "\u2026", "\\textellipsis"); +defineSymbol(math, main, inner, "\u2026", "\\mathellipsis"); +defineSymbol(symbols_text, main, inner, "\u2026", "\\ldots", true); +defineSymbol(math, main, inner, "\u2026", "\\ldots", true); +defineSymbol(math, main, inner, "\u22EF", "\\@cdots", true); +defineSymbol(math, main, inner, "\u22F1", "\\ddots", true); +defineSymbol(math, main, textord, "\u22EE", "\\varvdots"); // \vdots is a macro + +defineSymbol(math, main, accent, "\u02CA", "\\acute"); +defineSymbol(math, main, accent, "\u02CB", "\\grave"); +defineSymbol(math, main, accent, "\xA8", "\\ddot"); +defineSymbol(math, main, accent, "~", "\\tilde"); +defineSymbol(math, main, accent, "\u02C9", "\\bar"); +defineSymbol(math, main, accent, "\u02D8", "\\breve"); +defineSymbol(math, main, accent, "\u02C7", "\\check"); +defineSymbol(math, main, accent, "^", "\\hat"); +defineSymbol(math, main, accent, "\u20D7", "\\vec"); +defineSymbol(math, main, accent, "\u02D9", "\\dot"); +defineSymbol(math, main, accent, "\u02DA", "\\mathring"); // \imath and \jmath should be invariant to \mathrm, \mathbf, etc., so use PUA + +defineSymbol(math, main, mathord, "\uE131", "\\@imath"); +defineSymbol(math, main, mathord, "\uE237", "\\@jmath"); +defineSymbol(math, main, textord, "\u0131", "\u0131"); +defineSymbol(math, main, textord, "\u0237", "\u0237"); +defineSymbol(symbols_text, main, textord, "\u0131", "\\i", true); +defineSymbol(symbols_text, main, textord, "\u0237", "\\j", true); +defineSymbol(symbols_text, main, textord, "\xDF", "\\ss", true); +defineSymbol(symbols_text, main, textord, "\xE6", "\\ae", true); +defineSymbol(symbols_text, main, textord, "\u0153", "\\oe", true); +defineSymbol(symbols_text, main, textord, "\xF8", "\\o", true); +defineSymbol(symbols_text, main, textord, "\xC6", "\\AE", true); +defineSymbol(symbols_text, main, textord, "\u0152", "\\OE", true); +defineSymbol(symbols_text, main, textord, "\xD8", "\\O", true); +defineSymbol(symbols_text, main, accent, "\u02CA", "\\'"); // acute + +defineSymbol(symbols_text, main, accent, "\u02CB", "\\`"); // grave + +defineSymbol(symbols_text, main, accent, "\u02C6", "\\^"); // circumflex + +defineSymbol(symbols_text, main, accent, "\u02DC", "\\~"); // tilde + +defineSymbol(symbols_text, main, accent, "\u02C9", "\\="); // macron + +defineSymbol(symbols_text, main, accent, "\u02D8", "\\u"); // breve + +defineSymbol(symbols_text, main, accent, "\u02D9", "\\."); // dot above + +defineSymbol(symbols_text, main, accent, "\xB8", "\\c"); // cedilla + +defineSymbol(symbols_text, main, accent, "\u02DA", "\\r"); // ring above + +defineSymbol(symbols_text, main, accent, "\u02C7", "\\v"); // caron + +defineSymbol(symbols_text, main, accent, "\xA8", '\\"'); // diaresis + +defineSymbol(symbols_text, main, accent, "\u02DD", "\\H"); // double acute + +defineSymbol(symbols_text, main, accent, "\u25EF", "\\textcircled"); // \bigcirc glyph +// These ligatures are detected and created in Parser.js's `formLigatures`. + +var ligatures = { + "--": true, + "---": true, + "``": true, + "''": true +}; +defineSymbol(symbols_text, main, textord, "\u2013", "--", true); +defineSymbol(symbols_text, main, textord, "\u2013", "\\textendash"); +defineSymbol(symbols_text, main, textord, "\u2014", "---", true); +defineSymbol(symbols_text, main, textord, "\u2014", "\\textemdash"); +defineSymbol(symbols_text, main, textord, "\u2018", "`", true); +defineSymbol(symbols_text, main, textord, "\u2018", "\\textquoteleft"); +defineSymbol(symbols_text, main, textord, "\u2019", "'", true); +defineSymbol(symbols_text, main, textord, "\u2019", "\\textquoteright"); +defineSymbol(symbols_text, main, textord, "\u201C", "``", true); +defineSymbol(symbols_text, main, textord, "\u201C", "\\textquotedblleft"); +defineSymbol(symbols_text, main, textord, "\u201D", "''", true); +defineSymbol(symbols_text, main, textord, "\u201D", "\\textquotedblright"); // \degree from gensymb package + +defineSymbol(math, main, textord, "\xB0", "\\degree", true); +defineSymbol(symbols_text, main, textord, "\xB0", "\\degree"); // \textdegree from inputenc package + +defineSymbol(symbols_text, main, textord, "\xB0", "\\textdegree", true); // TODO: In LaTeX, \pounds can generate a different character in text and math +// mode, but among our fonts, only Main-Regular defines this character "163". + +defineSymbol(math, main, textord, "\xA3", "\\pounds"); +defineSymbol(math, main, textord, "\xA3", "\\mathsterling", true); +defineSymbol(symbols_text, main, textord, "\xA3", "\\pounds"); +defineSymbol(symbols_text, main, textord, "\xA3", "\\textsterling", true); +defineSymbol(math, ams, textord, "\u2720", "\\maltese"); +defineSymbol(symbols_text, ams, textord, "\u2720", "\\maltese"); // There are lots of symbols which are the same, so we add them in afterwards. +// All of these are textords in math mode + +var mathTextSymbols = "0123456789/@.\""; + +for (var i = 0; i < mathTextSymbols.length; i++) { + var ch = mathTextSymbols.charAt(i); + defineSymbol(math, main, textord, ch, ch); +} // All of these are textords in text mode + + +var textSymbols = "0123456789!@*()-=+\";:?/.,"; + +for (var _i = 0; _i < textSymbols.length; _i++) { + var _ch = textSymbols.charAt(_i); + + defineSymbol(symbols_text, main, textord, _ch, _ch); +} // All of these are textords in text mode, and mathords in math mode + + +var letters = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"; + +for (var _i2 = 0; _i2 < letters.length; _i2++) { + var _ch2 = letters.charAt(_i2); + + defineSymbol(math, main, mathord, _ch2, _ch2); + defineSymbol(symbols_text, main, textord, _ch2, _ch2); +} // Blackboard bold and script letters in Unicode range + + +defineSymbol(math, ams, textord, "C", "\u2102"); // blackboard bold + +defineSymbol(symbols_text, ams, textord, "C", "\u2102"); +defineSymbol(math, ams, textord, "H", "\u210D"); +defineSymbol(symbols_text, ams, textord, "H", "\u210D"); +defineSymbol(math, ams, textord, "N", "\u2115"); +defineSymbol(symbols_text, ams, textord, "N", "\u2115"); +defineSymbol(math, ams, textord, "P", "\u2119"); +defineSymbol(symbols_text, ams, textord, "P", "\u2119"); +defineSymbol(math, ams, textord, "Q", "\u211A"); +defineSymbol(symbols_text, ams, textord, "Q", "\u211A"); +defineSymbol(math, ams, textord, "R", "\u211D"); +defineSymbol(symbols_text, ams, textord, "R", "\u211D"); +defineSymbol(math, ams, textord, "Z", "\u2124"); +defineSymbol(symbols_text, ams, textord, "Z", "\u2124"); +defineSymbol(math, main, mathord, "h", "\u210E"); // italic h, Planck constant + +defineSymbol(symbols_text, main, mathord, "h", "\u210E"); // The next loop loads wide (surrogate pair) characters. +// We support some letters in the Unicode range U+1D400 to U+1D7FF, +// Mathematical Alphanumeric Symbols. +// Some editors do not deal well with wide characters. So don't write the +// string into this file. Instead, create the string from the surrogate pair. + +var wideChar = ""; + +for (var _i3 = 0; _i3 < letters.length; _i3++) { + var _ch3 = letters.charAt(_i3); // The hex numbers in the next line are a surrogate pair. + // 0xD835 is the high surrogate for all letters in the range we support. + // 0xDC00 is the low surrogate for bold A. + + + wideChar = String.fromCharCode(0xD835, 0xDC00 + _i3); // A-Z a-z bold + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(symbols_text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDC34 + _i3); // A-Z a-z italic + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(symbols_text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDC68 + _i3); // A-Z a-z bold italic + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(symbols_text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDD04 + _i3); // A-Z a-z Fractur + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(symbols_text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDDA0 + _i3); // A-Z a-z sans-serif + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(symbols_text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDDD4 + _i3); // A-Z a-z sans bold + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(symbols_text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDE08 + _i3); // A-Z a-z sans italic + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(symbols_text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDE70 + _i3); // A-Z a-z monospace + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(symbols_text, main, textord, _ch3, wideChar); + + if (_i3 < 26) { + // KaTeX fonts have only capital letters for blackboard bold and script. + // See exception for k below. + wideChar = String.fromCharCode(0xD835, 0xDD38 + _i3); // A-Z double struck + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(symbols_text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDC9C + _i3); // A-Z script + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(symbols_text, main, textord, _ch3, wideChar); + } // TODO: Add bold script when it is supported by a KaTeX font. + +} // "k" is the only double struck lower case letter in the KaTeX fonts. + + +wideChar = String.fromCharCode(0xD835, 0xDD5C); // k double struck + +defineSymbol(math, main, mathord, "k", wideChar); +defineSymbol(symbols_text, main, textord, "k", wideChar); // Next, some wide character numerals + +for (var _i4 = 0; _i4 < 10; _i4++) { + var _ch4 = _i4.toString(); + + wideChar = String.fromCharCode(0xD835, 0xDFCE + _i4); // 0-9 bold + + defineSymbol(math, main, mathord, _ch4, wideChar); + defineSymbol(symbols_text, main, textord, _ch4, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDFE2 + _i4); // 0-9 sans serif + + defineSymbol(math, main, mathord, _ch4, wideChar); + defineSymbol(symbols_text, main, textord, _ch4, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDFEC + _i4); // 0-9 bold sans + + defineSymbol(math, main, mathord, _ch4, wideChar); + defineSymbol(symbols_text, main, textord, _ch4, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDFF6 + _i4); // 0-9 monospace + + defineSymbol(math, main, mathord, _ch4, wideChar); + defineSymbol(symbols_text, main, textord, _ch4, wideChar); +} // We add these Latin-1 letters as symbols for backwards-compatibility, +// but they are not actually in the font, nor are they supported by the +// Unicode accent mechanism, so they fall back to Times font and look ugly. +// TODO(edemaine): Fix this. + + +var extraLatin = "\xD0\xDE\xFE"; + +for (var _i5 = 0; _i5 < extraLatin.length; _i5++) { + var _ch5 = extraLatin.charAt(_i5); + + defineSymbol(math, main, mathord, _ch5, _ch5); + defineSymbol(symbols_text, main, textord, _ch5, _ch5); +} +;// CONCATENATED MODULE: ./src/wide-character.js +/** + * This file provides support for Unicode range U+1D400 to U+1D7FF, + * Mathematical Alphanumeric Symbols. + * + * Function wideCharacterFont takes a wide character as input and returns + * the font information necessary to render it properly. + */ + +/** + * Data below is from https://www.unicode.org/charts/PDF/U1D400.pdf + * That document sorts characters into groups by font type, say bold or italic. + * + * In the arrays below, each subarray consists three elements: + * * The CSS class of that group when in math mode. + * * The CSS class of that group when in text mode. + * * The font name, so that KaTeX can get font metrics. + */ + +var wideLatinLetterData = [["mathbf", "textbf", "Main-Bold"], // A-Z bold upright +["mathbf", "textbf", "Main-Bold"], // a-z bold upright +["mathnormal", "textit", "Math-Italic"], // A-Z italic +["mathnormal", "textit", "Math-Italic"], // a-z italic +["boldsymbol", "boldsymbol", "Main-BoldItalic"], // A-Z bold italic +["boldsymbol", "boldsymbol", "Main-BoldItalic"], // a-z bold italic +// Map fancy A-Z letters to script, not calligraphic. +// This aligns with unicode-math and math fonts (except Cambria Math). +["mathscr", "textscr", "Script-Regular"], // A-Z script +["", "", ""], // a-z script. No font +["", "", ""], // A-Z bold script. No font +["", "", ""], // a-z bold script. No font +["mathfrak", "textfrak", "Fraktur-Regular"], // A-Z Fraktur +["mathfrak", "textfrak", "Fraktur-Regular"], // a-z Fraktur +["mathbb", "textbb", "AMS-Regular"], // A-Z double-struck +["mathbb", "textbb", "AMS-Regular"], // k double-struck +["", "", ""], // A-Z bold Fraktur No font metrics +["", "", ""], // a-z bold Fraktur. No font. +["mathsf", "textsf", "SansSerif-Regular"], // A-Z sans-serif +["mathsf", "textsf", "SansSerif-Regular"], // a-z sans-serif +["mathboldsf", "textboldsf", "SansSerif-Bold"], // A-Z bold sans-serif +["mathboldsf", "textboldsf", "SansSerif-Bold"], // a-z bold sans-serif +["mathitsf", "textitsf", "SansSerif-Italic"], // A-Z italic sans-serif +["mathitsf", "textitsf", "SansSerif-Italic"], // a-z italic sans-serif +["", "", ""], // A-Z bold italic sans. No font +["", "", ""], // a-z bold italic sans. No font +["mathtt", "texttt", "Typewriter-Regular"], // A-Z monospace +["mathtt", "texttt", "Typewriter-Regular"] // a-z monospace +]; +var wideNumeralData = [["mathbf", "textbf", "Main-Bold"], // 0-9 bold +["", "", ""], // 0-9 double-struck. No KaTeX font. +["mathsf", "textsf", "SansSerif-Regular"], // 0-9 sans-serif +["mathboldsf", "textboldsf", "SansSerif-Bold"], // 0-9 bold sans-serif +["mathtt", "texttt", "Typewriter-Regular"] // 0-9 monospace +]; +var wideCharacterFont = function wideCharacterFont(wideChar, mode) { + // IE doesn't support codePointAt(). So work with the surrogate pair. + var H = wideChar.charCodeAt(0); // high surrogate + + var L = wideChar.charCodeAt(1); // low surrogate + + var codePoint = (H - 0xD800) * 0x400 + (L - 0xDC00) + 0x10000; + var j = mode === "math" ? 0 : 1; // column index for CSS class. + + if (0x1D400 <= codePoint && codePoint < 0x1D6A4) { + // wideLatinLetterData contains exactly 26 chars on each row. + // So we can calculate the relevant row. No traverse necessary. + var i = Math.floor((codePoint - 0x1D400) / 26); + return [wideLatinLetterData[i][2], wideLatinLetterData[i][j]]; + } else if (0x1D7CE <= codePoint && codePoint <= 0x1D7FF) { + // Numerals, ten per row. + var _i = Math.floor((codePoint - 0x1D7CE) / 10); + + return [wideNumeralData[_i][2], wideNumeralData[_i][j]]; + } else if (codePoint === 0x1D6A5 || codePoint === 0x1D6A6) { + // dotless i or j + return [wideLatinLetterData[0][2], wideLatinLetterData[0][j]]; + } else if (0x1D6A6 < codePoint && codePoint < 0x1D7CE) { + // Greek letters. Not supported, yet. + return ["", ""]; + } else { + // We don't support any wide characters outside 1D400–1D7FF. + throw new src_ParseError("Unsupported character: " + wideChar); + } +}; +;// CONCATENATED MODULE: ./src/Options.js +/** + * This file contains information about the options that the Parser carries + * around with it while parsing. Data is held in an `Options` object, and when + * recursing, a new `Options` object can be created with the `.with*` and + * `.reset` functions. + */ + +var sizeStyleMap = [// Each element contains [textsize, scriptsize, scriptscriptsize]. +// The size mappings are taken from TeX with \normalsize=10pt. +[1, 1, 1], // size1: [5, 5, 5] \tiny +[2, 1, 1], // size2: [6, 5, 5] +[3, 1, 1], // size3: [7, 5, 5] \scriptsize +[4, 2, 1], // size4: [8, 6, 5] \footnotesize +[5, 2, 1], // size5: [9, 6, 5] \small +[6, 3, 1], // size6: [10, 7, 5] \normalsize +[7, 4, 2], // size7: [12, 8, 6] \large +[8, 6, 3], // size8: [14.4, 10, 7] \Large +[9, 7, 6], // size9: [17.28, 12, 10] \LARGE +[10, 8, 7], // size10: [20.74, 14.4, 12] \huge +[11, 10, 9] // size11: [24.88, 20.74, 17.28] \HUGE +]; +var sizeMultipliers = [// fontMetrics.js:getGlobalMetrics also uses size indexes, so if +// you change size indexes, change that function. +0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.2, 1.44, 1.728, 2.074, 2.488]; + +var sizeAtStyle = function sizeAtStyle(size, style) { + return style.size < 2 ? size : sizeStyleMap[size - 1][style.size - 1]; +}; // In these types, "" (empty string) means "no change". + + +/** + * This is the main options class. It contains the current style, size, color, + * and font. + * + * Options objects should not be modified. To create a new Options with + * different properties, call a `.having*` method. + */ +var Options = /*#__PURE__*/function () { + // A font family applies to a group of fonts (i.e. SansSerif), while a font + // represents a specific font (i.e. SansSerif Bold). + // See: https://tex.stackexchange.com/questions/22350/difference-between-textrm-and-mathrm + + /** + * The base size index. + */ + function Options(data) { + this.style = void 0; + this.color = void 0; + this.size = void 0; + this.textSize = void 0; + this.phantom = void 0; + this.font = void 0; + this.fontFamily = void 0; + this.fontWeight = void 0; + this.fontShape = void 0; + this.sizeMultiplier = void 0; + this.maxSize = void 0; + this.minRuleThickness = void 0; + this._fontMetrics = void 0; + this.style = data.style; + this.color = data.color; + this.size = data.size || Options.BASESIZE; + this.textSize = data.textSize || this.size; + this.phantom = !!data.phantom; + this.font = data.font || ""; + this.fontFamily = data.fontFamily || ""; + this.fontWeight = data.fontWeight || ''; + this.fontShape = data.fontShape || ''; + this.sizeMultiplier = sizeMultipliers[this.size - 1]; + this.maxSize = data.maxSize; + this.minRuleThickness = data.minRuleThickness; + this._fontMetrics = undefined; + } + /** + * Returns a new options object with the same properties as "this". Properties + * from "extension" will be copied to the new options object. + */ + + + var _proto = Options.prototype; + + _proto.extend = function extend(extension) { + var data = { + style: this.style, + size: this.size, + textSize: this.textSize, + color: this.color, + phantom: this.phantom, + font: this.font, + fontFamily: this.fontFamily, + fontWeight: this.fontWeight, + fontShape: this.fontShape, + maxSize: this.maxSize, + minRuleThickness: this.minRuleThickness + }; + + for (var key in extension) { + if (extension.hasOwnProperty(key)) { + data[key] = extension[key]; + } + } + + return new Options(data); + } + /** + * Return an options object with the given style. If `this.style === style`, + * returns `this`. + */ + ; + + _proto.havingStyle = function havingStyle(style) { + if (this.style === style) { + return this; + } else { + return this.extend({ + style: style, + size: sizeAtStyle(this.textSize, style) + }); + } + } + /** + * Return an options object with a cramped version of the current style. If + * the current style is cramped, returns `this`. + */ + ; + + _proto.havingCrampedStyle = function havingCrampedStyle() { + return this.havingStyle(this.style.cramp()); + } + /** + * Return an options object with the given size and in at least `\textstyle`. + * Returns `this` if appropriate. + */ + ; + + _proto.havingSize = function havingSize(size) { + if (this.size === size && this.textSize === size) { + return this; + } else { + return this.extend({ + style: this.style.text(), + size: size, + textSize: size, + sizeMultiplier: sizeMultipliers[size - 1] + }); + } + } + /** + * Like `this.havingSize(BASESIZE).havingStyle(style)`. If `style` is omitted, + * changes to at least `\textstyle`. + */ + ; + + _proto.havingBaseStyle = function havingBaseStyle(style) { + style = style || this.style.text(); + var wantSize = sizeAtStyle(Options.BASESIZE, style); + + if (this.size === wantSize && this.textSize === Options.BASESIZE && this.style === style) { + return this; + } else { + return this.extend({ + style: style, + size: wantSize + }); + } + } + /** + * Remove the effect of sizing changes such as \Huge. + * Keep the effect of the current style, such as \scriptstyle. + */ + ; + + _proto.havingBaseSizing = function havingBaseSizing() { + var size; + + switch (this.style.id) { + case 4: + case 5: + size = 3; // normalsize in scriptstyle + + break; + + case 6: + case 7: + size = 1; // normalsize in scriptscriptstyle + + break; + + default: + size = 6; + // normalsize in textstyle or displaystyle + } + + return this.extend({ + style: this.style.text(), + size: size + }); + } + /** + * Create a new options object with the given color. + */ + ; + + _proto.withColor = function withColor(color) { + return this.extend({ + color: color + }); + } + /** + * Create a new options object with "phantom" set to true. + */ + ; + + _proto.withPhantom = function withPhantom() { + return this.extend({ + phantom: true + }); + } + /** + * Creates a new options object with the given math font or old text font. + * @type {[type]} + */ + ; + + _proto.withFont = function withFont(font) { + return this.extend({ + font: font + }); + } + /** + * Create a new options objects with the given fontFamily. + */ + ; + + _proto.withTextFontFamily = function withTextFontFamily(fontFamily) { + return this.extend({ + fontFamily: fontFamily, + font: "" + }); + } + /** + * Creates a new options object with the given font weight + */ + ; + + _proto.withTextFontWeight = function withTextFontWeight(fontWeight) { + return this.extend({ + fontWeight: fontWeight, + font: "" + }); + } + /** + * Creates a new options object with the given font weight + */ + ; + + _proto.withTextFontShape = function withTextFontShape(fontShape) { + return this.extend({ + fontShape: fontShape, + font: "" + }); + } + /** + * Return the CSS sizing classes required to switch from enclosing options + * `oldOptions` to `this`. Returns an array of classes. + */ + ; + + _proto.sizingClasses = function sizingClasses(oldOptions) { + if (oldOptions.size !== this.size) { + return ["sizing", "reset-size" + oldOptions.size, "size" + this.size]; + } else { + return []; + } + } + /** + * Return the CSS sizing classes required to switch to the base size. Like + * `this.havingSize(BASESIZE).sizingClasses(this)`. + */ + ; + + _proto.baseSizingClasses = function baseSizingClasses() { + if (this.size !== Options.BASESIZE) { + return ["sizing", "reset-size" + this.size, "size" + Options.BASESIZE]; + } else { + return []; + } + } + /** + * Return the font metrics for this size. + */ + ; + + _proto.fontMetrics = function fontMetrics() { + if (!this._fontMetrics) { + this._fontMetrics = getGlobalMetrics(this.size); + } + + return this._fontMetrics; + } + /** + * Gets the CSS color of the current options object + */ + ; + + _proto.getColor = function getColor() { + if (this.phantom) { + return "transparent"; + } else { + return this.color; + } + }; + + return Options; +}(); + +Options.BASESIZE = 6; +/* harmony default export */ var src_Options = (Options); +;// CONCATENATED MODULE: ./src/units.js +/** + * This file does conversion between units. In particular, it provides + * calculateSize to convert other units into ems. + */ + + // This table gives the number of TeX pts in one of each *absolute* TeX unit. +// Thus, multiplying a length by this number converts the length from units +// into pts. Dividing the result by ptPerEm gives the number of ems +// *assuming* a font size of ptPerEm (normal size, normal style). + +var ptPerUnit = { + // https://en.wikibooks.org/wiki/LaTeX/Lengths and + // https://tex.stackexchange.com/a/8263 + "pt": 1, + // TeX point + "mm": 7227 / 2540, + // millimeter + "cm": 7227 / 254, + // centimeter + "in": 72.27, + // inch + "bp": 803 / 800, + // big (PostScript) points + "pc": 12, + // pica + "dd": 1238 / 1157, + // didot + "cc": 14856 / 1157, + // cicero (12 didot) + "nd": 685 / 642, + // new didot + "nc": 1370 / 107, + // new cicero (12 new didot) + "sp": 1 / 65536, + // scaled point (TeX's internal smallest unit) + // https://tex.stackexchange.com/a/41371 + "px": 803 / 800 // \pdfpxdimen defaults to 1 bp in pdfTeX and LuaTeX + +}; // Dictionary of relative units, for fast validity testing. + +var relativeUnit = { + "ex": true, + "em": true, + "mu": true +}; + +/** + * Determine whether the specified unit (either a string defining the unit + * or a "size" parse node containing a unit field) is valid. + */ +var validUnit = function validUnit(unit) { + if (typeof unit !== "string") { + unit = unit.unit; + } + + return unit in ptPerUnit || unit in relativeUnit || unit === "ex"; +}; +/* + * Convert a "size" parse node (with numeric "number" and string "unit" fields, + * as parsed by functions.js argType "size") into a CSS em value for the + * current style/scale. `options` gives the current options. + */ + +var calculateSize = function calculateSize(sizeValue, options) { + var scale; + + if (sizeValue.unit in ptPerUnit) { + // Absolute units + scale = ptPerUnit[sizeValue.unit] // Convert unit to pt + / options.fontMetrics().ptPerEm // Convert pt to CSS em + / options.sizeMultiplier; // Unscale to make absolute units + } else if (sizeValue.unit === "mu") { + // `mu` units scale with scriptstyle/scriptscriptstyle. + scale = options.fontMetrics().cssEmPerMu; + } else { + // Other relative units always refer to the *textstyle* font + // in the current size. + var unitOptions; + + if (options.style.isTight()) { + // isTight() means current style is script/scriptscript. + unitOptions = options.havingStyle(options.style.text()); + } else { + unitOptions = options; + } // TODO: In TeX these units are relative to the quad of the current + // *text* font, e.g. cmr10. KaTeX instead uses values from the + // comparably-sized *Computer Modern symbol* font. At 10pt, these + // match. At 7pt and 5pt, they differ: cmr7=1.138894, cmsy7=1.170641; + // cmr5=1.361133, cmsy5=1.472241. Consider $\scriptsize a\kern1emb$. + // TeX \showlists shows a kern of 1.13889 * fontsize; + // KaTeX shows a kern of 1.171 * fontsize. + + + if (sizeValue.unit === "ex") { + scale = unitOptions.fontMetrics().xHeight; + } else if (sizeValue.unit === "em") { + scale = unitOptions.fontMetrics().quad; + } else { + throw new src_ParseError("Invalid unit: '" + sizeValue.unit + "'"); + } + + if (unitOptions !== options) { + scale *= unitOptions.sizeMultiplier / options.sizeMultiplier; + } + } + + return Math.min(sizeValue.number * scale, options.maxSize); +}; +;// CONCATENATED MODULE: ./src/buildCommon.js +/* eslint no-console:0 */ + +/** + * This module contains general functions that can be used for building + * different kinds of domTree nodes in a consistent manner. + */ + + + + + + + +/** + * Looks up the given symbol in fontMetrics, after applying any symbol + * replacements defined in symbol.js + */ +var lookupSymbol = function lookupSymbol(value, // TODO(#963): Use a union type for this. +fontName, mode) { + // Replace the value with its replaced value from symbol.js + if (src_symbols[mode][value] && src_symbols[mode][value].replace) { + value = src_symbols[mode][value].replace; + } + + return { + value: value, + metrics: getCharacterMetrics(value, fontName, mode) + }; +}; +/** + * Makes a symbolNode after translation via the list of symbols in symbols.js. + * Correctly pulls out metrics for the character, and optionally takes a list of + * classes to be attached to the node. + * + * TODO: make argument order closer to makeSpan + * TODO: add a separate argument for math class (e.g. `mop`, `mbin`), which + * should if present come first in `classes`. + * TODO(#953): Make `options` mandatory and always pass it in. + */ + + +var makeSymbol = function makeSymbol(value, fontName, mode, options, classes) { + var lookup = lookupSymbol(value, fontName, mode); + var metrics = lookup.metrics; + value = lookup.value; + var symbolNode; + + if (metrics) { + var italic = metrics.italic; + + if (mode === "text" || options && options.font === "mathit") { + italic = 0; + } + + symbolNode = new SymbolNode(value, metrics.height, metrics.depth, italic, metrics.skew, metrics.width, classes); + } else { + // TODO(emily): Figure out a good way to only print this in development + typeof console !== "undefined" && console.warn("No character metrics " + ("for '" + value + "' in style '" + fontName + "' and mode '" + mode + "'")); + symbolNode = new SymbolNode(value, 0, 0, 0, 0, 0, classes); + } + + if (options) { + symbolNode.maxFontSize = options.sizeMultiplier; + + if (options.style.isTight()) { + symbolNode.classes.push("mtight"); + } + + var color = options.getColor(); + + if (color) { + symbolNode.style.color = color; + } + } + + return symbolNode; +}; +/** + * Makes a symbol in Main-Regular or AMS-Regular. + * Used for rel, bin, open, close, inner, and punct. + */ + + +var mathsym = function mathsym(value, mode, options, classes) { + if (classes === void 0) { + classes = []; + } + + // Decide what font to render the symbol in by its entry in the symbols + // table. + // Have a special case for when the value = \ because the \ is used as a + // textord in unsupported command errors but cannot be parsed as a regular + // text ordinal and is therefore not present as a symbol in the symbols + // table for text, as well as a special case for boldsymbol because it + // can be used for bold + and - + if (options.font === "boldsymbol" && lookupSymbol(value, "Main-Bold", mode).metrics) { + return makeSymbol(value, "Main-Bold", mode, options, classes.concat(["mathbf"])); + } else if (value === "\\" || src_symbols[mode][value].font === "main") { + return makeSymbol(value, "Main-Regular", mode, options, classes); + } else { + return makeSymbol(value, "AMS-Regular", mode, options, classes.concat(["amsrm"])); + } +}; +/** + * Determines which of the two font names (Main-Bold and Math-BoldItalic) and + * corresponding style tags (mathbf or boldsymbol) to use for font "boldsymbol", + * depending on the symbol. Use this function instead of fontMap for font + * "boldsymbol". + */ + + +var boldsymbol = function boldsymbol(value, mode, options, classes, type) { + if (type !== "textord" && lookupSymbol(value, "Math-BoldItalic", mode).metrics) { + return { + fontName: "Math-BoldItalic", + fontClass: "boldsymbol" + }; + } else { + // Some glyphs do not exist in Math-BoldItalic so we need to use + // Main-Bold instead. + return { + fontName: "Main-Bold", + fontClass: "mathbf" + }; + } +}; +/** + * Makes either a mathord or textord in the correct font and color. + */ + + +var makeOrd = function makeOrd(group, options, type) { + var mode = group.mode; + var text = group.text; + var classes = ["mord"]; // Math mode or Old font (i.e. \rm) + + var isFont = mode === "math" || mode === "text" && options.font; + var fontOrFamily = isFont ? options.font : options.fontFamily; + + if (text.charCodeAt(0) === 0xD835) { + // surrogate pairs get special treatment + var _wideCharacterFont = wideCharacterFont(text, mode), + wideFontName = _wideCharacterFont[0], + wideFontClass = _wideCharacterFont[1]; + + return makeSymbol(text, wideFontName, mode, options, classes.concat(wideFontClass)); + } else if (fontOrFamily) { + var fontName; + var fontClasses; + + if (fontOrFamily === "boldsymbol") { + var fontData = boldsymbol(text, mode, options, classes, type); + fontName = fontData.fontName; + fontClasses = [fontData.fontClass]; + } else if (isFont) { + fontName = fontMap[fontOrFamily].fontName; + fontClasses = [fontOrFamily]; + } else { + fontName = retrieveTextFontName(fontOrFamily, options.fontWeight, options.fontShape); + fontClasses = [fontOrFamily, options.fontWeight, options.fontShape]; + } + + if (lookupSymbol(text, fontName, mode).metrics) { + return makeSymbol(text, fontName, mode, options, classes.concat(fontClasses)); + } else if (ligatures.hasOwnProperty(text) && fontName.substr(0, 10) === "Typewriter") { + // Deconstruct ligatures in monospace fonts (\texttt, \tt). + var parts = []; + + for (var i = 0; i < text.length; i++) { + parts.push(makeSymbol(text[i], fontName, mode, options, classes.concat(fontClasses))); + } + + return makeFragment(parts); + } + } // Makes a symbol in the default font for mathords and textords. + + + if (type === "mathord") { + return makeSymbol(text, "Math-Italic", mode, options, classes.concat(["mathnormal"])); + } else if (type === "textord") { + var font = src_symbols[mode][text] && src_symbols[mode][text].font; + + if (font === "ams") { + var _fontName = retrieveTextFontName("amsrm", options.fontWeight, options.fontShape); + + return makeSymbol(text, _fontName, mode, options, classes.concat("amsrm", options.fontWeight, options.fontShape)); + } else if (font === "main" || !font) { + var _fontName2 = retrieveTextFontName("textrm", options.fontWeight, options.fontShape); + + return makeSymbol(text, _fontName2, mode, options, classes.concat(options.fontWeight, options.fontShape)); + } else { + // fonts added by plugins + var _fontName3 = retrieveTextFontName(font, options.fontWeight, options.fontShape); // We add font name as a css class + + + return makeSymbol(text, _fontName3, mode, options, classes.concat(_fontName3, options.fontWeight, options.fontShape)); + } + } else { + throw new Error("unexpected type: " + type + " in makeOrd"); + } +}; +/** + * Returns true if subsequent symbolNodes have the same classes, skew, maxFont, + * and styles. + */ + + +var canCombine = function canCombine(prev, next) { + if (createClass(prev.classes) !== createClass(next.classes) || prev.skew !== next.skew || prev.maxFontSize !== next.maxFontSize) { + return false; + } // If prev and next both are just "mbin"s or "mord"s we don't combine them + // so that the proper spacing can be preserved. + + + if (prev.classes.length === 1) { + var cls = prev.classes[0]; + + if (cls === "mbin" || cls === "mord") { + return false; + } + } + + for (var style in prev.style) { + if (prev.style.hasOwnProperty(style) && prev.style[style] !== next.style[style]) { + return false; + } + } + + for (var _style in next.style) { + if (next.style.hasOwnProperty(_style) && prev.style[_style] !== next.style[_style]) { + return false; + } + } + + return true; +}; +/** + * Combine consecutive domTree.symbolNodes into a single symbolNode. + * Note: this function mutates the argument. + */ + + +var tryCombineChars = function tryCombineChars(chars) { + for (var i = 0; i < chars.length - 1; i++) { + var prev = chars[i]; + var next = chars[i + 1]; + + if (prev instanceof SymbolNode && next instanceof SymbolNode && canCombine(prev, next)) { + prev.text += next.text; + prev.height = Math.max(prev.height, next.height); + prev.depth = Math.max(prev.depth, next.depth); // Use the last character's italic correction since we use + // it to add padding to the right of the span created from + // the combined characters. + + prev.italic = next.italic; + chars.splice(i + 1, 1); + i--; + } + } + + return chars; +}; +/** + * Calculate the height, depth, and maxFontSize of an element based on its + * children. + */ + + +var sizeElementFromChildren = function sizeElementFromChildren(elem) { + var height = 0; + var depth = 0; + var maxFontSize = 0; + + for (var i = 0; i < elem.children.length; i++) { + var child = elem.children[i]; + + if (child.height > height) { + height = child.height; + } + + if (child.depth > depth) { + depth = child.depth; + } + + if (child.maxFontSize > maxFontSize) { + maxFontSize = child.maxFontSize; + } + } + + elem.height = height; + elem.depth = depth; + elem.maxFontSize = maxFontSize; +}; +/** + * Makes a span with the given list of classes, list of children, and options. + * + * TODO(#953): Ensure that `options` is always provided (currently some call + * sites don't pass it) and make the type below mandatory. + * TODO: add a separate argument for math class (e.g. `mop`, `mbin`), which + * should if present come first in `classes`. + */ + + +var makeSpan = function makeSpan(classes, children, options, style) { + var span = new Span(classes, children, options, style); + sizeElementFromChildren(span); + return span; +}; // SVG one is simpler -- doesn't require height, depth, max-font setting. +// This is also a separate method for typesafety. + + +var makeSvgSpan = function makeSvgSpan(classes, children, options, style) { + return new Span(classes, children, options, style); +}; + +var makeLineSpan = function makeLineSpan(className, options, thickness) { + var line = makeSpan([className], [], options); + line.height = Math.max(thickness || options.fontMetrics().defaultRuleThickness, options.minRuleThickness); + line.style.borderBottomWidth = line.height + "em"; + line.maxFontSize = 1.0; + return line; +}; +/** + * Makes an anchor with the given href, list of classes, list of children, + * and options. + */ + + +var makeAnchor = function makeAnchor(href, classes, children, options) { + var anchor = new Anchor(href, classes, children, options); + sizeElementFromChildren(anchor); + return anchor; +}; +/** + * Makes a document fragment with the given list of children. + */ + + +var makeFragment = function makeFragment(children) { + var fragment = new DocumentFragment(children); + sizeElementFromChildren(fragment); + return fragment; +}; +/** + * Wraps group in a span if it's a document fragment, allowing to apply classes + * and styles + */ + + +var wrapFragment = function wrapFragment(group, options) { + if (group instanceof DocumentFragment) { + return makeSpan([], [group], options); + } + + return group; +}; // These are exact object types to catch typos in the names of the optional fields. + + +// Computes the updated `children` list and the overall depth. +// +// This helper function for makeVList makes it easier to enforce type safety by +// allowing early exits (returns) in the logic. +var getVListChildrenAndDepth = function getVListChildrenAndDepth(params) { + if (params.positionType === "individualShift") { + var oldChildren = params.children; + var children = [oldChildren[0]]; // Add in kerns to the list of params.children to get each element to be + // shifted to the correct specified shift + + var _depth = -oldChildren[0].shift - oldChildren[0].elem.depth; + + var currPos = _depth; + + for (var i = 1; i < oldChildren.length; i++) { + var diff = -oldChildren[i].shift - currPos - oldChildren[i].elem.depth; + var size = diff - (oldChildren[i - 1].elem.height + oldChildren[i - 1].elem.depth); + currPos = currPos + diff; + children.push({ + type: "kern", + size: size + }); + children.push(oldChildren[i]); + } + + return { + children: children, + depth: _depth + }; + } + + var depth; + + if (params.positionType === "top") { + // We always start at the bottom, so calculate the bottom by adding up + // all the sizes + var bottom = params.positionData; + + for (var _i = 0; _i < params.children.length; _i++) { + var child = params.children[_i]; + bottom -= child.type === "kern" ? child.size : child.elem.height + child.elem.depth; + } + + depth = bottom; + } else if (params.positionType === "bottom") { + depth = -params.positionData; + } else { + var firstChild = params.children[0]; + + if (firstChild.type !== "elem") { + throw new Error('First child must have type "elem".'); + } + + if (params.positionType === "shift") { + depth = -firstChild.elem.depth - params.positionData; + } else if (params.positionType === "firstBaseline") { + depth = -firstChild.elem.depth; + } else { + throw new Error("Invalid positionType " + params.positionType + "."); + } + } + + return { + children: params.children, + depth: depth + }; +}; +/** + * Makes a vertical list by stacking elements and kerns on top of each other. + * Allows for many different ways of specifying the positioning method. + * + * See VListParam documentation above. + */ + + +var makeVList = function makeVList(params, options) { + var _getVListChildrenAndD = getVListChildrenAndDepth(params), + children = _getVListChildrenAndD.children, + depth = _getVListChildrenAndD.depth; // Create a strut that is taller than any list item. The strut is added to + // each item, where it will determine the item's baseline. Since it has + // `overflow:hidden`, the strut's top edge will sit on the item's line box's + // top edge and the strut's bottom edge will sit on the item's baseline, + // with no additional line-height spacing. This allows the item baseline to + // be positioned precisely without worrying about font ascent and + // line-height. + + + var pstrutSize = 0; + + for (var i = 0; i < children.length; i++) { + var child = children[i]; + + if (child.type === "elem") { + var elem = child.elem; + pstrutSize = Math.max(pstrutSize, elem.maxFontSize, elem.height); + } + } + + pstrutSize += 2; + var pstrut = makeSpan(["pstrut"], []); + pstrut.style.height = pstrutSize + "em"; // Create a new list of actual children at the correct offsets + + var realChildren = []; + var minPos = depth; + var maxPos = depth; + var currPos = depth; + + for (var _i2 = 0; _i2 < children.length; _i2++) { + var _child = children[_i2]; + + if (_child.type === "kern") { + currPos += _child.size; + } else { + var _elem = _child.elem; + var classes = _child.wrapperClasses || []; + var style = _child.wrapperStyle || {}; + var childWrap = makeSpan(classes, [pstrut, _elem], undefined, style); + childWrap.style.top = -pstrutSize - currPos - _elem.depth + "em"; + + if (_child.marginLeft) { + childWrap.style.marginLeft = _child.marginLeft; + } + + if (_child.marginRight) { + childWrap.style.marginRight = _child.marginRight; + } + + realChildren.push(childWrap); + currPos += _elem.height + _elem.depth; + } + + minPos = Math.min(minPos, currPos); + maxPos = Math.max(maxPos, currPos); + } // The vlist contents go in a table-cell with `vertical-align:bottom`. + // This cell's bottom edge will determine the containing table's baseline + // without overly expanding the containing line-box. + + + var vlist = makeSpan(["vlist"], realChildren); + vlist.style.height = maxPos + "em"; // A second row is used if necessary to represent the vlist's depth. + + var rows; + + if (minPos < 0) { + // We will define depth in an empty span with display: table-cell. + // It should render with the height that we define. But Chrome, in + // contenteditable mode only, treats that span as if it contains some + // text content. And that min-height over-rides our desired height. + // So we put another empty span inside the depth strut span. + var emptySpan = makeSpan([], []); + var depthStrut = makeSpan(["vlist"], [emptySpan]); + depthStrut.style.height = -minPos + "em"; // Safari wants the first row to have inline content; otherwise it + // puts the bottom of the *second* row on the baseline. + + var topStrut = makeSpan(["vlist-s"], [new SymbolNode("\u200B")]); + rows = [makeSpan(["vlist-r"], [vlist, topStrut]), makeSpan(["vlist-r"], [depthStrut])]; + } else { + rows = [makeSpan(["vlist-r"], [vlist])]; + } + + var vtable = makeSpan(["vlist-t"], rows); + + if (rows.length === 2) { + vtable.classes.push("vlist-t2"); + } + + vtable.height = maxPos; + vtable.depth = -minPos; + return vtable; +}; // Glue is a concept from TeX which is a flexible space between elements in +// either a vertical or horizontal list. In KaTeX, at least for now, it's +// static space between elements in a horizontal layout. + + +var makeGlue = function makeGlue(measurement, options) { + // Make an empty span for the space + var rule = makeSpan(["mspace"], [], options); + var size = calculateSize(measurement, options); + rule.style.marginRight = size + "em"; + return rule; +}; // Takes font options, and returns the appropriate fontLookup name + + +var retrieveTextFontName = function retrieveTextFontName(fontFamily, fontWeight, fontShape) { + var baseFontName = ""; + + switch (fontFamily) { + case "amsrm": + baseFontName = "AMS"; + break; + + case "textrm": + baseFontName = "Main"; + break; + + case "textsf": + baseFontName = "SansSerif"; + break; + + case "texttt": + baseFontName = "Typewriter"; + break; + + default: + baseFontName = fontFamily; + // use fonts added by a plugin + } + + var fontStylesName; + + if (fontWeight === "textbf" && fontShape === "textit") { + fontStylesName = "BoldItalic"; + } else if (fontWeight === "textbf") { + fontStylesName = "Bold"; + } else if (fontWeight === "textit") { + fontStylesName = "Italic"; + } else { + fontStylesName = "Regular"; + } + + return baseFontName + "-" + fontStylesName; +}; +/** + * Maps TeX font commands to objects containing: + * - variant: string used for "mathvariant" attribute in buildMathML.js + * - fontName: the "style" parameter to fontMetrics.getCharacterMetrics + */ +// A map between tex font commands an MathML mathvariant attribute values + + +var fontMap = { + // styles + "mathbf": { + variant: "bold", + fontName: "Main-Bold" + }, + "mathrm": { + variant: "normal", + fontName: "Main-Regular" + }, + "textit": { + variant: "italic", + fontName: "Main-Italic" + }, + "mathit": { + variant: "italic", + fontName: "Main-Italic" + }, + "mathnormal": { + variant: "italic", + fontName: "Math-Italic" + }, + // "boldsymbol" is missing because they require the use of multiple fonts: + // Math-BoldItalic and Main-Bold. This is handled by a special case in + // makeOrd which ends up calling boldsymbol. + // families + "mathbb": { + variant: "double-struck", + fontName: "AMS-Regular" + }, + "mathcal": { + variant: "script", + fontName: "Caligraphic-Regular" + }, + "mathfrak": { + variant: "fraktur", + fontName: "Fraktur-Regular" + }, + "mathscr": { + variant: "script", + fontName: "Script-Regular" + }, + "mathsf": { + variant: "sans-serif", + fontName: "SansSerif-Regular" + }, + "mathtt": { + variant: "monospace", + fontName: "Typewriter-Regular" + } +}; +var svgData = { + // path, width, height + vec: ["vec", 0.471, 0.714], + // values from the font glyph + oiintSize1: ["oiintSize1", 0.957, 0.499], + // oval to overlay the integrand + oiintSize2: ["oiintSize2", 1.472, 0.659], + oiiintSize1: ["oiiintSize1", 1.304, 0.499], + oiiintSize2: ["oiiintSize2", 1.98, 0.659] +}; + +var staticSvg = function staticSvg(value, options) { + // Create a span with inline SVG for the element. + var _svgData$value = svgData[value], + pathName = _svgData$value[0], + width = _svgData$value[1], + height = _svgData$value[2]; + var path = new PathNode(pathName); + var svgNode = new SvgNode([path], { + "width": width + "em", + "height": height + "em", + // Override CSS rule `.katex svg { width: 100% }` + "style": "width:" + width + "em", + "viewBox": "0 0 " + 1000 * width + " " + 1000 * height, + "preserveAspectRatio": "xMinYMin" + }); + var span = makeSvgSpan(["overlay"], [svgNode], options); + span.height = height; + span.style.height = height + "em"; + span.style.width = width + "em"; + return span; +}; + +/* harmony default export */ var buildCommon = ({ + fontMap: fontMap, + makeSymbol: makeSymbol, + mathsym: mathsym, + makeSpan: makeSpan, + makeSvgSpan: makeSvgSpan, + makeLineSpan: makeLineSpan, + makeAnchor: makeAnchor, + makeFragment: makeFragment, + wrapFragment: wrapFragment, + makeVList: makeVList, + makeOrd: makeOrd, + makeGlue: makeGlue, + staticSvg: staticSvg, + svgData: svgData, + tryCombineChars: tryCombineChars +}); +;// CONCATENATED MODULE: ./src/spacingData.js +/** + * Describes spaces between different classes of atoms. + */ +var thinspace = { + number: 3, + unit: "mu" +}; +var mediumspace = { + number: 4, + unit: "mu" +}; +var thickspace = { + number: 5, + unit: "mu" +}; // Making the type below exact with all optional fields doesn't work due to +// - https://github.com/facebook/flow/issues/4582 +// - https://github.com/facebook/flow/issues/5688 +// However, since *all* fields are optional, $Shape<> works as suggested in 5688 +// above. + +// Spacing relationships for display and text styles +var spacings = { + mord: { + mop: thinspace, + mbin: mediumspace, + mrel: thickspace, + minner: thinspace + }, + mop: { + mord: thinspace, + mop: thinspace, + mrel: thickspace, + minner: thinspace + }, + mbin: { + mord: mediumspace, + mop: mediumspace, + mopen: mediumspace, + minner: mediumspace + }, + mrel: { + mord: thickspace, + mop: thickspace, + mopen: thickspace, + minner: thickspace + }, + mopen: {}, + mclose: { + mop: thinspace, + mbin: mediumspace, + mrel: thickspace, + minner: thinspace + }, + mpunct: { + mord: thinspace, + mop: thinspace, + mrel: thickspace, + mopen: thinspace, + mclose: thinspace, + mpunct: thinspace, + minner: thinspace + }, + minner: { + mord: thinspace, + mop: thinspace, + mbin: mediumspace, + mrel: thickspace, + mopen: thinspace, + mpunct: thinspace, + minner: thinspace + } +}; // Spacing relationships for script and scriptscript styles + +var tightSpacings = { + mord: { + mop: thinspace + }, + mop: { + mord: thinspace, + mop: thinspace + }, + mbin: {}, + mrel: {}, + mopen: {}, + mclose: { + mop: thinspace + }, + mpunct: {}, + minner: { + mop: thinspace + } +}; +;// CONCATENATED MODULE: ./src/defineFunction.js +/** Context provided to function handlers for error messages. */ +// Note: reverse the order of the return type union will cause a flow error. +// See https://github.com/facebook/flow/issues/3663. +// More general version of `HtmlBuilder` for nodes (e.g. \sum, accent types) +// whose presence impacts super/subscripting. In this case, ParseNode<"supsub"> +// delegates its HTML building to the HtmlBuilder corresponding to these nodes. + +/** + * Final function spec for use at parse time. + * This is almost identical to `FunctionPropSpec`, except it + * 1. includes the function handler, and + * 2. requires all arguments except argTypes. + * It is generated by `defineFunction()` below. + */ + +/** + * All registered functions. + * `functions.js` just exports this same dictionary again and makes it public. + * `Parser.js` requires this dictionary. + */ +var _functions = {}; +/** + * All HTML builders. Should be only used in the `define*` and the `build*ML` + * functions. + */ + +var _htmlGroupBuilders = {}; +/** + * All MathML builders. Should be only used in the `define*` and the `build*ML` + * functions. + */ + +var _mathmlGroupBuilders = {}; +function defineFunction(_ref) { + var type = _ref.type, + names = _ref.names, + props = _ref.props, + handler = _ref.handler, + htmlBuilder = _ref.htmlBuilder, + mathmlBuilder = _ref.mathmlBuilder; + // Set default values of functions + var data = { + type: type, + numArgs: props.numArgs, + argTypes: props.argTypes, + allowedInArgument: !!props.allowedInArgument, + allowedInText: !!props.allowedInText, + allowedInMath: props.allowedInMath === undefined ? true : props.allowedInMath, + numOptionalArgs: props.numOptionalArgs || 0, + infix: !!props.infix, + primitive: !!props.primitive, + handler: handler + }; + + for (var i = 0; i < names.length; ++i) { + _functions[names[i]] = data; + } + + if (type) { + if (htmlBuilder) { + _htmlGroupBuilders[type] = htmlBuilder; + } + + if (mathmlBuilder) { + _mathmlGroupBuilders[type] = mathmlBuilder; + } + } +} +/** + * Use this to register only the HTML and MathML builders for a function (e.g. + * if the function's ParseNode is generated in Parser.js rather than via a + * stand-alone handler provided to `defineFunction`). + */ + +function defineFunctionBuilders(_ref2) { + var type = _ref2.type, + htmlBuilder = _ref2.htmlBuilder, + mathmlBuilder = _ref2.mathmlBuilder; + defineFunction({ + type: type, + names: [], + props: { + numArgs: 0 + }, + handler: function handler() { + throw new Error('Should never be called.'); + }, + htmlBuilder: htmlBuilder, + mathmlBuilder: mathmlBuilder + }); +} +var normalizeArgument = function normalizeArgument(arg) { + return arg.type === "ordgroup" && arg.body.length === 1 ? arg.body[0] : arg; +}; // Since the corresponding buildHTML/buildMathML function expects a +// list of elements, we normalize for different kinds of arguments + +var ordargument = function ordargument(arg) { + return arg.type === "ordgroup" ? arg.body : [arg]; +}; +;// CONCATENATED MODULE: ./src/buildHTML.js +/** + * This file does the main work of building a domTree structure from a parse + * tree. The entry point is the `buildHTML` function, which takes a parse tree. + * Then, the buildExpression, buildGroup, and various groupBuilders functions + * are called, to produce a final HTML tree. + */ + + + + + + + + +var buildHTML_makeSpan = buildCommon.makeSpan; // Binary atoms (first class `mbin`) change into ordinary atoms (`mord`) +// depending on their surroundings. See TeXbook pg. 442-446, Rules 5 and 6, +// and the text before Rule 19. + +var binLeftCanceller = ["leftmost", "mbin", "mopen", "mrel", "mop", "mpunct"]; +var binRightCanceller = ["rightmost", "mrel", "mclose", "mpunct"]; +var styleMap = { + "display": src_Style.DISPLAY, + "text": src_Style.TEXT, + "script": src_Style.SCRIPT, + "scriptscript": src_Style.SCRIPTSCRIPT +}; +var DomEnum = { + mord: "mord", + mop: "mop", + mbin: "mbin", + mrel: "mrel", + mopen: "mopen", + mclose: "mclose", + mpunct: "mpunct", + minner: "minner" +}; + +/** + * Take a list of nodes, build them in order, and return a list of the built + * nodes. documentFragments are flattened into their contents, so the + * returned list contains no fragments. `isRealGroup` is true if `expression` + * is a real group (no atoms will be added on either side), as opposed to + * a partial group (e.g. one created by \color). `surrounding` is an array + * consisting type of nodes that will be added to the left and right. + */ +var buildExpression = function buildExpression(expression, options, isRealGroup, surrounding) { + if (surrounding === void 0) { + surrounding = [null, null]; + } + + // Parse expressions into `groups`. + var groups = []; + + for (var i = 0; i < expression.length; i++) { + var output = buildGroup(expression[i], options); + + if (output instanceof DocumentFragment) { + var children = output.children; + groups.push.apply(groups, children); + } else { + groups.push(output); + } + } // Combine consecutive domTree.symbolNodes into a single symbolNode. + + + buildCommon.tryCombineChars(groups); // If `expression` is a partial group, let the parent handle spacings + // to avoid processing groups multiple times. + + if (!isRealGroup) { + return groups; + } + + var glueOptions = options; + + if (expression.length === 1) { + var node = expression[0]; + + if (node.type === "sizing") { + glueOptions = options.havingSize(node.size); + } else if (node.type === "styling") { + glueOptions = options.havingStyle(styleMap[node.style]); + } + } // Dummy spans for determining spacings between surrounding atoms. + // If `expression` has no atoms on the left or right, class "leftmost" + // or "rightmost", respectively, is used to indicate it. + + + var dummyPrev = buildHTML_makeSpan([surrounding[0] || "leftmost"], [], options); + var dummyNext = buildHTML_makeSpan([surrounding[1] || "rightmost"], [], options); // TODO: These code assumes that a node's math class is the first element + // of its `classes` array. A later cleanup should ensure this, for + // instance by changing the signature of `makeSpan`. + // Before determining what spaces to insert, perform bin cancellation. + // Binary operators change to ordinary symbols in some contexts. + + var isRoot = isRealGroup === "root"; + traverseNonSpaceNodes(groups, function (node, prev) { + var prevType = prev.classes[0]; + var type = node.classes[0]; + + if (prevType === "mbin" && utils.contains(binRightCanceller, type)) { + prev.classes[0] = "mord"; + } else if (type === "mbin" && utils.contains(binLeftCanceller, prevType)) { + node.classes[0] = "mord"; + } + }, { + node: dummyPrev + }, dummyNext, isRoot); + traverseNonSpaceNodes(groups, function (node, prev) { + var prevType = getTypeOfDomTree(prev); + var type = getTypeOfDomTree(node); // 'mtight' indicates that the node is script or scriptscript style. + + var space = prevType && type ? node.hasClass("mtight") ? tightSpacings[prevType][type] : spacings[prevType][type] : null; + + if (space) { + // Insert glue (spacing) after the `prev`. + return buildCommon.makeGlue(space, glueOptions); + } + }, { + node: dummyPrev + }, dummyNext, isRoot); + return groups; +}; // Depth-first traverse non-space `nodes`, calling `callback` with the current and +// previous node as arguments, optionally returning a node to insert after the +// previous node. `prev` is an object with the previous node and `insertAfter` +// function to insert after it. `next` is a node that will be added to the right. +// Used for bin cancellation and inserting spacings. + +var traverseNonSpaceNodes = function traverseNonSpaceNodes(nodes, callback, prev, next, isRoot) { + if (next) { + // temporarily append the right node, if exists + nodes.push(next); + } + + var i = 0; + + for (; i < nodes.length; i++) { + var node = nodes[i]; + var partialGroup = checkPartialGroup(node); + + if (partialGroup) { + // Recursive DFS + // $FlowFixMe: make nodes a $ReadOnlyArray by returning a new array + traverseNonSpaceNodes(partialGroup.children, callback, prev, null, isRoot); + continue; + } // Ignore explicit spaces (e.g., \;, \,) when determining what implicit + // spacing should go between atoms of different classes + + + var nonspace = !node.hasClass("mspace"); + + if (nonspace) { + var result = callback(node, prev.node); + + if (result) { + if (prev.insertAfter) { + prev.insertAfter(result); + } else { + // insert at front + nodes.unshift(result); + i++; + } + } + } + + if (nonspace) { + prev.node = node; + } else if (isRoot && node.hasClass("newline")) { + prev.node = buildHTML_makeSpan(["leftmost"]); // treat like beginning of line + } + + prev.insertAfter = function (index) { + return function (n) { + nodes.splice(index + 1, 0, n); + i++; + }; + }(i); + } + + if (next) { + nodes.pop(); + } +}; // Check if given node is a partial group, i.e., does not affect spacing around. + + +var checkPartialGroup = function checkPartialGroup(node) { + if (node instanceof DocumentFragment || node instanceof Anchor || node instanceof Span && node.hasClass("enclosing")) { + return node; + } + + return null; +}; // Return the outermost node of a domTree. + + +var getOutermostNode = function getOutermostNode(node, side) { + var partialGroup = checkPartialGroup(node); + + if (partialGroup) { + var children = partialGroup.children; + + if (children.length) { + if (side === "right") { + return getOutermostNode(children[children.length - 1], "right"); + } else if (side === "left") { + return getOutermostNode(children[0], "left"); + } + } + } + + return node; +}; // Return math atom class (mclass) of a domTree. +// If `side` is given, it will get the type of the outermost node at given side. + + +var getTypeOfDomTree = function getTypeOfDomTree(node, side) { + if (!node) { + return null; + } + + if (side) { + node = getOutermostNode(node, side); + } // This makes a lot of assumptions as to where the type of atom + // appears. We should do a better job of enforcing this. + + + return DomEnum[node.classes[0]] || null; +}; +var makeNullDelimiter = function makeNullDelimiter(options, classes) { + var moreClasses = ["nulldelimiter"].concat(options.baseSizingClasses()); + return buildHTML_makeSpan(classes.concat(moreClasses)); +}; +/** + * buildGroup is the function that takes a group and calls the correct groupType + * function for it. It also handles the interaction of size and style changes + * between parents and children. + */ + +var buildGroup = function buildGroup(group, options, baseOptions) { + if (!group) { + return buildHTML_makeSpan(); + } + + if (_htmlGroupBuilders[group.type]) { + // Call the groupBuilders function + // $FlowFixMe + var groupNode = _htmlGroupBuilders[group.type](group, options); // If the size changed between the parent and the current group, account + // for that size difference. + + if (baseOptions && options.size !== baseOptions.size) { + groupNode = buildHTML_makeSpan(options.sizingClasses(baseOptions), [groupNode], options); + var multiplier = options.sizeMultiplier / baseOptions.sizeMultiplier; + groupNode.height *= multiplier; + groupNode.depth *= multiplier; + } + + return groupNode; + } else { + throw new src_ParseError("Got group of unknown type: '" + group.type + "'"); + } +}; +/** + * Combine an array of HTML DOM nodes (e.g., the output of `buildExpression`) + * into an unbreakable HTML node of class .base, with proper struts to + * guarantee correct vertical extent. `buildHTML` calls this repeatedly to + * make up the entire expression as a sequence of unbreakable units. + */ + +function buildHTMLUnbreakable(children, options) { + // Compute height and depth of this chunk. + var body = buildHTML_makeSpan(["base"], children, options); // Add strut, which ensures that the top of the HTML element falls at + // the height of the expression, and the bottom of the HTML element + // falls at the depth of the expression. + + var strut = buildHTML_makeSpan(["strut"]); + strut.style.height = body.height + body.depth + "em"; + strut.style.verticalAlign = -body.depth + "em"; + body.children.unshift(strut); + return body; +} +/** + * Take an entire parse tree, and build it into an appropriate set of HTML + * nodes. + */ + + +function buildHTML(tree, options) { + // Strip off outer tag wrapper for processing below. + var tag = null; + + if (tree.length === 1 && tree[0].type === "tag") { + tag = tree[0].tag; + tree = tree[0].body; + } // Build the expression contained in the tree + + + var expression = buildExpression(tree, options, "root"); + var eqnNum; + + if (expression.length === 2 && expression[1].hasClass("tag")) { + // An environment with automatic equation numbers, e.g. {gather}. + eqnNum = expression.pop(); + } + + var children = []; // Create one base node for each chunk between potential line breaks. + // The TeXBook [p.173] says "A formula will be broken only after a + // relation symbol like $=$ or $<$ or $\rightarrow$, or after a binary + // operation symbol like $+$ or $-$ or $\times$, where the relation or + // binary operation is on the ``outer level'' of the formula (i.e., not + // enclosed in {...} and not part of an \over construction)." + + var parts = []; + + for (var i = 0; i < expression.length; i++) { + parts.push(expression[i]); + + if (expression[i].hasClass("mbin") || expression[i].hasClass("mrel") || expression[i].hasClass("allowbreak")) { + // Put any post-operator glue on same line as operator. + // Watch for \nobreak along the way, and stop at \newline. + var nobreak = false; + + while (i < expression.length - 1 && expression[i + 1].hasClass("mspace") && !expression[i + 1].hasClass("newline")) { + i++; + parts.push(expression[i]); + + if (expression[i].hasClass("nobreak")) { + nobreak = true; + } + } // Don't allow break if \nobreak among the post-operator glue. + + + if (!nobreak) { + children.push(buildHTMLUnbreakable(parts, options)); + parts = []; + } + } else if (expression[i].hasClass("newline")) { + // Write the line except the newline + parts.pop(); + + if (parts.length > 0) { + children.push(buildHTMLUnbreakable(parts, options)); + parts = []; + } // Put the newline at the top level + + + children.push(expression[i]); + } + } + + if (parts.length > 0) { + children.push(buildHTMLUnbreakable(parts, options)); + } // Now, if there was a tag, build it too and append it as a final child. + + + var tagChild; + + if (tag) { + tagChild = buildHTMLUnbreakable(buildExpression(tag, options, true)); + tagChild.classes = ["tag"]; + children.push(tagChild); + } else if (eqnNum) { + children.push(eqnNum); + } + + var htmlNode = buildHTML_makeSpan(["katex-html"], children); + htmlNode.setAttribute("aria-hidden", "true"); // Adjust the strut of the tag to be the maximum height of all children + // (the height of the enclosing htmlNode) for proper vertical alignment. + + if (tagChild) { + var strut = tagChild.children[0]; + strut.style.height = htmlNode.height + htmlNode.depth + "em"; + strut.style.verticalAlign = -htmlNode.depth + "em"; + } + + return htmlNode; +} +;// CONCATENATED MODULE: ./src/mathMLTree.js +/** + * These objects store data about MathML nodes. This is the MathML equivalent + * of the types in domTree.js. Since MathML handles its own rendering, and + * since we're mainly using MathML to improve accessibility, we don't manage + * any of the styling state that the plain DOM nodes do. + * + * The `toNode` and `toMarkup` functions work simlarly to how they do in + * domTree.js, creating namespaced DOM nodes and HTML text markup respectively. + */ + + + +function newDocumentFragment(children) { + return new DocumentFragment(children); +} +/** + * This node represents a general purpose MathML node of any type. The + * constructor requires the type of node to create (for example, `"mo"` or + * `"mspace"`, corresponding to `` and `` tags). + */ + +var MathNode = /*#__PURE__*/function () { + function MathNode(type, children, classes) { + this.type = void 0; + this.attributes = void 0; + this.children = void 0; + this.classes = void 0; + this.type = type; + this.attributes = {}; + this.children = children || []; + this.classes = classes || []; + } + /** + * Sets an attribute on a MathML node. MathML depends on attributes to convey a + * semantic content, so this is used heavily. + */ + + + var _proto = MathNode.prototype; + + _proto.setAttribute = function setAttribute(name, value) { + this.attributes[name] = value; + } + /** + * Gets an attribute on a MathML node. + */ + ; + + _proto.getAttribute = function getAttribute(name) { + return this.attributes[name]; + } + /** + * Converts the math node into a MathML-namespaced DOM element. + */ + ; + + _proto.toNode = function toNode() { + var node = document.createElementNS("http://www.w3.org/1998/Math/MathML", this.type); + + for (var attr in this.attributes) { + if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) { + node.setAttribute(attr, this.attributes[attr]); + } + } + + if (this.classes.length > 0) { + node.className = createClass(this.classes); + } + + for (var i = 0; i < this.children.length; i++) { + node.appendChild(this.children[i].toNode()); + } + + return node; + } + /** + * Converts the math node into an HTML markup string. + */ + ; + + _proto.toMarkup = function toMarkup() { + var markup = "<" + this.type; // Add the attributes + + for (var attr in this.attributes) { + if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) { + markup += " " + attr + "=\""; + markup += utils.escape(this.attributes[attr]); + markup += "\""; + } + } + + if (this.classes.length > 0) { + markup += " class =\"" + utils.escape(createClass(this.classes)) + "\""; + } + + markup += ">"; + + for (var i = 0; i < this.children.length; i++) { + markup += this.children[i].toMarkup(); + } + + markup += ""; + return markup; + } + /** + * Converts the math node into a string, similar to innerText, but escaped. + */ + ; + + _proto.toText = function toText() { + return this.children.map(function (child) { + return child.toText(); + }).join(""); + }; + + return MathNode; +}(); +/** + * This node represents a piece of text. + */ + +var TextNode = /*#__PURE__*/function () { + function TextNode(text) { + this.text = void 0; + this.text = text; + } + /** + * Converts the text node into a DOM text node. + */ + + + var _proto2 = TextNode.prototype; + + _proto2.toNode = function toNode() { + return document.createTextNode(this.text); + } + /** + * Converts the text node into escaped HTML markup + * (representing the text itself). + */ + ; + + _proto2.toMarkup = function toMarkup() { + return utils.escape(this.toText()); + } + /** + * Converts the text node into a string + * (representing the text iteself). + */ + ; + + _proto2.toText = function toText() { + return this.text; + }; + + return TextNode; +}(); +/** + * This node represents a space, but may render as or as text, + * depending on the width. + */ + +var SpaceNode = /*#__PURE__*/function () { + /** + * Create a Space node with width given in CSS ems. + */ + function SpaceNode(width) { + this.width = void 0; + this.character = void 0; + this.width = width; // See https://www.w3.org/TR/2000/WD-MathML2-20000328/chapter6.html + // for a table of space-like characters. We use Unicode + // representations instead of &LongNames; as it's not clear how to + // make the latter via document.createTextNode. + + if (width >= 0.05555 && width <= 0.05556) { + this.character = "\u200A"; //   + } else if (width >= 0.1666 && width <= 0.1667) { + this.character = "\u2009"; //   + } else if (width >= 0.2222 && width <= 0.2223) { + this.character = "\u2005"; //   + } else if (width >= 0.2777 && width <= 0.2778) { + this.character = "\u2005\u200A"; //    + } else if (width >= -0.05556 && width <= -0.05555) { + this.character = "\u200A\u2063"; // ​ + } else if (width >= -0.1667 && width <= -0.1666) { + this.character = "\u2009\u2063"; // ​ + } else if (width >= -0.2223 && width <= -0.2222) { + this.character = "\u205F\u2063"; // ​ + } else if (width >= -0.2778 && width <= -0.2777) { + this.character = "\u2005\u2063"; // ​ + } else { + this.character = null; + } + } + /** + * Converts the math node into a MathML-namespaced DOM element. + */ + + + var _proto3 = SpaceNode.prototype; + + _proto3.toNode = function toNode() { + if (this.character) { + return document.createTextNode(this.character); + } else { + var node = document.createElementNS("http://www.w3.org/1998/Math/MathML", "mspace"); + node.setAttribute("width", this.width + "em"); + return node; + } + } + /** + * Converts the math node into an HTML markup string. + */ + ; + + _proto3.toMarkup = function toMarkup() { + if (this.character) { + return "" + this.character + ""; + } else { + return ""; + } + } + /** + * Converts the math node into a string, similar to innerText. + */ + ; + + _proto3.toText = function toText() { + if (this.character) { + return this.character; + } else { + return " "; + } + }; + + return SpaceNode; +}(); + +/* harmony default export */ var mathMLTree = ({ + MathNode: MathNode, + TextNode: TextNode, + SpaceNode: SpaceNode, + newDocumentFragment: newDocumentFragment +}); +;// CONCATENATED MODULE: ./src/buildMathML.js +/** + * This file converts a parse tree into a cooresponding MathML tree. The main + * entry point is the `buildMathML` function, which takes a parse tree from the + * parser. + */ + + + + + + + + + +/** + * Takes a symbol and converts it into a MathML text node after performing + * optional replacement from symbols.js. + */ +var makeText = function makeText(text, mode, options) { + if (src_symbols[mode][text] && src_symbols[mode][text].replace && text.charCodeAt(0) !== 0xD835 && !(ligatures.hasOwnProperty(text) && options && (options.fontFamily && options.fontFamily.substr(4, 2) === "tt" || options.font && options.font.substr(4, 2) === "tt"))) { + text = src_symbols[mode][text].replace; + } + + return new mathMLTree.TextNode(text); +}; +/** + * Wrap the given array of nodes in an node if needed, i.e., + * unless the array has length 1. Always returns a single node. + */ + +var makeRow = function makeRow(body) { + if (body.length === 1) { + return body[0]; + } else { + return new mathMLTree.MathNode("mrow", body); + } +}; +/** + * Returns the math variant as a string or null if none is required. + */ + +var getVariant = function getVariant(group, options) { + // Handle \text... font specifiers as best we can. + // MathML has a limited list of allowable mathvariant specifiers; see + // https://www.w3.org/TR/MathML3/chapter3.html#presm.commatt + if (options.fontFamily === "texttt") { + return "monospace"; + } else if (options.fontFamily === "textsf") { + if (options.fontShape === "textit" && options.fontWeight === "textbf") { + return "sans-serif-bold-italic"; + } else if (options.fontShape === "textit") { + return "sans-serif-italic"; + } else if (options.fontWeight === "textbf") { + return "bold-sans-serif"; + } else { + return "sans-serif"; + } + } else if (options.fontShape === "textit" && options.fontWeight === "textbf") { + return "bold-italic"; + } else if (options.fontShape === "textit") { + return "italic"; + } else if (options.fontWeight === "textbf") { + return "bold"; + } + + var font = options.font; + + if (!font || font === "mathnormal") { + return null; + } + + var mode = group.mode; + + if (font === "mathit") { + return "italic"; + } else if (font === "boldsymbol") { + return group.type === "textord" ? "bold" : "bold-italic"; + } else if (font === "mathbf") { + return "bold"; + } else if (font === "mathbb") { + return "double-struck"; + } else if (font === "mathfrak") { + return "fraktur"; + } else if (font === "mathscr" || font === "mathcal") { + // MathML makes no distinction between script and caligrahpic + return "script"; + } else if (font === "mathsf") { + return "sans-serif"; + } else if (font === "mathtt") { + return "monospace"; + } + + var text = group.text; + + if (utils.contains(["\\imath", "\\jmath"], text)) { + return null; + } + + if (src_symbols[mode][text] && src_symbols[mode][text].replace) { + text = src_symbols[mode][text].replace; + } + + var fontName = buildCommon.fontMap[font].fontName; + + if (getCharacterMetrics(text, fontName, mode)) { + return buildCommon.fontMap[font].variant; + } + + return null; +}; +/** + * Takes a list of nodes, builds them, and returns a list of the generated + * MathML nodes. Also combine consecutive outputs into a single + * tag. + */ + +var buildMathML_buildExpression = function buildExpression(expression, options, isOrdgroup) { + if (expression.length === 1) { + var group = buildMathML_buildGroup(expression[0], options); + + if (isOrdgroup && group instanceof MathNode && group.type === "mo") { + // When TeX writers want to suppress spacing on an operator, + // they often put the operator by itself inside braces. + group.setAttribute("lspace", "0em"); + group.setAttribute("rspace", "0em"); + } + + return [group]; + } + + var groups = []; + var lastGroup; + + for (var i = 0; i < expression.length; i++) { + var _group = buildMathML_buildGroup(expression[i], options); + + if (_group instanceof MathNode && lastGroup instanceof MathNode) { + // Concatenate adjacent s + if (_group.type === 'mtext' && lastGroup.type === 'mtext' && _group.getAttribute('mathvariant') === lastGroup.getAttribute('mathvariant')) { + var _lastGroup$children; + + (_lastGroup$children = lastGroup.children).push.apply(_lastGroup$children, _group.children); + + continue; // Concatenate adjacent s + } else if (_group.type === 'mn' && lastGroup.type === 'mn') { + var _lastGroup$children2; + + (_lastGroup$children2 = lastGroup.children).push.apply(_lastGroup$children2, _group.children); + + continue; // Concatenate ... followed by . + } else if (_group.type === 'mi' && _group.children.length === 1 && lastGroup.type === 'mn') { + var child = _group.children[0]; + + if (child instanceof TextNode && child.text === '.') { + var _lastGroup$children3; + + (_lastGroup$children3 = lastGroup.children).push.apply(_lastGroup$children3, _group.children); + + continue; + } + } else if (lastGroup.type === 'mi' && lastGroup.children.length === 1) { + var lastChild = lastGroup.children[0]; + + if (lastChild instanceof TextNode && lastChild.text === "\u0338" && (_group.type === 'mo' || _group.type === 'mi' || _group.type === 'mn')) { + var _child = _group.children[0]; + + if (_child instanceof TextNode && _child.text.length > 0) { + // Overlay with combining character long solidus + _child.text = _child.text.slice(0, 1) + "\u0338" + _child.text.slice(1); + groups.pop(); + } + } + } + } + + groups.push(_group); + lastGroup = _group; + } + + return groups; +}; +/** + * Equivalent to buildExpression, but wraps the elements in an + * if there's more than one. Returns a single node instead of an array. + */ + +var buildExpressionRow = function buildExpressionRow(expression, options, isOrdgroup) { + return makeRow(buildMathML_buildExpression(expression, options, isOrdgroup)); +}; +/** + * Takes a group from the parser and calls the appropriate groupBuilders function + * on it to produce a MathML node. + */ + +var buildMathML_buildGroup = function buildGroup(group, options) { + if (!group) { + return new mathMLTree.MathNode("mrow"); + } + + if (_mathmlGroupBuilders[group.type]) { + // Call the groupBuilders function + // $FlowFixMe + var result = _mathmlGroupBuilders[group.type](group, options); // $FlowFixMe + + return result; + } else { + throw new src_ParseError("Got group of unknown type: '" + group.type + "'"); + } +}; +/** + * Takes a full parse tree and settings and builds a MathML representation of + * it. In particular, we put the elements from building the parse tree into a + * tag so we can also include that TeX source as an annotation. + * + * Note that we actually return a domTree element with a `` inside it so + * we can do appropriate styling. + */ + +function buildMathML(tree, texExpression, options, isDisplayMode, forMathmlOnly) { + var expression = buildMathML_buildExpression(tree, options); // TODO: Make a pass thru the MathML similar to buildHTML.traverseNonSpaceNodes + // and add spacing nodes. This is necessary only adjacent to math operators + // like \sin or \lim or to subsup elements that contain math operators. + // MathML takes care of the other spacing issues. + // Wrap up the expression in an mrow so it is presented in the semantics + // tag correctly, unless it's a single or . + + var wrapper; + + if (expression.length === 1 && expression[0] instanceof MathNode && utils.contains(["mrow", "mtable"], expression[0].type)) { + wrapper = expression[0]; + } else { + wrapper = new mathMLTree.MathNode("mrow", expression); + } // Build a TeX annotation of the source + + + var annotation = new mathMLTree.MathNode("annotation", [new mathMLTree.TextNode(texExpression)]); + annotation.setAttribute("encoding", "application/x-tex"); + var semantics = new mathMLTree.MathNode("semantics", [wrapper, annotation]); + var math = new mathMLTree.MathNode("math", [semantics]); + math.setAttribute("xmlns", "http://www.w3.org/1998/Math/MathML"); + + if (isDisplayMode) { + math.setAttribute("display", "block"); + } // You can't style nodes, so we wrap the node in a span. + // NOTE: The span class is not typed to have nodes as children, and + // we don't want to make the children type more generic since the children + // of span are expected to have more fields in `buildHtml` contexts. + + + var wrapperClass = forMathmlOnly ? "katex" : "katex-mathml"; // $FlowFixMe + + return buildCommon.makeSpan([wrapperClass], [math]); +} +;// CONCATENATED MODULE: ./src/buildTree.js + + + + + + + +var optionsFromSettings = function optionsFromSettings(settings) { + return new src_Options({ + style: settings.displayMode ? src_Style.DISPLAY : src_Style.TEXT, + maxSize: settings.maxSize, + minRuleThickness: settings.minRuleThickness + }); +}; + +var displayWrap = function displayWrap(node, settings) { + if (settings.displayMode) { + var classes = ["katex-display"]; + + if (settings.leqno) { + classes.push("leqno"); + } + + if (settings.fleqn) { + classes.push("fleqn"); + } + + node = buildCommon.makeSpan(classes, [node]); + } + + return node; +}; + +var buildTree = function buildTree(tree, expression, settings) { + var options = optionsFromSettings(settings); + var katexNode; + + if (settings.output === "mathml") { + return buildMathML(tree, expression, options, settings.displayMode, true); + } else if (settings.output === "html") { + var htmlNode = buildHTML(tree, options); + katexNode = buildCommon.makeSpan(["katex"], [htmlNode]); + } else { + var mathMLNode = buildMathML(tree, expression, options, settings.displayMode, false); + + var _htmlNode = buildHTML(tree, options); + + katexNode = buildCommon.makeSpan(["katex"], [mathMLNode, _htmlNode]); + } + + return displayWrap(katexNode, settings); +}; +var buildHTMLTree = function buildHTMLTree(tree, expression, settings) { + var options = optionsFromSettings(settings); + var htmlNode = buildHTML(tree, options); + var katexNode = buildCommon.makeSpan(["katex"], [htmlNode]); + return displayWrap(katexNode, settings); +}; +/* harmony default export */ var src_buildTree = ((/* unused pure expression or super */ null && (buildTree))); +;// CONCATENATED MODULE: ./src/stretchy.js +/** + * This file provides support to buildMathML.js and buildHTML.js + * for stretchy wide elements rendered from SVG files + * and other CSS trickery. + */ + + + + +var stretchyCodePoint = { + widehat: "^", + widecheck: "ˇ", + widetilde: "~", + utilde: "~", + overleftarrow: "\u2190", + underleftarrow: "\u2190", + xleftarrow: "\u2190", + overrightarrow: "\u2192", + underrightarrow: "\u2192", + xrightarrow: "\u2192", + underbrace: "\u23DF", + overbrace: "\u23DE", + overgroup: "\u23E0", + undergroup: "\u23E1", + overleftrightarrow: "\u2194", + underleftrightarrow: "\u2194", + xleftrightarrow: "\u2194", + Overrightarrow: "\u21D2", + xRightarrow: "\u21D2", + overleftharpoon: "\u21BC", + xleftharpoonup: "\u21BC", + overrightharpoon: "\u21C0", + xrightharpoonup: "\u21C0", + xLeftarrow: "\u21D0", + xLeftrightarrow: "\u21D4", + xhookleftarrow: "\u21A9", + xhookrightarrow: "\u21AA", + xmapsto: "\u21A6", + xrightharpoondown: "\u21C1", + xleftharpoondown: "\u21BD", + xrightleftharpoons: "\u21CC", + xleftrightharpoons: "\u21CB", + xtwoheadleftarrow: "\u219E", + xtwoheadrightarrow: "\u21A0", + xlongequal: "=", + xtofrom: "\u21C4", + xrightleftarrows: "\u21C4", + xrightequilibrium: "\u21CC", + // Not a perfect match. + xleftequilibrium: "\u21CB", + // None better available. + "\\cdrightarrow": "\u2192", + "\\cdleftarrow": "\u2190", + "\\cdlongequal": "=" +}; + +var mathMLnode = function mathMLnode(label) { + var node = new mathMLTree.MathNode("mo", [new mathMLTree.TextNode(stretchyCodePoint[label.replace(/^\\/, '')])]); + node.setAttribute("stretchy", "true"); + return node; +}; // Many of the KaTeX SVG images have been adapted from glyphs in KaTeX fonts. +// Copyright (c) 2009-2010, Design Science, Inc. () +// Copyright (c) 2014-2017 Khan Academy () +// Licensed under the SIL Open Font License, Version 1.1. +// See \nhttp://scripts.sil.org/OFL +// Very Long SVGs +// Many of the KaTeX stretchy wide elements use a long SVG image and an +// overflow: hidden tactic to achieve a stretchy image while avoiding +// distortion of arrowheads or brace corners. +// The SVG typically contains a very long (400 em) arrow. +// The SVG is in a container span that has overflow: hidden, so the span +// acts like a window that exposes only part of the SVG. +// The SVG always has a longer, thinner aspect ratio than the container span. +// After the SVG fills 100% of the height of the container span, +// there is a long arrow shaft left over. That left-over shaft is not shown. +// Instead, it is sliced off because the span's CSS has overflow: hidden. +// Thus, the reader sees an arrow that matches the subject matter width +// without distortion. +// Some functions, such as \cancel, need to vary their aspect ratio. These +// functions do not get the overflow SVG treatment. +// Second Brush Stroke +// Low resolution monitors struggle to display images in fine detail. +// So browsers apply anti-aliasing. A long straight arrow shaft therefore +// will sometimes appear as if it has a blurred edge. +// To mitigate this, these SVG files contain a second "brush-stroke" on the +// arrow shafts. That is, a second long thin rectangular SVG path has been +// written directly on top of each arrow shaft. This reinforcement causes +// some of the screen pixels to display as black instead of the anti-aliased +// gray pixel that a single path would generate. So we get arrow shafts +// whose edges appear to be sharper. +// In the katexImagesData object just below, the dimensions all +// correspond to path geometry inside the relevant SVG. +// For example, \overrightarrow uses the same arrowhead as glyph U+2192 +// from the KaTeX Main font. The scaling factor is 1000. +// That is, inside the font, that arrowhead is 522 units tall, which +// corresponds to 0.522 em inside the document. + + +var katexImagesData = { + // path(s), minWidth, height, align + overrightarrow: [["rightarrow"], 0.888, 522, "xMaxYMin"], + overleftarrow: [["leftarrow"], 0.888, 522, "xMinYMin"], + underrightarrow: [["rightarrow"], 0.888, 522, "xMaxYMin"], + underleftarrow: [["leftarrow"], 0.888, 522, "xMinYMin"], + xrightarrow: [["rightarrow"], 1.469, 522, "xMaxYMin"], + "\\cdrightarrow": [["rightarrow"], 3.0, 522, "xMaxYMin"], + // CD minwwidth2.5pc + xleftarrow: [["leftarrow"], 1.469, 522, "xMinYMin"], + "\\cdleftarrow": [["leftarrow"], 3.0, 522, "xMinYMin"], + Overrightarrow: [["doublerightarrow"], 0.888, 560, "xMaxYMin"], + xRightarrow: [["doublerightarrow"], 1.526, 560, "xMaxYMin"], + xLeftarrow: [["doubleleftarrow"], 1.526, 560, "xMinYMin"], + overleftharpoon: [["leftharpoon"], 0.888, 522, "xMinYMin"], + xleftharpoonup: [["leftharpoon"], 0.888, 522, "xMinYMin"], + xleftharpoondown: [["leftharpoondown"], 0.888, 522, "xMinYMin"], + overrightharpoon: [["rightharpoon"], 0.888, 522, "xMaxYMin"], + xrightharpoonup: [["rightharpoon"], 0.888, 522, "xMaxYMin"], + xrightharpoondown: [["rightharpoondown"], 0.888, 522, "xMaxYMin"], + xlongequal: [["longequal"], 0.888, 334, "xMinYMin"], + "\\cdlongequal": [["longequal"], 3.0, 334, "xMinYMin"], + xtwoheadleftarrow: [["twoheadleftarrow"], 0.888, 334, "xMinYMin"], + xtwoheadrightarrow: [["twoheadrightarrow"], 0.888, 334, "xMaxYMin"], + overleftrightarrow: [["leftarrow", "rightarrow"], 0.888, 522], + overbrace: [["leftbrace", "midbrace", "rightbrace"], 1.6, 548], + underbrace: [["leftbraceunder", "midbraceunder", "rightbraceunder"], 1.6, 548], + underleftrightarrow: [["leftarrow", "rightarrow"], 0.888, 522], + xleftrightarrow: [["leftarrow", "rightarrow"], 1.75, 522], + xLeftrightarrow: [["doubleleftarrow", "doublerightarrow"], 1.75, 560], + xrightleftharpoons: [["leftharpoondownplus", "rightharpoonplus"], 1.75, 716], + xleftrightharpoons: [["leftharpoonplus", "rightharpoondownplus"], 1.75, 716], + xhookleftarrow: [["leftarrow", "righthook"], 1.08, 522], + xhookrightarrow: [["lefthook", "rightarrow"], 1.08, 522], + overlinesegment: [["leftlinesegment", "rightlinesegment"], 0.888, 522], + underlinesegment: [["leftlinesegment", "rightlinesegment"], 0.888, 522], + overgroup: [["leftgroup", "rightgroup"], 0.888, 342], + undergroup: [["leftgroupunder", "rightgroupunder"], 0.888, 342], + xmapsto: [["leftmapsto", "rightarrow"], 1.5, 522], + xtofrom: [["leftToFrom", "rightToFrom"], 1.75, 528], + // The next three arrows are from the mhchem package. + // In mhchem.sty, min-length is 2.0em. But these arrows might appear in the + // document as \xrightarrow or \xrightleftharpoons. Those have + // min-length = 1.75em, so we set min-length on these next three to match. + xrightleftarrows: [["baraboveleftarrow", "rightarrowabovebar"], 1.75, 901], + xrightequilibrium: [["baraboveshortleftharpoon", "rightharpoonaboveshortbar"], 1.75, 716], + xleftequilibrium: [["shortbaraboveleftharpoon", "shortrightharpoonabovebar"], 1.75, 716] +}; + +var groupLength = function groupLength(arg) { + if (arg.type === "ordgroup") { + return arg.body.length; + } else { + return 1; + } +}; + +var svgSpan = function svgSpan(group, options) { + // Create a span with inline SVG for the element. + function buildSvgSpan_() { + var viewBoxWidth = 400000; // default + + var label = group.label.substr(1); + + if (utils.contains(["widehat", "widecheck", "widetilde", "utilde"], label)) { + // Each type in the `if` statement corresponds to one of the ParseNode + // types below. This narrowing is required to access `grp.base`. + // $FlowFixMe + var grp = group; // There are four SVG images available for each function. + // Choose a taller image when there are more characters. + + var numChars = groupLength(grp.base); + var viewBoxHeight; + var pathName; + + var _height; + + if (numChars > 5) { + if (label === "widehat" || label === "widecheck") { + viewBoxHeight = 420; + viewBoxWidth = 2364; + _height = 0.42; + pathName = label + "4"; + } else { + viewBoxHeight = 312; + viewBoxWidth = 2340; + _height = 0.34; + pathName = "tilde4"; + } + } else { + var imgIndex = [1, 1, 2, 2, 3, 3][numChars]; + + if (label === "widehat" || label === "widecheck") { + viewBoxWidth = [0, 1062, 2364, 2364, 2364][imgIndex]; + viewBoxHeight = [0, 239, 300, 360, 420][imgIndex]; + _height = [0, 0.24, 0.3, 0.3, 0.36, 0.42][imgIndex]; + pathName = label + imgIndex; + } else { + viewBoxWidth = [0, 600, 1033, 2339, 2340][imgIndex]; + viewBoxHeight = [0, 260, 286, 306, 312][imgIndex]; + _height = [0, 0.26, 0.286, 0.3, 0.306, 0.34][imgIndex]; + pathName = "tilde" + imgIndex; + } + } + + var path = new PathNode(pathName); + var svgNode = new SvgNode([path], { + "width": "100%", + "height": _height + "em", + "viewBox": "0 0 " + viewBoxWidth + " " + viewBoxHeight, + "preserveAspectRatio": "none" + }); + return { + span: buildCommon.makeSvgSpan([], [svgNode], options), + minWidth: 0, + height: _height + }; + } else { + var spans = []; + var data = katexImagesData[label]; + var paths = data[0], + _minWidth = data[1], + _viewBoxHeight = data[2]; + + var _height2 = _viewBoxHeight / 1000; + + var numSvgChildren = paths.length; + var widthClasses; + var aligns; + + if (numSvgChildren === 1) { + // $FlowFixMe: All these cases must be of the 4-tuple type. + var align1 = data[3]; + widthClasses = ["hide-tail"]; + aligns = [align1]; + } else if (numSvgChildren === 2) { + widthClasses = ["halfarrow-left", "halfarrow-right"]; + aligns = ["xMinYMin", "xMaxYMin"]; + } else if (numSvgChildren === 3) { + widthClasses = ["brace-left", "brace-center", "brace-right"]; + aligns = ["xMinYMin", "xMidYMin", "xMaxYMin"]; + } else { + throw new Error("Correct katexImagesData or update code here to support\n " + numSvgChildren + " children."); + } + + for (var i = 0; i < numSvgChildren; i++) { + var _path = new PathNode(paths[i]); + + var _svgNode = new SvgNode([_path], { + "width": "400em", + "height": _height2 + "em", + "viewBox": "0 0 " + viewBoxWidth + " " + _viewBoxHeight, + "preserveAspectRatio": aligns[i] + " slice" + }); + + var _span = buildCommon.makeSvgSpan([widthClasses[i]], [_svgNode], options); + + if (numSvgChildren === 1) { + return { + span: _span, + minWidth: _minWidth, + height: _height2 + }; + } else { + _span.style.height = _height2 + "em"; + spans.push(_span); + } + } + + return { + span: buildCommon.makeSpan(["stretchy"], spans, options), + minWidth: _minWidth, + height: _height2 + }; + } + } // buildSvgSpan_() + + + var _buildSvgSpan_ = buildSvgSpan_(), + span = _buildSvgSpan_.span, + minWidth = _buildSvgSpan_.minWidth, + height = _buildSvgSpan_.height; // Note that we are returning span.depth = 0. + // Any adjustments relative to the baseline must be done in buildHTML. + + + span.height = height; + span.style.height = height + "em"; + + if (minWidth > 0) { + span.style.minWidth = minWidth + "em"; + } + + return span; +}; + +var encloseSpan = function encloseSpan(inner, label, topPad, bottomPad, options) { + // Return an image span for \cancel, \bcancel, \xcancel, \fbox, or \angl + var img; + var totalHeight = inner.height + inner.depth + topPad + bottomPad; + + if (/fbox|color|angl/.test(label)) { + img = buildCommon.makeSpan(["stretchy", label], [], options); + + if (label === "fbox") { + var color = options.color && options.getColor(); + + if (color) { + img.style.borderColor = color; + } + } + } else { + // \cancel, \bcancel, or \xcancel + // Since \cancel's SVG is inline and it omits the viewBox attribute, + // its stroke-width will not vary with span area. + var lines = []; + + if (/^[bx]cancel$/.test(label)) { + lines.push(new LineNode({ + "x1": "0", + "y1": "0", + "x2": "100%", + "y2": "100%", + "stroke-width": "0.046em" + })); + } + + if (/^x?cancel$/.test(label)) { + lines.push(new LineNode({ + "x1": "0", + "y1": "100%", + "x2": "100%", + "y2": "0", + "stroke-width": "0.046em" + })); + } + + var svgNode = new SvgNode(lines, { + "width": "100%", + "height": totalHeight + "em" + }); + img = buildCommon.makeSvgSpan([], [svgNode], options); + } + + img.height = totalHeight; + img.style.height = totalHeight + "em"; + return img; +}; + +/* harmony default export */ var stretchy = ({ + encloseSpan: encloseSpan, + mathMLnode: mathMLnode, + svgSpan: svgSpan +}); +;// CONCATENATED MODULE: ./src/parseNode.js + + +/** + * Asserts that the node is of the given type and returns it with stricter + * typing. Throws if the node's type does not match. + */ +function assertNodeType(node, type) { + if (!node || node.type !== type) { + throw new Error("Expected node of type " + type + ", but got " + (node ? "node of type " + node.type : String(node))); + } // $FlowFixMe, >=0.125 + + + return node; +} +/** + * Returns the node more strictly typed iff it is of the given type. Otherwise, + * returns null. + */ + +function assertSymbolNodeType(node) { + var typedNode = checkSymbolNodeType(node); + + if (!typedNode) { + throw new Error("Expected node of symbol group type, but got " + (node ? "node of type " + node.type : String(node))); + } + + return typedNode; +} +/** + * Returns the node more strictly typed iff it is of the given type. Otherwise, + * returns null. + */ + +function checkSymbolNodeType(node) { + if (node && (node.type === "atom" || NON_ATOMS.hasOwnProperty(node.type))) { + // $FlowFixMe + return node; + } + + return null; +} +;// CONCATENATED MODULE: ./src/functions/accent.js + + + + + + + + + +// NOTE: Unlike most `htmlBuilder`s, this one handles not only "accent", but +// also "supsub" since an accent can affect super/subscripting. +var htmlBuilder = function htmlBuilder(grp, options) { + // Accents are handled in the TeXbook pg. 443, rule 12. + var base; + var group; + var supSubGroup; + + if (grp && grp.type === "supsub") { + // If our base is a character box, and we have superscripts and + // subscripts, the supsub will defer to us. In particular, we want + // to attach the superscripts and subscripts to the inner body (so + // that the position of the superscripts and subscripts won't be + // affected by the height of the accent). We accomplish this by + // sticking the base of the accent into the base of the supsub, and + // rendering that, while keeping track of where the accent is. + // The real accent group is the base of the supsub group + group = assertNodeType(grp.base, "accent"); // The character box is the base of the accent group + + base = group.base; // Stick the character box into the base of the supsub group + + grp.base = base; // Rerender the supsub group with its new base, and store that + // result. + + supSubGroup = assertSpan(buildGroup(grp, options)); // reset original base + + grp.base = group; + } else { + group = assertNodeType(grp, "accent"); + base = group.base; + } // Build the base group + + + var body = buildGroup(base, options.havingCrampedStyle()); // Does the accent need to shift for the skew of a character? + + var mustShift = group.isShifty && utils.isCharacterBox(base); // Calculate the skew of the accent. This is based on the line "If the + // nucleus is not a single character, let s = 0; otherwise set s to the + // kern amount for the nucleus followed by the \skewchar of its font." + // Note that our skew metrics are just the kern between each character + // and the skewchar. + + var skew = 0; + + if (mustShift) { + // If the base is a character box, then we want the skew of the + // innermost character. To do that, we find the innermost character: + var baseChar = utils.getBaseElem(base); // Then, we render its group to get the symbol inside it + + var baseGroup = buildGroup(baseChar, options.havingCrampedStyle()); // Finally, we pull the skew off of the symbol. + + skew = assertSymbolDomNode(baseGroup).skew; // Note that we now throw away baseGroup, because the layers we + // removed with getBaseElem might contain things like \color which + // we can't get rid of. + // TODO(emily): Find a better way to get the skew + } + + var accentBelow = group.label === "\\c"; // calculate the amount of space between the body and the accent + + var clearance = accentBelow ? body.height + body.depth : Math.min(body.height, options.fontMetrics().xHeight); // Build the accent + + var accentBody; + + if (!group.isStretchy) { + var accent; + var width; + + if (group.label === "\\vec") { + // Before version 0.9, \vec used the combining font glyph U+20D7. + // But browsers, especially Safari, are not consistent in how they + // render combining characters when not preceded by a character. + // So now we use an SVG. + // If Safari reforms, we should consider reverting to the glyph. + accent = buildCommon.staticSvg("vec", options); + width = buildCommon.svgData.vec[1]; + } else { + accent = buildCommon.makeOrd({ + mode: group.mode, + text: group.label + }, options, "textord"); + accent = assertSymbolDomNode(accent); // Remove the italic correction of the accent, because it only serves to + // shift the accent over to a place we don't want. + + accent.italic = 0; + width = accent.width; + + if (accentBelow) { + clearance += accent.depth; + } + } + + accentBody = buildCommon.makeSpan(["accent-body"], [accent]); // "Full" accents expand the width of the resulting symbol to be + // at least the width of the accent, and overlap directly onto the + // character without any vertical offset. + + var accentFull = group.label === "\\textcircled"; + + if (accentFull) { + accentBody.classes.push('accent-full'); + clearance = body.height; + } // Shift the accent over by the skew. + + + var left = skew; // CSS defines `.katex .accent .accent-body:not(.accent-full) { width: 0 }` + // so that the accent doesn't contribute to the bounding box. + // We need to shift the character by its width (effectively half + // its width) to compensate. + + if (!accentFull) { + left -= width / 2; + } + + accentBody.style.left = left + "em"; // \textcircled uses the \bigcirc glyph, so it needs some + // vertical adjustment to match LaTeX. + + if (group.label === "\\textcircled") { + accentBody.style.top = ".2em"; + } + + accentBody = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: body + }, { + type: "kern", + size: -clearance + }, { + type: "elem", + elem: accentBody + }] + }, options); + } else { + accentBody = stretchy.svgSpan(group, options); + accentBody = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: body + }, { + type: "elem", + elem: accentBody, + wrapperClasses: ["svg-align"], + wrapperStyle: skew > 0 ? { + width: "calc(100% - " + 2 * skew + "em)", + marginLeft: 2 * skew + "em" + } : undefined + }] + }, options); + } + + var accentWrap = buildCommon.makeSpan(["mord", "accent"], [accentBody], options); + + if (supSubGroup) { + // Here, we replace the "base" child of the supsub with our newly + // generated accent. + supSubGroup.children[0] = accentWrap; // Since we don't rerun the height calculation after replacing the + // accent, we manually recalculate height. + + supSubGroup.height = Math.max(accentWrap.height, supSubGroup.height); // Accents should always be ords, even when their innards are not. + + supSubGroup.classes[0] = "mord"; + return supSubGroup; + } else { + return accentWrap; + } +}; + +var mathmlBuilder = function mathmlBuilder(group, options) { + var accentNode = group.isStretchy ? stretchy.mathMLnode(group.label) : new mathMLTree.MathNode("mo", [makeText(group.label, group.mode)]); + var node = new mathMLTree.MathNode("mover", [buildMathML_buildGroup(group.base, options), accentNode]); + node.setAttribute("accent", "true"); + return node; +}; + +var NON_STRETCHY_ACCENT_REGEX = new RegExp(["\\acute", "\\grave", "\\ddot", "\\tilde", "\\bar", "\\breve", "\\check", "\\hat", "\\vec", "\\dot", "\\mathring"].map(function (accent) { + return "\\" + accent; +}).join("|")); // Accents + +defineFunction({ + type: "accent", + names: ["\\acute", "\\grave", "\\ddot", "\\tilde", "\\bar", "\\breve", "\\check", "\\hat", "\\vec", "\\dot", "\\mathring", "\\widecheck", "\\widehat", "\\widetilde", "\\overrightarrow", "\\overleftarrow", "\\Overrightarrow", "\\overleftrightarrow", "\\overgroup", "\\overlinesegment", "\\overleftharpoon", "\\overrightharpoon"], + props: { + numArgs: 1 + }, + handler: function handler(context, args) { + var base = normalizeArgument(args[0]); + var isStretchy = !NON_STRETCHY_ACCENT_REGEX.test(context.funcName); + var isShifty = !isStretchy || context.funcName === "\\widehat" || context.funcName === "\\widetilde" || context.funcName === "\\widecheck"; + return { + type: "accent", + mode: context.parser.mode, + label: context.funcName, + isStretchy: isStretchy, + isShifty: isShifty, + base: base + }; + }, + htmlBuilder: htmlBuilder, + mathmlBuilder: mathmlBuilder +}); // Text-mode accents + +defineFunction({ + type: "accent", + names: ["\\'", "\\`", "\\^", "\\~", "\\=", "\\u", "\\.", '\\"', "\\c", "\\r", "\\H", "\\v", "\\textcircled"], + props: { + numArgs: 1, + allowedInText: true, + allowedInMath: true, + // unless in strict mode + argTypes: ["primitive"] + }, + handler: function handler(context, args) { + var base = args[0]; + var mode = context.parser.mode; + + if (mode === "math") { + context.parser.settings.reportNonstrict("mathVsTextAccents", "LaTeX's accent " + context.funcName + " works only in text mode"); + mode = "text"; + } + + return { + type: "accent", + mode: mode, + label: context.funcName, + isStretchy: false, + isShifty: true, + base: base + }; + }, + htmlBuilder: htmlBuilder, + mathmlBuilder: mathmlBuilder +}); +;// CONCATENATED MODULE: ./src/functions/accentunder.js +// Horizontal overlap functions + + + + + + +defineFunction({ + type: "accentUnder", + names: ["\\underleftarrow", "\\underrightarrow", "\\underleftrightarrow", "\\undergroup", "\\underlinesegment", "\\utilde"], + props: { + numArgs: 1 + }, + handler: function handler(_ref, args) { + var parser = _ref.parser, + funcName = _ref.funcName; + var base = args[0]; + return { + type: "accentUnder", + mode: parser.mode, + label: funcName, + base: base + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + // Treat under accents much like underlines. + var innerGroup = buildGroup(group.base, options); + var accentBody = stretchy.svgSpan(group, options); + var kern = group.label === "\\utilde" ? 0.12 : 0; // Generate the vlist, with the appropriate kerns + + var vlist = buildCommon.makeVList({ + positionType: "top", + positionData: innerGroup.height, + children: [{ + type: "elem", + elem: accentBody, + wrapperClasses: ["svg-align"] + }, { + type: "kern", + size: kern + }, { + type: "elem", + elem: innerGroup + }] + }, options); + return buildCommon.makeSpan(["mord", "accentunder"], [vlist], options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var accentNode = stretchy.mathMLnode(group.label); + var node = new mathMLTree.MathNode("munder", [buildMathML_buildGroup(group.base, options), accentNode]); + node.setAttribute("accentunder", "true"); + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/arrow.js + + + + + + + +// Helper function +var paddedNode = function paddedNode(group) { + var node = new mathMLTree.MathNode("mpadded", group ? [group] : []); + node.setAttribute("width", "+0.6em"); + node.setAttribute("lspace", "0.3em"); + return node; +}; // Stretchy arrows with an optional argument + + +defineFunction({ + type: "xArrow", + names: ["\\xleftarrow", "\\xrightarrow", "\\xLeftarrow", "\\xRightarrow", "\\xleftrightarrow", "\\xLeftrightarrow", "\\xhookleftarrow", "\\xhookrightarrow", "\\xmapsto", "\\xrightharpoondown", "\\xrightharpoonup", "\\xleftharpoondown", "\\xleftharpoonup", "\\xrightleftharpoons", "\\xleftrightharpoons", "\\xlongequal", "\\xtwoheadrightarrow", "\\xtwoheadleftarrow", "\\xtofrom", // The next 3 functions are here to support the mhchem extension. + // Direct use of these functions is discouraged and may break someday. + "\\xrightleftarrows", "\\xrightequilibrium", "\\xleftequilibrium", // The next 3 functions are here only to support the {CD} environment. + "\\\\cdrightarrow", "\\\\cdleftarrow", "\\\\cdlongequal"], + props: { + numArgs: 1, + numOptionalArgs: 1 + }, + handler: function handler(_ref, args, optArgs) { + var parser = _ref.parser, + funcName = _ref.funcName; + return { + type: "xArrow", + mode: parser.mode, + label: funcName, + body: args[0], + below: optArgs[0] + }; + }, + // Flow is unable to correctly infer the type of `group`, even though it's + // unamibiguously determined from the passed-in `type` above. + htmlBuilder: function htmlBuilder(group, options) { + var style = options.style; // Build the argument groups in the appropriate style. + // Ref: amsmath.dtx: \hbox{$\scriptstyle\mkern#3mu{#6}\mkern#4mu$}% + // Some groups can return document fragments. Handle those by wrapping + // them in a span. + + var newOptions = options.havingStyle(style.sup()); + var upperGroup = buildCommon.wrapFragment(buildGroup(group.body, newOptions, options), options); + var arrowPrefix = group.label.slice(0, 2) === "\\x" ? "x" : "cd"; + upperGroup.classes.push(arrowPrefix + "-arrow-pad"); + var lowerGroup; + + if (group.below) { + // Build the lower group + newOptions = options.havingStyle(style.sub()); + lowerGroup = buildCommon.wrapFragment(buildGroup(group.below, newOptions, options), options); + lowerGroup.classes.push(arrowPrefix + "-arrow-pad"); + } + + var arrowBody = stretchy.svgSpan(group, options); // Re shift: Note that stretchy.svgSpan returned arrowBody.depth = 0. + // The point we want on the math axis is at 0.5 * arrowBody.height. + + var arrowShift = -options.fontMetrics().axisHeight + 0.5 * arrowBody.height; // 2 mu kern. Ref: amsmath.dtx: #7\if0#2\else\mkern#2mu\fi + + var upperShift = -options.fontMetrics().axisHeight - 0.5 * arrowBody.height - 0.111; // 0.111 em = 2 mu + + if (upperGroup.depth > 0.25 || group.label === "\\xleftequilibrium") { + upperShift -= upperGroup.depth; // shift up if depth encroaches + } // Generate the vlist + + + var vlist; + + if (lowerGroup) { + var lowerShift = -options.fontMetrics().axisHeight + lowerGroup.height + 0.5 * arrowBody.height + 0.111; + vlist = buildCommon.makeVList({ + positionType: "individualShift", + children: [{ + type: "elem", + elem: upperGroup, + shift: upperShift + }, { + type: "elem", + elem: arrowBody, + shift: arrowShift + }, { + type: "elem", + elem: lowerGroup, + shift: lowerShift + }] + }, options); + } else { + vlist = buildCommon.makeVList({ + positionType: "individualShift", + children: [{ + type: "elem", + elem: upperGroup, + shift: upperShift + }, { + type: "elem", + elem: arrowBody, + shift: arrowShift + }] + }, options); + } // $FlowFixMe: Replace this with passing "svg-align" into makeVList. + + + vlist.children[0].children[0].children[1].classes.push("svg-align"); + return buildCommon.makeSpan(["mrel", "x-arrow"], [vlist], options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var arrowNode = stretchy.mathMLnode(group.label); + arrowNode.setAttribute("minsize", group.label.charAt(0) === "x" ? "1.75em" : "3.0em"); + var node; + + if (group.body) { + var upperNode = paddedNode(buildMathML_buildGroup(group.body, options)); + + if (group.below) { + var lowerNode = paddedNode(buildMathML_buildGroup(group.below, options)); + node = new mathMLTree.MathNode("munderover", [arrowNode, lowerNode, upperNode]); + } else { + node = new mathMLTree.MathNode("mover", [arrowNode, upperNode]); + } + } else if (group.below) { + var _lowerNode = paddedNode(buildMathML_buildGroup(group.below, options)); + + node = new mathMLTree.MathNode("munder", [arrowNode, _lowerNode]); + } else { + // This should never happen. + // Parser.js throws an error if there is no argument. + node = paddedNode(); + node = new mathMLTree.MathNode("mover", [arrowNode, node]); + } + + return node; + } +}); +;// CONCATENATED MODULE: ./src/environments/cd.js + + + + + + + +var cdArrowFunctionName = { + ">": "\\\\cdrightarrow", + "<": "\\\\cdleftarrow", + "=": "\\\\cdlongequal", + "A": "\\uparrow", + "V": "\\downarrow", + "|": "\\Vert", + ".": "no arrow" +}; + +var newCell = function newCell() { + // Create an empty cell, to be filled below with parse nodes. + // The parseTree from this module must be constructed like the + // one created by parseArray(), so an empty CD cell must + // be a ParseNode<"styling">. And CD is always displaystyle. + // So these values are fixed and flow can do implicit typing. + return { + type: "styling", + body: [], + mode: "math", + style: "display" + }; +}; + +var isStartOfArrow = function isStartOfArrow(node) { + return node.type === "textord" && node.text === "@"; +}; + +var isLabelEnd = function isLabelEnd(node, endChar) { + return (node.type === "mathord" || node.type === "atom") && node.text === endChar; +}; + +function cdArrow(arrowChar, labels, parser) { + // Return a parse tree of an arrow and its labels. + // This acts in a way similar to a macro expansion. + var funcName = cdArrowFunctionName[arrowChar]; + + switch (funcName) { + case "\\\\cdrightarrow": + case "\\\\cdleftarrow": + return parser.callFunction(funcName, [labels[0]], [labels[1]]); + + case "\\uparrow": + case "\\downarrow": + { + var leftLabel = parser.callFunction("\\\\cdleft", [labels[0]], []); + var bareArrow = { + type: "atom", + text: funcName, + mode: "math", + family: "rel" + }; + var sizedArrow = parser.callFunction("\\Big", [bareArrow], []); + var rightLabel = parser.callFunction("\\\\cdright", [labels[1]], []); + var arrowGroup = { + type: "ordgroup", + mode: "math", + body: [leftLabel, sizedArrow, rightLabel] + }; + return parser.callFunction("\\\\cdparent", [arrowGroup], []); + } + + case "\\\\cdlongequal": + return parser.callFunction("\\\\cdlongequal", [], []); + + case "\\Vert": + { + var arrow = { + type: "textord", + text: "\\Vert", + mode: "math" + }; + return parser.callFunction("\\Big", [arrow], []); + } + + default: + return { + type: "textord", + text: " ", + mode: "math" + }; + } +} + +function parseCD(parser) { + // Get the array's parse nodes with \\ temporarily mapped to \cr. + var parsedRows = []; + parser.gullet.beginGroup(); + parser.gullet.macros.set("\\cr", "\\\\\\relax"); + parser.gullet.beginGroup(); + + while (true) { + // eslint-disable-line no-constant-condition + // Get the parse nodes for the next row. + parsedRows.push(parser.parseExpression(false, "\\\\")); + parser.gullet.endGroup(); + parser.gullet.beginGroup(); + var next = parser.fetch().text; + + if (next === "&" || next === "\\\\") { + parser.consume(); + } else if (next === "\\end") { + if (parsedRows[parsedRows.length - 1].length === 0) { + parsedRows.pop(); // final row ended in \\ + } + + break; + } else { + throw new src_ParseError("Expected \\\\ or \\cr or \\end", parser.nextToken); + } + } + + var row = []; + var body = [row]; // Loop thru the parse nodes. Collect them into cells and arrows. + + for (var i = 0; i < parsedRows.length; i++) { + // Start a new row. + var rowNodes = parsedRows[i]; // Create the first cell. + + var cell = newCell(); + + for (var j = 0; j < rowNodes.length; j++) { + if (!isStartOfArrow(rowNodes[j])) { + // If a parseNode is not an arrow, it goes into a cell. + cell.body.push(rowNodes[j]); + } else { + // Parse node j is an "@", the start of an arrow. + // Before starting on the arrow, push the cell into `row`. + row.push(cell); // Now collect parseNodes into an arrow. + // The character after "@" defines the arrow type. + + j += 1; + var arrowChar = assertSymbolNodeType(rowNodes[j]).text; // Create two empty label nodes. We may or may not use them. + + var labels = new Array(2); + labels[0] = { + type: "ordgroup", + mode: "math", + body: [] + }; + labels[1] = { + type: "ordgroup", + mode: "math", + body: [] + }; // Process the arrow. + + if ("=|.".indexOf(arrowChar) > -1) {// Three "arrows", ``@=`, `@|`, and `@.`, do not take labels. + // Do nothing here. + } else if ("<>AV".indexOf(arrowChar) > -1) { + // Four arrows, `@>>>`, `@<<<`, `@AAA`, and `@VVV`, each take + // two optional labels. E.g. the right-point arrow syntax is + // really: @>{optional label}>{optional label}> + // Collect parseNodes into labels. + for (var labelNum = 0; labelNum < 2; labelNum++) { + var inLabel = true; + + for (var k = j + 1; k < rowNodes.length; k++) { + if (isLabelEnd(rowNodes[k], arrowChar)) { + inLabel = false; + j = k; + break; + } + + if (isStartOfArrow(rowNodes[k])) { + throw new src_ParseError("Missing a " + arrowChar + " character to complete a CD arrow.", rowNodes[k]); + } + + labels[labelNum].body.push(rowNodes[k]); + } + + if (inLabel) { + // isLabelEnd never returned a true. + throw new src_ParseError("Missing a " + arrowChar + " character to complete a CD arrow.", rowNodes[j]); + } + } + } else { + throw new src_ParseError("Expected one of \"<>AV=|.\" after @", rowNodes[j]); + } // Now join the arrow to its labels. + + + var arrow = cdArrow(arrowChar, labels, parser); // Wrap the arrow in ParseNode<"styling">. + // This is done to match parseArray() behavior. + + var wrappedArrow = { + type: "styling", + body: [arrow], + mode: "math", + style: "display" // CD is always displaystyle. + + }; + row.push(wrappedArrow); // In CD's syntax, cells are implicit. That is, everything that + // is not an arrow gets collected into a cell. So create an empty + // cell now. It will collect upcoming parseNodes. + + cell = newCell(); + } + } + + if (i % 2 === 0) { + // Even-numbered rows consist of: cell, arrow, cell, arrow, ... cell + // The last cell is not yet pushed into `row`, so: + row.push(cell); + } else { + // Odd-numbered rows consist of: vert arrow, empty cell, ... vert arrow + // Remove the empty cell that was placed at the beginning of `row`. + row.shift(); + } + + row = []; + body.push(row); + } // End row group + + + parser.gullet.endGroup(); // End array group defining \\ + + parser.gullet.endGroup(); // define column separation. + + var cols = new Array(body[0].length).fill({ + type: "align", + align: "c", + pregap: 0.25, + // CD package sets \enskip between columns. + postgap: 0.25 // So pre and post each get half an \enskip, i.e. 0.25em. + + }); + return { + type: "array", + mode: "math", + body: body, + arraystretch: 1, + addJot: true, + rowGaps: [null], + cols: cols, + colSeparationType: "CD", + hLinesBeforeRow: new Array(body.length + 1).fill([]) + }; +} // The functions below are not available for general use. +// They are here only for internal use by the {CD} environment in placing labels +// next to vertical arrows. +// We don't need any such functions for horizontal arrows because we can reuse +// the functionality that already exists for extensible arrows. + +defineFunction({ + type: "cdlabel", + names: ["\\\\cdleft", "\\\\cdright"], + props: { + numArgs: 1 + }, + handler: function handler(_ref, args) { + var parser = _ref.parser, + funcName = _ref.funcName; + return { + type: "cdlabel", + mode: parser.mode, + side: funcName.slice(4), + label: args[0] + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var newOptions = options.havingStyle(options.style.sup()); + var label = buildCommon.wrapFragment(buildGroup(group.label, newOptions, options), options); + label.classes.push("cd-label-" + group.side); + label.style.bottom = 0.8 - label.depth + "em"; // Zero out label height & depth, so vertical align of arrow is set + // by the arrow height, not by the label. + + label.height = 0; + label.depth = 0; + return label; + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var label = new mathMLTree.MathNode("mrow", [buildMathML_buildGroup(group.label, options)]); + label = new mathMLTree.MathNode("mpadded", [label]); + label.setAttribute("width", "0"); + + if (group.side === "left") { + label.setAttribute("lspace", "-1width"); + } // We have to guess at vertical alignment. We know the arrow is 1.8em tall, + // But we don't know the height or depth of the label. + + + label.setAttribute("voffset", "0.7em"); + label = new mathMLTree.MathNode("mstyle", [label]); + label.setAttribute("displaystyle", "false"); + label.setAttribute("scriptlevel", "1"); + return label; + } +}); +defineFunction({ + type: "cdlabelparent", + names: ["\\\\cdparent"], + props: { + numArgs: 1 + }, + handler: function handler(_ref2, args) { + var parser = _ref2.parser; + return { + type: "cdlabelparent", + mode: parser.mode, + fragment: args[0] + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + // Wrap the vertical arrow and its labels. + // The parent gets position: relative. The child gets position: absolute. + // So CSS can locate the label correctly. + var parent = buildCommon.wrapFragment(buildGroup(group.fragment, options), options); + parent.classes.push("cd-vert-arrow"); + return parent; + }, + mathmlBuilder: function mathmlBuilder(group, options) { + return new mathMLTree.MathNode("mrow", [buildMathML_buildGroup(group.fragment, options)]); + } +}); +;// CONCATENATED MODULE: ./src/functions/char.js + + + // \@char is an internal function that takes a grouped decimal argument like +// {123} and converts into symbol with code 123. It is used by the *macro* +// \char defined in macros.js. + +defineFunction({ + type: "textord", + names: ["\\@char"], + props: { + numArgs: 1, + allowedInText: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser; + var arg = assertNodeType(args[0], "ordgroup"); + var group = arg.body; + var number = ""; + + for (var i = 0; i < group.length; i++) { + var node = assertNodeType(group[i], "textord"); + number += node.text; + } + + var code = parseInt(number); + var text; + + if (isNaN(code)) { + throw new src_ParseError("\\@char has non-numeric argument " + number); // If we drop IE support, the following code could be replaced with + // text = String.fromCodePoint(code) + } else if (code < 0 || code >= 0x10ffff) { + throw new src_ParseError("\\@char with invalid code point " + number); + } else if (code <= 0xffff) { + text = String.fromCharCode(code); + } else { + // Astral code point; split into surrogate halves + code -= 0x10000; + text = String.fromCharCode((code >> 10) + 0xd800, (code & 0x3ff) + 0xdc00); + } + + return { + type: "textord", + mode: parser.mode, + text: text + }; + } +}); +;// CONCATENATED MODULE: ./src/functions/color.js + + + + + + + +var color_htmlBuilder = function htmlBuilder(group, options) { + var elements = buildExpression(group.body, options.withColor(group.color), false); // \color isn't supposed to affect the type of the elements it contains. + // To accomplish this, we wrap the results in a fragment, so the inner + // elements will be able to directly interact with their neighbors. For + // example, `\color{red}{2 +} 3` has the same spacing as `2 + 3` + + return buildCommon.makeFragment(elements); +}; + +var color_mathmlBuilder = function mathmlBuilder(group, options) { + var inner = buildMathML_buildExpression(group.body, options.withColor(group.color)); + var node = new mathMLTree.MathNode("mstyle", inner); + node.setAttribute("mathcolor", group.color); + return node; +}; + +defineFunction({ + type: "color", + names: ["\\textcolor"], + props: { + numArgs: 2, + allowedInText: true, + argTypes: ["color", "original"] + }, + handler: function handler(_ref, args) { + var parser = _ref.parser; + var color = assertNodeType(args[0], "color-token").color; + var body = args[1]; + return { + type: "color", + mode: parser.mode, + color: color, + body: ordargument(body) + }; + }, + htmlBuilder: color_htmlBuilder, + mathmlBuilder: color_mathmlBuilder +}); +defineFunction({ + type: "color", + names: ["\\color"], + props: { + numArgs: 1, + allowedInText: true, + argTypes: ["color"] + }, + handler: function handler(_ref2, args) { + var parser = _ref2.parser, + breakOnTokenText = _ref2.breakOnTokenText; + var color = assertNodeType(args[0], "color-token").color; // Set macro \current@color in current namespace to store the current + // color, mimicking the behavior of color.sty. + // This is currently used just to correctly color a \right + // that follows a \color command. + + parser.gullet.macros.set("\\current@color", color); // Parse out the implicit body that should be colored. + + var body = parser.parseExpression(true, breakOnTokenText); + return { + type: "color", + mode: parser.mode, + color: color, + body: body + }; + }, + htmlBuilder: color_htmlBuilder, + mathmlBuilder: color_mathmlBuilder +}); +;// CONCATENATED MODULE: ./src/functions/cr.js +// Row breaks within tabular environments, and line breaks at top level + + + + + // \DeclareRobustCommand\\{...\@xnewline} + +defineFunction({ + type: "cr", + names: ["\\\\"], + props: { + numArgs: 0, + numOptionalArgs: 1, + argTypes: ["size"], + allowedInText: true + }, + handler: function handler(_ref, args, optArgs) { + var parser = _ref.parser; + var size = optArgs[0]; + var newLine = !parser.settings.displayMode || !parser.settings.useStrictBehavior("newLineInDisplayMode", "In LaTeX, \\\\ or \\newline " + "does nothing in display mode"); + return { + type: "cr", + mode: parser.mode, + newLine: newLine, + size: size && assertNodeType(size, "size").value + }; + }, + // The following builders are called only at the top level, + // not within tabular/array environments. + htmlBuilder: function htmlBuilder(group, options) { + var span = buildCommon.makeSpan(["mspace"], [], options); + + if (group.newLine) { + span.classes.push("newline"); + + if (group.size) { + span.style.marginTop = calculateSize(group.size, options) + "em"; + } + } + + return span; + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var node = new mathMLTree.MathNode("mspace"); + + if (group.newLine) { + node.setAttribute("linebreak", "newline"); + + if (group.size) { + node.setAttribute("height", calculateSize(group.size, options) + "em"); + } + } + + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/def.js + + + +var globalMap = { + "\\global": "\\global", + "\\long": "\\\\globallong", + "\\\\globallong": "\\\\globallong", + "\\def": "\\gdef", + "\\gdef": "\\gdef", + "\\edef": "\\xdef", + "\\xdef": "\\xdef", + "\\let": "\\\\globallet", + "\\futurelet": "\\\\globalfuture" +}; + +var checkControlSequence = function checkControlSequence(tok) { + var name = tok.text; + + if (/^(?:[\\{}$&#^_]|EOF)$/.test(name)) { + throw new src_ParseError("Expected a control sequence", tok); + } + + return name; +}; + +var getRHS = function getRHS(parser) { + var tok = parser.gullet.popToken(); + + if (tok.text === "=") { + // consume optional equals + tok = parser.gullet.popToken(); + + if (tok.text === " ") { + // consume one optional space + tok = parser.gullet.popToken(); + } + } + + return tok; +}; + +var letCommand = function letCommand(parser, name, tok, global) { + var macro = parser.gullet.macros.get(tok.text); + + if (macro == null) { + // don't expand it later even if a macro with the same name is defined + // e.g., \let\foo=\frac \def\frac{\relax} \frac12 + tok.noexpand = true; + macro = { + tokens: [tok], + numArgs: 0, + // reproduce the same behavior in expansion + unexpandable: !parser.gullet.isExpandable(tok.text) + }; + } + + parser.gullet.macros.set(name, macro, global); +}; // -> | +// -> |\global +// -> | +// -> \global|\long|\outer + + +defineFunction({ + type: "internal", + names: ["\\global", "\\long", "\\\\globallong" // can’t be entered directly + ], + props: { + numArgs: 0, + allowedInText: true + }, + handler: function handler(_ref) { + var parser = _ref.parser, + funcName = _ref.funcName; + parser.consumeSpaces(); + var token = parser.fetch(); + + if (globalMap[token.text]) { + // KaTeX doesn't have \par, so ignore \long + if (funcName === "\\global" || funcName === "\\\\globallong") { + token.text = globalMap[token.text]; + } + + return assertNodeType(parser.parseFunction(), "internal"); + } + + throw new src_ParseError("Invalid token after macro prefix", token); + } +}); // Basic support for macro definitions: \def, \gdef, \edef, \xdef +// -> +// -> \def|\gdef|\edef|\xdef +// -> + +defineFunction({ + type: "internal", + names: ["\\def", "\\gdef", "\\edef", "\\xdef"], + props: { + numArgs: 0, + allowedInText: true, + primitive: true + }, + handler: function handler(_ref2) { + var parser = _ref2.parser, + funcName = _ref2.funcName; + var tok = parser.gullet.popToken(); + var name = tok.text; + + if (/^(?:[\\{}$&#^_]|EOF)$/.test(name)) { + throw new src_ParseError("Expected a control sequence", tok); + } + + var numArgs = 0; + var insert; + var delimiters = [[]]; // contains no braces + + while (parser.gullet.future().text !== "{") { + tok = parser.gullet.popToken(); + + if (tok.text === "#") { + // If the very last character of the is #, so that + // this # is immediately followed by {, TeX will behave as if the { + // had been inserted at the right end of both the parameter text + // and the replacement text. + if (parser.gullet.future().text === "{") { + insert = parser.gullet.future(); + delimiters[numArgs].push("{"); + break; + } // A parameter, the first appearance of # must be followed by 1, + // the next by 2, and so on; up to nine #’s are allowed + + + tok = parser.gullet.popToken(); + + if (!/^[1-9]$/.test(tok.text)) { + throw new src_ParseError("Invalid argument number \"" + tok.text + "\""); + } + + if (parseInt(tok.text) !== numArgs + 1) { + throw new src_ParseError("Argument number \"" + tok.text + "\" out of order"); + } + + numArgs++; + delimiters.push([]); + } else if (tok.text === "EOF") { + throw new src_ParseError("Expected a macro definition"); + } else { + delimiters[numArgs].push(tok.text); + } + } // replacement text, enclosed in '{' and '}' and properly nested + + + var _parser$gullet$consum = parser.gullet.consumeArg(), + tokens = _parser$gullet$consum.tokens; + + if (insert) { + tokens.unshift(insert); + } + + if (funcName === "\\edef" || funcName === "\\xdef") { + tokens = parser.gullet.expandTokens(tokens); + tokens.reverse(); // to fit in with stack order + } // Final arg is the expansion of the macro + + + parser.gullet.macros.set(name, { + tokens: tokens, + numArgs: numArgs, + delimiters: delimiters + }, funcName === globalMap[funcName]); + return { + type: "internal", + mode: parser.mode + }; + } +}); // -> +// -> \futurelet +// | \let +// -> |= + +defineFunction({ + type: "internal", + names: ["\\let", "\\\\globallet" // can’t be entered directly + ], + props: { + numArgs: 0, + allowedInText: true, + primitive: true + }, + handler: function handler(_ref3) { + var parser = _ref3.parser, + funcName = _ref3.funcName; + var name = checkControlSequence(parser.gullet.popToken()); + parser.gullet.consumeSpaces(); + var tok = getRHS(parser); + letCommand(parser, name, tok, funcName === "\\\\globallet"); + return { + type: "internal", + mode: parser.mode + }; + } +}); // ref: https://www.tug.org/TUGboat/tb09-3/tb22bechtolsheim.pdf + +defineFunction({ + type: "internal", + names: ["\\futurelet", "\\\\globalfuture" // can’t be entered directly + ], + props: { + numArgs: 0, + allowedInText: true, + primitive: true + }, + handler: function handler(_ref4) { + var parser = _ref4.parser, + funcName = _ref4.funcName; + var name = checkControlSequence(parser.gullet.popToken()); + var middle = parser.gullet.popToken(); + var tok = parser.gullet.popToken(); + letCommand(parser, name, tok, funcName === "\\\\globalfuture"); + parser.gullet.pushToken(tok); + parser.gullet.pushToken(middle); + return { + type: "internal", + mode: parser.mode + }; + } +}); +;// CONCATENATED MODULE: ./src/delimiter.js +/** + * This file deals with creating delimiters of various sizes. The TeXbook + * discusses these routines on page 441-442, in the "Another subroutine sets box + * x to a specified variable delimiter" paragraph. + * + * There are three main routines here. `makeSmallDelim` makes a delimiter in the + * normal font, but in either text, script, or scriptscript style. + * `makeLargeDelim` makes a delimiter in textstyle, but in one of the Size1, + * Size2, Size3, or Size4 fonts. `makeStackedDelim` makes a delimiter out of + * smaller pieces that are stacked on top of one another. + * + * The functions take a parameter `center`, which determines if the delimiter + * should be centered around the axis. + * + * Then, there are three exposed functions. `sizedDelim` makes a delimiter in + * one of the given sizes. This is used for things like `\bigl`. + * `customSizedDelim` makes a delimiter with a given total height+depth. It is + * called in places like `\sqrt`. `leftRightDelim` makes an appropriate + * delimiter which surrounds an expression of a given height an depth. It is + * used in `\left` and `\right`. + */ + + + + + + + + + + +/** + * Get the metrics for a given symbol and font, after transformation (i.e. + * after following replacement from symbols.js) + */ +var getMetrics = function getMetrics(symbol, font, mode) { + var replace = src_symbols.math[symbol] && src_symbols.math[symbol].replace; + var metrics = getCharacterMetrics(replace || symbol, font, mode); + + if (!metrics) { + throw new Error("Unsupported symbol " + symbol + " and font size " + font + "."); + } + + return metrics; +}; +/** + * Puts a delimiter span in a given style, and adds appropriate height, depth, + * and maxFontSizes. + */ + + +var styleWrap = function styleWrap(delim, toStyle, options, classes) { + var newOptions = options.havingBaseStyle(toStyle); + var span = buildCommon.makeSpan(classes.concat(newOptions.sizingClasses(options)), [delim], options); + var delimSizeMultiplier = newOptions.sizeMultiplier / options.sizeMultiplier; + span.height *= delimSizeMultiplier; + span.depth *= delimSizeMultiplier; + span.maxFontSize = newOptions.sizeMultiplier; + return span; +}; + +var centerSpan = function centerSpan(span, options, style) { + var newOptions = options.havingBaseStyle(style); + var shift = (1 - options.sizeMultiplier / newOptions.sizeMultiplier) * options.fontMetrics().axisHeight; + span.classes.push("delimcenter"); + span.style.top = shift + "em"; + span.height -= shift; + span.depth += shift; +}; +/** + * Makes a small delimiter. This is a delimiter that comes in the Main-Regular + * font, but is restyled to either be in textstyle, scriptstyle, or + * scriptscriptstyle. + */ + + +var makeSmallDelim = function makeSmallDelim(delim, style, center, options, mode, classes) { + var text = buildCommon.makeSymbol(delim, "Main-Regular", mode, options); + var span = styleWrap(text, style, options, classes); + + if (center) { + centerSpan(span, options, style); + } + + return span; +}; +/** + * Builds a symbol in the given font size (note size is an integer) + */ + + +var mathrmSize = function mathrmSize(value, size, mode, options) { + return buildCommon.makeSymbol(value, "Size" + size + "-Regular", mode, options); +}; +/** + * Makes a large delimiter. This is a delimiter that comes in the Size1, Size2, + * Size3, or Size4 fonts. It is always rendered in textstyle. + */ + + +var makeLargeDelim = function makeLargeDelim(delim, size, center, options, mode, classes) { + var inner = mathrmSize(delim, size, mode, options); + var span = styleWrap(buildCommon.makeSpan(["delimsizing", "size" + size], [inner], options), src_Style.TEXT, options, classes); + + if (center) { + centerSpan(span, options, src_Style.TEXT); + } + + return span; +}; +/** + * Make a span from a font glyph with the given offset and in the given font. + * This is used in makeStackedDelim to make the stacking pieces for the delimiter. + */ + + +var makeGlyphSpan = function makeGlyphSpan(symbol, font, mode) { + var sizeClass; // Apply the correct CSS class to choose the right font. + + if (font === "Size1-Regular") { + sizeClass = "delim-size1"; + } else + /* if (font === "Size4-Regular") */ + { + sizeClass = "delim-size4"; + } + + var corner = buildCommon.makeSpan(["delimsizinginner", sizeClass], [buildCommon.makeSpan([], [buildCommon.makeSymbol(symbol, font, mode)])]); // Since this will be passed into `makeVList` in the end, wrap the element + // in the appropriate tag that VList uses. + + return { + type: "elem", + elem: corner + }; +}; + +var makeInner = function makeInner(ch, height, options) { + // Create a span with inline SVG for the inner part of a tall stacked delimiter. + var width = fontMetricsData["Size4-Regular"][ch.charCodeAt(0)] ? fontMetricsData["Size4-Regular"][ch.charCodeAt(0)][4].toFixed(3) : fontMetricsData["Size1-Regular"][ch.charCodeAt(0)][4].toFixed(3); + var path = new PathNode("inner", innerPath(ch, Math.round(1000 * height))); + var svgNode = new SvgNode([path], { + "width": width + "em", + "height": height + "em", + // Override CSS rule `.katex svg { width: 100% }` + "style": "width:" + width + "em", + "viewBox": "0 0 " + 1000 * width + " " + Math.round(1000 * height), + "preserveAspectRatio": "xMinYMin" + }); + var span = buildCommon.makeSvgSpan([], [svgNode], options); + span.height = height; + span.style.height = height + "em"; + span.style.width = width + "em"; + return { + type: "elem", + elem: span + }; +}; // Helpers for makeStackedDelim + + +var lapInEms = 0.008; +var lap = { + type: "kern", + size: -1 * lapInEms +}; +var verts = ["|", "\\lvert", "\\rvert", "\\vert"]; +var doubleVerts = ["\\|", "\\lVert", "\\rVert", "\\Vert"]; +/** + * Make a stacked delimiter out of a given delimiter, with the total height at + * least `heightTotal`. This routine is mentioned on page 442 of the TeXbook. + */ + +var makeStackedDelim = function makeStackedDelim(delim, heightTotal, center, options, mode, classes) { + // There are four parts, the top, an optional middle, a repeated part, and a + // bottom. + var top; + var middle; + var repeat; + var bottom; + top = repeat = bottom = delim; + middle = null; // Also keep track of what font the delimiters are in + + var font = "Size1-Regular"; // We set the parts and font based on the symbol. Note that we use + // '\u23d0' instead of '|' and '\u2016' instead of '\\|' for the + // repeats of the arrows + + if (delim === "\\uparrow") { + repeat = bottom = "\u23D0"; + } else if (delim === "\\Uparrow") { + repeat = bottom = "\u2016"; + } else if (delim === "\\downarrow") { + top = repeat = "\u23D0"; + } else if (delim === "\\Downarrow") { + top = repeat = "\u2016"; + } else if (delim === "\\updownarrow") { + top = "\\uparrow"; + repeat = "\u23D0"; + bottom = "\\downarrow"; + } else if (delim === "\\Updownarrow") { + top = "\\Uparrow"; + repeat = "\u2016"; + bottom = "\\Downarrow"; + } else if (utils.contains(verts, delim)) { + repeat = "\u2223"; + } else if (utils.contains(doubleVerts, delim)) { + repeat = "\u2225"; + } else if (delim === "[" || delim === "\\lbrack") { + top = "\u23A1"; + repeat = "\u23A2"; + bottom = "\u23A3"; + font = "Size4-Regular"; + } else if (delim === "]" || delim === "\\rbrack") { + top = "\u23A4"; + repeat = "\u23A5"; + bottom = "\u23A6"; + font = "Size4-Regular"; + } else if (delim === "\\lfloor" || delim === "\u230A") { + repeat = top = "\u23A2"; + bottom = "\u23A3"; + font = "Size4-Regular"; + } else if (delim === "\\lceil" || delim === "\u2308") { + top = "\u23A1"; + repeat = bottom = "\u23A2"; + font = "Size4-Regular"; + } else if (delim === "\\rfloor" || delim === "\u230B") { + repeat = top = "\u23A5"; + bottom = "\u23A6"; + font = "Size4-Regular"; + } else if (delim === "\\rceil" || delim === "\u2309") { + top = "\u23A4"; + repeat = bottom = "\u23A5"; + font = "Size4-Regular"; + } else if (delim === "(" || delim === "\\lparen") { + top = "\u239B"; + repeat = "\u239C"; + bottom = "\u239D"; + font = "Size4-Regular"; + } else if (delim === ")" || delim === "\\rparen") { + top = "\u239E"; + repeat = "\u239F"; + bottom = "\u23A0"; + font = "Size4-Regular"; + } else if (delim === "\\{" || delim === "\\lbrace") { + top = "\u23A7"; + middle = "\u23A8"; + bottom = "\u23A9"; + repeat = "\u23AA"; + font = "Size4-Regular"; + } else if (delim === "\\}" || delim === "\\rbrace") { + top = "\u23AB"; + middle = "\u23AC"; + bottom = "\u23AD"; + repeat = "\u23AA"; + font = "Size4-Regular"; + } else if (delim === "\\lgroup" || delim === "\u27EE") { + top = "\u23A7"; + bottom = "\u23A9"; + repeat = "\u23AA"; + font = "Size4-Regular"; + } else if (delim === "\\rgroup" || delim === "\u27EF") { + top = "\u23AB"; + bottom = "\u23AD"; + repeat = "\u23AA"; + font = "Size4-Regular"; + } else if (delim === "\\lmoustache" || delim === "\u23B0") { + top = "\u23A7"; + bottom = "\u23AD"; + repeat = "\u23AA"; + font = "Size4-Regular"; + } else if (delim === "\\rmoustache" || delim === "\u23B1") { + top = "\u23AB"; + bottom = "\u23A9"; + repeat = "\u23AA"; + font = "Size4-Regular"; + } // Get the metrics of the four sections + + + var topMetrics = getMetrics(top, font, mode); + var topHeightTotal = topMetrics.height + topMetrics.depth; + var repeatMetrics = getMetrics(repeat, font, mode); + var repeatHeightTotal = repeatMetrics.height + repeatMetrics.depth; + var bottomMetrics = getMetrics(bottom, font, mode); + var bottomHeightTotal = bottomMetrics.height + bottomMetrics.depth; + var middleHeightTotal = 0; + var middleFactor = 1; + + if (middle !== null) { + var middleMetrics = getMetrics(middle, font, mode); + middleHeightTotal = middleMetrics.height + middleMetrics.depth; + middleFactor = 2; // repeat symmetrically above and below middle + } // Calcuate the minimal height that the delimiter can have. + // It is at least the size of the top, bottom, and optional middle combined. + + + var minHeight = topHeightTotal + bottomHeightTotal + middleHeightTotal; // Compute the number of copies of the repeat symbol we will need + + var repeatCount = Math.max(0, Math.ceil((heightTotal - minHeight) / (middleFactor * repeatHeightTotal))); // Compute the total height of the delimiter including all the symbols + + var realHeightTotal = minHeight + repeatCount * middleFactor * repeatHeightTotal; // The center of the delimiter is placed at the center of the axis. Note + // that in this context, "center" means that the delimiter should be + // centered around the axis in the current style, while normally it is + // centered around the axis in textstyle. + + var axisHeight = options.fontMetrics().axisHeight; + + if (center) { + axisHeight *= options.sizeMultiplier; + } // Calculate the depth + + + var depth = realHeightTotal / 2 - axisHeight; // Now, we start building the pieces that will go into the vlist + // Keep a list of the pieces of the stacked delimiter + + var stack = []; // Add the bottom symbol + + stack.push(makeGlyphSpan(bottom, font, mode)); + stack.push(lap); // overlap + + if (middle === null) { + // The middle section will be an SVG. Make it an extra 0.016em tall. + // We'll overlap by 0.008em at top and bottom. + var innerHeight = realHeightTotal - topHeightTotal - bottomHeightTotal + 2 * lapInEms; + stack.push(makeInner(repeat, innerHeight, options)); + } else { + // When there is a middle bit, we need the middle part and two repeated + // sections + var _innerHeight = (realHeightTotal - topHeightTotal - bottomHeightTotal - middleHeightTotal) / 2 + 2 * lapInEms; + + stack.push(makeInner(repeat, _innerHeight, options)); // Now insert the middle of the brace. + + stack.push(lap); + stack.push(makeGlyphSpan(middle, font, mode)); + stack.push(lap); + stack.push(makeInner(repeat, _innerHeight, options)); + } // Add the top symbol + + + stack.push(lap); + stack.push(makeGlyphSpan(top, font, mode)); // Finally, build the vlist + + var newOptions = options.havingBaseStyle(src_Style.TEXT); + var inner = buildCommon.makeVList({ + positionType: "bottom", + positionData: depth, + children: stack + }, newOptions); + return styleWrap(buildCommon.makeSpan(["delimsizing", "mult"], [inner], newOptions), src_Style.TEXT, options, classes); +}; // All surds have 0.08em padding above the viniculum inside the SVG. +// That keeps browser span height rounding error from pinching the line. + + +var vbPad = 80; // padding above the surd, measured inside the viewBox. + +var emPad = 0.08; // padding, in ems, measured in the document. + +var sqrtSvg = function sqrtSvg(sqrtName, height, viewBoxHeight, extraViniculum, options) { + var path = sqrtPath(sqrtName, extraViniculum, viewBoxHeight); + var pathNode = new PathNode(sqrtName, path); + var svg = new SvgNode([pathNode], { + // Note: 1000:1 ratio of viewBox to document em width. + "width": "400em", + "height": height + "em", + "viewBox": "0 0 400000 " + viewBoxHeight, + "preserveAspectRatio": "xMinYMin slice" + }); + return buildCommon.makeSvgSpan(["hide-tail"], [svg], options); +}; +/** + * Make a sqrt image of the given height, + */ + + +var makeSqrtImage = function makeSqrtImage(height, options) { + // Define a newOptions that removes the effect of size changes such as \Huge. + // We don't pick different a height surd for \Huge. For it, we scale up. + var newOptions = options.havingBaseSizing(); // Pick the desired surd glyph from a sequence of surds. + + var delim = traverseSequence("\\surd", height * newOptions.sizeMultiplier, stackLargeDelimiterSequence, newOptions); + var sizeMultiplier = newOptions.sizeMultiplier; // default + // The standard sqrt SVGs each have a 0.04em thick viniculum. + // If Settings.minRuleThickness is larger than that, we add extraViniculum. + + var extraViniculum = Math.max(0, options.minRuleThickness - options.fontMetrics().sqrtRuleThickness); // Create a span containing an SVG image of a sqrt symbol. + + var span; + var spanHeight = 0; + var texHeight = 0; + var viewBoxHeight = 0; + var advanceWidth; // We create viewBoxes with 80 units of "padding" above each surd. + // Then browser rounding error on the parent span height will not + // encroach on the ink of the viniculum. But that padding is not + // included in the TeX-like `height` used for calculation of + // vertical alignment. So texHeight = span.height < span.style.height. + + if (delim.type === "small") { + // Get an SVG that is derived from glyph U+221A in font KaTeX-Main. + // 1000 unit normal glyph height. + viewBoxHeight = 1000 + 1000 * extraViniculum + vbPad; + + if (height < 1.0) { + sizeMultiplier = 1.0; // mimic a \textfont radical + } else if (height < 1.4) { + sizeMultiplier = 0.7; // mimic a \scriptfont radical + } + + spanHeight = (1.0 + extraViniculum + emPad) / sizeMultiplier; + texHeight = (1.00 + extraViniculum) / sizeMultiplier; + span = sqrtSvg("sqrtMain", spanHeight, viewBoxHeight, extraViniculum, options); + span.style.minWidth = "0.853em"; + advanceWidth = 0.833 / sizeMultiplier; // from the font. + } else if (delim.type === "large") { + // These SVGs come from fonts: KaTeX_Size1, _Size2, etc. + viewBoxHeight = (1000 + vbPad) * sizeToMaxHeight[delim.size]; + texHeight = (sizeToMaxHeight[delim.size] + extraViniculum) / sizeMultiplier; + spanHeight = (sizeToMaxHeight[delim.size] + extraViniculum + emPad) / sizeMultiplier; + span = sqrtSvg("sqrtSize" + delim.size, spanHeight, viewBoxHeight, extraViniculum, options); + span.style.minWidth = "1.02em"; + advanceWidth = 1.0 / sizeMultiplier; // 1.0 from the font. + } else { + // Tall sqrt. In TeX, this would be stacked using multiple glyphs. + // We'll use a single SVG to accomplish the same thing. + spanHeight = height + extraViniculum + emPad; + texHeight = height + extraViniculum; + viewBoxHeight = Math.floor(1000 * height + extraViniculum) + vbPad; + span = sqrtSvg("sqrtTall", spanHeight, viewBoxHeight, extraViniculum, options); + span.style.minWidth = "0.742em"; + advanceWidth = 1.056; + } + + span.height = texHeight; + span.style.height = spanHeight + "em"; + return { + span: span, + advanceWidth: advanceWidth, + // Calculate the actual line width. + // This actually should depend on the chosen font -- e.g. \boldmath + // should use the thicker surd symbols from e.g. KaTeX_Main-Bold, and + // have thicker rules. + ruleWidth: (options.fontMetrics().sqrtRuleThickness + extraViniculum) * sizeMultiplier + }; +}; // There are three kinds of delimiters, delimiters that stack when they become +// too large + + +var stackLargeDelimiters = ["(", "\\lparen", ")", "\\rparen", "[", "\\lbrack", "]", "\\rbrack", "\\{", "\\lbrace", "\\}", "\\rbrace", "\\lfloor", "\\rfloor", "\u230A", "\u230B", "\\lceil", "\\rceil", "\u2308", "\u2309", "\\surd"]; // delimiters that always stack + +var stackAlwaysDelimiters = ["\\uparrow", "\\downarrow", "\\updownarrow", "\\Uparrow", "\\Downarrow", "\\Updownarrow", "|", "\\|", "\\vert", "\\Vert", "\\lvert", "\\rvert", "\\lVert", "\\rVert", "\\lgroup", "\\rgroup", "\u27EE", "\u27EF", "\\lmoustache", "\\rmoustache", "\u23B0", "\u23B1"]; // and delimiters that never stack + +var stackNeverDelimiters = ["<", ">", "\\langle", "\\rangle", "/", "\\backslash", "\\lt", "\\gt"]; // Metrics of the different sizes. Found by looking at TeX's output of +// $\bigl| // \Bigl| \biggl| \Biggl| \showlists$ +// Used to create stacked delimiters of appropriate sizes in makeSizedDelim. + +var sizeToMaxHeight = [0, 1.2, 1.8, 2.4, 3.0]; +/** + * Used to create a delimiter of a specific size, where `size` is 1, 2, 3, or 4. + */ + +var makeSizedDelim = function makeSizedDelim(delim, size, options, mode, classes) { + // < and > turn into \langle and \rangle in delimiters + if (delim === "<" || delim === "\\lt" || delim === "\u27E8") { + delim = "\\langle"; + } else if (delim === ">" || delim === "\\gt" || delim === "\u27E9") { + delim = "\\rangle"; + } // Sized delimiters are never centered. + + + if (utils.contains(stackLargeDelimiters, delim) || utils.contains(stackNeverDelimiters, delim)) { + return makeLargeDelim(delim, size, false, options, mode, classes); + } else if (utils.contains(stackAlwaysDelimiters, delim)) { + return makeStackedDelim(delim, sizeToMaxHeight[size], false, options, mode, classes); + } else { + throw new src_ParseError("Illegal delimiter: '" + delim + "'"); + } +}; +/** + * There are three different sequences of delimiter sizes that the delimiters + * follow depending on the kind of delimiter. This is used when creating custom + * sized delimiters to decide whether to create a small, large, or stacked + * delimiter. + * + * In real TeX, these sequences aren't explicitly defined, but are instead + * defined inside the font metrics. Since there are only three sequences that + * are possible for the delimiters that TeX defines, it is easier to just encode + * them explicitly here. + */ + + +// Delimiters that never stack try small delimiters and large delimiters only +var stackNeverDelimiterSequence = [{ + type: "small", + style: src_Style.SCRIPTSCRIPT +}, { + type: "small", + style: src_Style.SCRIPT +}, { + type: "small", + style: src_Style.TEXT +}, { + type: "large", + size: 1 +}, { + type: "large", + size: 2 +}, { + type: "large", + size: 3 +}, { + type: "large", + size: 4 +}]; // Delimiters that always stack try the small delimiters first, then stack + +var stackAlwaysDelimiterSequence = [{ + type: "small", + style: src_Style.SCRIPTSCRIPT +}, { + type: "small", + style: src_Style.SCRIPT +}, { + type: "small", + style: src_Style.TEXT +}, { + type: "stack" +}]; // Delimiters that stack when large try the small and then large delimiters, and +// stack afterwards + +var stackLargeDelimiterSequence = [{ + type: "small", + style: src_Style.SCRIPTSCRIPT +}, { + type: "small", + style: src_Style.SCRIPT +}, { + type: "small", + style: src_Style.TEXT +}, { + type: "large", + size: 1 +}, { + type: "large", + size: 2 +}, { + type: "large", + size: 3 +}, { + type: "large", + size: 4 +}, { + type: "stack" +}]; +/** + * Get the font used in a delimiter based on what kind of delimiter it is. + * TODO(#963) Use more specific font family return type once that is introduced. + */ + +var delimTypeToFont = function delimTypeToFont(type) { + if (type.type === "small") { + return "Main-Regular"; + } else if (type.type === "large") { + return "Size" + type.size + "-Regular"; + } else if (type.type === "stack") { + return "Size4-Regular"; + } else { + throw new Error("Add support for delim type '" + type.type + "' here."); + } +}; +/** + * Traverse a sequence of types of delimiters to decide what kind of delimiter + * should be used to create a delimiter of the given height+depth. + */ + + +var traverseSequence = function traverseSequence(delim, height, sequence, options) { + // Here, we choose the index we should start at in the sequences. In smaller + // sizes (which correspond to larger numbers in style.size) we start earlier + // in the sequence. Thus, scriptscript starts at index 3-3=0, script starts + // at index 3-2=1, text starts at 3-1=2, and display starts at min(2,3-0)=2 + var start = Math.min(2, 3 - options.style.size); + + for (var i = start; i < sequence.length; i++) { + if (sequence[i].type === "stack") { + // This is always the last delimiter, so we just break the loop now. + break; + } + + var metrics = getMetrics(delim, delimTypeToFont(sequence[i]), "math"); + var heightDepth = metrics.height + metrics.depth; // Small delimiters are scaled down versions of the same font, so we + // account for the style change size. + + if (sequence[i].type === "small") { + var newOptions = options.havingBaseStyle(sequence[i].style); + heightDepth *= newOptions.sizeMultiplier; + } // Check if the delimiter at this size works for the given height. + + + if (heightDepth > height) { + return sequence[i]; + } + } // If we reached the end of the sequence, return the last sequence element. + + + return sequence[sequence.length - 1]; +}; +/** + * Make a delimiter of a given height+depth, with optional centering. Here, we + * traverse the sequences, and create a delimiter that the sequence tells us to. + */ + + +var makeCustomSizedDelim = function makeCustomSizedDelim(delim, height, center, options, mode, classes) { + if (delim === "<" || delim === "\\lt" || delim === "\u27E8") { + delim = "\\langle"; + } else if (delim === ">" || delim === "\\gt" || delim === "\u27E9") { + delim = "\\rangle"; + } // Decide what sequence to use + + + var sequence; + + if (utils.contains(stackNeverDelimiters, delim)) { + sequence = stackNeverDelimiterSequence; + } else if (utils.contains(stackLargeDelimiters, delim)) { + sequence = stackLargeDelimiterSequence; + } else { + sequence = stackAlwaysDelimiterSequence; + } // Look through the sequence + + + var delimType = traverseSequence(delim, height, sequence, options); // Get the delimiter from font glyphs. + // Depending on the sequence element we decided on, call the + // appropriate function. + + if (delimType.type === "small") { + return makeSmallDelim(delim, delimType.style, center, options, mode, classes); + } else if (delimType.type === "large") { + return makeLargeDelim(delim, delimType.size, center, options, mode, classes); + } else + /* if (delimType.type === "stack") */ + { + return makeStackedDelim(delim, height, center, options, mode, classes); + } +}; +/** + * Make a delimiter for use with `\left` and `\right`, given a height and depth + * of an expression that the delimiters surround. + */ + + +var makeLeftRightDelim = function makeLeftRightDelim(delim, height, depth, options, mode, classes) { + // We always center \left/\right delimiters, so the axis is always shifted + var axisHeight = options.fontMetrics().axisHeight * options.sizeMultiplier; // Taken from TeX source, tex.web, function make_left_right + + var delimiterFactor = 901; + var delimiterExtend = 5.0 / options.fontMetrics().ptPerEm; + var maxDistFromAxis = Math.max(height - axisHeight, depth + axisHeight); + var totalHeight = Math.max( // In real TeX, calculations are done using integral values which are + // 65536 per pt, or 655360 per em. So, the division here truncates in + // TeX but doesn't here, producing different results. If we wanted to + // exactly match TeX's calculation, we could do + // Math.floor(655360 * maxDistFromAxis / 500) * + // delimiterFactor / 655360 + // (To see the difference, compare + // x^{x^{\left(\rule{0.1em}{0.68em}\right)}} + // in TeX and KaTeX) + maxDistFromAxis / 500 * delimiterFactor, 2 * maxDistFromAxis - delimiterExtend); // Finally, we defer to `makeCustomSizedDelim` with our calculated total + // height + + return makeCustomSizedDelim(delim, totalHeight, true, options, mode, classes); +}; + +/* harmony default export */ var delimiter = ({ + sqrtImage: makeSqrtImage, + sizedDelim: makeSizedDelim, + sizeToMaxHeight: sizeToMaxHeight, + customSizedDelim: makeCustomSizedDelim, + leftRightDelim: makeLeftRightDelim +}); +;// CONCATENATED MODULE: ./src/functions/delimsizing.js + + + + + + + + + +// Extra data needed for the delimiter handler down below +var delimiterSizes = { + "\\bigl": { + mclass: "mopen", + size: 1 + }, + "\\Bigl": { + mclass: "mopen", + size: 2 + }, + "\\biggl": { + mclass: "mopen", + size: 3 + }, + "\\Biggl": { + mclass: "mopen", + size: 4 + }, + "\\bigr": { + mclass: "mclose", + size: 1 + }, + "\\Bigr": { + mclass: "mclose", + size: 2 + }, + "\\biggr": { + mclass: "mclose", + size: 3 + }, + "\\Biggr": { + mclass: "mclose", + size: 4 + }, + "\\bigm": { + mclass: "mrel", + size: 1 + }, + "\\Bigm": { + mclass: "mrel", + size: 2 + }, + "\\biggm": { + mclass: "mrel", + size: 3 + }, + "\\Biggm": { + mclass: "mrel", + size: 4 + }, + "\\big": { + mclass: "mord", + size: 1 + }, + "\\Big": { + mclass: "mord", + size: 2 + }, + "\\bigg": { + mclass: "mord", + size: 3 + }, + "\\Bigg": { + mclass: "mord", + size: 4 + } +}; +var delimiters = ["(", "\\lparen", ")", "\\rparen", "[", "\\lbrack", "]", "\\rbrack", "\\{", "\\lbrace", "\\}", "\\rbrace", "\\lfloor", "\\rfloor", "\u230A", "\u230B", "\\lceil", "\\rceil", "\u2308", "\u2309", "<", ">", "\\langle", "\u27E8", "\\rangle", "\u27E9", "\\lt", "\\gt", "\\lvert", "\\rvert", "\\lVert", "\\rVert", "\\lgroup", "\\rgroup", "\u27EE", "\u27EF", "\\lmoustache", "\\rmoustache", "\u23B0", "\u23B1", "/", "\\backslash", "|", "\\vert", "\\|", "\\Vert", "\\uparrow", "\\Uparrow", "\\downarrow", "\\Downarrow", "\\updownarrow", "\\Updownarrow", "."]; + +// Delimiter functions +function checkDelimiter(delim, context) { + var symDelim = checkSymbolNodeType(delim); + + if (symDelim && utils.contains(delimiters, symDelim.text)) { + return symDelim; + } else if (symDelim) { + throw new src_ParseError("Invalid delimiter '" + symDelim.text + "' after '" + context.funcName + "'", delim); + } else { + throw new src_ParseError("Invalid delimiter type '" + delim.type + "'", delim); + } +} + +defineFunction({ + type: "delimsizing", + names: ["\\bigl", "\\Bigl", "\\biggl", "\\Biggl", "\\bigr", "\\Bigr", "\\biggr", "\\Biggr", "\\bigm", "\\Bigm", "\\biggm", "\\Biggm", "\\big", "\\Big", "\\bigg", "\\Bigg"], + props: { + numArgs: 1, + argTypes: ["primitive"] + }, + handler: function handler(context, args) { + var delim = checkDelimiter(args[0], context); + return { + type: "delimsizing", + mode: context.parser.mode, + size: delimiterSizes[context.funcName].size, + mclass: delimiterSizes[context.funcName].mclass, + delim: delim.text + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + if (group.delim === ".") { + // Empty delimiters still count as elements, even though they don't + // show anything. + return buildCommon.makeSpan([group.mclass]); + } // Use delimiter.sizedDelim to generate the delimiter. + + + return delimiter.sizedDelim(group.delim, group.size, options, group.mode, [group.mclass]); + }, + mathmlBuilder: function mathmlBuilder(group) { + var children = []; + + if (group.delim !== ".") { + children.push(makeText(group.delim, group.mode)); + } + + var node = new mathMLTree.MathNode("mo", children); + + if (group.mclass === "mopen" || group.mclass === "mclose") { + // Only some of the delimsizing functions act as fences, and they + // return "mopen" or "mclose" mclass. + node.setAttribute("fence", "true"); + } else { + // Explicitly disable fencing if it's not a fence, to override the + // defaults. + node.setAttribute("fence", "false"); + } + + node.setAttribute("stretchy", "true"); + node.setAttribute("minsize", delimiter.sizeToMaxHeight[group.size] + "em"); + node.setAttribute("maxsize", delimiter.sizeToMaxHeight[group.size] + "em"); + return node; + } +}); + +function assertParsed(group) { + if (!group.body) { + throw new Error("Bug: The leftright ParseNode wasn't fully parsed."); + } +} + +defineFunction({ + type: "leftright-right", + names: ["\\right"], + props: { + numArgs: 1, + primitive: true + }, + handler: function handler(context, args) { + // \left case below triggers parsing of \right in + // `const right = parser.parseFunction();` + // uses this return value. + var color = context.parser.gullet.macros.get("\\current@color"); + + if (color && typeof color !== "string") { + throw new src_ParseError("\\current@color set to non-string in \\right"); + } + + return { + type: "leftright-right", + mode: context.parser.mode, + delim: checkDelimiter(args[0], context).text, + color: color // undefined if not set via \color + + }; + } +}); +defineFunction({ + type: "leftright", + names: ["\\left"], + props: { + numArgs: 1, + primitive: true + }, + handler: function handler(context, args) { + var delim = checkDelimiter(args[0], context); + var parser = context.parser; // Parse out the implicit body + + ++parser.leftrightDepth; // parseExpression stops before '\\right' + + var body = parser.parseExpression(false); + --parser.leftrightDepth; // Check the next token + + parser.expect("\\right", false); + var right = assertNodeType(parser.parseFunction(), "leftright-right"); + return { + type: "leftright", + mode: parser.mode, + body: body, + left: delim.text, + right: right.delim, + rightColor: right.color + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + assertParsed(group); // Build the inner expression + + var inner = buildExpression(group.body, options, true, ["mopen", "mclose"]); + var innerHeight = 0; + var innerDepth = 0; + var hadMiddle = false; // Calculate its height and depth + + for (var i = 0; i < inner.length; i++) { + // Property `isMiddle` not defined on `span`. See comment in + // "middle"'s htmlBuilder. + // $FlowFixMe + if (inner[i].isMiddle) { + hadMiddle = true; + } else { + innerHeight = Math.max(inner[i].height, innerHeight); + innerDepth = Math.max(inner[i].depth, innerDepth); + } + } // The size of delimiters is the same, regardless of what style we are + // in. Thus, to correctly calculate the size of delimiter we need around + // a group, we scale down the inner size based on the size. + + + innerHeight *= options.sizeMultiplier; + innerDepth *= options.sizeMultiplier; + var leftDelim; + + if (group.left === ".") { + // Empty delimiters in \left and \right make null delimiter spaces. + leftDelim = makeNullDelimiter(options, ["mopen"]); + } else { + // Otherwise, use leftRightDelim to generate the correct sized + // delimiter. + leftDelim = delimiter.leftRightDelim(group.left, innerHeight, innerDepth, options, group.mode, ["mopen"]); + } // Add it to the beginning of the expression + + + inner.unshift(leftDelim); // Handle middle delimiters + + if (hadMiddle) { + for (var _i = 1; _i < inner.length; _i++) { + var middleDelim = inner[_i]; // Property `isMiddle` not defined on `span`. See comment in + // "middle"'s htmlBuilder. + // $FlowFixMe + + var isMiddle = middleDelim.isMiddle; + + if (isMiddle) { + // Apply the options that were active when \middle was called + inner[_i] = delimiter.leftRightDelim(isMiddle.delim, innerHeight, innerDepth, isMiddle.options, group.mode, []); + } + } + } + + var rightDelim; // Same for the right delimiter, but using color specified by \color + + if (group.right === ".") { + rightDelim = makeNullDelimiter(options, ["mclose"]); + } else { + var colorOptions = group.rightColor ? options.withColor(group.rightColor) : options; + rightDelim = delimiter.leftRightDelim(group.right, innerHeight, innerDepth, colorOptions, group.mode, ["mclose"]); + } // Add it to the end of the expression. + + + inner.push(rightDelim); + return buildCommon.makeSpan(["minner"], inner, options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + assertParsed(group); + var inner = buildMathML_buildExpression(group.body, options); + + if (group.left !== ".") { + var leftNode = new mathMLTree.MathNode("mo", [makeText(group.left, group.mode)]); + leftNode.setAttribute("fence", "true"); + inner.unshift(leftNode); + } + + if (group.right !== ".") { + var rightNode = new mathMLTree.MathNode("mo", [makeText(group.right, group.mode)]); + rightNode.setAttribute("fence", "true"); + + if (group.rightColor) { + rightNode.setAttribute("mathcolor", group.rightColor); + } + + inner.push(rightNode); + } + + return makeRow(inner); + } +}); +defineFunction({ + type: "middle", + names: ["\\middle"], + props: { + numArgs: 1, + primitive: true + }, + handler: function handler(context, args) { + var delim = checkDelimiter(args[0], context); + + if (!context.parser.leftrightDepth) { + throw new src_ParseError("\\middle without preceding \\left", delim); + } + + return { + type: "middle", + mode: context.parser.mode, + delim: delim.text + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var middleDelim; + + if (group.delim === ".") { + middleDelim = makeNullDelimiter(options, []); + } else { + middleDelim = delimiter.sizedDelim(group.delim, 1, options, group.mode, []); + var isMiddle = { + delim: group.delim, + options: options + }; // Property `isMiddle` not defined on `span`. It is only used in + // this file above. + // TODO: Fix this violation of the `span` type and possibly rename + // things since `isMiddle` sounds like a boolean, but is a struct. + // $FlowFixMe + + middleDelim.isMiddle = isMiddle; + } + + return middleDelim; + }, + mathmlBuilder: function mathmlBuilder(group, options) { + // A Firefox \middle will strech a character vertically only if it + // is in the fence part of the operator dictionary at: + // https://www.w3.org/TR/MathML3/appendixc.html. + // So we need to avoid U+2223 and use plain "|" instead. + var textNode = group.delim === "\\vert" || group.delim === "|" ? makeText("|", "text") : makeText(group.delim, group.mode); + var middleNode = new mathMLTree.MathNode("mo", [textNode]); + middleNode.setAttribute("fence", "true"); // MathML gives 5/18em spacing to each element. + // \middle should get delimiter spacing instead. + + middleNode.setAttribute("lspace", "0.05em"); + middleNode.setAttribute("rspace", "0.05em"); + return middleNode; + } +}); +;// CONCATENATED MODULE: ./src/functions/enclose.js + + + + + + + + + + + + +var enclose_htmlBuilder = function htmlBuilder(group, options) { + // \cancel, \bcancel, \xcancel, \sout, \fbox, \colorbox, \fcolorbox, \phase + // Some groups can return document fragments. Handle those by wrapping + // them in a span. + var inner = buildCommon.wrapFragment(buildGroup(group.body, options), options); + var label = group.label.substr(1); + var scale = options.sizeMultiplier; + var img; + var imgShift = 0; // In the LaTeX cancel package, line geometry is slightly different + // depending on whether the subject is wider than it is tall, or vice versa. + // We don't know the width of a group, so as a proxy, we test if + // the subject is a single character. This captures most of the + // subjects that should get the "tall" treatment. + + var isSingleChar = utils.isCharacterBox(group.body); + + if (label === "sout") { + img = buildCommon.makeSpan(["stretchy", "sout"]); + img.height = options.fontMetrics().defaultRuleThickness / scale; + imgShift = -0.5 * options.fontMetrics().xHeight; + } else if (label === "phase") { + // Set a couple of dimensions from the steinmetz package. + var lineWeight = calculateSize({ + number: 0.6, + unit: "pt" + }, options); + var clearance = calculateSize({ + number: 0.35, + unit: "ex" + }, options); // Prevent size changes like \Huge from affecting line thickness + + var newOptions = options.havingBaseSizing(); + scale = scale / newOptions.sizeMultiplier; + var angleHeight = inner.height + inner.depth + lineWeight + clearance; // Reserve a left pad for the angle. + + inner.style.paddingLeft = angleHeight / 2 + lineWeight + "em"; // Create an SVG + + var viewBoxHeight = Math.floor(1000 * angleHeight * scale); + var path = phasePath(viewBoxHeight); + var svgNode = new SvgNode([new PathNode("phase", path)], { + "width": "400em", + "height": viewBoxHeight / 1000 + "em", + "viewBox": "0 0 400000 " + viewBoxHeight, + "preserveAspectRatio": "xMinYMin slice" + }); // Wrap it in a span with overflow: hidden. + + img = buildCommon.makeSvgSpan(["hide-tail"], [svgNode], options); + img.style.height = angleHeight + "em"; + imgShift = inner.depth + lineWeight + clearance; + } else { + // Add horizontal padding + if (/cancel/.test(label)) { + if (!isSingleChar) { + inner.classes.push("cancel-pad"); + } + } else if (label === "angl") { + inner.classes.push("anglpad"); + } else { + inner.classes.push("boxpad"); + } // Add vertical padding + + + var topPad = 0; + var bottomPad = 0; + var ruleThickness = 0; // ref: cancel package: \advance\totalheight2\p@ % "+2" + + if (/box/.test(label)) { + ruleThickness = Math.max(options.fontMetrics().fboxrule, // default + options.minRuleThickness // User override. + ); + topPad = options.fontMetrics().fboxsep + (label === "colorbox" ? 0 : ruleThickness); + bottomPad = topPad; + } else if (label === "angl") { + ruleThickness = Math.max(options.fontMetrics().defaultRuleThickness, options.minRuleThickness); + topPad = 4 * ruleThickness; // gap = 3 × line, plus the line itself. + + bottomPad = Math.max(0, 0.25 - inner.depth); + } else { + topPad = isSingleChar ? 0.2 : 0; + bottomPad = topPad; + } + + img = stretchy.encloseSpan(inner, label, topPad, bottomPad, options); + + if (/fbox|boxed|fcolorbox/.test(label)) { + img.style.borderStyle = "solid"; + img.style.borderWidth = ruleThickness + "em"; + } else if (label === "angl" && ruleThickness !== 0.049) { + img.style.borderTopWidth = ruleThickness + "em"; + img.style.borderRightWidth = ruleThickness + "em"; + } + + imgShift = inner.depth + bottomPad; + + if (group.backgroundColor) { + img.style.backgroundColor = group.backgroundColor; + + if (group.borderColor) { + img.style.borderColor = group.borderColor; + } + } + } + + var vlist; + + if (group.backgroundColor) { + vlist = buildCommon.makeVList({ + positionType: "individualShift", + children: [// Put the color background behind inner; + { + type: "elem", + elem: img, + shift: imgShift + }, { + type: "elem", + elem: inner, + shift: 0 + }] + }, options); + } else { + var classes = /cancel|phase/.test(label) ? ["svg-align"] : []; + vlist = buildCommon.makeVList({ + positionType: "individualShift", + children: [// Write the \cancel stroke on top of inner. + { + type: "elem", + elem: inner, + shift: 0 + }, { + type: "elem", + elem: img, + shift: imgShift, + wrapperClasses: classes + }] + }, options); + } + + if (/cancel/.test(label)) { + // The cancel package documentation says that cancel lines add their height + // to the expression, but tests show that isn't how it actually works. + vlist.height = inner.height; + vlist.depth = inner.depth; + } + + if (/cancel/.test(label) && !isSingleChar) { + // cancel does not create horiz space for its line extension. + return buildCommon.makeSpan(["mord", "cancel-lap"], [vlist], options); + } else { + return buildCommon.makeSpan(["mord"], [vlist], options); + } +}; + +var enclose_mathmlBuilder = function mathmlBuilder(group, options) { + var fboxsep = 0; + var node = new mathMLTree.MathNode(group.label.indexOf("colorbox") > -1 ? "mpadded" : "menclose", [buildMathML_buildGroup(group.body, options)]); + + switch (group.label) { + case "\\cancel": + node.setAttribute("notation", "updiagonalstrike"); + break; + + case "\\bcancel": + node.setAttribute("notation", "downdiagonalstrike"); + break; + + case "\\phase": + node.setAttribute("notation", "phasorangle"); + break; + + case "\\sout": + node.setAttribute("notation", "horizontalstrike"); + break; + + case "\\fbox": + node.setAttribute("notation", "box"); + break; + + case "\\angl": + node.setAttribute("notation", "actuarial"); + break; + + case "\\fcolorbox": + case "\\colorbox": + // doesn't have a good notation option. So use + // instead. Set some attributes that come included with . + fboxsep = options.fontMetrics().fboxsep * options.fontMetrics().ptPerEm; + node.setAttribute("width", "+" + 2 * fboxsep + "pt"); + node.setAttribute("height", "+" + 2 * fboxsep + "pt"); + node.setAttribute("lspace", fboxsep + "pt"); // + + node.setAttribute("voffset", fboxsep + "pt"); + + if (group.label === "\\fcolorbox") { + var thk = Math.max(options.fontMetrics().fboxrule, // default + options.minRuleThickness // user override + ); + node.setAttribute("style", "border: " + thk + "em solid " + String(group.borderColor)); + } + + break; + + case "\\xcancel": + node.setAttribute("notation", "updiagonalstrike downdiagonalstrike"); + break; + } + + if (group.backgroundColor) { + node.setAttribute("mathbackground", group.backgroundColor); + } + + return node; +}; + +defineFunction({ + type: "enclose", + names: ["\\colorbox"], + props: { + numArgs: 2, + allowedInText: true, + argTypes: ["color", "text"] + }, + handler: function handler(_ref, args, optArgs) { + var parser = _ref.parser, + funcName = _ref.funcName; + var color = assertNodeType(args[0], "color-token").color; + var body = args[1]; + return { + type: "enclose", + mode: parser.mode, + label: funcName, + backgroundColor: color, + body: body + }; + }, + htmlBuilder: enclose_htmlBuilder, + mathmlBuilder: enclose_mathmlBuilder +}); +defineFunction({ + type: "enclose", + names: ["\\fcolorbox"], + props: { + numArgs: 3, + allowedInText: true, + argTypes: ["color", "color", "text"] + }, + handler: function handler(_ref2, args, optArgs) { + var parser = _ref2.parser, + funcName = _ref2.funcName; + var borderColor = assertNodeType(args[0], "color-token").color; + var backgroundColor = assertNodeType(args[1], "color-token").color; + var body = args[2]; + return { + type: "enclose", + mode: parser.mode, + label: funcName, + backgroundColor: backgroundColor, + borderColor: borderColor, + body: body + }; + }, + htmlBuilder: enclose_htmlBuilder, + mathmlBuilder: enclose_mathmlBuilder +}); +defineFunction({ + type: "enclose", + names: ["\\fbox"], + props: { + numArgs: 1, + argTypes: ["hbox"], + allowedInText: true + }, + handler: function handler(_ref3, args) { + var parser = _ref3.parser; + return { + type: "enclose", + mode: parser.mode, + label: "\\fbox", + body: args[0] + }; + } +}); +defineFunction({ + type: "enclose", + names: ["\\cancel", "\\bcancel", "\\xcancel", "\\sout", "\\phase"], + props: { + numArgs: 1 + }, + handler: function handler(_ref4, args) { + var parser = _ref4.parser, + funcName = _ref4.funcName; + var body = args[0]; + return { + type: "enclose", + mode: parser.mode, + label: funcName, + body: body + }; + }, + htmlBuilder: enclose_htmlBuilder, + mathmlBuilder: enclose_mathmlBuilder +}); +defineFunction({ + type: "enclose", + names: ["\\angl"], + props: { + numArgs: 1, + argTypes: ["hbox"], + allowedInText: false + }, + handler: function handler(_ref5, args) { + var parser = _ref5.parser; + return { + type: "enclose", + mode: parser.mode, + label: "\\angl", + body: args[0] + }; + } +}); +;// CONCATENATED MODULE: ./src/defineEnvironment.js + + +/** + * All registered environments. + * `environments.js` exports this same dictionary again and makes it public. + * `Parser.js` requires this dictionary via `environments.js`. + */ +var _environments = {}; +function defineEnvironment(_ref) { + var type = _ref.type, + names = _ref.names, + props = _ref.props, + handler = _ref.handler, + htmlBuilder = _ref.htmlBuilder, + mathmlBuilder = _ref.mathmlBuilder; + // Set default values of environments. + var data = { + type: type, + numArgs: props.numArgs || 0, + allowedInText: false, + numOptionalArgs: 0, + handler: handler + }; + + for (var i = 0; i < names.length; ++i) { + // TODO: The value type of _environments should be a type union of all + // possible `EnvSpec<>` possibilities instead of `EnvSpec<*>`, which is + // an existential type. + _environments[names[i]] = data; + } + + if (htmlBuilder) { + _htmlGroupBuilders[type] = htmlBuilder; + } + + if (mathmlBuilder) { + _mathmlGroupBuilders[type] = mathmlBuilder; + } +} +;// CONCATENATED MODULE: ./src/environments/array.js + + + + + + + + + + + + + + +// Helper functions +function getHLines(parser) { + // Return an array. The array length = number of hlines. + // Each element in the array tells if the line is dashed. + var hlineInfo = []; + parser.consumeSpaces(); + var nxt = parser.fetch().text; + + while (nxt === "\\hline" || nxt === "\\hdashline") { + parser.consume(); + hlineInfo.push(nxt === "\\hdashline"); + parser.consumeSpaces(); + nxt = parser.fetch().text; + } + + return hlineInfo; +} + +var validateAmsEnvironmentContext = function validateAmsEnvironmentContext(context) { + var settings = context.parser.settings; + + if (!settings.displayMode) { + throw new src_ParseError("{" + context.envName + "} can be used only in" + " display mode."); + } +}; +/** + * Parse the body of the environment, with rows delimited by \\ and + * columns delimited by &, and create a nested list in row-major order + * with one group per cell. If given an optional argument style + * ("text", "display", etc.), then each cell is cast into that style. + */ + + +function parseArray(parser, _ref, style) { + var hskipBeforeAndAfter = _ref.hskipBeforeAndAfter, + addJot = _ref.addJot, + cols = _ref.cols, + arraystretch = _ref.arraystretch, + colSeparationType = _ref.colSeparationType, + addEqnNum = _ref.addEqnNum, + singleRow = _ref.singleRow, + emptySingleRow = _ref.emptySingleRow, + maxNumCols = _ref.maxNumCols, + leqno = _ref.leqno; + parser.gullet.beginGroup(); + + if (!singleRow) { + // \cr is equivalent to \\ without the optional size argument (see below) + // TODO: provide helpful error when \cr is used outside array environment + parser.gullet.macros.set("\\cr", "\\\\\\relax"); + } // Get current arraystretch if it's not set by the environment + + + if (!arraystretch) { + var stretch = parser.gullet.expandMacroAsText("\\arraystretch"); + + if (stretch == null) { + // Default \arraystretch from lttab.dtx + arraystretch = 1; + } else { + arraystretch = parseFloat(stretch); + + if (!arraystretch || arraystretch < 0) { + throw new src_ParseError("Invalid \\arraystretch: " + stretch); + } + } + } // Start group for first cell + + + parser.gullet.beginGroup(); + var row = []; + var body = [row]; + var rowGaps = []; + var hLinesBeforeRow = []; // Test for \hline at the top of the array. + + hLinesBeforeRow.push(getHLines(parser)); + + while (true) { + // eslint-disable-line no-constant-condition + // Parse each cell in its own group (namespace) + var cell = parser.parseExpression(false, singleRow ? "\\end" : "\\\\"); + parser.gullet.endGroup(); + parser.gullet.beginGroup(); + cell = { + type: "ordgroup", + mode: parser.mode, + body: cell + }; + + if (style) { + cell = { + type: "styling", + mode: parser.mode, + style: style, + body: [cell] + }; + } + + row.push(cell); + var next = parser.fetch().text; + + if (next === "&") { + if (maxNumCols && row.length === maxNumCols) { + if (singleRow || colSeparationType) { + // {equation} or {split} + throw new src_ParseError("Too many tab characters: &", parser.nextToken); + } else { + // {array} environment + parser.settings.reportNonstrict("textEnv", "Too few columns " + "specified in the {array} column argument."); + } + } + + parser.consume(); + } else if (next === "\\end") { + // Arrays terminate newlines with `\crcr` which consumes a `\cr` if + // the last line is empty. However, AMS environments keep the + // empty row if it's the only one. + // NOTE: Currently, `cell` is the last item added into `row`. + if (row.length === 1 && cell.type === "styling" && cell.body[0].body.length === 0 && (body.length > 1 || !emptySingleRow)) { + body.pop(); + } + + if (hLinesBeforeRow.length < body.length + 1) { + hLinesBeforeRow.push([]); + } + + break; + } else if (next === "\\\\") { + parser.consume(); + var size = void 0; // \def\Let@{\let\\\math@cr} + // \def\math@cr{...\math@cr@} + // \def\math@cr@{\new@ifnextchar[\math@cr@@{\math@cr@@[\z@]}} + // \def\math@cr@@[#1]{...\math@cr@@@...} + // \def\math@cr@@@{\cr} + + if (parser.gullet.future().text !== " ") { + size = parser.parseSizeGroup(true); + } + + rowGaps.push(size ? size.value : null); // check for \hline(s) following the row separator + + hLinesBeforeRow.push(getHLines(parser)); + row = []; + body.push(row); + } else { + throw new src_ParseError("Expected & or \\\\ or \\cr or \\end", parser.nextToken); + } + } // End cell group + + + parser.gullet.endGroup(); // End array group defining \cr + + parser.gullet.endGroup(); + return { + type: "array", + mode: parser.mode, + addJot: addJot, + arraystretch: arraystretch, + body: body, + cols: cols, + rowGaps: rowGaps, + hskipBeforeAndAfter: hskipBeforeAndAfter, + hLinesBeforeRow: hLinesBeforeRow, + colSeparationType: colSeparationType, + addEqnNum: addEqnNum, + leqno: leqno + }; +} // Decides on a style for cells in an array according to whether the given +// environment name starts with the letter 'd'. + + +function dCellStyle(envName) { + if (envName.substr(0, 1) === "d") { + return "display"; + } else { + return "text"; + } +} + +var array_htmlBuilder = function htmlBuilder(group, options) { + var r; + var c; + var nr = group.body.length; + var hLinesBeforeRow = group.hLinesBeforeRow; + var nc = 0; + var body = new Array(nr); + var hlines = []; + var ruleThickness = Math.max( // From LaTeX \showthe\arrayrulewidth. Equals 0.04 em. + options.fontMetrics().arrayRuleWidth, options.minRuleThickness // User override. + ); // Horizontal spacing + + var pt = 1 / options.fontMetrics().ptPerEm; + var arraycolsep = 5 * pt; // default value, i.e. \arraycolsep in article.cls + + if (group.colSeparationType && group.colSeparationType === "small") { + // We're in a {smallmatrix}. Default column space is \thickspace, + // i.e. 5/18em = 0.2778em, per amsmath.dtx for {smallmatrix}. + // But that needs adjustment because LaTeX applies \scriptstyle to the + // entire array, including the colspace, but this function applies + // \scriptstyle only inside each element. + var localMultiplier = options.havingStyle(src_Style.SCRIPT).sizeMultiplier; + arraycolsep = 0.2778 * (localMultiplier / options.sizeMultiplier); + } // Vertical spacing + + + var baselineskip = group.colSeparationType === "CD" ? calculateSize({ + number: 3, + unit: "ex" + }, options) : 12 * pt; // see size10.clo + // Default \jot from ltmath.dtx + // TODO(edemaine): allow overriding \jot via \setlength (#687) + + var jot = 3 * pt; + var arrayskip = group.arraystretch * baselineskip; + var arstrutHeight = 0.7 * arrayskip; // \strutbox in ltfsstrc.dtx and + + var arstrutDepth = 0.3 * arrayskip; // \@arstrutbox in lttab.dtx + + var totalHeight = 0; // Set a position for \hline(s) at the top of the array, if any. + + function setHLinePos(hlinesInGap) { + for (var i = 0; i < hlinesInGap.length; ++i) { + if (i > 0) { + totalHeight += 0.25; + } + + hlines.push({ + pos: totalHeight, + isDashed: hlinesInGap[i] + }); + } + } + + setHLinePos(hLinesBeforeRow[0]); + + for (r = 0; r < group.body.length; ++r) { + var inrow = group.body[r]; + var height = arstrutHeight; // \@array adds an \@arstrut + + var depth = arstrutDepth; // to each tow (via the template) + + if (nc < inrow.length) { + nc = inrow.length; + } + + var outrow = new Array(inrow.length); + + for (c = 0; c < inrow.length; ++c) { + var elt = buildGroup(inrow[c], options); + + if (depth < elt.depth) { + depth = elt.depth; + } + + if (height < elt.height) { + height = elt.height; + } + + outrow[c] = elt; + } + + var rowGap = group.rowGaps[r]; + var gap = 0; + + if (rowGap) { + gap = calculateSize(rowGap, options); + + if (gap > 0) { + // \@argarraycr + gap += arstrutDepth; + + if (depth < gap) { + depth = gap; // \@xargarraycr + } + + gap = 0; + } + } // In AMS multiline environments such as aligned and gathered, rows + // correspond to lines that have additional \jot added to the + // \baselineskip via \openup. + + + if (group.addJot) { + depth += jot; + } + + outrow.height = height; + outrow.depth = depth; + totalHeight += height; + outrow.pos = totalHeight; + totalHeight += depth + gap; // \@yargarraycr + + body[r] = outrow; // Set a position for \hline(s), if any. + + setHLinePos(hLinesBeforeRow[r + 1]); + } + + var offset = totalHeight / 2 + options.fontMetrics().axisHeight; + var colDescriptions = group.cols || []; + var cols = []; + var colSep; + var colDescrNum; + var eqnNumSpans = []; + + if (group.addEqnNum) { + // An environment with automatic equation numbers. + // Create node(s) that will trigger CSS counter increment. + for (r = 0; r < nr; ++r) { + var rw = body[r]; + var shift = rw.pos - offset; + var eqnTag = buildCommon.makeSpan(["eqn-num"], [], options); + eqnTag.depth = rw.depth; + eqnTag.height = rw.height; + eqnNumSpans.push({ + type: "elem", + elem: eqnTag, + shift: shift + }); + } + } + + for (c = 0, colDescrNum = 0; // Continue while either there are more columns or more column + // descriptions, so trailing separators don't get lost. + c < nc || colDescrNum < colDescriptions.length; ++c, ++colDescrNum) { + var colDescr = colDescriptions[colDescrNum] || {}; + var firstSeparator = true; + + while (colDescr.type === "separator") { + // If there is more than one separator in a row, add a space + // between them. + if (!firstSeparator) { + colSep = buildCommon.makeSpan(["arraycolsep"], []); + colSep.style.width = options.fontMetrics().doubleRuleSep + "em"; + cols.push(colSep); + } + + if (colDescr.separator === "|" || colDescr.separator === ":") { + var lineType = colDescr.separator === "|" ? "solid" : "dashed"; + var separator = buildCommon.makeSpan(["vertical-separator"], [], options); + separator.style.height = totalHeight + "em"; + separator.style.borderRightWidth = ruleThickness + "em"; + separator.style.borderRightStyle = lineType; + separator.style.margin = "0 -" + ruleThickness / 2 + "em"; + separator.style.verticalAlign = -(totalHeight - offset) + "em"; + cols.push(separator); + } else { + throw new src_ParseError("Invalid separator type: " + colDescr.separator); + } + + colDescrNum++; + colDescr = colDescriptions[colDescrNum] || {}; + firstSeparator = false; + } + + if (c >= nc) { + continue; + } + + var sepwidth = void 0; + + if (c > 0 || group.hskipBeforeAndAfter) { + sepwidth = utils.deflt(colDescr.pregap, arraycolsep); + + if (sepwidth !== 0) { + colSep = buildCommon.makeSpan(["arraycolsep"], []); + colSep.style.width = sepwidth + "em"; + cols.push(colSep); + } + } + + var col = []; + + for (r = 0; r < nr; ++r) { + var row = body[r]; + var elem = row[c]; + + if (!elem) { + continue; + } + + var _shift = row.pos - offset; + + elem.depth = row.depth; + elem.height = row.height; + col.push({ + type: "elem", + elem: elem, + shift: _shift + }); + } + + col = buildCommon.makeVList({ + positionType: "individualShift", + children: col + }, options); + col = buildCommon.makeSpan(["col-align-" + (colDescr.align || "c")], [col]); + cols.push(col); + + if (c < nc - 1 || group.hskipBeforeAndAfter) { + sepwidth = utils.deflt(colDescr.postgap, arraycolsep); + + if (sepwidth !== 0) { + colSep = buildCommon.makeSpan(["arraycolsep"], []); + colSep.style.width = sepwidth + "em"; + cols.push(colSep); + } + } + } + + body = buildCommon.makeSpan(["mtable"], cols); // Add \hline(s), if any. + + if (hlines.length > 0) { + var line = buildCommon.makeLineSpan("hline", options, ruleThickness); + var dashes = buildCommon.makeLineSpan("hdashline", options, ruleThickness); + var vListElems = [{ + type: "elem", + elem: body, + shift: 0 + }]; + + while (hlines.length > 0) { + var hline = hlines.pop(); + var lineShift = hline.pos - offset; + + if (hline.isDashed) { + vListElems.push({ + type: "elem", + elem: dashes, + shift: lineShift + }); + } else { + vListElems.push({ + type: "elem", + elem: line, + shift: lineShift + }); + } + } + + body = buildCommon.makeVList({ + positionType: "individualShift", + children: vListElems + }, options); + } + + if (!group.addEqnNum) { + return buildCommon.makeSpan(["mord"], [body], options); + } else { + var eqnNumCol = buildCommon.makeVList({ + positionType: "individualShift", + children: eqnNumSpans + }, options); + eqnNumCol = buildCommon.makeSpan(["tag"], [eqnNumCol], options); + return buildCommon.makeFragment([body, eqnNumCol]); + } +}; + +var alignMap = { + c: "center ", + l: "left ", + r: "right " +}; + +var array_mathmlBuilder = function mathmlBuilder(group, options) { + var tbl = []; + var glue = new mathMLTree.MathNode("mtd", [], ["mtr-glue"]); + var tag = new mathMLTree.MathNode("mtd", [], ["mml-eqn-num"]); + + for (var i = 0; i < group.body.length; i++) { + var rw = group.body[i]; + var row = []; + + for (var j = 0; j < rw.length; j++) { + row.push(new mathMLTree.MathNode("mtd", [buildMathML_buildGroup(rw[j], options)])); + } + + if (group.addEqnNum) { + row.unshift(glue); + row.push(glue); + + if (group.leqno) { + row.unshift(tag); + } else { + row.push(tag); + } + } + + tbl.push(new mathMLTree.MathNode("mtr", row)); + } + + var table = new mathMLTree.MathNode("mtable", tbl); // Set column alignment, row spacing, column spacing, and + // array lines by setting attributes on the table element. + // Set the row spacing. In MathML, we specify a gap distance. + // We do not use rowGap[] because MathML automatically increases + // cell height with the height/depth of the element content. + // LaTeX \arraystretch multiplies the row baseline-to-baseline distance. + // We simulate this by adding (arraystretch - 1)em to the gap. This + // does a reasonable job of adjusting arrays containing 1 em tall content. + // The 0.16 and 0.09 values are found emprically. They produce an array + // similar to LaTeX and in which content does not interfere with \hines. + + var gap = group.arraystretch === 0.5 ? 0.1 // {smallmatrix}, {subarray} + : 0.16 + group.arraystretch - 1 + (group.addJot ? 0.09 : 0); + table.setAttribute("rowspacing", gap.toFixed(4) + "em"); // MathML table lines go only between cells. + // To place a line on an edge we'll use , if necessary. + + var menclose = ""; + var align = ""; + + if (group.cols && group.cols.length > 0) { + // Find column alignment, column spacing, and vertical lines. + var cols = group.cols; + var columnLines = ""; + var prevTypeWasAlign = false; + var iStart = 0; + var iEnd = cols.length; + + if (cols[0].type === "separator") { + menclose += "top "; + iStart = 1; + } + + if (cols[cols.length - 1].type === "separator") { + menclose += "bottom "; + iEnd -= 1; + } + + for (var _i = iStart; _i < iEnd; _i++) { + if (cols[_i].type === "align") { + align += alignMap[cols[_i].align]; + + if (prevTypeWasAlign) { + columnLines += "none "; + } + + prevTypeWasAlign = true; + } else if (cols[_i].type === "separator") { + // MathML accepts only single lines between cells. + // So we read only the first of consecutive separators. + if (prevTypeWasAlign) { + columnLines += cols[_i].separator === "|" ? "solid " : "dashed "; + prevTypeWasAlign = false; + } + } + } + + table.setAttribute("columnalign", align.trim()); + + if (/[sd]/.test(columnLines)) { + table.setAttribute("columnlines", columnLines.trim()); + } + } // Set column spacing. + + + if (group.colSeparationType === "align") { + var _cols = group.cols || []; + + var spacing = ""; + + for (var _i2 = 1; _i2 < _cols.length; _i2++) { + spacing += _i2 % 2 ? "0em " : "1em "; + } + + table.setAttribute("columnspacing", spacing.trim()); + } else if (group.colSeparationType === "alignat" || group.colSeparationType === "gather") { + table.setAttribute("columnspacing", "0em"); + } else if (group.colSeparationType === "small") { + table.setAttribute("columnspacing", "0.2778em"); + } else if (group.colSeparationType === "CD") { + table.setAttribute("columnspacing", "0.5em"); + } else { + table.setAttribute("columnspacing", "1em"); + } // Address \hline and \hdashline + + + var rowLines = ""; + var hlines = group.hLinesBeforeRow; + menclose += hlines[0].length > 0 ? "left " : ""; + menclose += hlines[hlines.length - 1].length > 0 ? "right " : ""; + + for (var _i3 = 1; _i3 < hlines.length - 1; _i3++) { + rowLines += hlines[_i3].length === 0 ? "none " // MathML accepts only a single line between rows. Read one element. + : hlines[_i3][0] ? "dashed " : "solid "; + } + + if (/[sd]/.test(rowLines)) { + table.setAttribute("rowlines", rowLines.trim()); + } + + if (menclose !== "") { + table = new mathMLTree.MathNode("menclose", [table]); + table.setAttribute("notation", menclose.trim()); + } + + if (group.arraystretch && group.arraystretch < 1) { + // A small array. Wrap in scriptstyle so row gap is not too large. + table = new mathMLTree.MathNode("mstyle", [table]); + table.setAttribute("scriptlevel", "1"); + } + + return table; +}; // Convenience function for align, align*, aligned, alignat, alignat*, alignedat. + + +var alignedHandler = function alignedHandler(context, args) { + if (context.envName.indexOf("ed") === -1) { + validateAmsEnvironmentContext(context); + } + + var cols = []; + var separationType = context.envName.indexOf("at") > -1 ? "alignat" : "align"; + var res = parseArray(context.parser, { + cols: cols, + addJot: true, + addEqnNum: context.envName === "align" || context.envName === "alignat", + emptySingleRow: true, + colSeparationType: separationType, + maxNumCols: context.envName === "split" ? 2 : undefined, + leqno: context.parser.settings.leqno + }, "display"); // Determining number of columns. + // 1. If the first argument is given, we use it as a number of columns, + // and makes sure that each row doesn't exceed that number. + // 2. Otherwise, just count number of columns = maximum number + // of cells in each row ("aligned" mode -- isAligned will be true). + // + // At the same time, prepend empty group {} at beginning of every second + // cell in each row (starting with second cell) so that operators become + // binary. This behavior is implemented in amsmath's \start@aligned. + + var numMaths; + var numCols = 0; + var emptyGroup = { + type: "ordgroup", + mode: context.mode, + body: [] + }; + + if (args[0] && args[0].type === "ordgroup") { + var arg0 = ""; + + for (var i = 0; i < args[0].body.length; i++) { + var textord = assertNodeType(args[0].body[i], "textord"); + arg0 += textord.text; + } + + numMaths = Number(arg0); + numCols = numMaths * 2; + } + + var isAligned = !numCols; + res.body.forEach(function (row) { + for (var _i4 = 1; _i4 < row.length; _i4 += 2) { + // Modify ordgroup node within styling node + var styling = assertNodeType(row[_i4], "styling"); + var ordgroup = assertNodeType(styling.body[0], "ordgroup"); + ordgroup.body.unshift(emptyGroup); + } + + if (!isAligned) { + // Case 1 + var curMaths = row.length / 2; + + if (numMaths < curMaths) { + throw new src_ParseError("Too many math in a row: " + ("expected " + numMaths + ", but got " + curMaths), row[0]); + } + } else if (numCols < row.length) { + // Case 2 + numCols = row.length; + } + }); // Adjusting alignment. + // In aligned mode, we add one \qquad between columns; + // otherwise we add nothing. + + for (var _i5 = 0; _i5 < numCols; ++_i5) { + var align = "r"; + var pregap = 0; + + if (_i5 % 2 === 1) { + align = "l"; + } else if (_i5 > 0 && isAligned) { + // "aligned" mode. + pregap = 1; // add one \quad + } + + cols[_i5] = { + type: "align", + align: align, + pregap: pregap, + postgap: 0 + }; + } + + res.colSeparationType = isAligned ? "align" : "alignat"; + return res; +}; // Arrays are part of LaTeX, defined in lttab.dtx so its documentation +// is part of the source2e.pdf file of LaTeX2e source documentation. +// {darray} is an {array} environment where cells are set in \displaystyle, +// as defined in nccmath.sty. + + +defineEnvironment({ + type: "array", + names: ["array", "darray"], + props: { + numArgs: 1 + }, + handler: function handler(context, args) { + // Since no types are specified above, the two possibilities are + // - The argument is wrapped in {} or [], in which case Parser's + // parseGroup() returns an "ordgroup" wrapping some symbol node. + // - The argument is a bare symbol node. + var symNode = checkSymbolNodeType(args[0]); + var colalign = symNode ? [args[0]] : assertNodeType(args[0], "ordgroup").body; + var cols = colalign.map(function (nde) { + var node = assertSymbolNodeType(nde); + var ca = node.text; + + if ("lcr".indexOf(ca) !== -1) { + return { + type: "align", + align: ca + }; + } else if (ca === "|") { + return { + type: "separator", + separator: "|" + }; + } else if (ca === ":") { + return { + type: "separator", + separator: ":" + }; + } + + throw new src_ParseError("Unknown column alignment: " + ca, nde); + }); + var res = { + cols: cols, + hskipBeforeAndAfter: true, + // \@preamble in lttab.dtx + maxNumCols: cols.length + }; + return parseArray(context.parser, res, dCellStyle(context.envName)); + }, + htmlBuilder: array_htmlBuilder, + mathmlBuilder: array_mathmlBuilder +}); // The matrix environments of amsmath builds on the array environment +// of LaTeX, which is discussed above. +// The mathtools package adds starred versions of the same environments. +// These have an optional argument to choose left|center|right justification. + +defineEnvironment({ + type: "array", + names: ["matrix", "pmatrix", "bmatrix", "Bmatrix", "vmatrix", "Vmatrix", "matrix*", "pmatrix*", "bmatrix*", "Bmatrix*", "vmatrix*", "Vmatrix*"], + props: { + numArgs: 0 + }, + handler: function handler(context) { + var delimiters = { + "matrix": null, + "pmatrix": ["(", ")"], + "bmatrix": ["[", "]"], + "Bmatrix": ["\\{", "\\}"], + "vmatrix": ["|", "|"], + "Vmatrix": ["\\Vert", "\\Vert"] + }[context.envName.replace("*", "")]; // \hskip -\arraycolsep in amsmath + + var colAlign = "c"; + var payload = { + hskipBeforeAndAfter: false, + cols: [{ + type: "align", + align: colAlign + }] + }; + + if (context.envName.charAt(context.envName.length - 1) === "*") { + // It's one of the mathtools starred functions. + // Parse the optional alignment argument. + var parser = context.parser; + parser.consumeSpaces(); + + if (parser.fetch().text === "[") { + parser.consume(); + parser.consumeSpaces(); + colAlign = parser.fetch().text; + + if ("lcr".indexOf(colAlign) === -1) { + throw new src_ParseError("Expected l or c or r", parser.nextToken); + } + + parser.consume(); + parser.consumeSpaces(); + parser.expect("]"); + parser.consume(); + payload.cols = [{ + type: "align", + align: colAlign + }]; + } + } + + var res = parseArray(context.parser, payload, dCellStyle(context.envName)); // Populate cols with the correct number of column alignment specs. + + var numCols = Math.max.apply(Math, [0].concat(res.body.map(function (row) { + return row.length; + }))); + res.cols = new Array(numCols).fill({ + type: "align", + align: colAlign + }); + return delimiters ? { + type: "leftright", + mode: context.mode, + body: [res], + left: delimiters[0], + right: delimiters[1], + rightColor: undefined // \right uninfluenced by \color in array + + } : res; + }, + htmlBuilder: array_htmlBuilder, + mathmlBuilder: array_mathmlBuilder +}); +defineEnvironment({ + type: "array", + names: ["smallmatrix"], + props: { + numArgs: 0 + }, + handler: function handler(context) { + var payload = { + arraystretch: 0.5 + }; + var res = parseArray(context.parser, payload, "script"); + res.colSeparationType = "small"; + return res; + }, + htmlBuilder: array_htmlBuilder, + mathmlBuilder: array_mathmlBuilder +}); +defineEnvironment({ + type: "array", + names: ["subarray"], + props: { + numArgs: 1 + }, + handler: function handler(context, args) { + // Parsing of {subarray} is similar to {array} + var symNode = checkSymbolNodeType(args[0]); + var colalign = symNode ? [args[0]] : assertNodeType(args[0], "ordgroup").body; + var cols = colalign.map(function (nde) { + var node = assertSymbolNodeType(nde); + var ca = node.text; // {subarray} only recognizes "l" & "c" + + if ("lc".indexOf(ca) !== -1) { + return { + type: "align", + align: ca + }; + } + + throw new src_ParseError("Unknown column alignment: " + ca, nde); + }); + + if (cols.length > 1) { + throw new src_ParseError("{subarray} can contain only one column"); + } + + var res = { + cols: cols, + hskipBeforeAndAfter: false, + arraystretch: 0.5 + }; + res = parseArray(context.parser, res, "script"); + + if (res.body.length > 0 && res.body[0].length > 1) { + throw new src_ParseError("{subarray} can contain only one column"); + } + + return res; + }, + htmlBuilder: array_htmlBuilder, + mathmlBuilder: array_mathmlBuilder +}); // A cases environment (in amsmath.sty) is almost equivalent to +// \def\arraystretch{1.2}% +// \left\{\begin{array}{@{}l@{\quad}l@{}} … \end{array}\right. +// {dcases} is a {cases} environment where cells are set in \displaystyle, +// as defined in mathtools.sty. +// {rcases} is another mathtools environment. It's brace is on the right side. + +defineEnvironment({ + type: "array", + names: ["cases", "dcases", "rcases", "drcases"], + props: { + numArgs: 0 + }, + handler: function handler(context) { + var payload = { + arraystretch: 1.2, + cols: [{ + type: "align", + align: "l", + pregap: 0, + // TODO(kevinb) get the current style. + // For now we use the metrics for TEXT style which is what we were + // doing before. Before attempting to get the current style we + // should look at TeX's behavior especially for \over and matrices. + postgap: 1.0 + /* 1em quad */ + + }, { + type: "align", + align: "l", + pregap: 0, + postgap: 0 + }] + }; + var res = parseArray(context.parser, payload, dCellStyle(context.envName)); + return { + type: "leftright", + mode: context.mode, + body: [res], + left: context.envName.indexOf("r") > -1 ? "." : "\\{", + right: context.envName.indexOf("r") > -1 ? "\\}" : ".", + rightColor: undefined + }; + }, + htmlBuilder: array_htmlBuilder, + mathmlBuilder: array_mathmlBuilder +}); // In the align environment, one uses ampersands, &, to specify number of +// columns in each row, and to locate spacing between each column. +// align gets automatic numbering. align* and aligned do not. +// The alignedat environment can be used in math mode. +// Note that we assume \nomallineskiplimit to be zero, +// so that \strut@ is the same as \strut. + +defineEnvironment({ + type: "array", + names: ["align", "align*", "aligned", "split"], + props: { + numArgs: 0 + }, + handler: alignedHandler, + htmlBuilder: array_htmlBuilder, + mathmlBuilder: array_mathmlBuilder +}); // A gathered environment is like an array environment with one centered +// column, but where rows are considered lines so get \jot line spacing +// and contents are set in \displaystyle. + +defineEnvironment({ + type: "array", + names: ["gathered", "gather", "gather*"], + props: { + numArgs: 0 + }, + handler: function handler(context) { + if (utils.contains(["gather", "gather*"], context.envName)) { + validateAmsEnvironmentContext(context); + } + + var res = { + cols: [{ + type: "align", + align: "c" + }], + addJot: true, + colSeparationType: "gather", + addEqnNum: context.envName === "gather", + emptySingleRow: true, + leqno: context.parser.settings.leqno + }; + return parseArray(context.parser, res, "display"); + }, + htmlBuilder: array_htmlBuilder, + mathmlBuilder: array_mathmlBuilder +}); // alignat environment is like an align environment, but one must explicitly +// specify maximum number of columns in each row, and can adjust spacing between +// each columns. + +defineEnvironment({ + type: "array", + names: ["alignat", "alignat*", "alignedat"], + props: { + numArgs: 1 + }, + handler: alignedHandler, + htmlBuilder: array_htmlBuilder, + mathmlBuilder: array_mathmlBuilder +}); +defineEnvironment({ + type: "array", + names: ["equation", "equation*"], + props: { + numArgs: 0 + }, + handler: function handler(context) { + validateAmsEnvironmentContext(context); + var res = { + addEqnNum: context.envName === "equation", + emptySingleRow: true, + singleRow: true, + maxNumCols: 1, + leqno: context.parser.settings.leqno + }; + return parseArray(context.parser, res, "display"); + }, + htmlBuilder: array_htmlBuilder, + mathmlBuilder: array_mathmlBuilder +}); +defineEnvironment({ + type: "array", + names: ["CD"], + props: { + numArgs: 0 + }, + handler: function handler(context) { + validateAmsEnvironmentContext(context); + return parseCD(context.parser); + }, + htmlBuilder: array_htmlBuilder, + mathmlBuilder: array_mathmlBuilder +}); // Catch \hline outside array environment + +defineFunction({ + type: "text", + // Doesn't matter what this is. + names: ["\\hline", "\\hdashline"], + props: { + numArgs: 0, + allowedInText: true, + allowedInMath: true + }, + handler: function handler(context, args) { + throw new src_ParseError(context.funcName + " valid only within array environment"); + } +}); +;// CONCATENATED MODULE: ./src/environments.js + +var environments = _environments; +/* harmony default export */ var src_environments = (environments); // All environment definitions should be imported below + + +;// CONCATENATED MODULE: ./src/functions/environment.js + + + + // Environment delimiters. HTML/MathML rendering is defined in the corresponding +// defineEnvironment definitions. + +defineFunction({ + type: "environment", + names: ["\\begin", "\\end"], + props: { + numArgs: 1, + argTypes: ["text"] + }, + handler: function handler(_ref, args) { + var parser = _ref.parser, + funcName = _ref.funcName; + var nameGroup = args[0]; + + if (nameGroup.type !== "ordgroup") { + throw new src_ParseError("Invalid environment name", nameGroup); + } + + var envName = ""; + + for (var i = 0; i < nameGroup.body.length; ++i) { + envName += assertNodeType(nameGroup.body[i], "textord").text; + } + + if (funcName === "\\begin") { + // begin...end is similar to left...right + if (!src_environments.hasOwnProperty(envName)) { + throw new src_ParseError("No such environment: " + envName, nameGroup); + } // Build the environment object. Arguments and other information will + // be made available to the begin and end methods using properties. + + + var env = src_environments[envName]; + + var _parser$parseArgument = parser.parseArguments("\\begin{" + envName + "}", env), + _args = _parser$parseArgument.args, + optArgs = _parser$parseArgument.optArgs; + + var context = { + mode: parser.mode, + envName: envName, + parser: parser + }; + var result = env.handler(context, _args, optArgs); + parser.expect("\\end", false); + var endNameToken = parser.nextToken; + var end = assertNodeType(parser.parseFunction(), "environment"); + + if (end.name !== envName) { + throw new src_ParseError("Mismatch: \\begin{" + envName + "} matched by \\end{" + end.name + "}", endNameToken); + } // $FlowFixMe, "environment" handler returns an environment ParseNode + + + return result; + } + + return { + type: "environment", + mode: parser.mode, + name: envName, + nameGroup: nameGroup + }; + } +}); +;// CONCATENATED MODULE: ./src/functions/mclass.js + + + + + + +var mclass_makeSpan = buildCommon.makeSpan; + +function mclass_htmlBuilder(group, options) { + var elements = buildExpression(group.body, options, true); + return mclass_makeSpan([group.mclass], elements, options); +} + +function mclass_mathmlBuilder(group, options) { + var node; + var inner = buildMathML_buildExpression(group.body, options); + + if (group.mclass === "minner") { + return mathMLTree.newDocumentFragment(inner); + } else if (group.mclass === "mord") { + if (group.isCharacterBox) { + node = inner[0]; + node.type = "mi"; + } else { + node = new mathMLTree.MathNode("mi", inner); + } + } else { + if (group.isCharacterBox) { + node = inner[0]; + node.type = "mo"; + } else { + node = new mathMLTree.MathNode("mo", inner); + } // Set spacing based on what is the most likely adjacent atom type. + // See TeXbook p170. + + + if (group.mclass === "mbin") { + node.attributes.lspace = "0.22em"; // medium space + + node.attributes.rspace = "0.22em"; + } else if (group.mclass === "mpunct") { + node.attributes.lspace = "0em"; + node.attributes.rspace = "0.17em"; // thinspace + } else if (group.mclass === "mopen" || group.mclass === "mclose") { + node.attributes.lspace = "0em"; + node.attributes.rspace = "0em"; + } // MathML default space is 5/18 em, so needs no action. + // Ref: https://developer.mozilla.org/en-US/docs/Web/MathML/Element/mo + + } + + return node; +} // Math class commands except \mathop + + +defineFunction({ + type: "mclass", + names: ["\\mathord", "\\mathbin", "\\mathrel", "\\mathopen", "\\mathclose", "\\mathpunct", "\\mathinner"], + props: { + numArgs: 1, + primitive: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser, + funcName = _ref.funcName; + var body = args[0]; + return { + type: "mclass", + mode: parser.mode, + mclass: "m" + funcName.substr(5), + // TODO(kevinb): don't prefix with 'm' + body: ordargument(body), + isCharacterBox: utils.isCharacterBox(body) + }; + }, + htmlBuilder: mclass_htmlBuilder, + mathmlBuilder: mclass_mathmlBuilder +}); +var binrelClass = function binrelClass(arg) { + // \binrel@ spacing varies with (bin|rel|ord) of the atom in the argument. + // (by rendering separately and with {}s before and after, and measuring + // the change in spacing). We'll do roughly the same by detecting the + // atom type directly. + var atom = arg.type === "ordgroup" && arg.body.length ? arg.body[0] : arg; + + if (atom.type === "atom" && (atom.family === "bin" || atom.family === "rel")) { + return "m" + atom.family; + } else { + return "mord"; + } +}; // \@binrel{x}{y} renders like y but as mbin/mrel/mord if x is mbin/mrel/mord. +// This is equivalent to \binrel@{x}\binrel@@{y} in AMSTeX. + +defineFunction({ + type: "mclass", + names: ["\\@binrel"], + props: { + numArgs: 2 + }, + handler: function handler(_ref2, args) { + var parser = _ref2.parser; + return { + type: "mclass", + mode: parser.mode, + mclass: binrelClass(args[0]), + body: ordargument(args[1]), + isCharacterBox: utils.isCharacterBox(args[1]) + }; + } +}); // Build a relation or stacked op by placing one symbol on top of another + +defineFunction({ + type: "mclass", + names: ["\\stackrel", "\\overset", "\\underset"], + props: { + numArgs: 2 + }, + handler: function handler(_ref3, args) { + var parser = _ref3.parser, + funcName = _ref3.funcName; + var baseArg = args[1]; + var shiftedArg = args[0]; + var mclass; + + if (funcName !== "\\stackrel") { + // LaTeX applies \binrel spacing to \overset and \underset. + mclass = binrelClass(baseArg); + } else { + mclass = "mrel"; // for \stackrel + } + + var baseOp = { + type: "op", + mode: baseArg.mode, + limits: true, + alwaysHandleSupSub: true, + parentIsSupSub: false, + symbol: false, + suppressBaseShift: funcName !== "\\stackrel", + body: ordargument(baseArg) + }; + var supsub = { + type: "supsub", + mode: shiftedArg.mode, + base: baseOp, + sup: funcName === "\\underset" ? null : shiftedArg, + sub: funcName === "\\underset" ? shiftedArg : null + }; + return { + type: "mclass", + mode: parser.mode, + mclass: mclass, + body: [supsub], + isCharacterBox: utils.isCharacterBox(supsub) + }; + }, + htmlBuilder: mclass_htmlBuilder, + mathmlBuilder: mclass_mathmlBuilder +}); +;// CONCATENATED MODULE: ./src/functions/font.js +// TODO(kevinb): implement \\sl and \\sc + + + + + + +var font_htmlBuilder = function htmlBuilder(group, options) { + var font = group.font; + var newOptions = options.withFont(font); + return buildGroup(group.body, newOptions); +}; + +var font_mathmlBuilder = function mathmlBuilder(group, options) { + var font = group.font; + var newOptions = options.withFont(font); + return buildMathML_buildGroup(group.body, newOptions); +}; + +var fontAliases = { + "\\Bbb": "\\mathbb", + "\\bold": "\\mathbf", + "\\frak": "\\mathfrak", + "\\bm": "\\boldsymbol" +}; +defineFunction({ + type: "font", + names: [// styles, except \boldsymbol defined below + "\\mathrm", "\\mathit", "\\mathbf", "\\mathnormal", // families + "\\mathbb", "\\mathcal", "\\mathfrak", "\\mathscr", "\\mathsf", "\\mathtt", // aliases, except \bm defined below + "\\Bbb", "\\bold", "\\frak"], + props: { + numArgs: 1, + allowedInArgument: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser, + funcName = _ref.funcName; + var body = normalizeArgument(args[0]); + var func = funcName; + + if (func in fontAliases) { + func = fontAliases[func]; + } + + return { + type: "font", + mode: parser.mode, + font: func.slice(1), + body: body + }; + }, + htmlBuilder: font_htmlBuilder, + mathmlBuilder: font_mathmlBuilder +}); +defineFunction({ + type: "mclass", + names: ["\\boldsymbol", "\\bm"], + props: { + numArgs: 1 + }, + handler: function handler(_ref2, args) { + var parser = _ref2.parser; + var body = args[0]; + var isCharacterBox = utils.isCharacterBox(body); // amsbsy.sty's \boldsymbol uses \binrel spacing to inherit the + // argument's bin|rel|ord status + + return { + type: "mclass", + mode: parser.mode, + mclass: binrelClass(body), + body: [{ + type: "font", + mode: parser.mode, + font: "boldsymbol", + body: body + }], + isCharacterBox: isCharacterBox + }; + } +}); // Old font changing functions + +defineFunction({ + type: "font", + names: ["\\rm", "\\sf", "\\tt", "\\bf", "\\it", "\\cal"], + props: { + numArgs: 0, + allowedInText: true + }, + handler: function handler(_ref3, args) { + var parser = _ref3.parser, + funcName = _ref3.funcName, + breakOnTokenText = _ref3.breakOnTokenText; + var mode = parser.mode; + var body = parser.parseExpression(true, breakOnTokenText); + var style = "math" + funcName.slice(1); + return { + type: "font", + mode: mode, + font: style, + body: { + type: "ordgroup", + mode: parser.mode, + body: body + } + }; + }, + htmlBuilder: font_htmlBuilder, + mathmlBuilder: font_mathmlBuilder +}); +;// CONCATENATED MODULE: ./src/functions/genfrac.js + + + + + + + + + + + +var adjustStyle = function adjustStyle(size, originalStyle) { + // Figure out what style this fraction should be in based on the + // function used + var style = originalStyle; + + if (size === "display") { + // Get display style as a default. + // If incoming style is sub/sup, use style.text() to get correct size. + style = style.id >= src_Style.SCRIPT.id ? style.text() : src_Style.DISPLAY; + } else if (size === "text" && style.size === src_Style.DISPLAY.size) { + // We're in a \tfrac but incoming style is displaystyle, so: + style = src_Style.TEXT; + } else if (size === "script") { + style = src_Style.SCRIPT; + } else if (size === "scriptscript") { + style = src_Style.SCRIPTSCRIPT; + } + + return style; +}; + +var genfrac_htmlBuilder = function htmlBuilder(group, options) { + // Fractions are handled in the TeXbook on pages 444-445, rules 15(a-e). + var style = adjustStyle(group.size, options.style); + var nstyle = style.fracNum(); + var dstyle = style.fracDen(); + var newOptions; + newOptions = options.havingStyle(nstyle); + var numerm = buildGroup(group.numer, newOptions, options); + + if (group.continued) { + // \cfrac inserts a \strut into the numerator. + // Get \strut dimensions from TeXbook page 353. + var hStrut = 8.5 / options.fontMetrics().ptPerEm; + var dStrut = 3.5 / options.fontMetrics().ptPerEm; + numerm.height = numerm.height < hStrut ? hStrut : numerm.height; + numerm.depth = numerm.depth < dStrut ? dStrut : numerm.depth; + } + + newOptions = options.havingStyle(dstyle); + var denomm = buildGroup(group.denom, newOptions, options); + var rule; + var ruleWidth; + var ruleSpacing; + + if (group.hasBarLine) { + if (group.barSize) { + ruleWidth = calculateSize(group.barSize, options); + rule = buildCommon.makeLineSpan("frac-line", options, ruleWidth); + } else { + rule = buildCommon.makeLineSpan("frac-line", options); + } + + ruleWidth = rule.height; + ruleSpacing = rule.height; + } else { + rule = null; + ruleWidth = 0; + ruleSpacing = options.fontMetrics().defaultRuleThickness; + } // Rule 15b + + + var numShift; + var clearance; + var denomShift; + + if (style.size === src_Style.DISPLAY.size || group.size === "display") { + numShift = options.fontMetrics().num1; + + if (ruleWidth > 0) { + clearance = 3 * ruleSpacing; + } else { + clearance = 7 * ruleSpacing; + } + + denomShift = options.fontMetrics().denom1; + } else { + if (ruleWidth > 0) { + numShift = options.fontMetrics().num2; + clearance = ruleSpacing; + } else { + numShift = options.fontMetrics().num3; + clearance = 3 * ruleSpacing; + } + + denomShift = options.fontMetrics().denom2; + } + + var frac; + + if (!rule) { + // Rule 15c + var candidateClearance = numShift - numerm.depth - (denomm.height - denomShift); + + if (candidateClearance < clearance) { + numShift += 0.5 * (clearance - candidateClearance); + denomShift += 0.5 * (clearance - candidateClearance); + } + + frac = buildCommon.makeVList({ + positionType: "individualShift", + children: [{ + type: "elem", + elem: denomm, + shift: denomShift + }, { + type: "elem", + elem: numerm, + shift: -numShift + }] + }, options); + } else { + // Rule 15d + var axisHeight = options.fontMetrics().axisHeight; + + if (numShift - numerm.depth - (axisHeight + 0.5 * ruleWidth) < clearance) { + numShift += clearance - (numShift - numerm.depth - (axisHeight + 0.5 * ruleWidth)); + } + + if (axisHeight - 0.5 * ruleWidth - (denomm.height - denomShift) < clearance) { + denomShift += clearance - (axisHeight - 0.5 * ruleWidth - (denomm.height - denomShift)); + } + + var midShift = -(axisHeight - 0.5 * ruleWidth); + frac = buildCommon.makeVList({ + positionType: "individualShift", + children: [{ + type: "elem", + elem: denomm, + shift: denomShift + }, { + type: "elem", + elem: rule, + shift: midShift + }, { + type: "elem", + elem: numerm, + shift: -numShift + }] + }, options); + } // Since we manually change the style sometimes (with \dfrac or \tfrac), + // account for the possible size change here. + + + newOptions = options.havingStyle(style); + frac.height *= newOptions.sizeMultiplier / options.sizeMultiplier; + frac.depth *= newOptions.sizeMultiplier / options.sizeMultiplier; // Rule 15e + + var delimSize; + + if (style.size === src_Style.DISPLAY.size) { + delimSize = options.fontMetrics().delim1; + } else if (style.size === src_Style.SCRIPTSCRIPT.size) { + delimSize = options.havingStyle(src_Style.SCRIPT).fontMetrics().delim2; + } else { + delimSize = options.fontMetrics().delim2; + } + + var leftDelim; + var rightDelim; + + if (group.leftDelim == null) { + leftDelim = makeNullDelimiter(options, ["mopen"]); + } else { + leftDelim = delimiter.customSizedDelim(group.leftDelim, delimSize, true, options.havingStyle(style), group.mode, ["mopen"]); + } + + if (group.continued) { + rightDelim = buildCommon.makeSpan([]); // zero width for \cfrac + } else if (group.rightDelim == null) { + rightDelim = makeNullDelimiter(options, ["mclose"]); + } else { + rightDelim = delimiter.customSizedDelim(group.rightDelim, delimSize, true, options.havingStyle(style), group.mode, ["mclose"]); + } + + return buildCommon.makeSpan(["mord"].concat(newOptions.sizingClasses(options)), [leftDelim, buildCommon.makeSpan(["mfrac"], [frac]), rightDelim], options); +}; + +var genfrac_mathmlBuilder = function mathmlBuilder(group, options) { + var node = new mathMLTree.MathNode("mfrac", [buildMathML_buildGroup(group.numer, options), buildMathML_buildGroup(group.denom, options)]); + + if (!group.hasBarLine) { + node.setAttribute("linethickness", "0px"); + } else if (group.barSize) { + var ruleWidth = calculateSize(group.barSize, options); + node.setAttribute("linethickness", ruleWidth + "em"); + } + + var style = adjustStyle(group.size, options.style); + + if (style.size !== options.style.size) { + node = new mathMLTree.MathNode("mstyle", [node]); + var isDisplay = style.size === src_Style.DISPLAY.size ? "true" : "false"; + node.setAttribute("displaystyle", isDisplay); + node.setAttribute("scriptlevel", "0"); + } + + if (group.leftDelim != null || group.rightDelim != null) { + var withDelims = []; + + if (group.leftDelim != null) { + var leftOp = new mathMLTree.MathNode("mo", [new mathMLTree.TextNode(group.leftDelim.replace("\\", ""))]); + leftOp.setAttribute("fence", "true"); + withDelims.push(leftOp); + } + + withDelims.push(node); + + if (group.rightDelim != null) { + var rightOp = new mathMLTree.MathNode("mo", [new mathMLTree.TextNode(group.rightDelim.replace("\\", ""))]); + rightOp.setAttribute("fence", "true"); + withDelims.push(rightOp); + } + + return makeRow(withDelims); + } + + return node; +}; + +defineFunction({ + type: "genfrac", + names: ["\\dfrac", "\\frac", "\\tfrac", "\\dbinom", "\\binom", "\\tbinom", "\\\\atopfrac", // can’t be entered directly + "\\\\bracefrac", "\\\\brackfrac" // ditto + ], + props: { + numArgs: 2, + allowedInArgument: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser, + funcName = _ref.funcName; + var numer = args[0]; + var denom = args[1]; + var hasBarLine; + var leftDelim = null; + var rightDelim = null; + var size = "auto"; + + switch (funcName) { + case "\\dfrac": + case "\\frac": + case "\\tfrac": + hasBarLine = true; + break; + + case "\\\\atopfrac": + hasBarLine = false; + break; + + case "\\dbinom": + case "\\binom": + case "\\tbinom": + hasBarLine = false; + leftDelim = "("; + rightDelim = ")"; + break; + + case "\\\\bracefrac": + hasBarLine = false; + leftDelim = "\\{"; + rightDelim = "\\}"; + break; + + case "\\\\brackfrac": + hasBarLine = false; + leftDelim = "["; + rightDelim = "]"; + break; + + default: + throw new Error("Unrecognized genfrac command"); + } + + switch (funcName) { + case "\\dfrac": + case "\\dbinom": + size = "display"; + break; + + case "\\tfrac": + case "\\tbinom": + size = "text"; + break; + } + + return { + type: "genfrac", + mode: parser.mode, + continued: false, + numer: numer, + denom: denom, + hasBarLine: hasBarLine, + leftDelim: leftDelim, + rightDelim: rightDelim, + size: size, + barSize: null + }; + }, + htmlBuilder: genfrac_htmlBuilder, + mathmlBuilder: genfrac_mathmlBuilder +}); +defineFunction({ + type: "genfrac", + names: ["\\cfrac"], + props: { + numArgs: 2 + }, + handler: function handler(_ref2, args) { + var parser = _ref2.parser, + funcName = _ref2.funcName; + var numer = args[0]; + var denom = args[1]; + return { + type: "genfrac", + mode: parser.mode, + continued: true, + numer: numer, + denom: denom, + hasBarLine: true, + leftDelim: null, + rightDelim: null, + size: "display", + barSize: null + }; + } +}); // Infix generalized fractions -- these are not rendered directly, but replaced +// immediately by one of the variants above. + +defineFunction({ + type: "infix", + names: ["\\over", "\\choose", "\\atop", "\\brace", "\\brack"], + props: { + numArgs: 0, + infix: true + }, + handler: function handler(_ref3) { + var parser = _ref3.parser, + funcName = _ref3.funcName, + token = _ref3.token; + var replaceWith; + + switch (funcName) { + case "\\over": + replaceWith = "\\frac"; + break; + + case "\\choose": + replaceWith = "\\binom"; + break; + + case "\\atop": + replaceWith = "\\\\atopfrac"; + break; + + case "\\brace": + replaceWith = "\\\\bracefrac"; + break; + + case "\\brack": + replaceWith = "\\\\brackfrac"; + break; + + default: + throw new Error("Unrecognized infix genfrac command"); + } + + return { + type: "infix", + mode: parser.mode, + replaceWith: replaceWith, + token: token + }; + } +}); +var stylArray = ["display", "text", "script", "scriptscript"]; + +var delimFromValue = function delimFromValue(delimString) { + var delim = null; + + if (delimString.length > 0) { + delim = delimString; + delim = delim === "." ? null : delim; + } + + return delim; +}; + +defineFunction({ + type: "genfrac", + names: ["\\genfrac"], + props: { + numArgs: 6, + allowedInArgument: true, + argTypes: ["math", "math", "size", "text", "math", "math"] + }, + handler: function handler(_ref4, args) { + var parser = _ref4.parser; + var numer = args[4]; + var denom = args[5]; // Look into the parse nodes to get the desired delimiters. + + var leftNode = normalizeArgument(args[0]); + var leftDelim = leftNode.type === "atom" && leftNode.family === "open" ? delimFromValue(leftNode.text) : null; + var rightNode = normalizeArgument(args[1]); + var rightDelim = rightNode.type === "atom" && rightNode.family === "close" ? delimFromValue(rightNode.text) : null; + var barNode = assertNodeType(args[2], "size"); + var hasBarLine; + var barSize = null; + + if (barNode.isBlank) { + // \genfrac acts differently than \above. + // \genfrac treats an empty size group as a signal to use a + // standard bar size. \above would see size = 0 and omit the bar. + hasBarLine = true; + } else { + barSize = barNode.value; + hasBarLine = barSize.number > 0; + } // Find out if we want displaystyle, textstyle, etc. + + + var size = "auto"; + var styl = args[3]; + + if (styl.type === "ordgroup") { + if (styl.body.length > 0) { + var textOrd = assertNodeType(styl.body[0], "textord"); + size = stylArray[Number(textOrd.text)]; + } + } else { + styl = assertNodeType(styl, "textord"); + size = stylArray[Number(styl.text)]; + } + + return { + type: "genfrac", + mode: parser.mode, + numer: numer, + denom: denom, + continued: false, + hasBarLine: hasBarLine, + barSize: barSize, + leftDelim: leftDelim, + rightDelim: rightDelim, + size: size + }; + }, + htmlBuilder: genfrac_htmlBuilder, + mathmlBuilder: genfrac_mathmlBuilder +}); // \above is an infix fraction that also defines a fraction bar size. + +defineFunction({ + type: "infix", + names: ["\\above"], + props: { + numArgs: 1, + argTypes: ["size"], + infix: true + }, + handler: function handler(_ref5, args) { + var parser = _ref5.parser, + funcName = _ref5.funcName, + token = _ref5.token; + return { + type: "infix", + mode: parser.mode, + replaceWith: "\\\\abovefrac", + size: assertNodeType(args[0], "size").value, + token: token + }; + } +}); +defineFunction({ + type: "genfrac", + names: ["\\\\abovefrac"], + props: { + numArgs: 3, + argTypes: ["math", "size", "math"] + }, + handler: function handler(_ref6, args) { + var parser = _ref6.parser, + funcName = _ref6.funcName; + var numer = args[0]; + var barSize = assert(assertNodeType(args[1], "infix").size); + var denom = args[2]; + var hasBarLine = barSize.number > 0; + return { + type: "genfrac", + mode: parser.mode, + numer: numer, + denom: denom, + continued: false, + hasBarLine: hasBarLine, + barSize: barSize, + leftDelim: null, + rightDelim: null, + size: "auto" + }; + }, + htmlBuilder: genfrac_htmlBuilder, + mathmlBuilder: genfrac_mathmlBuilder +}); +;// CONCATENATED MODULE: ./src/functions/horizBrace.js + + + + + + + + +// NOTE: Unlike most `htmlBuilder`s, this one handles not only "horizBrace", but +// also "supsub" since an over/underbrace can affect super/subscripting. +var horizBrace_htmlBuilder = function htmlBuilder(grp, options) { + var style = options.style; // Pull out the `ParseNode<"horizBrace">` if `grp` is a "supsub" node. + + var supSubGroup; + var group; + + if (grp.type === "supsub") { + // Ref: LaTeX source2e: }}}}\limits} + // i.e. LaTeX treats the brace similar to an op and passes it + // with \limits, so we need to assign supsub style. + supSubGroup = grp.sup ? buildGroup(grp.sup, options.havingStyle(style.sup()), options) : buildGroup(grp.sub, options.havingStyle(style.sub()), options); + group = assertNodeType(grp.base, "horizBrace"); + } else { + group = assertNodeType(grp, "horizBrace"); + } // Build the base group + + + var body = buildGroup(group.base, options.havingBaseStyle(src_Style.DISPLAY)); // Create the stretchy element + + var braceBody = stretchy.svgSpan(group, options); // Generate the vlist, with the appropriate kerns ┏━━━━━━━━┓ + // This first vlist contains the content and the brace: equation + + var vlist; + + if (group.isOver) { + vlist = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: body + }, { + type: "kern", + size: 0.1 + }, { + type: "elem", + elem: braceBody + }] + }, options); // $FlowFixMe: Replace this with passing "svg-align" into makeVList. + + vlist.children[0].children[0].children[1].classes.push("svg-align"); + } else { + vlist = buildCommon.makeVList({ + positionType: "bottom", + positionData: body.depth + 0.1 + braceBody.height, + children: [{ + type: "elem", + elem: braceBody + }, { + type: "kern", + size: 0.1 + }, { + type: "elem", + elem: body + }] + }, options); // $FlowFixMe: Replace this with passing "svg-align" into makeVList. + + vlist.children[0].children[0].children[0].classes.push("svg-align"); + } + + if (supSubGroup) { + // To write the supsub, wrap the first vlist in another vlist: + // They can't all go in the same vlist, because the note might be + // wider than the equation. We want the equation to control the + // brace width. + // note long note long note + // ┏━━━━━━━━┓ or ┏━━━┓ not ┏━━━━━━━━━┓ + // equation eqn eqn + var vSpan = buildCommon.makeSpan(["mord", group.isOver ? "mover" : "munder"], [vlist], options); + + if (group.isOver) { + vlist = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: vSpan + }, { + type: "kern", + size: 0.2 + }, { + type: "elem", + elem: supSubGroup + }] + }, options); + } else { + vlist = buildCommon.makeVList({ + positionType: "bottom", + positionData: vSpan.depth + 0.2 + supSubGroup.height + supSubGroup.depth, + children: [{ + type: "elem", + elem: supSubGroup + }, { + type: "kern", + size: 0.2 + }, { + type: "elem", + elem: vSpan + }] + }, options); + } + } + + return buildCommon.makeSpan(["mord", group.isOver ? "mover" : "munder"], [vlist], options); +}; + +var horizBrace_mathmlBuilder = function mathmlBuilder(group, options) { + var accentNode = stretchy.mathMLnode(group.label); + return new mathMLTree.MathNode(group.isOver ? "mover" : "munder", [buildMathML_buildGroup(group.base, options), accentNode]); +}; // Horizontal stretchy braces + + +defineFunction({ + type: "horizBrace", + names: ["\\overbrace", "\\underbrace"], + props: { + numArgs: 1 + }, + handler: function handler(_ref, args) { + var parser = _ref.parser, + funcName = _ref.funcName; + return { + type: "horizBrace", + mode: parser.mode, + label: funcName, + isOver: /^\\over/.test(funcName), + base: args[0] + }; + }, + htmlBuilder: horizBrace_htmlBuilder, + mathmlBuilder: horizBrace_mathmlBuilder +}); +;// CONCATENATED MODULE: ./src/functions/href.js + + + + + + +defineFunction({ + type: "href", + names: ["\\href"], + props: { + numArgs: 2, + argTypes: ["url", "original"], + allowedInText: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser; + var body = args[1]; + var href = assertNodeType(args[0], "url").url; + + if (!parser.settings.isTrusted({ + command: "\\href", + url: href + })) { + return parser.formatUnsupportedCmd("\\href"); + } + + return { + type: "href", + mode: parser.mode, + href: href, + body: ordargument(body) + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var elements = buildExpression(group.body, options, false); + return buildCommon.makeAnchor(group.href, [], elements, options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var math = buildExpressionRow(group.body, options); + + if (!(math instanceof MathNode)) { + math = new MathNode("mrow", [math]); + } + + math.setAttribute("href", group.href); + return math; + } +}); +defineFunction({ + type: "href", + names: ["\\url"], + props: { + numArgs: 1, + argTypes: ["url"], + allowedInText: true + }, + handler: function handler(_ref2, args) { + var parser = _ref2.parser; + var href = assertNodeType(args[0], "url").url; + + if (!parser.settings.isTrusted({ + command: "\\url", + url: href + })) { + return parser.formatUnsupportedCmd("\\url"); + } + + var chars = []; + + for (var i = 0; i < href.length; i++) { + var c = href[i]; + + if (c === "~") { + c = "\\textasciitilde"; + } + + chars.push({ + type: "textord", + mode: "text", + text: c + }); + } + + var body = { + type: "text", + mode: parser.mode, + font: "\\texttt", + body: chars + }; + return { + type: "href", + mode: parser.mode, + href: href, + body: ordargument(body) + }; + } +}); +;// CONCATENATED MODULE: ./src/functions/hbox.js + + + + + // \hbox is provided for compatibility with LaTeX \vcenter. +// In LaTeX, \vcenter can act only on a box, as in +// \vcenter{\hbox{$\frac{a+b}{\dfrac{c}{d}}$}} +// This function by itself doesn't do anything but prevent a soft line break. + +defineFunction({ + type: "hbox", + names: ["\\hbox"], + props: { + numArgs: 1, + argTypes: ["text"], + allowedInText: true, + primitive: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser; + return { + type: "hbox", + mode: parser.mode, + body: ordargument(args[0]) + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var elements = buildExpression(group.body, options, false); + return buildCommon.makeFragment(elements); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + return new mathMLTree.MathNode("mrow", buildMathML_buildExpression(group.body, options)); + } +}); +;// CONCATENATED MODULE: ./src/functions/html.js + + + + + + +defineFunction({ + type: "html", + names: ["\\htmlClass", "\\htmlId", "\\htmlStyle", "\\htmlData"], + props: { + numArgs: 2, + argTypes: ["raw", "original"], + allowedInText: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser, + funcName = _ref.funcName, + token = _ref.token; + var value = assertNodeType(args[0], "raw").string; + var body = args[1]; + + if (parser.settings.strict) { + parser.settings.reportNonstrict("htmlExtension", "HTML extension is disabled on strict mode"); + } + + var trustContext; + var attributes = {}; + + switch (funcName) { + case "\\htmlClass": + attributes.class = value; + trustContext = { + command: "\\htmlClass", + class: value + }; + break; + + case "\\htmlId": + attributes.id = value; + trustContext = { + command: "\\htmlId", + id: value + }; + break; + + case "\\htmlStyle": + attributes.style = value; + trustContext = { + command: "\\htmlStyle", + style: value + }; + break; + + case "\\htmlData": + { + var data = value.split(","); + + for (var i = 0; i < data.length; i++) { + var keyVal = data[i].split("="); + + if (keyVal.length !== 2) { + throw new src_ParseError("Error parsing key-value for \\htmlData"); + } + + attributes["data-" + keyVal[0].trim()] = keyVal[1].trim(); + } + + trustContext = { + command: "\\htmlData", + attributes: attributes + }; + break; + } + + default: + throw new Error("Unrecognized html command"); + } + + if (!parser.settings.isTrusted(trustContext)) { + return parser.formatUnsupportedCmd(funcName); + } + + return { + type: "html", + mode: parser.mode, + attributes: attributes, + body: ordargument(body) + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var elements = buildExpression(group.body, options, false); + var classes = ["enclosing"]; + + if (group.attributes.class) { + classes.push.apply(classes, group.attributes.class.trim().split(/\s+/)); + } + + var span = buildCommon.makeSpan(classes, elements, options); + + for (var attr in group.attributes) { + if (attr !== "class" && group.attributes.hasOwnProperty(attr)) { + span.setAttribute(attr, group.attributes[attr]); + } + } + + return span; + }, + mathmlBuilder: function mathmlBuilder(group, options) { + return buildExpressionRow(group.body, options); + } +}); +;// CONCATENATED MODULE: ./src/functions/htmlmathml.js + + + + +defineFunction({ + type: "htmlmathml", + names: ["\\html@mathml"], + props: { + numArgs: 2, + allowedInText: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser; + return { + type: "htmlmathml", + mode: parser.mode, + html: ordargument(args[0]), + mathml: ordargument(args[1]) + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var elements = buildExpression(group.html, options, false); + return buildCommon.makeFragment(elements); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + return buildExpressionRow(group.mathml, options); + } +}); +;// CONCATENATED MODULE: ./src/functions/includegraphics.js + + + + + + + +var sizeData = function sizeData(str) { + if (/^[-+]? *(\d+(\.\d*)?|\.\d+)$/.test(str)) { + // str is a number with no unit specified. + // default unit is bp, per graphix package. + return { + number: +str, + unit: "bp" + }; + } else { + var match = /([-+]?) *(\d+(?:\.\d*)?|\.\d+) *([a-z]{2})/.exec(str); + + if (!match) { + throw new src_ParseError("Invalid size: '" + str + "' in \\includegraphics"); + } + + var data = { + number: +(match[1] + match[2]), + // sign + magnitude, cast to number + unit: match[3] + }; + + if (!validUnit(data)) { + throw new src_ParseError("Invalid unit: '" + data.unit + "' in \\includegraphics."); + } + + return data; + } +}; + +defineFunction({ + type: "includegraphics", + names: ["\\includegraphics"], + props: { + numArgs: 1, + numOptionalArgs: 1, + argTypes: ["raw", "url"], + allowedInText: false + }, + handler: function handler(_ref, args, optArgs) { + var parser = _ref.parser; + var width = { + number: 0, + unit: "em" + }; + var height = { + number: 0.9, + unit: "em" + }; // sorta character sized. + + var totalheight = { + number: 0, + unit: "em" + }; + var alt = ""; + + if (optArgs[0]) { + var attributeStr = assertNodeType(optArgs[0], "raw").string; // Parser.js does not parse key/value pairs. We get a string. + + var attributes = attributeStr.split(","); + + for (var i = 0; i < attributes.length; i++) { + var keyVal = attributes[i].split("="); + + if (keyVal.length === 2) { + var str = keyVal[1].trim(); + + switch (keyVal[0].trim()) { + case "alt": + alt = str; + break; + + case "width": + width = sizeData(str); + break; + + case "height": + height = sizeData(str); + break; + + case "totalheight": + totalheight = sizeData(str); + break; + + default: + throw new src_ParseError("Invalid key: '" + keyVal[0] + "' in \\includegraphics."); + } + } + } + } + + var src = assertNodeType(args[0], "url").url; + + if (alt === "") { + // No alt given. Use the file name. Strip away the path. + alt = src; + alt = alt.replace(/^.*[\\/]/, ''); + alt = alt.substring(0, alt.lastIndexOf('.')); + } + + if (!parser.settings.isTrusted({ + command: "\\includegraphics", + url: src + })) { + return parser.formatUnsupportedCmd("\\includegraphics"); + } + + return { + type: "includegraphics", + mode: parser.mode, + alt: alt, + width: width, + height: height, + totalheight: totalheight, + src: src + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var height = calculateSize(group.height, options); + var depth = 0; + + if (group.totalheight.number > 0) { + depth = calculateSize(group.totalheight, options) - height; + depth = Number(depth.toFixed(2)); + } + + var width = 0; + + if (group.width.number > 0) { + width = calculateSize(group.width, options); + } + + var style = { + height: height + depth + "em" + }; + + if (width > 0) { + style.width = width + "em"; + } + + if (depth > 0) { + style.verticalAlign = -depth + "em"; + } + + var node = new Img(group.src, group.alt, style); + node.height = height; + node.depth = depth; + return node; + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var node = new mathMLTree.MathNode("mglyph", []); + node.setAttribute("alt", group.alt); + var height = calculateSize(group.height, options); + var depth = 0; + + if (group.totalheight.number > 0) { + depth = calculateSize(group.totalheight, options) - height; + depth = depth.toFixed(2); + node.setAttribute("valign", "-" + depth + "em"); + } + + node.setAttribute("height", height + depth + "em"); + + if (group.width.number > 0) { + var width = calculateSize(group.width, options); + node.setAttribute("width", width + "em"); + } + + node.setAttribute("src", group.src); + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/kern.js +// Horizontal spacing commands + + + + + // TODO: \hskip and \mskip should support plus and minus in lengths + +defineFunction({ + type: "kern", + names: ["\\kern", "\\mkern", "\\hskip", "\\mskip"], + props: { + numArgs: 1, + argTypes: ["size"], + primitive: true, + allowedInText: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser, + funcName = _ref.funcName; + var size = assertNodeType(args[0], "size"); + + if (parser.settings.strict) { + var mathFunction = funcName[1] === 'm'; // \mkern, \mskip + + var muUnit = size.value.unit === 'mu'; + + if (mathFunction) { + if (!muUnit) { + parser.settings.reportNonstrict("mathVsTextUnits", "LaTeX's " + funcName + " supports only mu units, " + ("not " + size.value.unit + " units")); + } + + if (parser.mode !== "math") { + parser.settings.reportNonstrict("mathVsTextUnits", "LaTeX's " + funcName + " works only in math mode"); + } + } else { + // !mathFunction + if (muUnit) { + parser.settings.reportNonstrict("mathVsTextUnits", "LaTeX's " + funcName + " doesn't support mu units"); + } + } + } + + return { + type: "kern", + mode: parser.mode, + dimension: size.value + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + return buildCommon.makeGlue(group.dimension, options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var dimension = calculateSize(group.dimension, options); + return new mathMLTree.SpaceNode(dimension); + } +}); +;// CONCATENATED MODULE: ./src/functions/lap.js +// Horizontal overlap functions + + + + + +defineFunction({ + type: "lap", + names: ["\\mathllap", "\\mathrlap", "\\mathclap"], + props: { + numArgs: 1, + allowedInText: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser, + funcName = _ref.funcName; + var body = args[0]; + return { + type: "lap", + mode: parser.mode, + alignment: funcName.slice(5), + body: body + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + // mathllap, mathrlap, mathclap + var inner; + + if (group.alignment === "clap") { + // ref: https://www.math.lsu.edu/~aperlis/publications/mathclap/ + inner = buildCommon.makeSpan([], [buildGroup(group.body, options)]); // wrap, since CSS will center a .clap > .inner > span + + inner = buildCommon.makeSpan(["inner"], [inner], options); + } else { + inner = buildCommon.makeSpan(["inner"], [buildGroup(group.body, options)]); + } + + var fix = buildCommon.makeSpan(["fix"], []); + var node = buildCommon.makeSpan([group.alignment], [inner, fix], options); // At this point, we have correctly set horizontal alignment of the + // two items involved in the lap. + // Next, use a strut to set the height of the HTML bounding box. + // Otherwise, a tall argument may be misplaced. + // This code resolved issue #1153 + + var strut = buildCommon.makeSpan(["strut"]); + strut.style.height = node.height + node.depth + "em"; + strut.style.verticalAlign = -node.depth + "em"; + node.children.unshift(strut); // Next, prevent vertical misplacement when next to something tall. + // This code resolves issue #1234 + + node = buildCommon.makeSpan(["thinbox"], [node], options); + return buildCommon.makeSpan(["mord", "vbox"], [node], options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + // mathllap, mathrlap, mathclap + var node = new mathMLTree.MathNode("mpadded", [buildMathML_buildGroup(group.body, options)]); + + if (group.alignment !== "rlap") { + var offset = group.alignment === "llap" ? "-1" : "-0.5"; + node.setAttribute("lspace", offset + "width"); + } + + node.setAttribute("width", "0px"); + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/math.js + + // Switching from text mode back to math mode + +defineFunction({ + type: "styling", + names: ["\\(", "$"], + props: { + numArgs: 0, + allowedInText: true, + allowedInMath: false + }, + handler: function handler(_ref, args) { + var funcName = _ref.funcName, + parser = _ref.parser; + var outerMode = parser.mode; + parser.switchMode("math"); + var close = funcName === "\\(" ? "\\)" : "$"; + var body = parser.parseExpression(false, close); + parser.expect(close); + parser.switchMode(outerMode); + return { + type: "styling", + mode: parser.mode, + style: "text", + body: body + }; + } +}); // Check for extra closing math delimiters + +defineFunction({ + type: "text", + // Doesn't matter what this is. + names: ["\\)", "\\]"], + props: { + numArgs: 0, + allowedInText: true, + allowedInMath: false + }, + handler: function handler(context, args) { + throw new src_ParseError("Mismatched " + context.funcName); + } +}); +;// CONCATENATED MODULE: ./src/functions/mathchoice.js + + + + + + +var chooseMathStyle = function chooseMathStyle(group, options) { + switch (options.style.size) { + case src_Style.DISPLAY.size: + return group.display; + + case src_Style.TEXT.size: + return group.text; + + case src_Style.SCRIPT.size: + return group.script; + + case src_Style.SCRIPTSCRIPT.size: + return group.scriptscript; + + default: + return group.text; + } +}; + +defineFunction({ + type: "mathchoice", + names: ["\\mathchoice"], + props: { + numArgs: 4, + primitive: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser; + return { + type: "mathchoice", + mode: parser.mode, + display: ordargument(args[0]), + text: ordargument(args[1]), + script: ordargument(args[2]), + scriptscript: ordargument(args[3]) + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var body = chooseMathStyle(group, options); + var elements = buildExpression(body, options, false); + return buildCommon.makeFragment(elements); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var body = chooseMathStyle(group, options); + return buildExpressionRow(body, options); + } +}); +;// CONCATENATED MODULE: ./src/functions/utils/assembleSupSub.js + + + +// For an operator with limits, assemble the base, sup, and sub into a span. +var assembleSupSub = function assembleSupSub(base, supGroup, subGroup, options, style, slant, baseShift) { + base = buildCommon.makeSpan([], [base]); + var subIsSingleCharacter = subGroup && utils.isCharacterBox(subGroup); + var sub; + var sup; // We manually have to handle the superscripts and subscripts. This, + // aside from the kern calculations, is copied from supsub. + + if (supGroup) { + var elem = buildGroup(supGroup, options.havingStyle(style.sup()), options); + sup = { + elem: elem, + kern: Math.max(options.fontMetrics().bigOpSpacing1, options.fontMetrics().bigOpSpacing3 - elem.depth) + }; + } + + if (subGroup) { + var _elem = buildGroup(subGroup, options.havingStyle(style.sub()), options); + + sub = { + elem: _elem, + kern: Math.max(options.fontMetrics().bigOpSpacing2, options.fontMetrics().bigOpSpacing4 - _elem.height) + }; + } // Build the final group as a vlist of the possible subscript, base, + // and possible superscript. + + + var finalGroup; + + if (sup && sub) { + var bottom = options.fontMetrics().bigOpSpacing5 + sub.elem.height + sub.elem.depth + sub.kern + base.depth + baseShift; + finalGroup = buildCommon.makeVList({ + positionType: "bottom", + positionData: bottom, + children: [{ + type: "kern", + size: options.fontMetrics().bigOpSpacing5 + }, { + type: "elem", + elem: sub.elem, + marginLeft: -slant + "em" + }, { + type: "kern", + size: sub.kern + }, { + type: "elem", + elem: base + }, { + type: "kern", + size: sup.kern + }, { + type: "elem", + elem: sup.elem, + marginLeft: slant + "em" + }, { + type: "kern", + size: options.fontMetrics().bigOpSpacing5 + }] + }, options); + } else if (sub) { + var top = base.height - baseShift; // Shift the limits by the slant of the symbol. Note + // that we are supposed to shift the limits by 1/2 of the slant, + // but since we are centering the limits adding a full slant of + // margin will shift by 1/2 that. + + finalGroup = buildCommon.makeVList({ + positionType: "top", + positionData: top, + children: [{ + type: "kern", + size: options.fontMetrics().bigOpSpacing5 + }, { + type: "elem", + elem: sub.elem, + marginLeft: -slant + "em" + }, { + type: "kern", + size: sub.kern + }, { + type: "elem", + elem: base + }] + }, options); + } else if (sup) { + var _bottom = base.depth + baseShift; + + finalGroup = buildCommon.makeVList({ + positionType: "bottom", + positionData: _bottom, + children: [{ + type: "elem", + elem: base + }, { + type: "kern", + size: sup.kern + }, { + type: "elem", + elem: sup.elem, + marginLeft: slant + "em" + }, { + type: "kern", + size: options.fontMetrics().bigOpSpacing5 + }] + }, options); + } else { + // This case probably shouldn't occur (this would mean the + // supsub was sending us a group with no superscript or + // subscript) but be safe. + return base; + } + + var parts = [finalGroup]; + + if (sub && slant !== 0 && !subIsSingleCharacter) { + // A negative margin-left was applied to the lower limit. + // Avoid an overlap by placing a spacer on the left on the group. + var spacer = buildCommon.makeSpan(["mspace"], [], options); + spacer.style.marginRight = slant + "em"; + parts.unshift(spacer); + } + + return buildCommon.makeSpan(["mop", "op-limits"], parts, options); +}; +;// CONCATENATED MODULE: ./src/functions/op.js +// Limits, symbols + + + + + + + + + + +// Most operators have a large successor symbol, but these don't. +var noSuccessor = ["\\smallint"]; // NOTE: Unlike most `htmlBuilder`s, this one handles not only "op", but also +// "supsub" since some of them (like \int) can affect super/subscripting. + +var op_htmlBuilder = function htmlBuilder(grp, options) { + // Operators are handled in the TeXbook pg. 443-444, rule 13(a). + var supGroup; + var subGroup; + var hasLimits = false; + var group; + + if (grp.type === "supsub") { + // If we have limits, supsub will pass us its group to handle. Pull + // out the superscript and subscript and set the group to the op in + // its base. + supGroup = grp.sup; + subGroup = grp.sub; + group = assertNodeType(grp.base, "op"); + hasLimits = true; + } else { + group = assertNodeType(grp, "op"); + } + + var style = options.style; + var large = false; + + if (style.size === src_Style.DISPLAY.size && group.symbol && !utils.contains(noSuccessor, group.name)) { + // Most symbol operators get larger in displaystyle (rule 13) + large = true; + } + + var base; + + if (group.symbol) { + // If this is a symbol, create the symbol. + var fontName = large ? "Size2-Regular" : "Size1-Regular"; + var stash = ""; + + if (group.name === "\\oiint" || group.name === "\\oiiint") { + // No font glyphs yet, so use a glyph w/o the oval. + // TODO: When font glyphs are available, delete this code. + stash = group.name.substr(1); + group.name = stash === "oiint" ? "\\iint" : "\\iiint"; + } + + base = buildCommon.makeSymbol(group.name, fontName, "math", options, ["mop", "op-symbol", large ? "large-op" : "small-op"]); + + if (stash.length > 0) { + // We're in \oiint or \oiiint. Overlay the oval. + // TODO: When font glyphs are available, delete this code. + var italic = base.italic; + var oval = buildCommon.staticSvg(stash + "Size" + (large ? "2" : "1"), options); + base = buildCommon.makeVList({ + positionType: "individualShift", + children: [{ + type: "elem", + elem: base, + shift: 0 + }, { + type: "elem", + elem: oval, + shift: large ? 0.08 : 0 + }] + }, options); + group.name = "\\" + stash; + base.classes.unshift("mop"); // $FlowFixMe + + base.italic = italic; + } + } else if (group.body) { + // If this is a list, compose that list. + var inner = buildExpression(group.body, options, true); + + if (inner.length === 1 && inner[0] instanceof SymbolNode) { + base = inner[0]; + base.classes[0] = "mop"; // replace old mclass + } else { + base = buildCommon.makeSpan(["mop"], inner, options); + } + } else { + // Otherwise, this is a text operator. Build the text from the + // operator's name. + var output = []; + + for (var i = 1; i < group.name.length; i++) { + output.push(buildCommon.mathsym(group.name[i], group.mode, options)); + } + + base = buildCommon.makeSpan(["mop"], output, options); + } // If content of op is a single symbol, shift it vertically. + + + var baseShift = 0; + var slant = 0; + + if ((base instanceof SymbolNode || group.name === "\\oiint" || group.name === "\\oiiint") && !group.suppressBaseShift) { + // We suppress the shift of the base of \overset and \underset. Otherwise, + // shift the symbol so its center lies on the axis (rule 13). It + // appears that our fonts have the centers of the symbols already + // almost on the axis, so these numbers are very small. Note we + // don't actually apply this here, but instead it is used either in + // the vlist creation or separately when there are no limits. + baseShift = (base.height - base.depth) / 2 - options.fontMetrics().axisHeight; // The slant of the symbol is just its italic correction. + // $FlowFixMe + + slant = base.italic; + } + + if (hasLimits) { + return assembleSupSub(base, supGroup, subGroup, options, style, slant, baseShift); + } else { + if (baseShift) { + base.style.position = "relative"; + base.style.top = baseShift + "em"; + } + + return base; + } +}; + +var op_mathmlBuilder = function mathmlBuilder(group, options) { + var node; + + if (group.symbol) { + // This is a symbol. Just add the symbol. + node = new MathNode("mo", [makeText(group.name, group.mode)]); + + if (utils.contains(noSuccessor, group.name)) { + node.setAttribute("largeop", "false"); + } + } else if (group.body) { + // This is an operator with children. Add them. + node = new MathNode("mo", buildMathML_buildExpression(group.body, options)); + } else { + // This is a text operator. Add all of the characters from the + // operator's name. + node = new MathNode("mi", [new TextNode(group.name.slice(1))]); // Append an ⁡. + // ref: https://www.w3.org/TR/REC-MathML/chap3_2.html#sec3.2.4 + + var operator = new MathNode("mo", [makeText("\u2061", "text")]); + + if (group.parentIsSupSub) { + node = new MathNode("mrow", [node, operator]); + } else { + node = newDocumentFragment([node, operator]); + } + } + + return node; +}; + +var singleCharBigOps = { + "\u220F": "\\prod", + "\u2210": "\\coprod", + "\u2211": "\\sum", + "\u22C0": "\\bigwedge", + "\u22C1": "\\bigvee", + "\u22C2": "\\bigcap", + "\u22C3": "\\bigcup", + "\u2A00": "\\bigodot", + "\u2A01": "\\bigoplus", + "\u2A02": "\\bigotimes", + "\u2A04": "\\biguplus", + "\u2A06": "\\bigsqcup" +}; +defineFunction({ + type: "op", + names: ["\\coprod", "\\bigvee", "\\bigwedge", "\\biguplus", "\\bigcap", "\\bigcup", "\\intop", "\\prod", "\\sum", "\\bigotimes", "\\bigoplus", "\\bigodot", "\\bigsqcup", "\\smallint", "\u220F", "\u2210", "\u2211", "\u22C0", "\u22C1", "\u22C2", "\u22C3", "\u2A00", "\u2A01", "\u2A02", "\u2A04", "\u2A06"], + props: { + numArgs: 0 + }, + handler: function handler(_ref, args) { + var parser = _ref.parser, + funcName = _ref.funcName; + var fName = funcName; + + if (fName.length === 1) { + fName = singleCharBigOps[fName]; + } + + return { + type: "op", + mode: parser.mode, + limits: true, + parentIsSupSub: false, + symbol: true, + name: fName + }; + }, + htmlBuilder: op_htmlBuilder, + mathmlBuilder: op_mathmlBuilder +}); // Note: calling defineFunction with a type that's already been defined only +// works because the same htmlBuilder and mathmlBuilder are being used. + +defineFunction({ + type: "op", + names: ["\\mathop"], + props: { + numArgs: 1, + primitive: true + }, + handler: function handler(_ref2, args) { + var parser = _ref2.parser; + var body = args[0]; + return { + type: "op", + mode: parser.mode, + limits: false, + parentIsSupSub: false, + symbol: false, + body: ordargument(body) + }; + }, + htmlBuilder: op_htmlBuilder, + mathmlBuilder: op_mathmlBuilder +}); // There are 2 flags for operators; whether they produce limits in +// displaystyle, and whether they are symbols and should grow in +// displaystyle. These four groups cover the four possible choices. + +var singleCharIntegrals = { + "\u222B": "\\int", + "\u222C": "\\iint", + "\u222D": "\\iiint", + "\u222E": "\\oint", + "\u222F": "\\oiint", + "\u2230": "\\oiiint" +}; // No limits, not symbols + +defineFunction({ + type: "op", + names: ["\\arcsin", "\\arccos", "\\arctan", "\\arctg", "\\arcctg", "\\arg", "\\ch", "\\cos", "\\cosec", "\\cosh", "\\cot", "\\cotg", "\\coth", "\\csc", "\\ctg", "\\cth", "\\deg", "\\dim", "\\exp", "\\hom", "\\ker", "\\lg", "\\ln", "\\log", "\\sec", "\\sin", "\\sinh", "\\sh", "\\tan", "\\tanh", "\\tg", "\\th"], + props: { + numArgs: 0 + }, + handler: function handler(_ref3) { + var parser = _ref3.parser, + funcName = _ref3.funcName; + return { + type: "op", + mode: parser.mode, + limits: false, + parentIsSupSub: false, + symbol: false, + name: funcName + }; + }, + htmlBuilder: op_htmlBuilder, + mathmlBuilder: op_mathmlBuilder +}); // Limits, not symbols + +defineFunction({ + type: "op", + names: ["\\det", "\\gcd", "\\inf", "\\lim", "\\max", "\\min", "\\Pr", "\\sup"], + props: { + numArgs: 0 + }, + handler: function handler(_ref4) { + var parser = _ref4.parser, + funcName = _ref4.funcName; + return { + type: "op", + mode: parser.mode, + limits: true, + parentIsSupSub: false, + symbol: false, + name: funcName + }; + }, + htmlBuilder: op_htmlBuilder, + mathmlBuilder: op_mathmlBuilder +}); // No limits, symbols + +defineFunction({ + type: "op", + names: ["\\int", "\\iint", "\\iiint", "\\oint", "\\oiint", "\\oiiint", "\u222B", "\u222C", "\u222D", "\u222E", "\u222F", "\u2230"], + props: { + numArgs: 0 + }, + handler: function handler(_ref5) { + var parser = _ref5.parser, + funcName = _ref5.funcName; + var fName = funcName; + + if (fName.length === 1) { + fName = singleCharIntegrals[fName]; + } + + return { + type: "op", + mode: parser.mode, + limits: false, + parentIsSupSub: false, + symbol: true, + name: fName + }; + }, + htmlBuilder: op_htmlBuilder, + mathmlBuilder: op_mathmlBuilder +}); +;// CONCATENATED MODULE: ./src/defineMacro.js + + +/** + * All registered global/built-in macros. + * `macros.js` exports this same dictionary again and makes it public. + * `Parser.js` requires this dictionary via `macros.js`. + */ +var _macros = {}; // This function might one day accept an additional argument and do more things. + +function defineMacro(name, body) { + _macros[name] = body; +} +;// CONCATENATED MODULE: ./src/functions/operatorname.js + + + + + + + + + +// NOTE: Unlike most `htmlBuilder`s, this one handles not only +// "operatorname", but also "supsub" since \operatorname* can +// affect super/subscripting. +var operatorname_htmlBuilder = function htmlBuilder(grp, options) { + // Operators are handled in the TeXbook pg. 443-444, rule 13(a). + var supGroup; + var subGroup; + var hasLimits = false; + var group; + + if (grp.type === "supsub") { + // If we have limits, supsub will pass us its group to handle. Pull + // out the superscript and subscript and set the group to the op in + // its base. + supGroup = grp.sup; + subGroup = grp.sub; + group = assertNodeType(grp.base, "operatorname"); + hasLimits = true; + } else { + group = assertNodeType(grp, "operatorname"); + } + + var base; + + if (group.body.length > 0) { + var body = group.body.map(function (child) { + // $FlowFixMe: Check if the node has a string `text` property. + var childText = child.text; + + if (typeof childText === "string") { + return { + type: "textord", + mode: child.mode, + text: childText + }; + } else { + return child; + } + }); // Consolidate function names into symbol characters. + + var expression = buildExpression(body, options.withFont("mathrm"), true); + + for (var i = 0; i < expression.length; i++) { + var child = expression[i]; + + if (child instanceof SymbolNode) { + // Per amsopn package, + // change minus to hyphen and \ast to asterisk + child.text = child.text.replace(/\u2212/, "-").replace(/\u2217/, "*"); + } + } + + base = buildCommon.makeSpan(["mop"], expression, options); + } else { + base = buildCommon.makeSpan(["mop"], [], options); + } + + if (hasLimits) { + return assembleSupSub(base, supGroup, subGroup, options, options.style, 0, 0); + } else { + return base; + } +}; + +var operatorname_mathmlBuilder = function mathmlBuilder(group, options) { + // The steps taken here are similar to the html version. + var expression = buildMathML_buildExpression(group.body, options.withFont("mathrm")); // Is expression a string or has it something like a fraction? + + var isAllString = true; // default + + for (var i = 0; i < expression.length; i++) { + var node = expression[i]; + + if (node instanceof mathMLTree.SpaceNode) {// Do nothing + } else if (node instanceof mathMLTree.MathNode) { + switch (node.type) { + case "mi": + case "mn": + case "ms": + case "mspace": + case "mtext": + break; + // Do nothing yet. + + case "mo": + { + var child = node.children[0]; + + if (node.children.length === 1 && child instanceof mathMLTree.TextNode) { + child.text = child.text.replace(/\u2212/, "-").replace(/\u2217/, "*"); + } else { + isAllString = false; + } + + break; + } + + default: + isAllString = false; + } + } else { + isAllString = false; + } + } + + if (isAllString) { + // Write a single TextNode instead of multiple nested tags. + var word = expression.map(function (node) { + return node.toText(); + }).join(""); + expression = [new mathMLTree.TextNode(word)]; + } + + var identifier = new mathMLTree.MathNode("mi", expression); + identifier.setAttribute("mathvariant", "normal"); // \u2061 is the same as ⁡ + // ref: https://www.w3schools.com/charsets/ref_html_entities_a.asp + + var operator = new mathMLTree.MathNode("mo", [makeText("\u2061", "text")]); + + if (group.parentIsSupSub) { + return new mathMLTree.MathNode("mrow", [identifier, operator]); + } else { + return mathMLTree.newDocumentFragment([identifier, operator]); + } +}; // \operatorname +// amsopn.dtx: \mathop{#1\kern\z@\operator@font#3}\newmcodes@ + + +defineFunction({ + type: "operatorname", + names: ["\\operatorname@", "\\operatornamewithlimits"], + props: { + numArgs: 1 + }, + handler: function handler(_ref, args) { + var parser = _ref.parser, + funcName = _ref.funcName; + var body = args[0]; + return { + type: "operatorname", + mode: parser.mode, + body: ordargument(body), + alwaysHandleSupSub: funcName === "\\operatornamewithlimits", + limits: false, + parentIsSupSub: false + }; + }, + htmlBuilder: operatorname_htmlBuilder, + mathmlBuilder: operatorname_mathmlBuilder +}); +defineMacro("\\operatorname", "\\@ifstar\\operatornamewithlimits\\operatorname@"); +;// CONCATENATED MODULE: ./src/functions/ordgroup.js + + + + +defineFunctionBuilders({ + type: "ordgroup", + htmlBuilder: function htmlBuilder(group, options) { + if (group.semisimple) { + return buildCommon.makeFragment(buildExpression(group.body, options, false)); + } + + return buildCommon.makeSpan(["mord"], buildExpression(group.body, options, true), options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + return buildExpressionRow(group.body, options, true); + } +}); +;// CONCATENATED MODULE: ./src/functions/overline.js + + + + + +defineFunction({ + type: "overline", + names: ["\\overline"], + props: { + numArgs: 1 + }, + handler: function handler(_ref, args) { + var parser = _ref.parser; + var body = args[0]; + return { + type: "overline", + mode: parser.mode, + body: body + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + // Overlines are handled in the TeXbook pg 443, Rule 9. + // Build the inner group in the cramped style. + var innerGroup = buildGroup(group.body, options.havingCrampedStyle()); // Create the line above the body + + var line = buildCommon.makeLineSpan("overline-line", options); // Generate the vlist, with the appropriate kerns + + var defaultRuleThickness = options.fontMetrics().defaultRuleThickness; + var vlist = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: innerGroup + }, { + type: "kern", + size: 3 * defaultRuleThickness + }, { + type: "elem", + elem: line + }, { + type: "kern", + size: defaultRuleThickness + }] + }, options); + return buildCommon.makeSpan(["mord", "overline"], [vlist], options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var operator = new mathMLTree.MathNode("mo", [new mathMLTree.TextNode("\u203E")]); + operator.setAttribute("stretchy", "true"); + var node = new mathMLTree.MathNode("mover", [buildMathML_buildGroup(group.body, options), operator]); + node.setAttribute("accent", "true"); + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/phantom.js + + + + + +defineFunction({ + type: "phantom", + names: ["\\phantom"], + props: { + numArgs: 1, + allowedInText: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser; + var body = args[0]; + return { + type: "phantom", + mode: parser.mode, + body: ordargument(body) + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var elements = buildExpression(group.body, options.withPhantom(), false); // \phantom isn't supposed to affect the elements it contains. + // See "color" for more details. + + return buildCommon.makeFragment(elements); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var inner = buildMathML_buildExpression(group.body, options); + return new mathMLTree.MathNode("mphantom", inner); + } +}); +defineFunction({ + type: "hphantom", + names: ["\\hphantom"], + props: { + numArgs: 1, + allowedInText: true + }, + handler: function handler(_ref2, args) { + var parser = _ref2.parser; + var body = args[0]; + return { + type: "hphantom", + mode: parser.mode, + body: body + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var node = buildCommon.makeSpan([], [buildGroup(group.body, options.withPhantom())]); + node.height = 0; + node.depth = 0; + + if (node.children) { + for (var i = 0; i < node.children.length; i++) { + node.children[i].height = 0; + node.children[i].depth = 0; + } + } // See smash for comment re: use of makeVList + + + node = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: node + }] + }, options); // For spacing, TeX treats \smash as a math group (same spacing as ord). + + return buildCommon.makeSpan(["mord"], [node], options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var inner = buildMathML_buildExpression(ordargument(group.body), options); + var phantom = new mathMLTree.MathNode("mphantom", inner); + var node = new mathMLTree.MathNode("mpadded", [phantom]); + node.setAttribute("height", "0px"); + node.setAttribute("depth", "0px"); + return node; + } +}); +defineFunction({ + type: "vphantom", + names: ["\\vphantom"], + props: { + numArgs: 1, + allowedInText: true + }, + handler: function handler(_ref3, args) { + var parser = _ref3.parser; + var body = args[0]; + return { + type: "vphantom", + mode: parser.mode, + body: body + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var inner = buildCommon.makeSpan(["inner"], [buildGroup(group.body, options.withPhantom())]); + var fix = buildCommon.makeSpan(["fix"], []); + return buildCommon.makeSpan(["mord", "rlap"], [inner, fix], options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var inner = buildMathML_buildExpression(ordargument(group.body), options); + var phantom = new mathMLTree.MathNode("mphantom", inner); + var node = new mathMLTree.MathNode("mpadded", [phantom]); + node.setAttribute("width", "0px"); + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/raisebox.js + + + + + + + // Box manipulation + +defineFunction({ + type: "raisebox", + names: ["\\raisebox"], + props: { + numArgs: 2, + argTypes: ["size", "hbox"], + allowedInText: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser; + var amount = assertNodeType(args[0], "size").value; + var body = args[1]; + return { + type: "raisebox", + mode: parser.mode, + dy: amount, + body: body + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var body = buildGroup(group.body, options); + var dy = calculateSize(group.dy, options); + return buildCommon.makeVList({ + positionType: "shift", + positionData: -dy, + children: [{ + type: "elem", + elem: body + }] + }, options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var node = new mathMLTree.MathNode("mpadded", [buildMathML_buildGroup(group.body, options)]); + var dy = group.dy.number + group.dy.unit; + node.setAttribute("voffset", dy); + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/rule.js + + + + + +defineFunction({ + type: "rule", + names: ["\\rule"], + props: { + numArgs: 2, + numOptionalArgs: 1, + argTypes: ["size", "size", "size"] + }, + handler: function handler(_ref, args, optArgs) { + var parser = _ref.parser; + var shift = optArgs[0]; + var width = assertNodeType(args[0], "size"); + var height = assertNodeType(args[1], "size"); + return { + type: "rule", + mode: parser.mode, + shift: shift && assertNodeType(shift, "size").value, + width: width.value, + height: height.value + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + // Make an empty span for the rule + var rule = buildCommon.makeSpan(["mord", "rule"], [], options); // Calculate the shift, width, and height of the rule, and account for units + + var width = calculateSize(group.width, options); + var height = calculateSize(group.height, options); + var shift = group.shift ? calculateSize(group.shift, options) : 0; // Style the rule to the right size + + rule.style.borderRightWidth = width + "em"; + rule.style.borderTopWidth = height + "em"; + rule.style.bottom = shift + "em"; // Record the height and width + + rule.width = width; + rule.height = height + shift; + rule.depth = -shift; // Font size is the number large enough that the browser will + // reserve at least `absHeight` space above the baseline. + // The 1.125 factor was empirically determined + + rule.maxFontSize = height * 1.125 * options.sizeMultiplier; + return rule; + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var width = calculateSize(group.width, options); + var height = calculateSize(group.height, options); + var shift = group.shift ? calculateSize(group.shift, options) : 0; + var color = options.color && options.getColor() || "black"; + var rule = new mathMLTree.MathNode("mspace"); + rule.setAttribute("mathbackground", color); + rule.setAttribute("width", width + "em"); + rule.setAttribute("height", height + "em"); + var wrapper = new mathMLTree.MathNode("mpadded", [rule]); + + if (shift >= 0) { + wrapper.setAttribute("height", "+" + shift + "em"); + } else { + wrapper.setAttribute("height", shift + "em"); + wrapper.setAttribute("depth", "+" + -shift + "em"); + } + + wrapper.setAttribute("voffset", shift + "em"); + return wrapper; + } +}); +;// CONCATENATED MODULE: ./src/functions/sizing.js + + + + + +function sizingGroup(value, options, baseOptions) { + var inner = buildExpression(value, options, false); + var multiplier = options.sizeMultiplier / baseOptions.sizeMultiplier; // Add size-resetting classes to the inner list and set maxFontSize + // manually. Handle nested size changes. + + for (var i = 0; i < inner.length; i++) { + var pos = inner[i].classes.indexOf("sizing"); + + if (pos < 0) { + Array.prototype.push.apply(inner[i].classes, options.sizingClasses(baseOptions)); + } else if (inner[i].classes[pos + 1] === "reset-size" + options.size) { + // This is a nested size change: e.g., inner[i] is the "b" in + // `\Huge a \small b`. Override the old size (the `reset-` class) + // but not the new size. + inner[i].classes[pos + 1] = "reset-size" + baseOptions.size; + } + + inner[i].height *= multiplier; + inner[i].depth *= multiplier; + } + + return buildCommon.makeFragment(inner); +} +var sizeFuncs = ["\\tiny", "\\sixptsize", "\\scriptsize", "\\footnotesize", "\\small", "\\normalsize", "\\large", "\\Large", "\\LARGE", "\\huge", "\\Huge"]; +var sizing_htmlBuilder = function htmlBuilder(group, options) { + // Handle sizing operators like \Huge. Real TeX doesn't actually allow + // these functions inside of math expressions, so we do some special + // handling. + var newOptions = options.havingSize(group.size); + return sizingGroup(group.body, newOptions, options); +}; +defineFunction({ + type: "sizing", + names: sizeFuncs, + props: { + numArgs: 0, + allowedInText: true + }, + handler: function handler(_ref, args) { + var breakOnTokenText = _ref.breakOnTokenText, + funcName = _ref.funcName, + parser = _ref.parser; + var body = parser.parseExpression(false, breakOnTokenText); + return { + type: "sizing", + mode: parser.mode, + // Figure out what size to use based on the list of functions above + size: sizeFuncs.indexOf(funcName) + 1, + body: body + }; + }, + htmlBuilder: sizing_htmlBuilder, + mathmlBuilder: function mathmlBuilder(group, options) { + var newOptions = options.havingSize(group.size); + var inner = buildMathML_buildExpression(group.body, newOptions); + var node = new mathMLTree.MathNode("mstyle", inner); // TODO(emily): This doesn't produce the correct size for nested size + // changes, because we don't keep state of what style we're currently + // in, so we can't reset the size to normal before changing it. Now + // that we're passing an options parameter we should be able to fix + // this. + + node.setAttribute("mathsize", newOptions.sizeMultiplier + "em"); + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/smash.js +// smash, with optional [tb], as in AMS + + + + + + +defineFunction({ + type: "smash", + names: ["\\smash"], + props: { + numArgs: 1, + numOptionalArgs: 1, + allowedInText: true + }, + handler: function handler(_ref, args, optArgs) { + var parser = _ref.parser; + var smashHeight = false; + var smashDepth = false; + var tbArg = optArgs[0] && assertNodeType(optArgs[0], "ordgroup"); + + if (tbArg) { + // Optional [tb] argument is engaged. + // ref: amsmath: \renewcommand{\smash}[1][tb]{% + // def\mb@t{\ht}\def\mb@b{\dp}\def\mb@tb{\ht\z@\z@\dp}% + var letter = ""; + + for (var i = 0; i < tbArg.body.length; ++i) { + var node = tbArg.body[i]; // $FlowFixMe: Not every node type has a `text` property. + + letter = node.text; + + if (letter === "t") { + smashHeight = true; + } else if (letter === "b") { + smashDepth = true; + } else { + smashHeight = false; + smashDepth = false; + break; + } + } + } else { + smashHeight = true; + smashDepth = true; + } + + var body = args[0]; + return { + type: "smash", + mode: parser.mode, + body: body, + smashHeight: smashHeight, + smashDepth: smashDepth + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var node = buildCommon.makeSpan([], [buildGroup(group.body, options)]); + + if (!group.smashHeight && !group.smashDepth) { + return node; + } + + if (group.smashHeight) { + node.height = 0; // In order to influence makeVList, we have to reset the children. + + if (node.children) { + for (var i = 0; i < node.children.length; i++) { + node.children[i].height = 0; + } + } + } + + if (group.smashDepth) { + node.depth = 0; + + if (node.children) { + for (var _i = 0; _i < node.children.length; _i++) { + node.children[_i].depth = 0; + } + } + } // At this point, we've reset the TeX-like height and depth values. + // But the span still has an HTML line height. + // makeVList applies "display: table-cell", which prevents the browser + // from acting on that line height. So we'll call makeVList now. + + + var smashedNode = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: node + }] + }, options); // For spacing, TeX treats \hphantom as a math group (same spacing as ord). + + return buildCommon.makeSpan(["mord"], [smashedNode], options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var node = new mathMLTree.MathNode("mpadded", [buildMathML_buildGroup(group.body, options)]); + + if (group.smashHeight) { + node.setAttribute("height", "0px"); + } + + if (group.smashDepth) { + node.setAttribute("depth", "0px"); + } + + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/sqrt.js + + + + + + + +defineFunction({ + type: "sqrt", + names: ["\\sqrt"], + props: { + numArgs: 1, + numOptionalArgs: 1 + }, + handler: function handler(_ref, args, optArgs) { + var parser = _ref.parser; + var index = optArgs[0]; + var body = args[0]; + return { + type: "sqrt", + mode: parser.mode, + body: body, + index: index + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + // Square roots are handled in the TeXbook pg. 443, Rule 11. + // First, we do the same steps as in overline to build the inner group + // and line + var inner = buildGroup(group.body, options.havingCrampedStyle()); + + if (inner.height === 0) { + // Render a small surd. + inner.height = options.fontMetrics().xHeight; + } // Some groups can return document fragments. Handle those by wrapping + // them in a span. + + + inner = buildCommon.wrapFragment(inner, options); // Calculate the minimum size for the \surd delimiter + + var metrics = options.fontMetrics(); + var theta = metrics.defaultRuleThickness; + var phi = theta; + + if (options.style.id < src_Style.TEXT.id) { + phi = options.fontMetrics().xHeight; + } // Calculate the clearance between the body and line + + + var lineClearance = theta + phi / 4; + var minDelimiterHeight = inner.height + inner.depth + lineClearance + theta; // Create a sqrt SVG of the required minimum size + + var _delimiter$sqrtImage = delimiter.sqrtImage(minDelimiterHeight, options), + img = _delimiter$sqrtImage.span, + ruleWidth = _delimiter$sqrtImage.ruleWidth, + advanceWidth = _delimiter$sqrtImage.advanceWidth; + + var delimDepth = img.height - ruleWidth; // Adjust the clearance based on the delimiter size + + if (delimDepth > inner.height + inner.depth + lineClearance) { + lineClearance = (lineClearance + delimDepth - inner.height - inner.depth) / 2; + } // Shift the sqrt image + + + var imgShift = img.height - inner.height - lineClearance - ruleWidth; + inner.style.paddingLeft = advanceWidth + "em"; // Overlay the image and the argument. + + var body = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: inner, + wrapperClasses: ["svg-align"] + }, { + type: "kern", + size: -(inner.height + imgShift) + }, { + type: "elem", + elem: img + }, { + type: "kern", + size: ruleWidth + }] + }, options); + + if (!group.index) { + return buildCommon.makeSpan(["mord", "sqrt"], [body], options); + } else { + // Handle the optional root index + // The index is always in scriptscript style + var newOptions = options.havingStyle(src_Style.SCRIPTSCRIPT); + var rootm = buildGroup(group.index, newOptions, options); // The amount the index is shifted by. This is taken from the TeX + // source, in the definition of `\r@@t`. + + var toShift = 0.6 * (body.height - body.depth); // Build a VList with the superscript shifted up correctly + + var rootVList = buildCommon.makeVList({ + positionType: "shift", + positionData: -toShift, + children: [{ + type: "elem", + elem: rootm + }] + }, options); // Add a class surrounding it so we can add on the appropriate + // kerning + + var rootVListWrap = buildCommon.makeSpan(["root"], [rootVList]); + return buildCommon.makeSpan(["mord", "sqrt"], [rootVListWrap, body], options); + } + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var body = group.body, + index = group.index; + return index ? new mathMLTree.MathNode("mroot", [buildMathML_buildGroup(body, options), buildMathML_buildGroup(index, options)]) : new mathMLTree.MathNode("msqrt", [buildMathML_buildGroup(body, options)]); + } +}); +;// CONCATENATED MODULE: ./src/functions/styling.js + + + + + +var styling_styleMap = { + "display": src_Style.DISPLAY, + "text": src_Style.TEXT, + "script": src_Style.SCRIPT, + "scriptscript": src_Style.SCRIPTSCRIPT +}; +defineFunction({ + type: "styling", + names: ["\\displaystyle", "\\textstyle", "\\scriptstyle", "\\scriptscriptstyle"], + props: { + numArgs: 0, + allowedInText: true, + primitive: true + }, + handler: function handler(_ref, args) { + var breakOnTokenText = _ref.breakOnTokenText, + funcName = _ref.funcName, + parser = _ref.parser; + // parse out the implicit body + var body = parser.parseExpression(true, breakOnTokenText); // TODO: Refactor to avoid duplicating styleMap in multiple places (e.g. + // here and in buildHTML and de-dupe the enumeration of all the styles). + // $FlowFixMe: The names above exactly match the styles. + + var style = funcName.slice(1, funcName.length - 5); + return { + type: "styling", + mode: parser.mode, + // Figure out what style to use by pulling out the style from + // the function name + style: style, + body: body + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + // Style changes are handled in the TeXbook on pg. 442, Rule 3. + var newStyle = styling_styleMap[group.style]; + var newOptions = options.havingStyle(newStyle).withFont(''); + return sizingGroup(group.body, newOptions, options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + // Figure out what style we're changing to. + var newStyle = styling_styleMap[group.style]; + var newOptions = options.havingStyle(newStyle); + var inner = buildMathML_buildExpression(group.body, newOptions); + var node = new mathMLTree.MathNode("mstyle", inner); + var styleAttributes = { + "display": ["0", "true"], + "text": ["0", "false"], + "script": ["1", "false"], + "scriptscript": ["2", "false"] + }; + var attr = styleAttributes[group.style]; + node.setAttribute("scriptlevel", attr[0]); + node.setAttribute("displaystyle", attr[1]); + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/supsub.js + + + + + + + + + + + + + +/** + * Sometimes, groups perform special rules when they have superscripts or + * subscripts attached to them. This function lets the `supsub` group know that + * Sometimes, groups perform special rules when they have superscripts or + * its inner element should handle the superscripts and subscripts instead of + * handling them itself. + */ +var htmlBuilderDelegate = function htmlBuilderDelegate(group, options) { + var base = group.base; + + if (!base) { + return null; + } else if (base.type === "op") { + // Operators handle supsubs differently when they have limits + // (e.g. `\displaystyle\sum_2^3`) + var delegate = base.limits && (options.style.size === src_Style.DISPLAY.size || base.alwaysHandleSupSub); + return delegate ? op_htmlBuilder : null; + } else if (base.type === "operatorname") { + var _delegate = base.alwaysHandleSupSub && (options.style.size === src_Style.DISPLAY.size || base.limits); + + return _delegate ? operatorname_htmlBuilder : null; + } else if (base.type === "accent") { + return utils.isCharacterBox(base.base) ? htmlBuilder : null; + } else if (base.type === "horizBrace") { + var isSup = !group.sub; + return isSup === base.isOver ? horizBrace_htmlBuilder : null; + } else { + return null; + } +}; // Super scripts and subscripts, whose precise placement can depend on other +// functions that precede them. + + +defineFunctionBuilders({ + type: "supsub", + htmlBuilder: function htmlBuilder(group, options) { + // Superscript and subscripts are handled in the TeXbook on page + // 445-446, rules 18(a-f). + // Here is where we defer to the inner group if it should handle + // superscripts and subscripts itself. + var builderDelegate = htmlBuilderDelegate(group, options); + + if (builderDelegate) { + return builderDelegate(group, options); + } + + var valueBase = group.base, + valueSup = group.sup, + valueSub = group.sub; + var base = buildGroup(valueBase, options); + var supm; + var subm; + var metrics = options.fontMetrics(); // Rule 18a + + var supShift = 0; + var subShift = 0; + var isCharacterBox = valueBase && utils.isCharacterBox(valueBase); + + if (valueSup) { + var newOptions = options.havingStyle(options.style.sup()); + supm = buildGroup(valueSup, newOptions, options); + + if (!isCharacterBox) { + supShift = base.height - newOptions.fontMetrics().supDrop * newOptions.sizeMultiplier / options.sizeMultiplier; + } + } + + if (valueSub) { + var _newOptions = options.havingStyle(options.style.sub()); + + subm = buildGroup(valueSub, _newOptions, options); + + if (!isCharacterBox) { + subShift = base.depth + _newOptions.fontMetrics().subDrop * _newOptions.sizeMultiplier / options.sizeMultiplier; + } + } // Rule 18c + + + var minSupShift; + + if (options.style === src_Style.DISPLAY) { + minSupShift = metrics.sup1; + } else if (options.style.cramped) { + minSupShift = metrics.sup3; + } else { + minSupShift = metrics.sup2; + } // scriptspace is a font-size-independent size, so scale it + // appropriately for use as the marginRight. + + + var multiplier = options.sizeMultiplier; + var marginRight = 0.5 / metrics.ptPerEm / multiplier + "em"; + var marginLeft = null; + + if (subm) { + // Subscripts shouldn't be shifted by the base's italic correction. + // Account for that by shifting the subscript back the appropriate + // amount. Note we only do this when the base is a single symbol. + var isOiint = group.base && group.base.type === "op" && group.base.name && (group.base.name === "\\oiint" || group.base.name === "\\oiiint"); + + if (base instanceof SymbolNode || isOiint) { + // $FlowFixMe + marginLeft = -base.italic + "em"; + } + } + + var supsub; + + if (supm && subm) { + supShift = Math.max(supShift, minSupShift, supm.depth + 0.25 * metrics.xHeight); + subShift = Math.max(subShift, metrics.sub2); + var ruleWidth = metrics.defaultRuleThickness; // Rule 18e + + var maxWidth = 4 * ruleWidth; + + if (supShift - supm.depth - (subm.height - subShift) < maxWidth) { + subShift = maxWidth - (supShift - supm.depth) + subm.height; + var psi = 0.8 * metrics.xHeight - (supShift - supm.depth); + + if (psi > 0) { + supShift += psi; + subShift -= psi; + } + } + + var vlistElem = [{ + type: "elem", + elem: subm, + shift: subShift, + marginRight: marginRight, + marginLeft: marginLeft + }, { + type: "elem", + elem: supm, + shift: -supShift, + marginRight: marginRight + }]; + supsub = buildCommon.makeVList({ + positionType: "individualShift", + children: vlistElem + }, options); + } else if (subm) { + // Rule 18b + subShift = Math.max(subShift, metrics.sub1, subm.height - 0.8 * metrics.xHeight); + var _vlistElem = [{ + type: "elem", + elem: subm, + marginLeft: marginLeft, + marginRight: marginRight + }]; + supsub = buildCommon.makeVList({ + positionType: "shift", + positionData: subShift, + children: _vlistElem + }, options); + } else if (supm) { + // Rule 18c, d + supShift = Math.max(supShift, minSupShift, supm.depth + 0.25 * metrics.xHeight); + supsub = buildCommon.makeVList({ + positionType: "shift", + positionData: -supShift, + children: [{ + type: "elem", + elem: supm, + marginRight: marginRight + }] + }, options); + } else { + throw new Error("supsub must have either sup or sub."); + } // Wrap the supsub vlist in a span.msupsub to reset text-align. + + + var mclass = getTypeOfDomTree(base, "right") || "mord"; + return buildCommon.makeSpan([mclass], [base, buildCommon.makeSpan(["msupsub"], [supsub])], options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + // Is the inner group a relevant horizonal brace? + var isBrace = false; + var isOver; + var isSup; + + if (group.base && group.base.type === "horizBrace") { + isSup = !!group.sup; + + if (isSup === group.base.isOver) { + isBrace = true; + isOver = group.base.isOver; + } + } + + if (group.base && (group.base.type === "op" || group.base.type === "operatorname")) { + group.base.parentIsSupSub = true; + } + + var children = [buildMathML_buildGroup(group.base, options)]; + + if (group.sub) { + children.push(buildMathML_buildGroup(group.sub, options)); + } + + if (group.sup) { + children.push(buildMathML_buildGroup(group.sup, options)); + } + + var nodeType; + + if (isBrace) { + nodeType = isOver ? "mover" : "munder"; + } else if (!group.sub) { + var base = group.base; + + if (base && base.type === "op" && base.limits && (options.style === src_Style.DISPLAY || base.alwaysHandleSupSub)) { + nodeType = "mover"; + } else if (base && base.type === "operatorname" && base.alwaysHandleSupSub && (base.limits || options.style === src_Style.DISPLAY)) { + nodeType = "mover"; + } else { + nodeType = "msup"; + } + } else if (!group.sup) { + var _base = group.base; + + if (_base && _base.type === "op" && _base.limits && (options.style === src_Style.DISPLAY || _base.alwaysHandleSupSub)) { + nodeType = "munder"; + } else if (_base && _base.type === "operatorname" && _base.alwaysHandleSupSub && (_base.limits || options.style === src_Style.DISPLAY)) { + nodeType = "munder"; + } else { + nodeType = "msub"; + } + } else { + var _base2 = group.base; + + if (_base2 && _base2.type === "op" && _base2.limits && options.style === src_Style.DISPLAY) { + nodeType = "munderover"; + } else if (_base2 && _base2.type === "operatorname" && _base2.alwaysHandleSupSub && (options.style === src_Style.DISPLAY || _base2.limits)) { + nodeType = "munderover"; + } else { + nodeType = "msubsup"; + } + } + + return new mathMLTree.MathNode(nodeType, children); + } +}); +;// CONCATENATED MODULE: ./src/functions/symbolsOp.js + + + + // Operator ParseNodes created in Parser.js from symbol Groups in src/symbols.js. + +defineFunctionBuilders({ + type: "atom", + htmlBuilder: function htmlBuilder(group, options) { + return buildCommon.mathsym(group.text, group.mode, options, ["m" + group.family]); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var node = new mathMLTree.MathNode("mo", [makeText(group.text, group.mode)]); + + if (group.family === "bin") { + var variant = getVariant(group, options); + + if (variant === "bold-italic") { + node.setAttribute("mathvariant", variant); + } + } else if (group.family === "punct") { + node.setAttribute("separator", "true"); + } else if (group.family === "open" || group.family === "close") { + // Delims built here should not stretch vertically. + // See delimsizing.js for stretchy delims. + node.setAttribute("stretchy", "false"); + } + + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/symbolsOrd.js + + + + +// "mathord" and "textord" ParseNodes created in Parser.js from symbol Groups in +// src/symbols.js. +var defaultVariant = { + "mi": "italic", + "mn": "normal", + "mtext": "normal" +}; +defineFunctionBuilders({ + type: "mathord", + htmlBuilder: function htmlBuilder(group, options) { + return buildCommon.makeOrd(group, options, "mathord"); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var node = new mathMLTree.MathNode("mi", [makeText(group.text, group.mode, options)]); + var variant = getVariant(group, options) || "italic"; + + if (variant !== defaultVariant[node.type]) { + node.setAttribute("mathvariant", variant); + } + + return node; + } +}); +defineFunctionBuilders({ + type: "textord", + htmlBuilder: function htmlBuilder(group, options) { + return buildCommon.makeOrd(group, options, "textord"); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var text = makeText(group.text, group.mode, options); + var variant = getVariant(group, options) || "normal"; + var node; + + if (group.mode === 'text') { + node = new mathMLTree.MathNode("mtext", [text]); + } else if (/[0-9]/.test(group.text)) { + node = new mathMLTree.MathNode("mn", [text]); + } else if (group.text === "\\prime") { + node = new mathMLTree.MathNode("mo", [text]); + } else { + node = new mathMLTree.MathNode("mi", [text]); + } + + if (variant !== defaultVariant[node.type]) { + node.setAttribute("mathvariant", variant); + } + + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/symbolsSpacing.js + + + + // A map of CSS-based spacing functions to their CSS class. + +var cssSpace = { + "\\nobreak": "nobreak", + "\\allowbreak": "allowbreak" +}; // A lookup table to determine whether a spacing function/symbol should be +// treated like a regular space character. If a symbol or command is a key +// in this table, then it should be a regular space character. Furthermore, +// the associated value may have a `className` specifying an extra CSS class +// to add to the created `span`. + +var regularSpace = { + " ": {}, + "\\ ": {}, + "~": { + className: "nobreak" + }, + "\\space": {}, + "\\nobreakspace": { + className: "nobreak" + } +}; // ParseNode<"spacing"> created in Parser.js from the "spacing" symbol Groups in +// src/symbols.js. + +defineFunctionBuilders({ + type: "spacing", + htmlBuilder: function htmlBuilder(group, options) { + if (regularSpace.hasOwnProperty(group.text)) { + var className = regularSpace[group.text].className || ""; // Spaces are generated by adding an actual space. Each of these + // things has an entry in the symbols table, so these will be turned + // into appropriate outputs. + + if (group.mode === "text") { + var ord = buildCommon.makeOrd(group, options, "textord"); + ord.classes.push(className); + return ord; + } else { + return buildCommon.makeSpan(["mspace", className], [buildCommon.mathsym(group.text, group.mode, options)], options); + } + } else if (cssSpace.hasOwnProperty(group.text)) { + // Spaces based on just a CSS class. + return buildCommon.makeSpan(["mspace", cssSpace[group.text]], [], options); + } else { + throw new src_ParseError("Unknown type of space \"" + group.text + "\""); + } + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var node; + + if (regularSpace.hasOwnProperty(group.text)) { + node = new mathMLTree.MathNode("mtext", [new mathMLTree.TextNode("\xA0")]); + } else if (cssSpace.hasOwnProperty(group.text)) { + // CSS-based MathML spaces (\nobreak, \allowbreak) are ignored + return new mathMLTree.MathNode("mspace"); + } else { + throw new src_ParseError("Unknown type of space \"" + group.text + "\""); + } + + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/tag.js + + + + +var pad = function pad() { + var padNode = new mathMLTree.MathNode("mtd", []); + padNode.setAttribute("width", "50%"); + return padNode; +}; + +defineFunctionBuilders({ + type: "tag", + mathmlBuilder: function mathmlBuilder(group, options) { + var table = new mathMLTree.MathNode("mtable", [new mathMLTree.MathNode("mtr", [pad(), new mathMLTree.MathNode("mtd", [buildExpressionRow(group.body, options)]), pad(), new mathMLTree.MathNode("mtd", [buildExpressionRow(group.tag, options)])])]); + table.setAttribute("width", "100%"); + return table; // TODO: Left-aligned tags. + // Currently, the group and options passed here do not contain + // enough info to set tag alignment. `leqno` is in Settings but it is + // not passed to Options. On the HTML side, leqno is + // set by a CSS class applied in buildTree.js. That would have worked + // in MathML if browsers supported . Since they don't, we + // need to rewrite the way this function is called. + } +}); +;// CONCATENATED MODULE: ./src/functions/text.js + + + + // Non-mathy text, possibly in a font + +var textFontFamilies = { + "\\text": undefined, + "\\textrm": "textrm", + "\\textsf": "textsf", + "\\texttt": "texttt", + "\\textnormal": "textrm" +}; +var textFontWeights = { + "\\textbf": "textbf", + "\\textmd": "textmd" +}; +var textFontShapes = { + "\\textit": "textit", + "\\textup": "textup" +}; + +var optionsWithFont = function optionsWithFont(group, options) { + var font = group.font; // Checks if the argument is a font family or a font style. + + if (!font) { + return options; + } else if (textFontFamilies[font]) { + return options.withTextFontFamily(textFontFamilies[font]); + } else if (textFontWeights[font]) { + return options.withTextFontWeight(textFontWeights[font]); + } else { + return options.withTextFontShape(textFontShapes[font]); + } +}; + +defineFunction({ + type: "text", + names: [// Font families + "\\text", "\\textrm", "\\textsf", "\\texttt", "\\textnormal", // Font weights + "\\textbf", "\\textmd", // Font Shapes + "\\textit", "\\textup"], + props: { + numArgs: 1, + argTypes: ["text"], + allowedInArgument: true, + allowedInText: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser, + funcName = _ref.funcName; + var body = args[0]; + return { + type: "text", + mode: parser.mode, + body: ordargument(body), + font: funcName + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var newOptions = optionsWithFont(group, options); + var inner = buildExpression(group.body, newOptions, true); + return buildCommon.makeSpan(["mord", "text"], inner, newOptions); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var newOptions = optionsWithFont(group, options); + return buildExpressionRow(group.body, newOptions); + } +}); +;// CONCATENATED MODULE: ./src/functions/underline.js + + + + + +defineFunction({ + type: "underline", + names: ["\\underline"], + props: { + numArgs: 1, + allowedInText: true + }, + handler: function handler(_ref, args) { + var parser = _ref.parser; + return { + type: "underline", + mode: parser.mode, + body: args[0] + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + // Underlines are handled in the TeXbook pg 443, Rule 10. + // Build the inner group. + var innerGroup = buildGroup(group.body, options); // Create the line to go below the body + + var line = buildCommon.makeLineSpan("underline-line", options); // Generate the vlist, with the appropriate kerns + + var defaultRuleThickness = options.fontMetrics().defaultRuleThickness; + var vlist = buildCommon.makeVList({ + positionType: "top", + positionData: innerGroup.height, + children: [{ + type: "kern", + size: defaultRuleThickness + }, { + type: "elem", + elem: line + }, { + type: "kern", + size: 3 * defaultRuleThickness + }, { + type: "elem", + elem: innerGroup + }] + }, options); + return buildCommon.makeSpan(["mord", "underline"], [vlist], options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var operator = new mathMLTree.MathNode("mo", [new mathMLTree.TextNode("\u203E")]); + operator.setAttribute("stretchy", "true"); + var node = new mathMLTree.MathNode("munder", [buildMathML_buildGroup(group.body, options), operator]); + node.setAttribute("accentunder", "true"); + return node; + } +}); +;// CONCATENATED MODULE: ./src/functions/vcenter.js + + + + + // \vcenter: Vertically center the argument group on the math axis. + +defineFunction({ + type: "vcenter", + names: ["\\vcenter"], + props: { + numArgs: 1, + argTypes: ["original"], + // In LaTeX, \vcenter can act only on a box. + allowedInText: false + }, + handler: function handler(_ref, args) { + var parser = _ref.parser; + return { + type: "vcenter", + mode: parser.mode, + body: args[0] + }; + }, + htmlBuilder: function htmlBuilder(group, options) { + var body = buildGroup(group.body, options); + var axisHeight = options.fontMetrics().axisHeight; + var dy = 0.5 * (body.height - axisHeight - (body.depth + axisHeight)); + return buildCommon.makeVList({ + positionType: "shift", + positionData: dy, + children: [{ + type: "elem", + elem: body + }] + }, options); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + // There is no way to do this in MathML. + // Write a class as a breadcrumb in case some post-processor wants + // to perform a vcenter adjustment. + return new mathMLTree.MathNode("mpadded", [buildMathML_buildGroup(group.body, options)], ["vcenter"]); + } +}); +;// CONCATENATED MODULE: ./src/functions/verb.js + + + + +defineFunction({ + type: "verb", + names: ["\\verb"], + props: { + numArgs: 0, + allowedInText: true + }, + handler: function handler(context, args, optArgs) { + // \verb and \verb* are dealt with directly in Parser.js. + // If we end up here, it's because of a failure to match the two delimiters + // in the regex in Lexer.js. LaTeX raises the following error when \verb is + // terminated by end of line (or file). + throw new src_ParseError("\\verb ended by end of line instead of matching delimiter"); + }, + htmlBuilder: function htmlBuilder(group, options) { + var text = makeVerb(group); + var body = []; // \verb enters text mode and therefore is sized like \textstyle + + var newOptions = options.havingStyle(options.style.text()); + + for (var i = 0; i < text.length; i++) { + var c = text[i]; + + if (c === '~') { + c = '\\textasciitilde'; + } + + body.push(buildCommon.makeSymbol(c, "Typewriter-Regular", group.mode, newOptions, ["mord", "texttt"])); + } + + return buildCommon.makeSpan(["mord", "text"].concat(newOptions.sizingClasses(options)), buildCommon.tryCombineChars(body), newOptions); + }, + mathmlBuilder: function mathmlBuilder(group, options) { + var text = new mathMLTree.TextNode(makeVerb(group)); + var node = new mathMLTree.MathNode("mtext", [text]); + node.setAttribute("mathvariant", "monospace"); + return node; + } +}); +/** + * Converts verb group into body string. + * + * \verb* replaces each space with an open box \u2423 + * \verb replaces each space with a no-break space \xA0 + */ + +var makeVerb = function makeVerb(group) { + return group.body.replace(/ /g, group.star ? "\u2423" : '\xA0'); +}; +;// CONCATENATED MODULE: ./src/functions.js +/** Include this to ensure that all functions are defined. */ + +var functions = _functions; +/* harmony default export */ var src_functions = (functions); // TODO(kevinb): have functions return an object and call defineFunction with +// that object in this file instead of relying on side-effects. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +;// CONCATENATED MODULE: ./src/SourceLocation.js +/** + * Lexing or parsing positional information for error reporting. + * This object is immutable. + */ +var SourceLocation = /*#__PURE__*/function () { + // The + prefix indicates that these fields aren't writeable + // Lexer holding the input string. + // Start offset, zero-based inclusive. + // End offset, zero-based exclusive. + function SourceLocation(lexer, start, end) { + this.lexer = void 0; + this.start = void 0; + this.end = void 0; + this.lexer = lexer; + this.start = start; + this.end = end; + } + /** + * Merges two `SourceLocation`s from location providers, given they are + * provided in order of appearance. + * - Returns the first one's location if only the first is provided. + * - Returns a merged range of the first and the last if both are provided + * and their lexers match. + * - Otherwise, returns null. + */ + + + SourceLocation.range = function range(first, second) { + if (!second) { + return first && first.loc; + } else if (!first || !first.loc || !second.loc || first.loc.lexer !== second.loc.lexer) { + return null; + } else { + return new SourceLocation(first.loc.lexer, first.loc.start, second.loc.end); + } + }; + + return SourceLocation; +}(); + + +;// CONCATENATED MODULE: ./src/Token.js + +/** + * Interface required to break circular dependency between Token, Lexer, and + * ParseError. + */ + +/** + * The resulting token returned from `lex`. + * + * It consists of the token text plus some position information. + * The position information is essentially a range in an input string, + * but instead of referencing the bare input string, we refer to the lexer. + * That way it is possible to attach extra metadata to the input string, + * like for example a file name or similar. + * + * The position information is optional, so it is OK to construct synthetic + * tokens if appropriate. Not providing available position information may + * lead to degraded error reporting, though. + */ +var Token = /*#__PURE__*/function () { + // don't expand the token + // used in \noexpand + function Token(text, // the text of this token + loc) { + this.text = void 0; + this.loc = void 0; + this.noexpand = void 0; + this.treatAsRelax = void 0; + this.text = text; + this.loc = loc; + } + /** + * Given a pair of tokens (this and endToken), compute a `Token` encompassing + * the whole input range enclosed by these two. + */ + + + var _proto = Token.prototype; + + _proto.range = function range(endToken, // last token of the range, inclusive + text // the text of the newly constructed token + ) { + return new Token(text, SourceLocation.range(this, endToken)); + }; + + return Token; +}(); +;// CONCATENATED MODULE: ./src/Lexer.js +/** + * The Lexer class handles tokenizing the input in various ways. Since our + * parser expects us to be able to backtrack, the lexer allows lexing from any + * given starting point. + * + * Its main exposed function is the `lex` function, which takes a position to + * lex from and a type of token to lex. It defers to the appropriate `_innerLex` + * function. + * + * The various `_innerLex` functions perform the actual lexing of different + * kinds. + */ + + + + +/* The following tokenRegex + * - matches typical whitespace (but not NBSP etc.) using its first group + * - does not match any control character \x00-\x1f except whitespace + * - does not match a bare backslash + * - matches any ASCII character except those just mentioned + * - does not match the BMP private use area \uE000-\uF8FF + * - does not match bare surrogate code units + * - matches any BMP character except for those just described + * - matches any valid Unicode surrogate pair + * - matches a backslash followed by one or more whitespace characters + * - matches a backslash followed by one or more letters then whitespace + * - matches a backslash followed by any BMP character + * Capturing groups: + * [1] regular whitespace + * [2] backslash followed by whitespace + * [3] anything else, which may include: + * [4] left character of \verb* + * [5] left character of \verb + * [6] backslash followed by word, excluding any trailing whitespace + * Just because the Lexer matches something doesn't mean it's valid input: + * If there is no matching function or symbol definition, the Parser will + * still reject the input. + */ +var spaceRegexString = "[ \r\n\t]"; +var controlWordRegexString = "\\\\[a-zA-Z@]+"; +var controlSymbolRegexString = "\\\\[^\uD800-\uDFFF]"; +var controlWordWhitespaceRegexString = "(" + controlWordRegexString + ")" + spaceRegexString + "*"; +var controlSpaceRegexString = "\\\\(\n|[ \r\t]+\n?)[ \r\t]*"; +var combiningDiacriticalMarkString = "[\u0300-\u036F]"; +var combiningDiacriticalMarksEndRegex = new RegExp(combiningDiacriticalMarkString + "+$"); +var tokenRegexString = "(" + spaceRegexString + "+)|" + ( // whitespace +controlSpaceRegexString + "|") + // \whitespace +"([!-\\[\\]-\u2027\u202A-\uD7FF\uF900-\uFFFF]" + ( // single codepoint +combiningDiacriticalMarkString + "*") + // ...plus accents +"|[\uD800-\uDBFF][\uDC00-\uDFFF]" + ( // surrogate pair +combiningDiacriticalMarkString + "*") + // ...plus accents +"|\\\\verb\\*([^]).*?\\4" + // \verb* +"|\\\\verb([^*a-zA-Z]).*?\\5" + ( // \verb unstarred +"|" + controlWordWhitespaceRegexString) + ( // \macroName + spaces +"|" + controlSymbolRegexString + ")"); // \\, \', etc. + +/** Main Lexer class */ + +var Lexer = /*#__PURE__*/function () { + // Category codes. The lexer only supports comment characters (14) for now. + // MacroExpander additionally distinguishes active (13). + function Lexer(input, settings) { + this.input = void 0; + this.settings = void 0; + this.tokenRegex = void 0; + this.catcodes = void 0; + // Separate accents from characters + this.input = input; + this.settings = settings; + this.tokenRegex = new RegExp(tokenRegexString, 'g'); + this.catcodes = { + "%": 14, + // comment character + "~": 13 // active character + + }; + } + + var _proto = Lexer.prototype; + + _proto.setCatcode = function setCatcode(char, code) { + this.catcodes[char] = code; + } + /** + * This function lexes a single token. + */ + ; + + _proto.lex = function lex() { + var input = this.input; + var pos = this.tokenRegex.lastIndex; + + if (pos === input.length) { + return new Token("EOF", new SourceLocation(this, pos, pos)); + } + + var match = this.tokenRegex.exec(input); + + if (match === null || match.index !== pos) { + throw new src_ParseError("Unexpected character: '" + input[pos] + "'", new Token(input[pos], new SourceLocation(this, pos, pos + 1))); + } + + var text = match[6] || match[3] || (match[2] ? "\\ " : " "); + + if (this.catcodes[text] === 14) { + // comment character + var nlIndex = input.indexOf('\n', this.tokenRegex.lastIndex); + + if (nlIndex === -1) { + this.tokenRegex.lastIndex = input.length; // EOF + + this.settings.reportNonstrict("commentAtEnd", "% comment has no terminating newline; LaTeX would " + "fail because of commenting the end of math mode (e.g. $)"); + } else { + this.tokenRegex.lastIndex = nlIndex + 1; + } + + return this.lex(); + } + + return new Token(text, new SourceLocation(this, pos, this.tokenRegex.lastIndex)); + }; + + return Lexer; +}(); + + +;// CONCATENATED MODULE: ./src/Namespace.js +/** + * A `Namespace` refers to a space of nameable things like macros or lengths, + * which can be `set` either globally or local to a nested group, using an + * undo stack similar to how TeX implements this functionality. + * Performance-wise, `get` and local `set` take constant time, while global + * `set` takes time proportional to the depth of group nesting. + */ + + +var Namespace = /*#__PURE__*/function () { + /** + * Both arguments are optional. The first argument is an object of + * built-in mappings which never change. The second argument is an object + * of initial (global-level) mappings, which will constantly change + * according to any global/top-level `set`s done. + */ + function Namespace(builtins, globalMacros) { + if (builtins === void 0) { + builtins = {}; + } + + if (globalMacros === void 0) { + globalMacros = {}; + } + + this.current = void 0; + this.builtins = void 0; + this.undefStack = void 0; + this.current = globalMacros; + this.builtins = builtins; + this.undefStack = []; + } + /** + * Start a new nested group, affecting future local `set`s. + */ + + + var _proto = Namespace.prototype; + + _proto.beginGroup = function beginGroup() { + this.undefStack.push({}); + } + /** + * End current nested group, restoring values before the group began. + */ + ; + + _proto.endGroup = function endGroup() { + if (this.undefStack.length === 0) { + throw new src_ParseError("Unbalanced namespace destruction: attempt " + "to pop global namespace; please report this as a bug"); + } + + var undefs = this.undefStack.pop(); + + for (var undef in undefs) { + if (undefs.hasOwnProperty(undef)) { + if (undefs[undef] === undefined) { + delete this.current[undef]; + } else { + this.current[undef] = undefs[undef]; + } + } + } + } + /** + * Ends all currently nested groups (if any), restoring values before the + * groups began. Useful in case of an error in the middle of parsing. + */ + ; + + _proto.endGroups = function endGroups() { + while (this.undefStack.length > 0) { + this.endGroup(); + } + } + /** + * Detect whether `name` has a definition. Equivalent to + * `get(name) != null`. + */ + ; + + _proto.has = function has(name) { + return this.current.hasOwnProperty(name) || this.builtins.hasOwnProperty(name); + } + /** + * Get the current value of a name, or `undefined` if there is no value. + * + * Note: Do not use `if (namespace.get(...))` to detect whether a macro + * is defined, as the definition may be the empty string which evaluates + * to `false` in JavaScript. Use `if (namespace.get(...) != null)` or + * `if (namespace.has(...))`. + */ + ; + + _proto.get = function get(name) { + if (this.current.hasOwnProperty(name)) { + return this.current[name]; + } else { + return this.builtins[name]; + } + } + /** + * Set the current value of a name, and optionally set it globally too. + * Local set() sets the current value and (when appropriate) adds an undo + * operation to the undo stack. Global set() may change the undo + * operation at every level, so takes time linear in their number. + */ + ; + + _proto.set = function set(name, value, global) { + if (global === void 0) { + global = false; + } + + if (global) { + // Global set is equivalent to setting in all groups. Simulate this + // by destroying any undos currently scheduled for this name, + // and adding an undo with the *new* value (in case it later gets + // locally reset within this environment). + for (var i = 0; i < this.undefStack.length; i++) { + delete this.undefStack[i][name]; + } + + if (this.undefStack.length > 0) { + this.undefStack[this.undefStack.length - 1][name] = value; + } + } else { + // Undo this set at end of this group (possibly to `undefined`), + // unless an undo is already in place, in which case that older + // value is the correct one. + var top = this.undefStack[this.undefStack.length - 1]; + + if (top && !top.hasOwnProperty(name)) { + top[name] = this.current[name]; + } + } + + this.current[name] = value; + }; + + return Namespace; +}(); + + +;// CONCATENATED MODULE: ./src/macros.js +/** + * Predefined macros for KaTeX. + * This can be used to define some commands in terms of others. + */ +// Export global macros object from defineMacro + +var macros = _macros; +/* harmony default export */ var src_macros = (macros); + + + + + ////////////////////////////////////////////////////////////////////// +// macro tools + +defineMacro("\\noexpand", function (context) { + // The expansion is the token itself; but that token is interpreted + // as if its meaning were ‘\relax’ if it is a control sequence that + // would ordinarily be expanded by TeX’s expansion rules. + var t = context.popToken(); + + if (context.isExpandable(t.text)) { + t.noexpand = true; + t.treatAsRelax = true; + } + + return { + tokens: [t], + numArgs: 0 + }; +}); +defineMacro("\\expandafter", function (context) { + // TeX first reads the token that comes immediately after \expandafter, + // without expanding it; let’s call this token t. Then TeX reads the + // token that comes after t (and possibly more tokens, if that token + // has an argument), replacing it by its expansion. Finally TeX puts + // t back in front of that expansion. + var t = context.popToken(); + context.expandOnce(true); // expand only an expandable token + + return { + tokens: [t], + numArgs: 0 + }; +}); // LaTeX's \@firstoftwo{#1}{#2} expands to #1, skipping #2 +// TeX source: \long\def\@firstoftwo#1#2{#1} + +defineMacro("\\@firstoftwo", function (context) { + var args = context.consumeArgs(2); + return { + tokens: args[0], + numArgs: 0 + }; +}); // LaTeX's \@secondoftwo{#1}{#2} expands to #2, skipping #1 +// TeX source: \long\def\@secondoftwo#1#2{#2} + +defineMacro("\\@secondoftwo", function (context) { + var args = context.consumeArgs(2); + return { + tokens: args[1], + numArgs: 0 + }; +}); // LaTeX's \@ifnextchar{#1}{#2}{#3} looks ahead to the next (unexpanded) +// symbol that isn't a space, consuming any spaces but not consuming the +// first nonspace character. If that nonspace character matches #1, then +// the macro expands to #2; otherwise, it expands to #3. + +defineMacro("\\@ifnextchar", function (context) { + var args = context.consumeArgs(3); // symbol, if, else + + context.consumeSpaces(); + var nextToken = context.future(); + + if (args[0].length === 1 && args[0][0].text === nextToken.text) { + return { + tokens: args[1], + numArgs: 0 + }; + } else { + return { + tokens: args[2], + numArgs: 0 + }; + } +}); // LaTeX's \@ifstar{#1}{#2} looks ahead to the next (unexpanded) symbol. +// If it is `*`, then it consumes the symbol, and the macro expands to #1; +// otherwise, the macro expands to #2 (without consuming the symbol). +// TeX source: \def\@ifstar#1{\@ifnextchar *{\@firstoftwo{#1}}} + +defineMacro("\\@ifstar", "\\@ifnextchar *{\\@firstoftwo{#1}}"); // LaTeX's \TextOrMath{#1}{#2} expands to #1 in text mode, #2 in math mode + +defineMacro("\\TextOrMath", function (context) { + var args = context.consumeArgs(2); + + if (context.mode === 'text') { + return { + tokens: args[0], + numArgs: 0 + }; + } else { + return { + tokens: args[1], + numArgs: 0 + }; + } +}); // Lookup table for parsing numbers in base 8 through 16 + +var digitToNumber = { + "0": 0, + "1": 1, + "2": 2, + "3": 3, + "4": 4, + "5": 5, + "6": 6, + "7": 7, + "8": 8, + "9": 9, + "a": 10, + "A": 10, + "b": 11, + "B": 11, + "c": 12, + "C": 12, + "d": 13, + "D": 13, + "e": 14, + "E": 14, + "f": 15, + "F": 15 +}; // TeX \char makes a literal character (catcode 12) using the following forms: +// (see The TeXBook, p. 43) +// \char123 -- decimal +// \char'123 -- octal +// \char"123 -- hex +// \char`x -- character that can be written (i.e. isn't active) +// \char`\x -- character that cannot be written (e.g. %) +// These all refer to characters from the font, so we turn them into special +// calls to a function \@char dealt with in the Parser. + +defineMacro("\\char", function (context) { + var token = context.popToken(); + var base; + var number = ''; + + if (token.text === "'") { + base = 8; + token = context.popToken(); + } else if (token.text === '"') { + base = 16; + token = context.popToken(); + } else if (token.text === "`") { + token = context.popToken(); + + if (token.text[0] === "\\") { + number = token.text.charCodeAt(1); + } else if (token.text === "EOF") { + throw new src_ParseError("\\char` missing argument"); + } else { + number = token.text.charCodeAt(0); + } + } else { + base = 10; + } + + if (base) { + // Parse a number in the given base, starting with first `token`. + number = digitToNumber[token.text]; + + if (number == null || number >= base) { + throw new src_ParseError("Invalid base-" + base + " digit " + token.text); + } + + var digit; + + while ((digit = digitToNumber[context.future().text]) != null && digit < base) { + number *= base; + number += digit; + context.popToken(); + } + } + + return "\\@char{" + number + "}"; +}); // \newcommand{\macro}[args]{definition} +// \renewcommand{\macro}[args]{definition} +// TODO: Optional arguments: \newcommand{\macro}[args][default]{definition} + +var newcommand = function newcommand(context, existsOK, nonexistsOK) { + var arg = context.consumeArg().tokens; + + if (arg.length !== 1) { + throw new src_ParseError("\\newcommand's first argument must be a macro name"); + } + + var name = arg[0].text; + var exists = context.isDefined(name); + + if (exists && !existsOK) { + throw new src_ParseError("\\newcommand{" + name + "} attempting to redefine " + (name + "; use \\renewcommand")); + } + + if (!exists && !nonexistsOK) { + throw new src_ParseError("\\renewcommand{" + name + "} when command " + name + " " + "does not yet exist; use \\newcommand"); + } + + var numArgs = 0; + arg = context.consumeArg().tokens; + + if (arg.length === 1 && arg[0].text === "[") { + var argText = ''; + var token = context.expandNextToken(); + + while (token.text !== "]" && token.text !== "EOF") { + // TODO: Should properly expand arg, e.g., ignore {}s + argText += token.text; + token = context.expandNextToken(); + } + + if (!argText.match(/^\s*[0-9]+\s*$/)) { + throw new src_ParseError("Invalid number of arguments: " + argText); + } + + numArgs = parseInt(argText); + arg = context.consumeArg().tokens; + } // Final arg is the expansion of the macro + + + context.macros.set(name, { + tokens: arg, + numArgs: numArgs + }); + return ''; +}; + +defineMacro("\\newcommand", function (context) { + return newcommand(context, false, true); +}); +defineMacro("\\renewcommand", function (context) { + return newcommand(context, true, false); +}); +defineMacro("\\providecommand", function (context) { + return newcommand(context, true, true); +}); // terminal (console) tools + +defineMacro("\\message", function (context) { + var arg = context.consumeArgs(1)[0]; // eslint-disable-next-line no-console + + console.log(arg.reverse().map(function (token) { + return token.text; + }).join("")); + return ''; +}); +defineMacro("\\errmessage", function (context) { + var arg = context.consumeArgs(1)[0]; // eslint-disable-next-line no-console + + console.error(arg.reverse().map(function (token) { + return token.text; + }).join("")); + return ''; +}); +defineMacro("\\show", function (context) { + var tok = context.popToken(); + var name = tok.text; // eslint-disable-next-line no-console + + console.log(tok, context.macros.get(name), src_functions[name], src_symbols.math[name], src_symbols.text[name]); + return ''; +}); ////////////////////////////////////////////////////////////////////// +// Grouping +// \let\bgroup={ \let\egroup=} + +defineMacro("\\bgroup", "{"); +defineMacro("\\egroup", "}"); // Symbols from latex.ltx: +// \def~{\nobreakspace{}} +// \def\lq{`} +// \def\rq{'} +// \def \aa {\r a} +// \def \AA {\r A} + +defineMacro("~", "\\nobreakspace"); +defineMacro("\\lq", "`"); +defineMacro("\\rq", "'"); +defineMacro("\\aa", "\\r a"); +defineMacro("\\AA", "\\r A"); // Copyright (C) and registered (R) symbols. Use raw symbol in MathML. +// \DeclareTextCommandDefault{\textcopyright}{\textcircled{c}} +// \DeclareTextCommandDefault{\textregistered}{\textcircled{% +// \check@mathfonts\fontsize\sf@size\z@\math@fontsfalse\selectfont R}} +// \DeclareRobustCommand{\copyright}{% +// \ifmmode{\nfss@text{\textcopyright}}\else\textcopyright\fi} + +defineMacro("\\textcopyright", "\\html@mathml{\\textcircled{c}}{\\char`©}"); +defineMacro("\\copyright", "\\TextOrMath{\\textcopyright}{\\text{\\textcopyright}}"); +defineMacro("\\textregistered", "\\html@mathml{\\textcircled{\\scriptsize R}}{\\char`®}"); // Characters omitted from Unicode range 1D400–1D7FF + +defineMacro("\u212C", "\\mathscr{B}"); // script + +defineMacro("\u2130", "\\mathscr{E}"); +defineMacro("\u2131", "\\mathscr{F}"); +defineMacro("\u210B", "\\mathscr{H}"); +defineMacro("\u2110", "\\mathscr{I}"); +defineMacro("\u2112", "\\mathscr{L}"); +defineMacro("\u2133", "\\mathscr{M}"); +defineMacro("\u211B", "\\mathscr{R}"); +defineMacro("\u212D", "\\mathfrak{C}"); // Fraktur + +defineMacro("\u210C", "\\mathfrak{H}"); +defineMacro("\u2128", "\\mathfrak{Z}"); // Define \Bbbk with a macro that works in both HTML and MathML. + +defineMacro("\\Bbbk", "\\Bbb{k}"); // Unicode middle dot +// The KaTeX fonts do not contain U+00B7. Instead, \cdotp displays +// the dot at U+22C5 and gives it punct spacing. + +defineMacro("\xB7", "\\cdotp"); // \llap and \rlap render their contents in text mode + +defineMacro("\\llap", "\\mathllap{\\textrm{#1}}"); +defineMacro("\\rlap", "\\mathrlap{\\textrm{#1}}"); +defineMacro("\\clap", "\\mathclap{\\textrm{#1}}"); // \mathstrut from the TeXbook, p 360 + +defineMacro("\\mathstrut", "\\vphantom{(}"); // \underbar from TeXbook p 353 + +defineMacro("\\underbar", "\\underline{\\text{#1}}"); // \not is defined by base/fontmath.ltx via +// \DeclareMathSymbol{\not}{\mathrel}{symbols}{"36} +// It's thus treated like a \mathrel, but defined by a symbol that has zero +// width but extends to the right. We use \rlap to get that spacing. +// For MathML we write U+0338 here. buildMathML.js will then do the overlay. + +defineMacro("\\not", '\\html@mathml{\\mathrel{\\mathrlap\\@not}}{\\char"338}'); // Negated symbols from base/fontmath.ltx: +// \def\neq{\not=} \let\ne=\neq +// \DeclareRobustCommand +// \notin{\mathrel{\m@th\mathpalette\c@ncel\in}} +// \def\c@ncel#1#2{\m@th\ooalign{$\hfil#1\mkern1mu/\hfil$\crcr$#1#2$}} + +defineMacro("\\neq", "\\html@mathml{\\mathrel{\\not=}}{\\mathrel{\\char`≠}}"); +defineMacro("\\ne", "\\neq"); +defineMacro("\u2260", "\\neq"); +defineMacro("\\notin", "\\html@mathml{\\mathrel{{\\in}\\mathllap{/\\mskip1mu}}}" + "{\\mathrel{\\char`∉}}"); +defineMacro("\u2209", "\\notin"); // Unicode stacked relations + +defineMacro("\u2258", "\\html@mathml{" + "\\mathrel{=\\kern{-1em}\\raisebox{0.4em}{$\\scriptsize\\frown$}}" + "}{\\mathrel{\\char`\u2258}}"); +defineMacro("\u2259", "\\html@mathml{\\stackrel{\\tiny\\wedge}{=}}{\\mathrel{\\char`\u2258}}"); +defineMacro("\u225A", "\\html@mathml{\\stackrel{\\tiny\\vee}{=}}{\\mathrel{\\char`\u225A}}"); +defineMacro("\u225B", "\\html@mathml{\\stackrel{\\scriptsize\\star}{=}}" + "{\\mathrel{\\char`\u225B}}"); +defineMacro("\u225D", "\\html@mathml{\\stackrel{\\tiny\\mathrm{def}}{=}}" + "{\\mathrel{\\char`\u225D}}"); +defineMacro("\u225E", "\\html@mathml{\\stackrel{\\tiny\\mathrm{m}}{=}}" + "{\\mathrel{\\char`\u225E}}"); +defineMacro("\u225F", "\\html@mathml{\\stackrel{\\tiny?}{=}}{\\mathrel{\\char`\u225F}}"); // Misc Unicode + +defineMacro("\u27C2", "\\perp"); +defineMacro("\u203C", "\\mathclose{!\\mkern-0.8mu!}"); +defineMacro("\u220C", "\\notni"); +defineMacro("\u231C", "\\ulcorner"); +defineMacro("\u231D", "\\urcorner"); +defineMacro("\u231E", "\\llcorner"); +defineMacro("\u231F", "\\lrcorner"); +defineMacro("\xA9", "\\copyright"); +defineMacro("\xAE", "\\textregistered"); +defineMacro("\uFE0F", "\\textregistered"); // The KaTeX fonts have corners at codepoints that don't match Unicode. +// For MathML purposes, use the Unicode code point. + +defineMacro("\\ulcorner", "\\html@mathml{\\@ulcorner}{\\mathop{\\char\"231c}}"); +defineMacro("\\urcorner", "\\html@mathml{\\@urcorner}{\\mathop{\\char\"231d}}"); +defineMacro("\\llcorner", "\\html@mathml{\\@llcorner}{\\mathop{\\char\"231e}}"); +defineMacro("\\lrcorner", "\\html@mathml{\\@lrcorner}{\\mathop{\\char\"231f}}"); ////////////////////////////////////////////////////////////////////// +// LaTeX_2ε +// \vdots{\vbox{\baselineskip4\p@ \lineskiplimit\z@ +// \kern6\p@\hbox{.}\hbox{.}\hbox{.}}} +// We'll call \varvdots, which gets a glyph from symbols.js. +// The zero-width rule gets us an equivalent to the vertical 6pt kern. + +defineMacro("\\vdots", "\\mathord{\\varvdots\\rule{0pt}{15pt}}"); +defineMacro("\u22EE", "\\vdots"); ////////////////////////////////////////////////////////////////////// +// amsmath.sty +// http://mirrors.concertpass.com/tex-archive/macros/latex/required/amsmath/amsmath.pdf +// Italic Greek capital letters. AMS defines these with \DeclareMathSymbol, +// but they are equivalent to \mathit{\Letter}. + +defineMacro("\\varGamma", "\\mathit{\\Gamma}"); +defineMacro("\\varDelta", "\\mathit{\\Delta}"); +defineMacro("\\varTheta", "\\mathit{\\Theta}"); +defineMacro("\\varLambda", "\\mathit{\\Lambda}"); +defineMacro("\\varXi", "\\mathit{\\Xi}"); +defineMacro("\\varPi", "\\mathit{\\Pi}"); +defineMacro("\\varSigma", "\\mathit{\\Sigma}"); +defineMacro("\\varUpsilon", "\\mathit{\\Upsilon}"); +defineMacro("\\varPhi", "\\mathit{\\Phi}"); +defineMacro("\\varPsi", "\\mathit{\\Psi}"); +defineMacro("\\varOmega", "\\mathit{\\Omega}"); //\newcommand{\substack}[1]{\subarray{c}#1\endsubarray} + +defineMacro("\\substack", "\\begin{subarray}{c}#1\\end{subarray}"); // \renewcommand{\colon}{\nobreak\mskip2mu\mathpunct{}\nonscript +// \mkern-\thinmuskip{:}\mskip6muplus1mu\relax} + +defineMacro("\\colon", "\\nobreak\\mskip2mu\\mathpunct{}" + "\\mathchoice{\\mkern-3mu}{\\mkern-3mu}{}{}{:}\\mskip6mu"); // \newcommand{\boxed}[1]{\fbox{\m@th$\displaystyle#1$}} + +defineMacro("\\boxed", "\\fbox{$\\displaystyle{#1}$}"); // \def\iff{\DOTSB\;\Longleftrightarrow\;} +// \def\implies{\DOTSB\;\Longrightarrow\;} +// \def\impliedby{\DOTSB\;\Longleftarrow\;} + +defineMacro("\\iff", "\\DOTSB\\;\\Longleftrightarrow\\;"); +defineMacro("\\implies", "\\DOTSB\\;\\Longrightarrow\\;"); +defineMacro("\\impliedby", "\\DOTSB\\;\\Longleftarrow\\;"); // AMSMath's automatic \dots, based on \mdots@@ macro. + +var dotsByToken = { + ',': '\\dotsc', + '\\not': '\\dotsb', + // \keybin@ checks for the following: + '+': '\\dotsb', + '=': '\\dotsb', + '<': '\\dotsb', + '>': '\\dotsb', + '-': '\\dotsb', + '*': '\\dotsb', + ':': '\\dotsb', + // Symbols whose definition starts with \DOTSB: + '\\DOTSB': '\\dotsb', + '\\coprod': '\\dotsb', + '\\bigvee': '\\dotsb', + '\\bigwedge': '\\dotsb', + '\\biguplus': '\\dotsb', + '\\bigcap': '\\dotsb', + '\\bigcup': '\\dotsb', + '\\prod': '\\dotsb', + '\\sum': '\\dotsb', + '\\bigotimes': '\\dotsb', + '\\bigoplus': '\\dotsb', + '\\bigodot': '\\dotsb', + '\\bigsqcup': '\\dotsb', + '\\And': '\\dotsb', + '\\longrightarrow': '\\dotsb', + '\\Longrightarrow': '\\dotsb', + '\\longleftarrow': '\\dotsb', + '\\Longleftarrow': '\\dotsb', + '\\longleftrightarrow': '\\dotsb', + '\\Longleftrightarrow': '\\dotsb', + '\\mapsto': '\\dotsb', + '\\longmapsto': '\\dotsb', + '\\hookrightarrow': '\\dotsb', + '\\doteq': '\\dotsb', + // Symbols whose definition starts with \mathbin: + '\\mathbin': '\\dotsb', + // Symbols whose definition starts with \mathrel: + '\\mathrel': '\\dotsb', + '\\relbar': '\\dotsb', + '\\Relbar': '\\dotsb', + '\\xrightarrow': '\\dotsb', + '\\xleftarrow': '\\dotsb', + // Symbols whose definition starts with \DOTSI: + '\\DOTSI': '\\dotsi', + '\\int': '\\dotsi', + '\\oint': '\\dotsi', + '\\iint': '\\dotsi', + '\\iiint': '\\dotsi', + '\\iiiint': '\\dotsi', + '\\idotsint': '\\dotsi', + // Symbols whose definition starts with \DOTSX: + '\\DOTSX': '\\dotsx' +}; +defineMacro("\\dots", function (context) { + // TODO: If used in text mode, should expand to \textellipsis. + // However, in KaTeX, \textellipsis and \ldots behave the same + // (in text mode), and it's unlikely we'd see any of the math commands + // that affect the behavior of \dots when in text mode. So fine for now + // (until we support \ifmmode ... \else ... \fi). + var thedots = '\\dotso'; + var next = context.expandAfterFuture().text; + + if (next in dotsByToken) { + thedots = dotsByToken[next]; + } else if (next.substr(0, 4) === '\\not') { + thedots = '\\dotsb'; + } else if (next in src_symbols.math) { + if (utils.contains(['bin', 'rel'], src_symbols.math[next].group)) { + thedots = '\\dotsb'; + } + } + + return thedots; +}); +var spaceAfterDots = { + // \rightdelim@ checks for the following: + ')': true, + ']': true, + '\\rbrack': true, + '\\}': true, + '\\rbrace': true, + '\\rangle': true, + '\\rceil': true, + '\\rfloor': true, + '\\rgroup': true, + '\\rmoustache': true, + '\\right': true, + '\\bigr': true, + '\\biggr': true, + '\\Bigr': true, + '\\Biggr': true, + // \extra@ also tests for the following: + '$': true, + // \extrap@ checks for the following: + ';': true, + '.': true, + ',': true +}; +defineMacro("\\dotso", function (context) { + var next = context.future().text; + + if (next in spaceAfterDots) { + return "\\ldots\\,"; + } else { + return "\\ldots"; + } +}); +defineMacro("\\dotsc", function (context) { + var next = context.future().text; // \dotsc uses \extra@ but not \extrap@, instead specially checking for + // ';' and '.', but doesn't check for ','. + + if (next in spaceAfterDots && next !== ',') { + return "\\ldots\\,"; + } else { + return "\\ldots"; + } +}); +defineMacro("\\cdots", function (context) { + var next = context.future().text; + + if (next in spaceAfterDots) { + return "\\@cdots\\,"; + } else { + return "\\@cdots"; + } +}); +defineMacro("\\dotsb", "\\cdots"); +defineMacro("\\dotsm", "\\cdots"); +defineMacro("\\dotsi", "\\!\\cdots"); // amsmath doesn't actually define \dotsx, but \dots followed by a macro +// starting with \DOTSX implies \dotso, and then \extra@ detects this case +// and forces the added `\,`. + +defineMacro("\\dotsx", "\\ldots\\,"); // \let\DOTSI\relax +// \let\DOTSB\relax +// \let\DOTSX\relax + +defineMacro("\\DOTSI", "\\relax"); +defineMacro("\\DOTSB", "\\relax"); +defineMacro("\\DOTSX", "\\relax"); // Spacing, based on amsmath.sty's override of LaTeX defaults +// \DeclareRobustCommand{\tmspace}[3]{% +// \ifmmode\mskip#1#2\else\kern#1#3\fi\relax} + +defineMacro("\\tmspace", "\\TextOrMath{\\kern#1#3}{\\mskip#1#2}\\relax"); // \renewcommand{\,}{\tmspace+\thinmuskip{.1667em}} +// TODO: math mode should use \thinmuskip + +defineMacro("\\,", "\\tmspace+{3mu}{.1667em}"); // \let\thinspace\, + +defineMacro("\\thinspace", "\\,"); // \def\>{\mskip\medmuskip} +// \renewcommand{\:}{\tmspace+\medmuskip{.2222em}} +// TODO: \> and math mode of \: should use \medmuskip = 4mu plus 2mu minus 4mu + +defineMacro("\\>", "\\mskip{4mu}"); +defineMacro("\\:", "\\tmspace+{4mu}{.2222em}"); // \let\medspace\: + +defineMacro("\\medspace", "\\:"); // \renewcommand{\;}{\tmspace+\thickmuskip{.2777em}} +// TODO: math mode should use \thickmuskip = 5mu plus 5mu + +defineMacro("\\;", "\\tmspace+{5mu}{.2777em}"); // \let\thickspace\; + +defineMacro("\\thickspace", "\\;"); // \renewcommand{\!}{\tmspace-\thinmuskip{.1667em}} +// TODO: math mode should use \thinmuskip + +defineMacro("\\!", "\\tmspace-{3mu}{.1667em}"); // \let\negthinspace\! + +defineMacro("\\negthinspace", "\\!"); // \newcommand{\negmedspace}{\tmspace-\medmuskip{.2222em}} +// TODO: math mode should use \medmuskip + +defineMacro("\\negmedspace", "\\tmspace-{4mu}{.2222em}"); // \newcommand{\negthickspace}{\tmspace-\thickmuskip{.2777em}} +// TODO: math mode should use \thickmuskip + +defineMacro("\\negthickspace", "\\tmspace-{5mu}{.277em}"); // \def\enspace{\kern.5em } + +defineMacro("\\enspace", "\\kern.5em "); // \def\enskip{\hskip.5em\relax} + +defineMacro("\\enskip", "\\hskip.5em\\relax"); // \def\quad{\hskip1em\relax} + +defineMacro("\\quad", "\\hskip1em\\relax"); // \def\qquad{\hskip2em\relax} + +defineMacro("\\qquad", "\\hskip2em\\relax"); // \tag@in@display form of \tag + +defineMacro("\\tag", "\\@ifstar\\tag@literal\\tag@paren"); +defineMacro("\\tag@paren", "\\tag@literal{({#1})}"); +defineMacro("\\tag@literal", function (context) { + if (context.macros.get("\\df@tag")) { + throw new src_ParseError("Multiple \\tag"); + } + + return "\\gdef\\df@tag{\\text{#1}}"; +}); // \renewcommand{\bmod}{\nonscript\mskip-\medmuskip\mkern5mu\mathbin +// {\operator@font mod}\penalty900 +// \mkern5mu\nonscript\mskip-\medmuskip} +// \newcommand{\pod}[1]{\allowbreak +// \if@display\mkern18mu\else\mkern8mu\fi(#1)} +// \renewcommand{\pmod}[1]{\pod{{\operator@font mod}\mkern6mu#1}} +// \newcommand{\mod}[1]{\allowbreak\if@display\mkern18mu +// \else\mkern12mu\fi{\operator@font mod}\,\,#1} +// TODO: math mode should use \medmuskip = 4mu plus 2mu minus 4mu + +defineMacro("\\bmod", "\\mathchoice{\\mskip1mu}{\\mskip1mu}{\\mskip5mu}{\\mskip5mu}" + "\\mathbin{\\rm mod}" + "\\mathchoice{\\mskip1mu}{\\mskip1mu}{\\mskip5mu}{\\mskip5mu}"); +defineMacro("\\pod", "\\allowbreak" + "\\mathchoice{\\mkern18mu}{\\mkern8mu}{\\mkern8mu}{\\mkern8mu}(#1)"); +defineMacro("\\pmod", "\\pod{{\\rm mod}\\mkern6mu#1}"); +defineMacro("\\mod", "\\allowbreak" + "\\mathchoice{\\mkern18mu}{\\mkern12mu}{\\mkern12mu}{\\mkern12mu}" + "{\\rm mod}\\,\\,#1"); // \pmb -- A simulation of bold. +// The version in ambsy.sty works by typesetting three copies of the argument +// with small offsets. We use two copies. We omit the vertical offset because +// of rendering problems that makeVList encounters in Safari. + +defineMacro("\\pmb", "\\html@mathml{" + "\\@binrel{#1}{\\mathrlap{#1}\\kern0.5px#1}}" + "{\\mathbf{#1}}"); ////////////////////////////////////////////////////////////////////// +// LaTeX source2e +// \expandafter\let\expandafter\@normalcr +// \csname\expandafter\@gobble\string\\ \endcsname +// \DeclareRobustCommand\newline{\@normalcr\relax} + +defineMacro("\\newline", "\\\\\\relax"); // \def\TeX{T\kern-.1667em\lower.5ex\hbox{E}\kern-.125emX\@} +// TODO: Doesn't normally work in math mode because \@ fails. KaTeX doesn't +// support \@ yet, so that's omitted, and we add \text so that the result +// doesn't look funny in math mode. + +defineMacro("\\TeX", "\\textrm{\\html@mathml{" + "T\\kern-.1667em\\raisebox{-.5ex}{E}\\kern-.125emX" + "}{TeX}}"); // \DeclareRobustCommand{\LaTeX}{L\kern-.36em% +// {\sbox\z@ T% +// \vbox to\ht\z@{\hbox{\check@mathfonts +// \fontsize\sf@size\z@ +// \math@fontsfalse\selectfont +// A}% +// \vss}% +// }% +// \kern-.15em% +// \TeX} +// This code aligns the top of the A with the T (from the perspective of TeX's +// boxes, though visually the A appears to extend above slightly). +// We compute the corresponding \raisebox when A is rendered in \normalsize +// \scriptstyle, which has a scale factor of 0.7 (see Options.js). + +var latexRaiseA = fontMetricsData["Main-Regular"]["T".charCodeAt(0)][1] - 0.7 * fontMetricsData["Main-Regular"]["A".charCodeAt(0)][1] + "em"; +defineMacro("\\LaTeX", "\\textrm{\\html@mathml{" + ("L\\kern-.36em\\raisebox{" + latexRaiseA + "}{\\scriptstyle A}") + "\\kern-.15em\\TeX}{LaTeX}}"); // New KaTeX logo based on tweaking LaTeX logo + +defineMacro("\\KaTeX", "\\textrm{\\html@mathml{" + ("K\\kern-.17em\\raisebox{" + latexRaiseA + "}{\\scriptstyle A}") + "\\kern-.15em\\TeX}{KaTeX}}"); // \DeclareRobustCommand\hspace{\@ifstar\@hspacer\@hspace} +// \def\@hspace#1{\hskip #1\relax} +// \def\@hspacer#1{\vrule \@width\z@\nobreak +// \hskip #1\hskip \z@skip} + +defineMacro("\\hspace", "\\@ifstar\\@hspacer\\@hspace"); +defineMacro("\\@hspace", "\\hskip #1\\relax"); +defineMacro("\\@hspacer", "\\rule{0pt}{0pt}\\hskip #1\\relax"); ////////////////////////////////////////////////////////////////////// +// mathtools.sty +//\providecommand\ordinarycolon{:} + +defineMacro("\\ordinarycolon", ":"); //\def\vcentcolon{\mathrel{\mathop\ordinarycolon}} +//TODO(edemaine): Not yet centered. Fix via \raisebox or #726 + +defineMacro("\\vcentcolon", "\\mathrel{\\mathop\\ordinarycolon}"); // \providecommand*\dblcolon{\vcentcolon\mathrel{\mkern-.9mu}\vcentcolon} + +defineMacro("\\dblcolon", "\\html@mathml{" + "\\mathrel{\\vcentcolon\\mathrel{\\mkern-.9mu}\\vcentcolon}}" + "{\\mathop{\\char\"2237}}"); // \providecommand*\coloneqq{\vcentcolon\mathrel{\mkern-1.2mu}=} + +defineMacro("\\coloneqq", "\\html@mathml{" + "\\mathrel{\\vcentcolon\\mathrel{\\mkern-1.2mu}=}}" + "{\\mathop{\\char\"2254}}"); // ≔ +// \providecommand*\Coloneqq{\dblcolon\mathrel{\mkern-1.2mu}=} + +defineMacro("\\Coloneqq", "\\html@mathml{" + "\\mathrel{\\dblcolon\\mathrel{\\mkern-1.2mu}=}}" + "{\\mathop{\\char\"2237\\char\"3d}}"); // \providecommand*\coloneq{\vcentcolon\mathrel{\mkern-1.2mu}\mathrel{-}} + +defineMacro("\\coloneq", "\\html@mathml{" + "\\mathrel{\\vcentcolon\\mathrel{\\mkern-1.2mu}\\mathrel{-}}}" + "{\\mathop{\\char\"3a\\char\"2212}}"); // \providecommand*\Coloneq{\dblcolon\mathrel{\mkern-1.2mu}\mathrel{-}} + +defineMacro("\\Coloneq", "\\html@mathml{" + "\\mathrel{\\dblcolon\\mathrel{\\mkern-1.2mu}\\mathrel{-}}}" + "{\\mathop{\\char\"2237\\char\"2212}}"); // \providecommand*\eqqcolon{=\mathrel{\mkern-1.2mu}\vcentcolon} + +defineMacro("\\eqqcolon", "\\html@mathml{" + "\\mathrel{=\\mathrel{\\mkern-1.2mu}\\vcentcolon}}" + "{\\mathop{\\char\"2255}}"); // ≕ +// \providecommand*\Eqqcolon{=\mathrel{\mkern-1.2mu}\dblcolon} + +defineMacro("\\Eqqcolon", "\\html@mathml{" + "\\mathrel{=\\mathrel{\\mkern-1.2mu}\\dblcolon}}" + "{\\mathop{\\char\"3d\\char\"2237}}"); // \providecommand*\eqcolon{\mathrel{-}\mathrel{\mkern-1.2mu}\vcentcolon} + +defineMacro("\\eqcolon", "\\html@mathml{" + "\\mathrel{\\mathrel{-}\\mathrel{\\mkern-1.2mu}\\vcentcolon}}" + "{\\mathop{\\char\"2239}}"); // \providecommand*\Eqcolon{\mathrel{-}\mathrel{\mkern-1.2mu}\dblcolon} + +defineMacro("\\Eqcolon", "\\html@mathml{" + "\\mathrel{\\mathrel{-}\\mathrel{\\mkern-1.2mu}\\dblcolon}}" + "{\\mathop{\\char\"2212\\char\"2237}}"); // \providecommand*\colonapprox{\vcentcolon\mathrel{\mkern-1.2mu}\approx} + +defineMacro("\\colonapprox", "\\html@mathml{" + "\\mathrel{\\vcentcolon\\mathrel{\\mkern-1.2mu}\\approx}}" + "{\\mathop{\\char\"3a\\char\"2248}}"); // \providecommand*\Colonapprox{\dblcolon\mathrel{\mkern-1.2mu}\approx} + +defineMacro("\\Colonapprox", "\\html@mathml{" + "\\mathrel{\\dblcolon\\mathrel{\\mkern-1.2mu}\\approx}}" + "{\\mathop{\\char\"2237\\char\"2248}}"); // \providecommand*\colonsim{\vcentcolon\mathrel{\mkern-1.2mu}\sim} + +defineMacro("\\colonsim", "\\html@mathml{" + "\\mathrel{\\vcentcolon\\mathrel{\\mkern-1.2mu}\\sim}}" + "{\\mathop{\\char\"3a\\char\"223c}}"); // \providecommand*\Colonsim{\dblcolon\mathrel{\mkern-1.2mu}\sim} + +defineMacro("\\Colonsim", "\\html@mathml{" + "\\mathrel{\\dblcolon\\mathrel{\\mkern-1.2mu}\\sim}}" + "{\\mathop{\\char\"2237\\char\"223c}}"); // Some Unicode characters are implemented with macros to mathtools functions. + +defineMacro("\u2237", "\\dblcolon"); // :: + +defineMacro("\u2239", "\\eqcolon"); // -: + +defineMacro("\u2254", "\\coloneqq"); // := + +defineMacro("\u2255", "\\eqqcolon"); // =: + +defineMacro("\u2A74", "\\Coloneqq"); // ::= +////////////////////////////////////////////////////////////////////// +// colonequals.sty +// Alternate names for mathtools's macros: + +defineMacro("\\ratio", "\\vcentcolon"); +defineMacro("\\coloncolon", "\\dblcolon"); +defineMacro("\\colonequals", "\\coloneqq"); +defineMacro("\\coloncolonequals", "\\Coloneqq"); +defineMacro("\\equalscolon", "\\eqqcolon"); +defineMacro("\\equalscoloncolon", "\\Eqqcolon"); +defineMacro("\\colonminus", "\\coloneq"); +defineMacro("\\coloncolonminus", "\\Coloneq"); +defineMacro("\\minuscolon", "\\eqcolon"); +defineMacro("\\minuscoloncolon", "\\Eqcolon"); // \colonapprox name is same in mathtools and colonequals. + +defineMacro("\\coloncolonapprox", "\\Colonapprox"); // \colonsim name is same in mathtools and colonequals. + +defineMacro("\\coloncolonsim", "\\Colonsim"); // Additional macros, implemented by analogy with mathtools definitions: + +defineMacro("\\simcolon", "\\mathrel{\\sim\\mathrel{\\mkern-1.2mu}\\vcentcolon}"); +defineMacro("\\simcoloncolon", "\\mathrel{\\sim\\mathrel{\\mkern-1.2mu}\\dblcolon}"); +defineMacro("\\approxcolon", "\\mathrel{\\approx\\mathrel{\\mkern-1.2mu}\\vcentcolon}"); +defineMacro("\\approxcoloncolon", "\\mathrel{\\approx\\mathrel{\\mkern-1.2mu}\\dblcolon}"); // Present in newtxmath, pxfonts and txfonts + +defineMacro("\\notni", "\\html@mathml{\\not\\ni}{\\mathrel{\\char`\u220C}}"); +defineMacro("\\limsup", "\\DOTSB\\operatorname*{lim\\,sup}"); +defineMacro("\\liminf", "\\DOTSB\\operatorname*{lim\\,inf}"); ////////////////////////////////////////////////////////////////////// +// From amsopn.sty + +defineMacro("\\injlim", "\\DOTSB\\operatorname*{inj\\,lim}"); +defineMacro("\\projlim", "\\DOTSB\\operatorname*{proj\\,lim}"); +defineMacro("\\varlimsup", "\\DOTSB\\operatorname*{\\overline{lim}}"); +defineMacro("\\varliminf", "\\DOTSB\\operatorname*{\\underline{lim}}"); +defineMacro("\\varinjlim", "\\DOTSB\\operatorname*{\\underrightarrow{lim}}"); +defineMacro("\\varprojlim", "\\DOTSB\\operatorname*{\\underleftarrow{lim}}"); ////////////////////////////////////////////////////////////////////// +// MathML alternates for KaTeX glyphs in the Unicode private area + +defineMacro("\\gvertneqq", "\\html@mathml{\\@gvertneqq}{\u2269}"); +defineMacro("\\lvertneqq", "\\html@mathml{\\@lvertneqq}{\u2268}"); +defineMacro("\\ngeqq", "\\html@mathml{\\@ngeqq}{\u2271}"); +defineMacro("\\ngeqslant", "\\html@mathml{\\@ngeqslant}{\u2271}"); +defineMacro("\\nleqq", "\\html@mathml{\\@nleqq}{\u2270}"); +defineMacro("\\nleqslant", "\\html@mathml{\\@nleqslant}{\u2270}"); +defineMacro("\\nshortmid", "\\html@mathml{\\@nshortmid}{∤}"); +defineMacro("\\nshortparallel", "\\html@mathml{\\@nshortparallel}{∦}"); +defineMacro("\\nsubseteqq", "\\html@mathml{\\@nsubseteqq}{\u2288}"); +defineMacro("\\nsupseteqq", "\\html@mathml{\\@nsupseteqq}{\u2289}"); +defineMacro("\\varsubsetneq", "\\html@mathml{\\@varsubsetneq}{⊊}"); +defineMacro("\\varsubsetneqq", "\\html@mathml{\\@varsubsetneqq}{⫋}"); +defineMacro("\\varsupsetneq", "\\html@mathml{\\@varsupsetneq}{⊋}"); +defineMacro("\\varsupsetneqq", "\\html@mathml{\\@varsupsetneqq}{⫌}"); +defineMacro("\\imath", "\\html@mathml{\\@imath}{\u0131}"); +defineMacro("\\jmath", "\\html@mathml{\\@jmath}{\u0237}"); ////////////////////////////////////////////////////////////////////// +// stmaryrd and semantic +// The stmaryrd and semantic packages render the next four items by calling a +// glyph. Those glyphs do not exist in the KaTeX fonts. Hence the macros. + +defineMacro("\\llbracket", "\\html@mathml{" + "\\mathopen{[\\mkern-3.2mu[}}" + "{\\mathopen{\\char`\u27E6}}"); +defineMacro("\\rrbracket", "\\html@mathml{" + "\\mathclose{]\\mkern-3.2mu]}}" + "{\\mathclose{\\char`\u27E7}}"); +defineMacro("\u27E6", "\\llbracket"); // blackboard bold [ + +defineMacro("\u27E7", "\\rrbracket"); // blackboard bold ] + +defineMacro("\\lBrace", "\\html@mathml{" + "\\mathopen{\\{\\mkern-3.2mu[}}" + "{\\mathopen{\\char`\u2983}}"); +defineMacro("\\rBrace", "\\html@mathml{" + "\\mathclose{]\\mkern-3.2mu\\}}}" + "{\\mathclose{\\char`\u2984}}"); +defineMacro("\u2983", "\\lBrace"); // blackboard bold { + +defineMacro("\u2984", "\\rBrace"); // blackboard bold } +// TODO: Create variable sized versions of the last two items. I believe that +// will require new font glyphs. +// The stmaryrd function `\minuso` provides a "Plimsoll" symbol that +// superimposes the characters \circ and \mathminus. Used in chemistry. + +defineMacro("\\minuso", "\\mathbin{\\html@mathml{" + "{\\mathrlap{\\mathchoice{\\kern{0.145em}}{\\kern{0.145em}}" + "{\\kern{0.1015em}}{\\kern{0.0725em}}\\circ}{-}}}" + "{\\char`⦵}}"); +defineMacro("⦵", "\\minuso"); ////////////////////////////////////////////////////////////////////// +// texvc.sty +// The texvc package contains macros available in mediawiki pages. +// We omit the functions deprecated at +// https://en.wikipedia.org/wiki/Help:Displaying_a_formula#Deprecated_syntax +// We also omit texvc's \O, which conflicts with \text{\O} + +defineMacro("\\darr", "\\downarrow"); +defineMacro("\\dArr", "\\Downarrow"); +defineMacro("\\Darr", "\\Downarrow"); +defineMacro("\\lang", "\\langle"); +defineMacro("\\rang", "\\rangle"); +defineMacro("\\uarr", "\\uparrow"); +defineMacro("\\uArr", "\\Uparrow"); +defineMacro("\\Uarr", "\\Uparrow"); +defineMacro("\\N", "\\mathbb{N}"); +defineMacro("\\R", "\\mathbb{R}"); +defineMacro("\\Z", "\\mathbb{Z}"); +defineMacro("\\alef", "\\aleph"); +defineMacro("\\alefsym", "\\aleph"); +defineMacro("\\Alpha", "\\mathrm{A}"); +defineMacro("\\Beta", "\\mathrm{B}"); +defineMacro("\\bull", "\\bullet"); +defineMacro("\\Chi", "\\mathrm{X}"); +defineMacro("\\clubs", "\\clubsuit"); +defineMacro("\\cnums", "\\mathbb{C}"); +defineMacro("\\Complex", "\\mathbb{C}"); +defineMacro("\\Dagger", "\\ddagger"); +defineMacro("\\diamonds", "\\diamondsuit"); +defineMacro("\\empty", "\\emptyset"); +defineMacro("\\Epsilon", "\\mathrm{E}"); +defineMacro("\\Eta", "\\mathrm{H}"); +defineMacro("\\exist", "\\exists"); +defineMacro("\\harr", "\\leftrightarrow"); +defineMacro("\\hArr", "\\Leftrightarrow"); +defineMacro("\\Harr", "\\Leftrightarrow"); +defineMacro("\\hearts", "\\heartsuit"); +defineMacro("\\image", "\\Im"); +defineMacro("\\infin", "\\infty"); +defineMacro("\\Iota", "\\mathrm{I}"); +defineMacro("\\isin", "\\in"); +defineMacro("\\Kappa", "\\mathrm{K}"); +defineMacro("\\larr", "\\leftarrow"); +defineMacro("\\lArr", "\\Leftarrow"); +defineMacro("\\Larr", "\\Leftarrow"); +defineMacro("\\lrarr", "\\leftrightarrow"); +defineMacro("\\lrArr", "\\Leftrightarrow"); +defineMacro("\\Lrarr", "\\Leftrightarrow"); +defineMacro("\\Mu", "\\mathrm{M}"); +defineMacro("\\natnums", "\\mathbb{N}"); +defineMacro("\\Nu", "\\mathrm{N}"); +defineMacro("\\Omicron", "\\mathrm{O}"); +defineMacro("\\plusmn", "\\pm"); +defineMacro("\\rarr", "\\rightarrow"); +defineMacro("\\rArr", "\\Rightarrow"); +defineMacro("\\Rarr", "\\Rightarrow"); +defineMacro("\\real", "\\Re"); +defineMacro("\\reals", "\\mathbb{R}"); +defineMacro("\\Reals", "\\mathbb{R}"); +defineMacro("\\Rho", "\\mathrm{P}"); +defineMacro("\\sdot", "\\cdot"); +defineMacro("\\sect", "\\S"); +defineMacro("\\spades", "\\spadesuit"); +defineMacro("\\sub", "\\subset"); +defineMacro("\\sube", "\\subseteq"); +defineMacro("\\supe", "\\supseteq"); +defineMacro("\\Tau", "\\mathrm{T}"); +defineMacro("\\thetasym", "\\vartheta"); // TODO: defineMacro("\\varcoppa", "\\\mbox{\\coppa}"); + +defineMacro("\\weierp", "\\wp"); +defineMacro("\\Zeta", "\\mathrm{Z}"); ////////////////////////////////////////////////////////////////////// +// statmath.sty +// https://ctan.math.illinois.edu/macros/latex/contrib/statmath/statmath.pdf + +defineMacro("\\argmin", "\\DOTSB\\operatorname*{arg\\,min}"); +defineMacro("\\argmax", "\\DOTSB\\operatorname*{arg\\,max}"); +defineMacro("\\plim", "\\DOTSB\\mathop{\\operatorname{plim}}\\limits"); ////////////////////////////////////////////////////////////////////// +// braket.sty +// http://ctan.math.washington.edu/tex-archive/macros/latex/contrib/braket/braket.pdf + +defineMacro("\\bra", "\\mathinner{\\langle{#1}|}"); +defineMacro("\\ket", "\\mathinner{|{#1}\\rangle}"); +defineMacro("\\braket", "\\mathinner{\\langle{#1}\\rangle}"); +defineMacro("\\Bra", "\\left\\langle#1\\right|"); +defineMacro("\\Ket", "\\left|#1\\right\\rangle"); ////////////////////////////////////////////////////////////////////// +// actuarialangle.dtx + +defineMacro("\\angln", "{\\angl n}"); // Custom Khan Academy colors, should be moved to an optional package + +defineMacro("\\blue", "\\textcolor{##6495ed}{#1}"); +defineMacro("\\orange", "\\textcolor{##ffa500}{#1}"); +defineMacro("\\pink", "\\textcolor{##ff00af}{#1}"); +defineMacro("\\red", "\\textcolor{##df0030}{#1}"); +defineMacro("\\green", "\\textcolor{##28ae7b}{#1}"); +defineMacro("\\gray", "\\textcolor{gray}{#1}"); +defineMacro("\\purple", "\\textcolor{##9d38bd}{#1}"); +defineMacro("\\blueA", "\\textcolor{##ccfaff}{#1}"); +defineMacro("\\blueB", "\\textcolor{##80f6ff}{#1}"); +defineMacro("\\blueC", "\\textcolor{##63d9ea}{#1}"); +defineMacro("\\blueD", "\\textcolor{##11accd}{#1}"); +defineMacro("\\blueE", "\\textcolor{##0c7f99}{#1}"); +defineMacro("\\tealA", "\\textcolor{##94fff5}{#1}"); +defineMacro("\\tealB", "\\textcolor{##26edd5}{#1}"); +defineMacro("\\tealC", "\\textcolor{##01d1c1}{#1}"); +defineMacro("\\tealD", "\\textcolor{##01a995}{#1}"); +defineMacro("\\tealE", "\\textcolor{##208170}{#1}"); +defineMacro("\\greenA", "\\textcolor{##b6ffb0}{#1}"); +defineMacro("\\greenB", "\\textcolor{##8af281}{#1}"); +defineMacro("\\greenC", "\\textcolor{##74cf70}{#1}"); +defineMacro("\\greenD", "\\textcolor{##1fab54}{#1}"); +defineMacro("\\greenE", "\\textcolor{##0d923f}{#1}"); +defineMacro("\\goldA", "\\textcolor{##ffd0a9}{#1}"); +defineMacro("\\goldB", "\\textcolor{##ffbb71}{#1}"); +defineMacro("\\goldC", "\\textcolor{##ff9c39}{#1}"); +defineMacro("\\goldD", "\\textcolor{##e07d10}{#1}"); +defineMacro("\\goldE", "\\textcolor{##a75a05}{#1}"); +defineMacro("\\redA", "\\textcolor{##fca9a9}{#1}"); +defineMacro("\\redB", "\\textcolor{##ff8482}{#1}"); +defineMacro("\\redC", "\\textcolor{##f9685d}{#1}"); +defineMacro("\\redD", "\\textcolor{##e84d39}{#1}"); +defineMacro("\\redE", "\\textcolor{##bc2612}{#1}"); +defineMacro("\\maroonA", "\\textcolor{##ffbde0}{#1}"); +defineMacro("\\maroonB", "\\textcolor{##ff92c6}{#1}"); +defineMacro("\\maroonC", "\\textcolor{##ed5fa6}{#1}"); +defineMacro("\\maroonD", "\\textcolor{##ca337c}{#1}"); +defineMacro("\\maroonE", "\\textcolor{##9e034e}{#1}"); +defineMacro("\\purpleA", "\\textcolor{##ddd7ff}{#1}"); +defineMacro("\\purpleB", "\\textcolor{##c6b9fc}{#1}"); +defineMacro("\\purpleC", "\\textcolor{##aa87ff}{#1}"); +defineMacro("\\purpleD", "\\textcolor{##7854ab}{#1}"); +defineMacro("\\purpleE", "\\textcolor{##543b78}{#1}"); +defineMacro("\\mintA", "\\textcolor{##f5f9e8}{#1}"); +defineMacro("\\mintB", "\\textcolor{##edf2df}{#1}"); +defineMacro("\\mintC", "\\textcolor{##e0e5cc}{#1}"); +defineMacro("\\grayA", "\\textcolor{##f6f7f7}{#1}"); +defineMacro("\\grayB", "\\textcolor{##f0f1f2}{#1}"); +defineMacro("\\grayC", "\\textcolor{##e3e5e6}{#1}"); +defineMacro("\\grayD", "\\textcolor{##d6d8da}{#1}"); +defineMacro("\\grayE", "\\textcolor{##babec2}{#1}"); +defineMacro("\\grayF", "\\textcolor{##888d93}{#1}"); +defineMacro("\\grayG", "\\textcolor{##626569}{#1}"); +defineMacro("\\grayH", "\\textcolor{##3b3e40}{#1}"); +defineMacro("\\grayI", "\\textcolor{##21242c}{#1}"); +defineMacro("\\kaBlue", "\\textcolor{##314453}{#1}"); +defineMacro("\\kaGreen", "\\textcolor{##71B307}{#1}"); +;// CONCATENATED MODULE: ./src/MacroExpander.js +/** + * This file contains the “gullet” where macros are expanded + * until only non-macro tokens remain. + */ + + + + + + + +// List of commands that act like macros but aren't defined as a macro, +// function, or symbol. Used in `isDefined`. +var implicitCommands = { + "\\relax": true, + // MacroExpander.js + "^": true, + // Parser.js + "_": true, + // Parser.js + "\\limits": true, + // Parser.js + "\\nolimits": true // Parser.js + +}; + +var MacroExpander = /*#__PURE__*/function () { + function MacroExpander(input, settings, mode) { + this.settings = void 0; + this.expansionCount = void 0; + this.lexer = void 0; + this.macros = void 0; + this.stack = void 0; + this.mode = void 0; + this.settings = settings; + this.expansionCount = 0; + this.feed(input); // Make new global namespace + + this.macros = new Namespace(src_macros, settings.macros); + this.mode = mode; + this.stack = []; // contains tokens in REVERSE order + } + /** + * Feed a new input string to the same MacroExpander + * (with existing macros etc.). + */ + + + var _proto = MacroExpander.prototype; + + _proto.feed = function feed(input) { + this.lexer = new Lexer(input, this.settings); + } + /** + * Switches between "text" and "math" modes. + */ + ; + + _proto.switchMode = function switchMode(newMode) { + this.mode = newMode; + } + /** + * Start a new group nesting within all namespaces. + */ + ; + + _proto.beginGroup = function beginGroup() { + this.macros.beginGroup(); + } + /** + * End current group nesting within all namespaces. + */ + ; + + _proto.endGroup = function endGroup() { + this.macros.endGroup(); + } + /** + * Ends all currently nested groups (if any), restoring values before the + * groups began. Useful in case of an error in the middle of parsing. + */ + ; + + _proto.endGroups = function endGroups() { + this.macros.endGroups(); + } + /** + * Returns the topmost token on the stack, without expanding it. + * Similar in behavior to TeX's `\futurelet`. + */ + ; + + _proto.future = function future() { + if (this.stack.length === 0) { + this.pushToken(this.lexer.lex()); + } + + return this.stack[this.stack.length - 1]; + } + /** + * Remove and return the next unexpanded token. + */ + ; + + _proto.popToken = function popToken() { + this.future(); // ensure non-empty stack + + return this.stack.pop(); + } + /** + * Add a given token to the token stack. In particular, this get be used + * to put back a token returned from one of the other methods. + */ + ; + + _proto.pushToken = function pushToken(token) { + this.stack.push(token); + } + /** + * Append an array of tokens to the token stack. + */ + ; + + _proto.pushTokens = function pushTokens(tokens) { + var _this$stack; + + (_this$stack = this.stack).push.apply(_this$stack, tokens); + } + /** + * Find an macro argument without expanding tokens and append the array of + * tokens to the token stack. Uses Token as a container for the result. + */ + ; + + _proto.scanArgument = function scanArgument(isOptional) { + var start; + var end; + var tokens; + + if (isOptional) { + this.consumeSpaces(); // \@ifnextchar gobbles any space following it + + if (this.future().text !== "[") { + return null; + } + + start = this.popToken(); // don't include [ in tokens + + var _this$consumeArg = this.consumeArg(["]"]); + + tokens = _this$consumeArg.tokens; + end = _this$consumeArg.end; + } else { + var _this$consumeArg2 = this.consumeArg(); + + tokens = _this$consumeArg2.tokens; + start = _this$consumeArg2.start; + end = _this$consumeArg2.end; + } // indicate the end of an argument + + + this.pushToken(new Token("EOF", end.loc)); + this.pushTokens(tokens); + return start.range(end, ""); + } + /** + * Consume all following space tokens, without expansion. + */ + ; + + _proto.consumeSpaces = function consumeSpaces() { + for (;;) { + var token = this.future(); + + if (token.text === " ") { + this.stack.pop(); + } else { + break; + } + } + } + /** + * Consume an argument from the token stream, and return the resulting array + * of tokens and start/end token. + */ + ; + + _proto.consumeArg = function consumeArg(delims) { + // The argument for a delimited parameter is the shortest (possibly + // empty) sequence of tokens with properly nested {...} groups that is + // followed ... by this particular list of non-parameter tokens. + // The argument for an undelimited parameter is the next nonblank + // token, unless that token is ‘{’, when the argument will be the + // entire {...} group that follows. + var tokens = []; + var isDelimited = delims && delims.length > 0; + + if (!isDelimited) { + // Ignore spaces between arguments. As the TeXbook says: + // "After you have said ‘\def\row#1#2{...}’, you are allowed to + // put spaces between the arguments (e.g., ‘\row x n’), because + // TeX doesn’t use single spaces as undelimited arguments." + this.consumeSpaces(); + } + + var start = this.future(); + var tok; + var depth = 0; + var match = 0; + + do { + tok = this.popToken(); + tokens.push(tok); + + if (tok.text === "{") { + ++depth; + } else if (tok.text === "}") { + --depth; + + if (depth === -1) { + throw new src_ParseError("Extra }", tok); + } + } else if (tok.text === "EOF") { + throw new src_ParseError("Unexpected end of input in a macro argument" + ", expected '" + (delims && isDelimited ? delims[match] : "}") + "'", tok); + } + + if (delims && isDelimited) { + if ((depth === 0 || depth === 1 && delims[match] === "{") && tok.text === delims[match]) { + ++match; + + if (match === delims.length) { + // don't include delims in tokens + tokens.splice(-match, match); + break; + } + } else { + match = 0; + } + } + } while (depth !== 0 || isDelimited); // If the argument found ... has the form ‘{}’, + // ... the outermost braces enclosing the argument are removed + + + if (start.text === "{" && tokens[tokens.length - 1].text === "}") { + tokens.pop(); + tokens.shift(); + } + + tokens.reverse(); // to fit in with stack order + + return { + tokens: tokens, + start: start, + end: tok + }; + } + /** + * Consume the specified number of (delimited) arguments from the token + * stream and return the resulting array of arguments. + */ + ; + + _proto.consumeArgs = function consumeArgs(numArgs, delimiters) { + if (delimiters) { + if (delimiters.length !== numArgs + 1) { + throw new src_ParseError("The length of delimiters doesn't match the number of args!"); + } + + var delims = delimiters[0]; + + for (var i = 0; i < delims.length; i++) { + var tok = this.popToken(); + + if (delims[i] !== tok.text) { + throw new src_ParseError("Use of the macro doesn't match its definition", tok); + } + } + } + + var args = []; + + for (var _i = 0; _i < numArgs; _i++) { + args.push(this.consumeArg(delimiters && delimiters[_i + 1]).tokens); + } + + return args; + } + /** + * Expand the next token only once if possible. + * + * If the token is expanded, the resulting tokens will be pushed onto + * the stack in reverse order and will be returned as an array, + * also in reverse order. + * + * If not, the next token will be returned without removing it + * from the stack. This case can be detected by a `Token` return value + * instead of an `Array` return value. + * + * In either case, the next token will be on the top of the stack, + * or the stack will be empty. + * + * Used to implement `expandAfterFuture` and `expandNextToken`. + * + * If expandableOnly, only expandable tokens are expanded and + * an undefined control sequence results in an error. + */ + ; + + _proto.expandOnce = function expandOnce(expandableOnly) { + var topToken = this.popToken(); + var name = topToken.text; + var expansion = !topToken.noexpand ? this._getExpansion(name) : null; + + if (expansion == null || expandableOnly && expansion.unexpandable) { + if (expandableOnly && expansion == null && name[0] === "\\" && !this.isDefined(name)) { + throw new src_ParseError("Undefined control sequence: " + name); + } + + this.pushToken(topToken); + return topToken; + } + + this.expansionCount++; + + if (this.expansionCount > this.settings.maxExpand) { + throw new src_ParseError("Too many expansions: infinite loop or " + "need to increase maxExpand setting"); + } + + var tokens = expansion.tokens; + var args = this.consumeArgs(expansion.numArgs, expansion.delimiters); + + if (expansion.numArgs) { + // paste arguments in place of the placeholders + tokens = tokens.slice(); // make a shallow copy + + for (var i = tokens.length - 1; i >= 0; --i) { + var tok = tokens[i]; + + if (tok.text === "#") { + if (i === 0) { + throw new src_ParseError("Incomplete placeholder at end of macro body", tok); + } + + tok = tokens[--i]; // next token on stack + + if (tok.text === "#") { + // ## → # + tokens.splice(i + 1, 1); // drop first # + } else if (/^[1-9]$/.test(tok.text)) { + var _tokens; + + // replace the placeholder with the indicated argument + (_tokens = tokens).splice.apply(_tokens, [i, 2].concat(args[+tok.text - 1])); + } else { + throw new src_ParseError("Not a valid argument number", tok); + } + } + } + } // Concatenate expansion onto top of stack. + + + this.pushTokens(tokens); + return tokens; + } + /** + * Expand the next token only once (if possible), and return the resulting + * top token on the stack (without removing anything from the stack). + * Similar in behavior to TeX's `\expandafter\futurelet`. + * Equivalent to expandOnce() followed by future(). + */ + ; + + _proto.expandAfterFuture = function expandAfterFuture() { + this.expandOnce(); + return this.future(); + } + /** + * Recursively expand first token, then return first non-expandable token. + */ + ; + + _proto.expandNextToken = function expandNextToken() { + for (;;) { + var expanded = this.expandOnce(); // expandOnce returns Token if and only if it's fully expanded. + + if (expanded instanceof Token) { + // \relax stops the expansion, but shouldn't get returned (a + // null return value couldn't get implemented as a function). + // the token after \noexpand is interpreted as if its meaning + // were ‘\relax’ + if (expanded.text === "\\relax" || expanded.treatAsRelax) { + this.stack.pop(); + } else { + return this.stack.pop(); // === expanded + } + } + } // Flow unable to figure out that this pathway is impossible. + // https://github.com/facebook/flow/issues/4808 + + + throw new Error(); // eslint-disable-line no-unreachable + } + /** + * Fully expand the given macro name and return the resulting list of + * tokens, or return `undefined` if no such macro is defined. + */ + ; + + _proto.expandMacro = function expandMacro(name) { + return this.macros.has(name) ? this.expandTokens([new Token(name)]) : undefined; + } + /** + * Fully expand the given token stream and return the resulting list of tokens + */ + ; + + _proto.expandTokens = function expandTokens(tokens) { + var output = []; + var oldStackLength = this.stack.length; + this.pushTokens(tokens); + + while (this.stack.length > oldStackLength) { + var expanded = this.expandOnce(true); // expand only expandable tokens + // expandOnce returns Token if and only if it's fully expanded. + + if (expanded instanceof Token) { + if (expanded.treatAsRelax) { + // the expansion of \noexpand is the token itself + expanded.noexpand = false; + expanded.treatAsRelax = false; + } + + output.push(this.stack.pop()); + } + } + + return output; + } + /** + * Fully expand the given macro name and return the result as a string, + * or return `undefined` if no such macro is defined. + */ + ; + + _proto.expandMacroAsText = function expandMacroAsText(name) { + var tokens = this.expandMacro(name); + + if (tokens) { + return tokens.map(function (token) { + return token.text; + }).join(""); + } else { + return tokens; + } + } + /** + * Returns the expanded macro as a reversed array of tokens and a macro + * argument count. Or returns `null` if no such macro. + */ + ; + + _proto._getExpansion = function _getExpansion(name) { + var definition = this.macros.get(name); + + if (definition == null) { + // mainly checking for undefined here + return definition; + } // If a single character has an associated catcode other than 13 + // (active character), then don't expand it. + + + if (name.length === 1) { + var catcode = this.lexer.catcodes[name]; + + if (catcode != null && catcode !== 13) { + return; + } + } + + var expansion = typeof definition === "function" ? definition(this) : definition; + + if (typeof expansion === "string") { + var numArgs = 0; + + if (expansion.indexOf("#") !== -1) { + var stripped = expansion.replace(/##/g, ""); + + while (stripped.indexOf("#" + (numArgs + 1)) !== -1) { + ++numArgs; + } + } + + var bodyLexer = new Lexer(expansion, this.settings); + var tokens = []; + var tok = bodyLexer.lex(); + + while (tok.text !== "EOF") { + tokens.push(tok); + tok = bodyLexer.lex(); + } + + tokens.reverse(); // to fit in with stack using push and pop + + var expanded = { + tokens: tokens, + numArgs: numArgs + }; + return expanded; + } + + return expansion; + } + /** + * Determine whether a command is currently "defined" (has some + * functionality), meaning that it's a macro (in the current group), + * a function, a symbol, or one of the special commands listed in + * `implicitCommands`. + */ + ; + + _proto.isDefined = function isDefined(name) { + return this.macros.has(name) || src_functions.hasOwnProperty(name) || src_symbols.math.hasOwnProperty(name) || src_symbols.text.hasOwnProperty(name) || implicitCommands.hasOwnProperty(name); + } + /** + * Determine whether a command is expandable. + */ + ; + + _proto.isExpandable = function isExpandable(name) { + var macro = this.macros.get(name); + return macro != null ? typeof macro === "string" || typeof macro === "function" || !macro.unexpandable : src_functions.hasOwnProperty(name) && !src_functions[name].primitive; + }; + + return MacroExpander; +}(); + + +;// CONCATENATED MODULE: ./src/Parser.js +/* eslint no-constant-condition:0 */ + + + + + + + + + + // Pre-evaluate both modules as unicodeSymbols require String.normalize() + +var unicodeAccents = { + "́": { + "text": "\\'", + "math": "\\acute" + }, + "̀": { + "text": "\\`", + "math": "\\grave" + }, + "̈": { + "text": "\\\"", + "math": "\\ddot" + }, + "̃": { + "text": "\\~", + "math": "\\tilde" + }, + "̄": { + "text": "\\=", + "math": "\\bar" + }, + "̆": { + "text": "\\u", + "math": "\\breve" + }, + "̌": { + "text": "\\v", + "math": "\\check" + }, + "̂": { + "text": "\\^", + "math": "\\hat" + }, + "̇": { + "text": "\\.", + "math": "\\dot" + }, + "̊": { + "text": "\\r", + "math": "\\mathring" + }, + "̋": { + "text": "\\H" + }, + "̧": { + "text": "\\c" + } +}; +var unicodeSymbols = { + "á": "á", + "à": "à", + "ä": "ä", + "ǟ": "ǟ", + "ã": "ã", + "ā": "ā", + "ă": "ă", + "ắ": "ắ", + "ằ": "ằ", + "ẵ": "ẵ", + "ǎ": "ǎ", + "â": "â", + "ấ": "ấ", + "ầ": "ầ", + "ẫ": "ẫ", + "ȧ": "ȧ", + "ǡ": "ǡ", + "å": "å", + "ǻ": "ǻ", + "ḃ": "ḃ", + "ć": "ć", + "ḉ": "ḉ", + "č": "č", + "ĉ": "ĉ", + "ċ": "ċ", + "ç": "ç", + "ď": "ď", + "ḋ": "ḋ", + "ḑ": "ḑ", + "é": "é", + "è": "è", + "ë": "ë", + "ẽ": "ẽ", + "ē": "ē", + "ḗ": "ḗ", + "ḕ": "ḕ", + "ĕ": "ĕ", + "ḝ": "ḝ", + "ě": "ě", + "ê": "ê", + "ế": "ế", + "ề": "ề", + "ễ": "ễ", + "ė": "ė", + "ȩ": "ȩ", + "ḟ": "ḟ", + "ǵ": "ǵ", + "ḡ": "ḡ", + "ğ": "ğ", + "ǧ": "ǧ", + "ĝ": "ĝ", + "ġ": "ġ", + "ģ": "ģ", + "ḧ": "ḧ", + "ȟ": "ȟ", + "ĥ": "ĥ", + "ḣ": "ḣ", + "ḩ": "ḩ", + "í": "í", + "ì": "ì", + "ï": "ï", + "ḯ": "ḯ", + "ĩ": "ĩ", + "ī": "ī", + "ĭ": "ĭ", + "ǐ": "ǐ", + "î": "î", + "ǰ": "ǰ", + "ĵ": "ĵ", + "ḱ": "ḱ", + "ǩ": "ǩ", + "ķ": "ķ", + "ĺ": "ĺ", + "ľ": "ľ", + "ļ": "ļ", + "ḿ": "ḿ", + "ṁ": "ṁ", + "ń": "ń", + "ǹ": "ǹ", + "ñ": "ñ", + "ň": "ň", + "ṅ": "ṅ", + "ņ": "ņ", + "ó": "ó", + "ò": "ò", + "ö": "ö", + "ȫ": "ȫ", + "õ": "õ", + "ṍ": "ṍ", + "ṏ": "ṏ", + "ȭ": "ȭ", + "ō": "ō", + "ṓ": "ṓ", + "ṑ": "ṑ", + "ŏ": "ŏ", + "ǒ": "ǒ", + "ô": "ô", + "ố": "ố", + "ồ": "ồ", + "ỗ": "ỗ", + "ȯ": "ȯ", + "ȱ": "ȱ", + "ő": "ő", + "ṕ": "ṕ", + "ṗ": "ṗ", + "ŕ": "ŕ", + "ř": "ř", + "ṙ": "ṙ", + "ŗ": "ŗ", + "ś": "ś", + "ṥ": "ṥ", + "š": "š", + "ṧ": "ṧ", + "ŝ": "ŝ", + "ṡ": "ṡ", + "ş": "ş", + "ẗ": "ẗ", + "ť": "ť", + "ṫ": "ṫ", + "ţ": "ţ", + "ú": "ú", + "ù": "ù", + "ü": "ü", + "ǘ": "ǘ", + "ǜ": "ǜ", + "ǖ": "ǖ", + "ǚ": "ǚ", + "ũ": "ũ", + "ṹ": "ṹ", + "ū": "ū", + "ṻ": "ṻ", + "ŭ": "ŭ", + "ǔ": "ǔ", + "û": "û", + "ů": "ů", + "ű": "ű", + "ṽ": "ṽ", + "ẃ": "ẃ", + "ẁ": "ẁ", + "ẅ": "ẅ", + "ŵ": "ŵ", + "ẇ": "ẇ", + "ẘ": "ẘ", + "ẍ": "ẍ", + "ẋ": "ẋ", + "ý": "ý", + "ỳ": "ỳ", + "ÿ": "ÿ", + "ỹ": "ỹ", + "ȳ": "ȳ", + "ŷ": "ŷ", + "ẏ": "ẏ", + "ẙ": "ẙ", + "ź": "ź", + "ž": "ž", + "ẑ": "ẑ", + "ż": "ż", + "Á": "Á", + "À": "À", + "Ä": "Ä", + "Ǟ": "Ǟ", + "Ã": "Ã", + "Ā": "Ā", + "Ă": "Ă", + "Ắ": "Ắ", + "Ằ": "Ằ", + "Ẵ": "Ẵ", + "Ǎ": "Ǎ", + "Â": "Â", + "Ấ": "Ấ", + "Ầ": "Ầ", + "Ẫ": "Ẫ", + "Ȧ": "Ȧ", + "Ǡ": "Ǡ", + "Å": "Å", + "Ǻ": "Ǻ", + "Ḃ": "Ḃ", + "Ć": "Ć", + "Ḉ": "Ḉ", + "Č": "Č", + "Ĉ": "Ĉ", + "Ċ": "Ċ", + "Ç": "Ç", + "Ď": "Ď", + "Ḋ": "Ḋ", + "Ḑ": "Ḑ", + "É": "É", + "È": "È", + "Ë": "Ë", + "Ẽ": "Ẽ", + "Ē": "Ē", + "Ḗ": "Ḗ", + "Ḕ": "Ḕ", + "Ĕ": "Ĕ", + "Ḝ": "Ḝ", + "Ě": "Ě", + "Ê": "Ê", + "Ế": "Ế", + "Ề": "Ề", + "Ễ": "Ễ", + "Ė": "Ė", + "Ȩ": "Ȩ", + "Ḟ": "Ḟ", + "Ǵ": "Ǵ", + "Ḡ": "Ḡ", + "Ğ": "Ğ", + "Ǧ": "Ǧ", + "Ĝ": "Ĝ", + "Ġ": "Ġ", + "Ģ": "Ģ", + "Ḧ": "Ḧ", + "Ȟ": "Ȟ", + "Ĥ": "Ĥ", + "Ḣ": "Ḣ", + "Ḩ": "Ḩ", + "Í": "Í", + "Ì": "Ì", + "Ï": "Ï", + "Ḯ": "Ḯ", + "Ĩ": "Ĩ", + "Ī": "Ī", + "Ĭ": "Ĭ", + "Ǐ": "Ǐ", + "Î": "Î", + "İ": "İ", + "Ĵ": "Ĵ", + "Ḱ": "Ḱ", + "Ǩ": "Ǩ", + "Ķ": "Ķ", + "Ĺ": "Ĺ", + "Ľ": "Ľ", + "Ļ": "Ļ", + "Ḿ": "Ḿ", + "Ṁ": "Ṁ", + "Ń": "Ń", + "Ǹ": "Ǹ", + "Ñ": "Ñ", + "Ň": "Ň", + "Ṅ": "Ṅ", + "Ņ": "Ņ", + "Ó": "Ó", + "Ò": "Ò", + "Ö": "Ö", + "Ȫ": "Ȫ", + "Õ": "Õ", + "Ṍ": "Ṍ", + "Ṏ": "Ṏ", + "Ȭ": "Ȭ", + "Ō": "Ō", + "Ṓ": "Ṓ", + "Ṑ": "Ṑ", + "Ŏ": "Ŏ", + "Ǒ": "Ǒ", + "Ô": "Ô", + "Ố": "Ố", + "Ồ": "Ồ", + "Ỗ": "Ỗ", + "Ȯ": "Ȯ", + "Ȱ": "Ȱ", + "Ő": "Ő", + "Ṕ": "Ṕ", + "Ṗ": "Ṗ", + "Ŕ": "Ŕ", + "Ř": "Ř", + "Ṙ": "Ṙ", + "Ŗ": "Ŗ", + "Ś": "Ś", + "Ṥ": "Ṥ", + "Š": "Š", + "Ṧ": "Ṧ", + "Ŝ": "Ŝ", + "Ṡ": "Ṡ", + "Ş": "Ş", + "Ť": "Ť", + "Ṫ": "Ṫ", + "Ţ": "Ţ", + "Ú": "Ú", + "Ù": "Ù", + "Ü": "Ü", + "Ǘ": "Ǘ", + "Ǜ": "Ǜ", + "Ǖ": "Ǖ", + "Ǚ": "Ǚ", + "Ũ": "Ũ", + "Ṹ": "Ṹ", + "Ū": "Ū", + "Ṻ": "Ṻ", + "Ŭ": "Ŭ", + "Ǔ": "Ǔ", + "Û": "Û", + "Ů": "Ů", + "Ű": "Ű", + "Ṽ": "Ṽ", + "Ẃ": "Ẃ", + "Ẁ": "Ẁ", + "Ẅ": "Ẅ", + "Ŵ": "Ŵ", + "Ẇ": "Ẇ", + "Ẍ": "Ẍ", + "Ẋ": "Ẋ", + "Ý": "Ý", + "Ỳ": "Ỳ", + "Ÿ": "Ÿ", + "Ỹ": "Ỹ", + "Ȳ": "Ȳ", + "Ŷ": "Ŷ", + "Ẏ": "Ẏ", + "Ź": "Ź", + "Ž": "Ž", + "Ẑ": "Ẑ", + "Ż": "Ż", + "ά": "ά", + "ὰ": "ὰ", + "ᾱ": "ᾱ", + "ᾰ": "ᾰ", + "έ": "έ", + "ὲ": "ὲ", + "ή": "ή", + "ὴ": "ὴ", + "ί": "ί", + "ὶ": "ὶ", + "ϊ": "ϊ", + "ΐ": "ΐ", + "ῒ": "ῒ", + "ῑ": "ῑ", + "ῐ": "ῐ", + "ό": "ό", + "ὸ": "ὸ", + "ύ": "ύ", + "ὺ": "ὺ", + "ϋ": "ϋ", + "ΰ": "ΰ", + "ῢ": "ῢ", + "ῡ": "ῡ", + "ῠ": "ῠ", + "ώ": "ώ", + "ὼ": "ὼ", + "Ύ": "Ύ", + "Ὺ": "Ὺ", + "Ϋ": "Ϋ", + "Ῡ": "Ῡ", + "Ῠ": "Ῠ", + "Ώ": "Ώ", + "Ὼ": "Ὼ" +}; + +/** + * This file contains the parser used to parse out a TeX expression from the + * input. Since TeX isn't context-free, standard parsers don't work particularly + * well. + * + * The strategy of this parser is as such: + * + * The main functions (the `.parse...` ones) take a position in the current + * parse string to parse tokens from. The lexer (found in Lexer.js, stored at + * this.gullet.lexer) also supports pulling out tokens at arbitrary places. When + * individual tokens are needed at a position, the lexer is called to pull out a + * token, which is then used. + * + * The parser has a property called "mode" indicating the mode that + * the parser is currently in. Currently it has to be one of "math" or + * "text", which denotes whether the current environment is a math-y + * one or a text-y one (e.g. inside \text). Currently, this serves to + * limit the functions which can be used in text mode. + * + * The main functions then return an object which contains the useful data that + * was parsed at its given point, and a new position at the end of the parsed + * data. The main functions can call each other and continue the parsing by + * using the returned position as a new starting point. + * + * There are also extra `.handle...` functions, which pull out some reused + * functionality into self-contained functions. + * + * The functions return ParseNodes. + */ +var Parser = /*#__PURE__*/function () { + function Parser(input, settings) { + this.mode = void 0; + this.gullet = void 0; + this.settings = void 0; + this.leftrightDepth = void 0; + this.nextToken = void 0; + // Start in math mode + this.mode = "math"; // Create a new macro expander (gullet) and (indirectly via that) also a + // new lexer (mouth) for this parser (stomach, in the language of TeX) + + this.gullet = new MacroExpander(input, settings, this.mode); // Store the settings for use in parsing + + this.settings = settings; // Count leftright depth (for \middle errors) + + this.leftrightDepth = 0; + } + /** + * Checks a result to make sure it has the right type, and throws an + * appropriate error otherwise. + */ + + + var _proto = Parser.prototype; + + _proto.expect = function expect(text, consume) { + if (consume === void 0) { + consume = true; + } + + if (this.fetch().text !== text) { + throw new src_ParseError("Expected '" + text + "', got '" + this.fetch().text + "'", this.fetch()); + } + + if (consume) { + this.consume(); + } + } + /** + * Discards the current lookahead token, considering it consumed. + */ + ; + + _proto.consume = function consume() { + this.nextToken = null; + } + /** + * Return the current lookahead token, or if there isn't one (at the + * beginning, or if the previous lookahead token was consume()d), + * fetch the next token as the new lookahead token and return it. + */ + ; + + _proto.fetch = function fetch() { + if (this.nextToken == null) { + this.nextToken = this.gullet.expandNextToken(); + } + + return this.nextToken; + } + /** + * Switches between "text" and "math" modes. + */ + ; + + _proto.switchMode = function switchMode(newMode) { + this.mode = newMode; + this.gullet.switchMode(newMode); + } + /** + * Main parsing function, which parses an entire input. + */ + ; + + _proto.parse = function parse() { + if (!this.settings.globalGroup) { + // Create a group namespace for the math expression. + // (LaTeX creates a new group for every $...$, $$...$$, \[...\].) + this.gullet.beginGroup(); + } // Use old \color behavior (same as LaTeX's \textcolor) if requested. + // We do this within the group for the math expression, so it doesn't + // pollute settings.macros. + + + if (this.settings.colorIsTextColor) { + this.gullet.macros.set("\\color", "\\textcolor"); + } + + try { + // Try to parse the input + var parse = this.parseExpression(false); // If we succeeded, make sure there's an EOF at the end + + this.expect("EOF"); // End the group namespace for the expression + + if (!this.settings.globalGroup) { + this.gullet.endGroup(); + } + + return parse; // Close any leftover groups in case of a parse error. + } finally { + this.gullet.endGroups(); + } + }; + + /** + * Parses an "expression", which is a list of atoms. + * + * `breakOnInfix`: Should the parsing stop when we hit infix nodes? This + * happens when functions have higher precendence han infix + * nodes in implicit parses. + * + * `breakOnTokenText`: The text of the token that the expression should end + * with, or `null` if something else should end the + * expression. + */ + _proto.parseExpression = function parseExpression(breakOnInfix, breakOnTokenText) { + var body = []; // Keep adding atoms to the body until we can't parse any more atoms (either + // we reached the end, a }, or a \right) + + while (true) { + // Ignore spaces in math mode + if (this.mode === "math") { + this.consumeSpaces(); + } + + var lex = this.fetch(); + + if (Parser.endOfExpression.indexOf(lex.text) !== -1) { + break; + } + + if (breakOnTokenText && lex.text === breakOnTokenText) { + break; + } + + if (breakOnInfix && src_functions[lex.text] && src_functions[lex.text].infix) { + break; + } + + var atom = this.parseAtom(breakOnTokenText); + + if (!atom) { + break; + } else if (atom.type === "internal") { + continue; + } + + body.push(atom); + } + + if (this.mode === "text") { + this.formLigatures(body); + } + + return this.handleInfixNodes(body); + } + /** + * Rewrites infix operators such as \over with corresponding commands such + * as \frac. + * + * There can only be one infix operator per group. If there's more than one + * then the expression is ambiguous. This can be resolved by adding {}. + */ + ; + + _proto.handleInfixNodes = function handleInfixNodes(body) { + var overIndex = -1; + var funcName; + + for (var i = 0; i < body.length; i++) { + if (body[i].type === "infix") { + if (overIndex !== -1) { + throw new src_ParseError("only one infix operator per group", body[i].token); + } + + overIndex = i; + funcName = body[i].replaceWith; + } + } + + if (overIndex !== -1 && funcName) { + var numerNode; + var denomNode; + var numerBody = body.slice(0, overIndex); + var denomBody = body.slice(overIndex + 1); + + if (numerBody.length === 1 && numerBody[0].type === "ordgroup") { + numerNode = numerBody[0]; + } else { + numerNode = { + type: "ordgroup", + mode: this.mode, + body: numerBody + }; + } + + if (denomBody.length === 1 && denomBody[0].type === "ordgroup") { + denomNode = denomBody[0]; + } else { + denomNode = { + type: "ordgroup", + mode: this.mode, + body: denomBody + }; + } + + var node; + + if (funcName === "\\\\abovefrac") { + node = this.callFunction(funcName, [numerNode, body[overIndex], denomNode], []); + } else { + node = this.callFunction(funcName, [numerNode, denomNode], []); + } + + return [node]; + } else { + return body; + } + } + /** + * Handle a subscript or superscript with nice errors. + */ + ; + + _proto.handleSupSubscript = function handleSupSubscript(name // For error reporting. + ) { + var symbolToken = this.fetch(); + var symbol = symbolToken.text; + this.consume(); + this.consumeSpaces(); // ignore spaces before sup/subscript argument + + var group = this.parseGroup(name); + + if (!group) { + throw new src_ParseError("Expected group after '" + symbol + "'", symbolToken); + } + + return group; + } + /** + * Converts the textual input of an unsupported command into a text node + * contained within a color node whose color is determined by errorColor + */ + ; + + _proto.formatUnsupportedCmd = function formatUnsupportedCmd(text) { + var textordArray = []; + + for (var i = 0; i < text.length; i++) { + textordArray.push({ + type: "textord", + mode: "text", + text: text[i] + }); + } + + var textNode = { + type: "text", + mode: this.mode, + body: textordArray + }; + var colorNode = { + type: "color", + mode: this.mode, + color: this.settings.errorColor, + body: [textNode] + }; + return colorNode; + } + /** + * Parses a group with optional super/subscripts. + */ + ; + + _proto.parseAtom = function parseAtom(breakOnTokenText) { + // The body of an atom is an implicit group, so that things like + // \left(x\right)^2 work correctly. + var base = this.parseGroup("atom", breakOnTokenText); // In text mode, we don't have superscripts or subscripts + + if (this.mode === "text") { + return base; + } // Note that base may be empty (i.e. null) at this point. + + + var superscript; + var subscript; + + while (true) { + // Guaranteed in math mode, so eat any spaces first. + this.consumeSpaces(); // Lex the first token + + var lex = this.fetch(); + + if (lex.text === "\\limits" || lex.text === "\\nolimits") { + // We got a limit control + if (base && base.type === "op") { + var limits = lex.text === "\\limits"; + base.limits = limits; + base.alwaysHandleSupSub = true; + } else if (base && base.type === "operatorname") { + if (base.alwaysHandleSupSub) { + base.limits = lex.text === "\\limits"; + } + } else { + throw new src_ParseError("Limit controls must follow a math operator", lex); + } + + this.consume(); + } else if (lex.text === "^") { + // We got a superscript start + if (superscript) { + throw new src_ParseError("Double superscript", lex); + } + + superscript = this.handleSupSubscript("superscript"); + } else if (lex.text === "_") { + // We got a subscript start + if (subscript) { + throw new src_ParseError("Double subscript", lex); + } + + subscript = this.handleSupSubscript("subscript"); + } else if (lex.text === "'") { + // We got a prime + if (superscript) { + throw new src_ParseError("Double superscript", lex); + } + + var prime = { + type: "textord", + mode: this.mode, + text: "\\prime" + }; // Many primes can be grouped together, so we handle this here + + var primes = [prime]; + this.consume(); // Keep lexing tokens until we get something that's not a prime + + while (this.fetch().text === "'") { + // For each one, add another prime to the list + primes.push(prime); + this.consume(); + } // If there's a superscript following the primes, combine that + // superscript in with the primes. + + + if (this.fetch().text === "^") { + primes.push(this.handleSupSubscript("superscript")); + } // Put everything into an ordgroup as the superscript + + + superscript = { + type: "ordgroup", + mode: this.mode, + body: primes + }; + } else { + // If it wasn't ^, _, or ', stop parsing super/subscripts + break; + } + } // Base must be set if superscript or subscript are set per logic above, + // but need to check here for type check to pass. + + + if (superscript || subscript) { + // If we got either a superscript or subscript, create a supsub + return { + type: "supsub", + mode: this.mode, + base: base, + sup: superscript, + sub: subscript + }; + } else { + // Otherwise return the original body + return base; + } + } + /** + * Parses an entire function, including its base and all of its arguments. + */ + ; + + _proto.parseFunction = function parseFunction(breakOnTokenText, name // For determining its context + ) { + var token = this.fetch(); + var func = token.text; + var funcData = src_functions[func]; + + if (!funcData) { + return null; + } + + this.consume(); // consume command token + + if (name && name !== "atom" && !funcData.allowedInArgument) { + throw new src_ParseError("Got function '" + func + "' with no arguments" + (name ? " as " + name : ""), token); + } else if (this.mode === "text" && !funcData.allowedInText) { + throw new src_ParseError("Can't use function '" + func + "' in text mode", token); + } else if (this.mode === "math" && funcData.allowedInMath === false) { + throw new src_ParseError("Can't use function '" + func + "' in math mode", token); + } + + var _this$parseArguments = this.parseArguments(func, funcData), + args = _this$parseArguments.args, + optArgs = _this$parseArguments.optArgs; + + return this.callFunction(func, args, optArgs, token, breakOnTokenText); + } + /** + * Call a function handler with a suitable context and arguments. + */ + ; + + _proto.callFunction = function callFunction(name, args, optArgs, token, breakOnTokenText) { + var context = { + funcName: name, + parser: this, + token: token, + breakOnTokenText: breakOnTokenText + }; + var func = src_functions[name]; + + if (func && func.handler) { + return func.handler(context, args, optArgs); + } else { + throw new src_ParseError("No function handler for " + name); + } + } + /** + * Parses the arguments of a function or environment + */ + ; + + _proto.parseArguments = function parseArguments(func, // Should look like "\name" or "\begin{name}". + funcData) { + var totalArgs = funcData.numArgs + funcData.numOptionalArgs; + + if (totalArgs === 0) { + return { + args: [], + optArgs: [] + }; + } + + var args = []; + var optArgs = []; + + for (var i = 0; i < totalArgs; i++) { + var argType = funcData.argTypes && funcData.argTypes[i]; + var isOptional = i < funcData.numOptionalArgs; + + if (funcData.primitive && argType == null || // \sqrt expands into primitive if optional argument doesn't exist + funcData.type === "sqrt" && i === 1 && optArgs[0] == null) { + argType = "primitive"; + } + + var arg = this.parseGroupOfType("argument to '" + func + "'", argType, isOptional); + + if (isOptional) { + optArgs.push(arg); + } else if (arg != null) { + args.push(arg); + } else { + // should be unreachable + throw new src_ParseError("Null argument, please report this as a bug"); + } + } + + return { + args: args, + optArgs: optArgs + }; + } + /** + * Parses a group when the mode is changing. + */ + ; + + _proto.parseGroupOfType = function parseGroupOfType(name, type, optional) { + switch (type) { + case "color": + return this.parseColorGroup(optional); + + case "size": + return this.parseSizeGroup(optional); + + case "url": + return this.parseUrlGroup(optional); + + case "math": + case "text": + return this.parseArgumentGroup(optional, type); + + case "hbox": + { + // hbox argument type wraps the argument in the equivalent of + // \hbox, which is like \text but switching to \textstyle size. + var group = this.parseArgumentGroup(optional, "text"); + return group != null ? { + type: "styling", + mode: group.mode, + body: [group], + style: "text" // simulate \textstyle + + } : null; + } + + case "raw": + { + var token = this.parseStringGroup("raw", optional); + return token != null ? { + type: "raw", + mode: "text", + string: token.text + } : null; + } + + case "primitive": + { + if (optional) { + throw new src_ParseError("A primitive argument cannot be optional"); + } + + var _group = this.parseGroup(name); + + if (_group == null) { + throw new src_ParseError("Expected group as " + name, this.fetch()); + } + + return _group; + } + + case "original": + case null: + case undefined: + return this.parseArgumentGroup(optional); + + default: + throw new src_ParseError("Unknown group type as " + name, this.fetch()); + } + } + /** + * Discard any space tokens, fetching the next non-space token. + */ + ; + + _proto.consumeSpaces = function consumeSpaces() { + while (this.fetch().text === " ") { + this.consume(); + } + } + /** + * Parses a group, essentially returning the string formed by the + * brace-enclosed tokens plus some position information. + */ + ; + + _proto.parseStringGroup = function parseStringGroup(modeName, // Used to describe the mode in error messages. + optional) { + var argToken = this.gullet.scanArgument(optional); + + if (argToken == null) { + return null; + } + + var str = ""; + var nextToken; + + while ((nextToken = this.fetch()).text !== "EOF") { + str += nextToken.text; + this.consume(); + } + + this.consume(); // consume the end of the argument + + argToken.text = str; + return argToken; + } + /** + * Parses a regex-delimited group: the largest sequence of tokens + * whose concatenated strings match `regex`. Returns the string + * formed by the tokens plus some position information. + */ + ; + + _proto.parseRegexGroup = function parseRegexGroup(regex, modeName // Used to describe the mode in error messages. + ) { + var firstToken = this.fetch(); + var lastToken = firstToken; + var str = ""; + var nextToken; + + while ((nextToken = this.fetch()).text !== "EOF" && regex.test(str + nextToken.text)) { + lastToken = nextToken; + str += lastToken.text; + this.consume(); + } + + if (str === "") { + throw new src_ParseError("Invalid " + modeName + ": '" + firstToken.text + "'", firstToken); + } + + return firstToken.range(lastToken, str); + } + /** + * Parses a color description. + */ + ; + + _proto.parseColorGroup = function parseColorGroup(optional) { + var res = this.parseStringGroup("color", optional); + + if (res == null) { + return null; + } + + var match = /^(#[a-f0-9]{3}|#?[a-f0-9]{6}|[a-z]+)$/i.exec(res.text); + + if (!match) { + throw new src_ParseError("Invalid color: '" + res.text + "'", res); + } + + var color = match[0]; + + if (/^[0-9a-f]{6}$/i.test(color)) { + // We allow a 6-digit HTML color spec without a leading "#". + // This follows the xcolor package's HTML color model. + // Predefined color names are all missed by this RegEx pattern. + color = "#" + color; + } + + return { + type: "color-token", + mode: this.mode, + color: color + }; + } + /** + * Parses a size specification, consisting of magnitude and unit. + */ + ; + + _proto.parseSizeGroup = function parseSizeGroup(optional) { + var res; + var isBlank = false; // don't expand before parseStringGroup + + this.gullet.consumeSpaces(); + + if (!optional && this.gullet.future().text !== "{") { + res = this.parseRegexGroup(/^[-+]? *(?:$|\d+|\d+\.\d*|\.\d*) *[a-z]{0,2} *$/, "size"); + } else { + res = this.parseStringGroup("size", optional); + } + + if (!res) { + return null; + } + + if (!optional && res.text.length === 0) { + // Because we've tested for what is !optional, this block won't + // affect \kern, \hspace, etc. It will capture the mandatory arguments + // to \genfrac and \above. + res.text = "0pt"; // Enable \above{} + + isBlank = true; // This is here specifically for \genfrac + } + + var match = /([-+]?) *(\d+(?:\.\d*)?|\.\d+) *([a-z]{2})/.exec(res.text); + + if (!match) { + throw new src_ParseError("Invalid size: '" + res.text + "'", res); + } + + var data = { + number: +(match[1] + match[2]), + // sign + magnitude, cast to number + unit: match[3] + }; + + if (!validUnit(data)) { + throw new src_ParseError("Invalid unit: '" + data.unit + "'", res); + } + + return { + type: "size", + mode: this.mode, + value: data, + isBlank: isBlank + }; + } + /** + * Parses an URL, checking escaped letters and allowed protocols, + * and setting the catcode of % as an active character (as in \hyperref). + */ + ; + + _proto.parseUrlGroup = function parseUrlGroup(optional) { + this.gullet.lexer.setCatcode("%", 13); // active character + + this.gullet.lexer.setCatcode("~", 12); // other character + + var res = this.parseStringGroup("url", optional); + this.gullet.lexer.setCatcode("%", 14); // comment character + + this.gullet.lexer.setCatcode("~", 13); // active character + + if (res == null) { + return null; + } // hyperref package allows backslashes alone in href, but doesn't + // generate valid links in such cases; we interpret this as + // "undefined" behaviour, and keep them as-is. Some browser will + // replace backslashes with forward slashes. + + + var url = res.text.replace(/\\([#$%&~_^{}])/g, '$1'); + return { + type: "url", + mode: this.mode, + url: url + }; + } + /** + * Parses an argument with the mode specified. + */ + ; + + _proto.parseArgumentGroup = function parseArgumentGroup(optional, mode) { + var argToken = this.gullet.scanArgument(optional); + + if (argToken == null) { + return null; + } + + var outerMode = this.mode; + + if (mode) { + // Switch to specified mode + this.switchMode(mode); + } + + this.gullet.beginGroup(); + var expression = this.parseExpression(false, "EOF"); // TODO: find an alternative way to denote the end + + this.expect("EOF"); // expect the end of the argument + + this.gullet.endGroup(); + var result = { + type: "ordgroup", + mode: this.mode, + loc: argToken.loc, + body: expression + }; + + if (mode) { + // Switch mode back + this.switchMode(outerMode); + } + + return result; + } + /** + * Parses an ordinary group, which is either a single nucleus (like "x") + * or an expression in braces (like "{x+y}") or an implicit group, a group + * that starts at the current position, and ends right before a higher explicit + * group ends, or at EOF. + */ + ; + + _proto.parseGroup = function parseGroup(name, // For error reporting. + breakOnTokenText) { + var firstToken = this.fetch(); + var text = firstToken.text; + var result; // Try to parse an open brace or \begingroup + + if (text === "{" || text === "\\begingroup") { + this.consume(); + var groupEnd = text === "{" ? "}" : "\\endgroup"; + this.gullet.beginGroup(); // If we get a brace, parse an expression + + var expression = this.parseExpression(false, groupEnd); + var lastToken = this.fetch(); + this.expect(groupEnd); // Check that we got a matching closing brace + + this.gullet.endGroup(); + result = { + type: "ordgroup", + mode: this.mode, + loc: SourceLocation.range(firstToken, lastToken), + body: expression, + // A group formed by \begingroup...\endgroup is a semi-simple group + // which doesn't affect spacing in math mode, i.e., is transparent. + // https://tex.stackexchange.com/questions/1930/when-should-one- + // use-begingroup-instead-of-bgroup + semisimple: text === "\\begingroup" || undefined + }; + } else { + // If there exists a function with this name, parse the function. + // Otherwise, just return a nucleus + result = this.parseFunction(breakOnTokenText, name) || this.parseSymbol(); + + if (result == null && text[0] === "\\" && !implicitCommands.hasOwnProperty(text)) { + if (this.settings.throwOnError) { + throw new src_ParseError("Undefined control sequence: " + text, firstToken); + } + + result = this.formatUnsupportedCmd(text); + this.consume(); + } + } + + return result; + } + /** + * Form ligature-like combinations of characters for text mode. + * This includes inputs like "--", "---", "``" and "''". + * The result will simply replace multiple textord nodes with a single + * character in each value by a single textord node having multiple + * characters in its value. The representation is still ASCII source. + * The group will be modified in place. + */ + ; + + _proto.formLigatures = function formLigatures(group) { + var n = group.length - 1; + + for (var i = 0; i < n; ++i) { + var a = group[i]; // $FlowFixMe: Not every node type has a `text` property. + + var v = a.text; + + if (v === "-" && group[i + 1].text === "-") { + if (i + 1 < n && group[i + 2].text === "-") { + group.splice(i, 3, { + type: "textord", + mode: "text", + loc: SourceLocation.range(a, group[i + 2]), + text: "---" + }); + n -= 2; + } else { + group.splice(i, 2, { + type: "textord", + mode: "text", + loc: SourceLocation.range(a, group[i + 1]), + text: "--" + }); + n -= 1; + } + } + + if ((v === "'" || v === "`") && group[i + 1].text === v) { + group.splice(i, 2, { + type: "textord", + mode: "text", + loc: SourceLocation.range(a, group[i + 1]), + text: v + v + }); + n -= 1; + } + } + } + /** + * Parse a single symbol out of the string. Here, we handle single character + * symbols and special functions like \verb. + */ + ; + + _proto.parseSymbol = function parseSymbol() { + var nucleus = this.fetch(); + var text = nucleus.text; + + if (/^\\verb[^a-zA-Z]/.test(text)) { + this.consume(); + var arg = text.slice(5); + var star = arg.charAt(0) === "*"; + + if (star) { + arg = arg.slice(1); + } // Lexer's tokenRegex is constructed to always have matching + // first/last characters. + + + if (arg.length < 2 || arg.charAt(0) !== arg.slice(-1)) { + throw new src_ParseError("\\verb assertion failed --\n please report what input caused this bug"); + } + + arg = arg.slice(1, -1); // remove first and last char + + return { + type: "verb", + mode: "text", + body: arg, + star: star + }; + } // At this point, we should have a symbol, possibly with accents. + // First expand any accented base symbol according to unicodeSymbols. + + + if (unicodeSymbols.hasOwnProperty(text[0]) && !src_symbols[this.mode][text[0]]) { + // This behavior is not strict (XeTeX-compatible) in math mode. + if (this.settings.strict && this.mode === "math") { + this.settings.reportNonstrict("unicodeTextInMathMode", "Accented Unicode text character \"" + text[0] + "\" used in " + "math mode", nucleus); + } + + text = unicodeSymbols[text[0]] + text.substr(1); + } // Strip off any combining characters + + + var match = combiningDiacriticalMarksEndRegex.exec(text); + + if (match) { + text = text.substring(0, match.index); + + if (text === 'i') { + text = "\u0131"; // dotless i, in math and text mode + } else if (text === 'j') { + text = "\u0237"; // dotless j, in math and text mode + } + } // Recognize base symbol + + + var symbol; + + if (src_symbols[this.mode][text]) { + if (this.settings.strict && this.mode === 'math' && extraLatin.indexOf(text) >= 0) { + this.settings.reportNonstrict("unicodeTextInMathMode", "Latin-1/Unicode text character \"" + text[0] + "\" used in " + "math mode", nucleus); + } + + var group = src_symbols[this.mode][text].group; + var loc = SourceLocation.range(nucleus); + var s; + + if (ATOMS.hasOwnProperty(group)) { + // $FlowFixMe + var family = group; + s = { + type: "atom", + mode: this.mode, + family: family, + loc: loc, + text: text + }; + } else { + // $FlowFixMe + s = { + type: group, + mode: this.mode, + loc: loc, + text: text + }; + } // $FlowFixMe + + + symbol = s; + } else if (text.charCodeAt(0) >= 0x80) { + // no symbol for e.g. ^ + if (this.settings.strict) { + if (!supportedCodepoint(text.charCodeAt(0))) { + this.settings.reportNonstrict("unknownSymbol", "Unrecognized Unicode character \"" + text[0] + "\"" + (" (" + text.charCodeAt(0) + ")"), nucleus); + } else if (this.mode === "math") { + this.settings.reportNonstrict("unicodeTextInMathMode", "Unicode text character \"" + text[0] + "\" used in math mode", nucleus); + } + } // All nonmathematical Unicode characters are rendered as if they + // are in text mode (wrapped in \text) because that's what it + // takes to render them in LaTeX. Setting `mode: this.mode` is + // another natural choice (the user requested math mode), but + // this makes it more difficult for getCharacterMetrics() to + // distinguish Unicode characters without metrics and those for + // which we want to simulate the letter M. + + + symbol = { + type: "textord", + mode: "text", + loc: SourceLocation.range(nucleus), + text: text + }; + } else { + return null; // EOF, ^, _, {, }, etc. + } + + this.consume(); // Transform combining characters into accents + + if (match) { + for (var i = 0; i < match[0].length; i++) { + var accent = match[0][i]; + + if (!unicodeAccents[accent]) { + throw new src_ParseError("Unknown accent ' " + accent + "'", nucleus); + } + + var command = unicodeAccents[accent][this.mode] || unicodeAccents[accent].text; + + if (!command) { + throw new src_ParseError("Accent " + accent + " unsupported in " + this.mode + " mode", nucleus); + } + + symbol = { + type: "accent", + mode: this.mode, + loc: SourceLocation.range(nucleus), + label: command, + isStretchy: false, + isShifty: true, + // $FlowFixMe + base: symbol + }; + } + } // $FlowFixMe + + + return symbol; + }; + + return Parser; +}(); + +Parser.endOfExpression = ["}", "\\endgroup", "\\end", "\\right", "&"]; + +;// CONCATENATED MODULE: ./src/parseTree.js +/** + * Provides a single function for parsing an expression using a Parser + * TODO(emily): Remove this + */ + + + +/** + * Parses an expression using a Parser, then returns the parsed result. + */ +var parseTree = function parseTree(toParse, settings) { + if (!(typeof toParse === 'string' || toParse instanceof String)) { + throw new TypeError('KaTeX can only parse string typed expression'); + } + + var parser = new Parser(toParse, settings); // Blank out any \df@tag to avoid spurious "Duplicate \tag" errors + + delete parser.gullet.macros.current["\\df@tag"]; + var tree = parser.parse(); // Prevent a color definition from persisting between calls to katex.render(). + + delete parser.gullet.macros.current["\\current@color"]; + delete parser.gullet.macros.current["\\color"]; // If the input used \tag, it will set the \df@tag macro to the tag. + // In this case, we separately parse the tag and wrap the tree. + + if (parser.gullet.macros.get("\\df@tag")) { + if (!settings.displayMode) { + throw new src_ParseError("\\tag works only in display equations"); + } + + parser.gullet.feed("\\df@tag"); + tree = [{ + type: "tag", + mode: "text", + body: tree, + tag: parser.parse() + }]; + } + + return tree; +}; + +/* harmony default export */ var src_parseTree = (parseTree); +;// CONCATENATED MODULE: ./katex.js +/* eslint no-console:0 */ + +/** + * This is the main entry point for KaTeX. Here, we expose functions for + * rendering expressions either to DOM nodes or to markup strings. + * + * We also expose the ParseError class to check if errors thrown from KaTeX are + * errors in the expression, or errors in javascript handling. + */ + + + + + + + + + + +/** + * Parse and build an expression, and place that expression in the DOM node + * given. + */ +var render = function render(expression, baseNode, options) { + baseNode.textContent = ""; + var node = renderToDomTree(expression, options).toNode(); + baseNode.appendChild(node); +}; // KaTeX's styles don't work properly in quirks mode. Print out an error, and +// disable rendering. + + +if (typeof document !== "undefined") { + if (document.compatMode !== "CSS1Compat") { + typeof console !== "undefined" && console.warn("Warning: KaTeX doesn't work in quirks mode. Make sure your " + "website has a suitable doctype."); + + render = function render() { + throw new src_ParseError("KaTeX doesn't work in quirks mode."); + }; + } +} +/** + * Parse and build an expression, and return the markup for that. + */ + + +var renderToString = function renderToString(expression, options) { + var markup = renderToDomTree(expression, options).toMarkup(); + return markup; +}; +/** + * Parse an expression and return the parse tree. + */ + + +var generateParseTree = function generateParseTree(expression, options) { + var settings = new Settings(options); + return src_parseTree(expression, settings); +}; +/** + * If the given error is a KaTeX ParseError and options.throwOnError is false, + * renders the invalid LaTeX as a span with hover title giving the KaTeX + * error message. Otherwise, simply throws the error. + */ + + +var renderError = function renderError(error, expression, options) { + if (options.throwOnError || !(error instanceof src_ParseError)) { + throw error; + } + + var node = buildCommon.makeSpan(["katex-error"], [new SymbolNode(expression)]); + node.setAttribute("title", error.toString()); + node.setAttribute("style", "color:" + options.errorColor); + return node; +}; +/** + * Generates and returns the katex build tree. This is used for advanced + * use cases (like rendering to custom output). + */ + + +var renderToDomTree = function renderToDomTree(expression, options) { + var settings = new Settings(options); + + try { + var tree = src_parseTree(expression, settings); + return buildTree(tree, expression, settings); + } catch (error) { + return renderError(error, expression, settings); + } +}; +/** + * Generates and returns the katex build tree, with just HTML (no MathML). + * This is used for advanced use cases (like rendering to custom output). + */ + + +var renderToHTMLTree = function renderToHTMLTree(expression, options) { + var settings = new Settings(options); + + try { + var tree = src_parseTree(expression, settings); + return buildHTMLTree(tree, expression, settings); + } catch (error) { + return renderError(error, expression, settings); + } +}; + +/* harmony default export */ var katex = ({ + /** + * Current KaTeX version + */ + version: "0.13.19", + + /** + * Renders the given LaTeX into an HTML+MathML combination, and adds + * it as a child to the specified DOM node. + */ + render: render, + + /** + * Renders the given LaTeX into an HTML+MathML combination string, + * for sending to the client. + */ + renderToString: renderToString, + + /** + * KaTeX error, usually during parsing. + */ + ParseError: src_ParseError, + + /** + * Parses the given LaTeX into KaTeX's internal parse tree structure, + * without rendering to HTML or MathML. + * + * NOTE: This method is not currently recommended for public use. + * The internal tree representation is unstable and is very likely + * to change. Use at your own risk. + */ + __parse: generateParseTree, + + /** + * Renders the given LaTeX into an HTML+MathML internal DOM tree + * representation, without flattening that representation to a string. + * + * NOTE: This method is not currently recommended for public use. + * The internal tree representation is unstable and is very likely + * to change. Use at your own risk. + */ + __renderToDomTree: renderToDomTree, + + /** + * Renders the given LaTeX into an HTML internal DOM tree representation, + * without MathML and without flattening that representation to a string. + * + * NOTE: This method is not currently recommended for public use. + * The internal tree representation is unstable and is very likely + * to change. Use at your own risk. + */ + __renderToHTMLTree: renderToHTMLTree, + + /** + * extends internal font metrics object with a new object + * each key in the new object represents a font name + */ + __setFontMetrics: setFontMetrics, + + /** + * adds a new symbol to builtin symbols table + */ + __defineSymbol: defineSymbol, + + /** + * adds a new macro to builtin macro list + */ + __defineMacro: defineMacro, + + /** + * Expose the dom tree node types, which can be useful for type checking nodes. + * + * NOTE: This method is not currently recommended for public use. + * The internal tree representation is unstable and is very likely + * to change. Use at your own risk. + */ + __domTree: { + Span: Span, + Anchor: Anchor, + SymbolNode: SymbolNode, + SvgNode: SvgNode, + PathNode: PathNode, + LineNode: LineNode + } +}); +;// CONCATENATED MODULE: ./katex.webpack.js +/** + * This is the webpack entry point for KaTeX. As ECMAScript, flow[1] and jest[2] + * doesn't support CSS modules natively, a separate entry point is used and + * it is not flowtyped. + * + * [1] https://gist.github.com/lambdahands/d19e0da96285b749f0ef + * [2] https://facebook.github.io/jest/docs/en/webpack.html + */ + + +/* harmony default export */ var katex_webpack = (katex); +__webpack_exports__ = __webpack_exports__["default"]; +/******/ return __webpack_exports__; +/******/ })() +; +}); \ No newline at end of file diff --git a/core/bikeshed/katex/dist/katex.min.css b/core/bikeshed/katex/dist/katex.min.css new file mode 100644 index 00000000..e0c115d5 --- /dev/null +++ b/core/bikeshed/katex/dist/katex.min.css @@ -0,0 +1 @@ +@font-face{font-family:KaTeX_AMS;font-style:normal;font-weight:400;src:url(fonts/KaTeX_AMS-Regular.woff2) format("woff2"),url(fonts/KaTeX_AMS-Regular.woff) format("woff"),url(fonts/KaTeX_AMS-Regular.ttf) 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e(e,t){this.mode=void 0,this.gullet=void 0,this.settings=void 0,this.leftrightDepth=void 0,this.nextToken=void 0,this.mode="math",this.gullet=new Gn(e,t,this.mode),this.settings=t,this.leftrightDepth=0}var t=e.prototype;return t.expect=function(e,t){if(void 0===t&&(t=!0),this.fetch().text!==e)throw new n("Expected '"+e+"', got '"+this.fetch().text+"'",this.fetch());t&&this.consume()},t.consume=function(){this.nextToken=null},t.fetch=function(){return null==this.nextToken&&(this.nextToken=this.gullet.expandNextToken()),this.nextToken},t.switchMode=function(e){this.mode=e,this.gullet.switchMode(e)},t.parse=function(){this.settings.globalGroup||this.gullet.beginGroup(),this.settings.colorIsTextColor&&this.gullet.macros.set("\\color","\\textcolor");try{var e=this.parseExpression(!1);return this.expect("EOF"),this.settings.globalGroup||this.gullet.endGroup(),e}finally{this.gullet.endGroups()}},t.parseExpression=function(t,r){for(var n=[];;){"math"===this.mode&&this.consumeSpaces();var a=this.fetch();if(-1!==e.endOfExpression.indexOf(a.text))break;if(r&&a.text===r)break;if(t&&Nn[a.text]&&Nn[a.text].infix)break;var i=this.parseAtom(r);if(!i)break;"internal"!==i.type&&n.push(i)}return"text"===this.mode&&this.formLigatures(n),this.handleInfixNodes(n)},t.handleInfixNodes=function(e){for(var t,r=-1,a=0;a=0&&this.settings.reportNonstrict("unicodeTextInMathMode",'Latin-1/Unicode text character "'+t[0]+'" used in math mode',e);var s,l=X[this.mode][t].group,h=qn.range(e);if(U.hasOwnProperty(l)){var m=l;s={type:"atom",mode:this.mode,family:m,loc:h,text:t}}else s={type:l,mode:this.mode,loc:h,text:t};i=s}else{if(!(t.charCodeAt(0)>=128))return null;this.settings.strict&&(w(t.charCodeAt(0))?"math"===this.mode&&this.settings.reportNonstrict("unicodeTextInMathMode",'Unicode text character "'+t[0]+'" used in math mode',e):this.settings.reportNonstrict("unknownSymbol",'Unrecognized Unicode character "'+t[0]+'" ('+t.charCodeAt(0)+")",e)),i={type:"textord",mode:"text",loc:qn.range(e),text:t}}if(this.consume(),o)for(var c=0;c 15) { + left = "…" + input.slice(start - 15, start); + } else { + left = input.slice(0, start); + } + + var right; + + if (end + 15 < input.length) { + right = input.slice(end, end + 15) + "…"; + } else { + right = input.slice(end); + } + + error += left + underlined + right; + } // Some hackery to make ParseError a prototype of Error + // See http://stackoverflow.com/a/8460753 + + + var self = new Error(error); + self.name = "ParseError"; // $FlowFixMe + + self.__proto__ = ParseError.prototype; // $FlowFixMe + + self.position = start; + return self; + } + +} // $FlowFixMe More hackery + + +ParseError.prototype.__proto__ = Error.prototype; + +/** + * This file contains a list of utility functions which are useful in other + * files. + */ + +/** + * Return whether an element is contained in a list + */ +var contains = function contains(list, elem) { + return list.indexOf(elem) !== -1; +}; +/** + * Provide a default value if a setting is undefined + * NOTE: Couldn't use `T` as the output type due to facebook/flow#5022. + */ + + +var deflt = function deflt(setting, defaultIfUndefined) { + return setting === undefined ? defaultIfUndefined : setting; +}; // hyphenate and escape adapted from Facebook's React under Apache 2 license + + +var uppercase = /([A-Z])/g; + +var hyphenate = function hyphenate(str) { + return str.replace(uppercase, "-$1").toLowerCase(); +}; + +var ESCAPE_LOOKUP = { + "&": "&", + ">": ">", + "<": "<", + "\"": """, + "'": "'" +}; +var ESCAPE_REGEX = /[&><"']/g; +/** + * Escapes text to prevent scripting attacks. + */ + +function escape(text) { + return String(text).replace(ESCAPE_REGEX, match => ESCAPE_LOOKUP[match]); +} +/** + * Sometimes we want to pull out the innermost element of a group. In most + * cases, this will just be the group itself, but when ordgroups and colors have + * a single element, we want to pull that out. + */ + + +var getBaseElem = function getBaseElem(group) { + if (group.type === "ordgroup") { + if (group.body.length === 1) { + return getBaseElem(group.body[0]); + } else { + return group; + } + } else if (group.type === "color") { + if (group.body.length === 1) { + return getBaseElem(group.body[0]); + } else { + return group; + } + } else if (group.type === "font") { + return getBaseElem(group.body); + } else { + return group; + } +}; +/** + * TeXbook algorithms often reference "character boxes", which are simply groups + * with a single character in them. To decide if something is a character box, + * we find its innermost group, and see if it is a single character. + */ + + +var isCharacterBox = function isCharacterBox(group) { + var baseElem = getBaseElem(group); // These are all they types of groups which hold single characters + + return baseElem.type === "mathord" || baseElem.type === "textord" || baseElem.type === "atom"; +}; + +var assert = function assert(value) { + if (!value) { + throw new Error('Expected non-null, but got ' + String(value)); + } + + return value; +}; +/** + * Return the protocol of a URL, or "_relative" if the URL does not specify a + * protocol (and thus is relative). + */ + +var protocolFromUrl = function protocolFromUrl(url) { + var protocol = /^\s*([^\\/#]*?)(?::|�*58|�*3a)/i.exec(url); + return protocol != null ? protocol[1] : "_relative"; +}; +var utils = { + contains, + deflt, + escape, + hyphenate, + getBaseElem, + isCharacterBox, + protocolFromUrl +}; + +/* eslint no-console:0 */ + +/** + * The main Settings object + * + * The current options stored are: + * - displayMode: Whether the expression should be typeset as inline math + * (false, the default), meaning that the math starts in + * \textstyle and is placed in an inline-block); or as display + * math (true), meaning that the math starts in \displaystyle + * and is placed in a block with vertical margin. + */ +class Settings { + constructor(options) { + this.displayMode = void 0; + this.output = void 0; + this.leqno = void 0; + this.fleqn = void 0; + this.throwOnError = void 0; + this.errorColor = void 0; + this.macros = void 0; + this.minRuleThickness = void 0; + this.colorIsTextColor = void 0; + this.strict = void 0; + this.trust = void 0; + this.maxSize = void 0; + this.maxExpand = void 0; + this.globalGroup = void 0; + // allow null options + options = options || {}; + this.displayMode = utils.deflt(options.displayMode, false); + this.output = utils.deflt(options.output, "htmlAndMathml"); + this.leqno = utils.deflt(options.leqno, false); + this.fleqn = utils.deflt(options.fleqn, false); + this.throwOnError = utils.deflt(options.throwOnError, true); + this.errorColor = utils.deflt(options.errorColor, "#cc0000"); + this.macros = options.macros || {}; + this.minRuleThickness = Math.max(0, utils.deflt(options.minRuleThickness, 0)); + this.colorIsTextColor = utils.deflt(options.colorIsTextColor, false); + this.strict = utils.deflt(options.strict, "warn"); + this.trust = utils.deflt(options.trust, false); + this.maxSize = Math.max(0, utils.deflt(options.maxSize, Infinity)); + this.maxExpand = Math.max(0, utils.deflt(options.maxExpand, 1000)); + this.globalGroup = utils.deflt(options.globalGroup, false); + } + /** + * Report nonstrict (non-LaTeX-compatible) input. + * Can safely not be called if `this.strict` is false in JavaScript. + */ + + + reportNonstrict(errorCode, errorMsg, token) { + var strict = this.strict; + + if (typeof strict === "function") { + // Allow return value of strict function to be boolean or string + // (or null/undefined, meaning no further processing). + strict = strict(errorCode, errorMsg, token); + } + + if (!strict || strict === "ignore") { + return; + } else if (strict === true || strict === "error") { + throw new ParseError("LaTeX-incompatible input and strict mode is set to 'error': " + (errorMsg + " [" + errorCode + "]"), token); + } else if (strict === "warn") { + typeof console !== "undefined" && console.warn("LaTeX-incompatible input and strict mode is set to 'warn': " + (errorMsg + " [" + errorCode + "]")); + } else { + // won't happen in type-safe code + typeof console !== "undefined" && console.warn("LaTeX-incompatible input and strict mode is set to " + ("unrecognized '" + strict + "': " + errorMsg + " [" + errorCode + "]")); + } + } + /** + * Check whether to apply strict (LaTeX-adhering) behavior for unusual + * input (like `\\`). Unlike `nonstrict`, will not throw an error; + * instead, "error" translates to a return value of `true`, while "ignore" + * translates to a return value of `false`. May still print a warning: + * "warn" prints a warning and returns `false`. + * This is for the second category of `errorCode`s listed in the README. + */ + + + useStrictBehavior(errorCode, errorMsg, token) { + var strict = this.strict; + + if (typeof strict === "function") { + // Allow return value of strict function to be boolean or string + // (or null/undefined, meaning no further processing). + // But catch any exceptions thrown by function, treating them + // like "error". + try { + strict = strict(errorCode, errorMsg, token); + } catch (error) { + strict = "error"; + } + } + + if (!strict || strict === "ignore") { + return false; + } else if (strict === true || strict === "error") { + return true; + } else if (strict === "warn") { + typeof console !== "undefined" && console.warn("LaTeX-incompatible input and strict mode is set to 'warn': " + (errorMsg + " [" + errorCode + "]")); + return false; + } else { + // won't happen in type-safe code + typeof console !== "undefined" && console.warn("LaTeX-incompatible input and strict mode is set to " + ("unrecognized '" + strict + "': " + errorMsg + " [" + errorCode + "]")); + return false; + } + } + /** + * Check whether to test potentially dangerous input, and return + * `true` (trusted) or `false` (untrusted). The sole argument `context` + * should be an object with `command` field specifying the relevant LaTeX + * command (as a string starting with `\`), and any other arguments, etc. + * If `context` has a `url` field, a `protocol` field will automatically + * get added by this function (changing the specified object). + */ + + + isTrusted(context) { + if (context.url && !context.protocol) { + context.protocol = utils.protocolFromUrl(context.url); + } + + var trust = typeof this.trust === "function" ? this.trust(context) : this.trust; + return Boolean(trust); + } + +} + +/** + * This file contains information and classes for the various kinds of styles + * used in TeX. It provides a generic `Style` class, which holds information + * about a specific style. It then provides instances of all the different kinds + * of styles possible, and provides functions to move between them and get + * information about them. + */ + +/** + * The main style class. Contains a unique id for the style, a size (which is + * the same for cramped and uncramped version of a style), and a cramped flag. + */ +class Style { + constructor(id, size, cramped) { + this.id = void 0; + this.size = void 0; + this.cramped = void 0; + this.id = id; + this.size = size; + this.cramped = cramped; + } + /** + * Get the style of a superscript given a base in the current style. + */ + + + sup() { + return styles[sup[this.id]]; + } + /** + * Get the style of a subscript given a base in the current style. + */ + + + sub() { + return styles[sub[this.id]]; + } + /** + * Get the style of a fraction numerator given the fraction in the current + * style. + */ + + + fracNum() { + return styles[fracNum[this.id]]; + } + /** + * Get the style of a fraction denominator given the fraction in the current + * style. + */ + + + fracDen() { + return styles[fracDen[this.id]]; + } + /** + * Get the cramped version of a style (in particular, cramping a cramped style + * doesn't change the style). + */ + + + cramp() { + return styles[cramp[this.id]]; + } + /** + * Get a text or display version of this style. + */ + + + text() { + return styles[text$1[this.id]]; + } + /** + * Return true if this style is tightly spaced (scriptstyle/scriptscriptstyle) + */ + + + isTight() { + return this.size >= 2; + } + +} // Export an interface for type checking, but don't expose the implementation. +// This way, no more styles can be generated. + + +// IDs of the different styles +var D = 0; +var Dc = 1; +var T = 2; +var Tc = 3; +var S = 4; +var Sc = 5; +var SS = 6; +var SSc = 7; // Instances of the different styles + +var styles = [new Style(D, 0, false), new Style(Dc, 0, true), new Style(T, 1, false), new Style(Tc, 1, true), new Style(S, 2, false), new Style(Sc, 2, true), new Style(SS, 3, false), new Style(SSc, 3, true)]; // Lookup tables for switching from one style to another + +var sup = [S, Sc, S, Sc, SS, SSc, SS, SSc]; +var sub = [Sc, Sc, Sc, Sc, SSc, SSc, SSc, SSc]; +var fracNum = [T, Tc, S, Sc, SS, SSc, SS, SSc]; +var fracDen = [Tc, Tc, Sc, Sc, SSc, SSc, SSc, SSc]; +var cramp = [Dc, Dc, Tc, Tc, Sc, Sc, SSc, SSc]; +var text$1 = [D, Dc, T, Tc, T, Tc, T, Tc]; // We only export some of the styles. + +var Style$1 = { + DISPLAY: styles[D], + TEXT: styles[T], + SCRIPT: styles[S], + SCRIPTSCRIPT: styles[SS] +}; + +/* + * This file defines the Unicode scripts and script families that we + * support. To add new scripts or families, just add a new entry to the + * scriptData array below. Adding scripts to the scriptData array allows + * characters from that script to appear in \text{} environments. + */ + +/** + * Each script or script family has a name and an array of blocks. + * Each block is an array of two numbers which specify the start and + * end points (inclusive) of a block of Unicode codepoints. + */ + +/** + * Unicode block data for the families of scripts we support in \text{}. + * Scripts only need to appear here if they do not have font metrics. + */ +var scriptData = [{ + // Latin characters beyond the Latin-1 characters we have metrics for. + // Needed for Czech, Hungarian and Turkish text, for example. + name: 'latin', + blocks: [[0x0100, 0x024f], // Latin Extended-A and Latin Extended-B + [0x0300, 0x036f] // Combining Diacritical marks + ] +}, { + // The Cyrillic script used by Russian and related languages. + // A Cyrillic subset used to be supported as explicitly defined + // symbols in symbols.js + name: 'cyrillic', + blocks: [[0x0400, 0x04ff]] +}, { + // Armenian + name: 'armenian', + blocks: [[0x0530, 0x058F]] +}, { + // The Brahmic scripts of South and Southeast Asia + // Devanagari (0900–097F) + // Bengali (0980–09FF) + // Gurmukhi (0A00–0A7F) + // Gujarati (0A80–0AFF) + // Oriya (0B00–0B7F) + // Tamil (0B80–0BFF) + // Telugu (0C00–0C7F) + // Kannada (0C80–0CFF) + // Malayalam (0D00–0D7F) + // Sinhala (0D80–0DFF) + // Thai (0E00–0E7F) + // Lao (0E80–0EFF) + // Tibetan (0F00–0FFF) + // Myanmar (1000–109F) + name: 'brahmic', + blocks: [[0x0900, 0x109F]] +}, { + name: 'georgian', + blocks: [[0x10A0, 0x10ff]] +}, { + // Chinese and Japanese. + // The "k" in cjk is for Korean, but we've separated Korean out + name: "cjk", + blocks: [[0x3000, 0x30FF], // CJK symbols and punctuation, Hiragana, Katakana + [0x4E00, 0x9FAF], // CJK ideograms + [0xFF00, 0xFF60] // Fullwidth punctuation + // TODO: add halfwidth Katakana and Romanji glyphs + ] +}, { + // Korean + name: 'hangul', + blocks: [[0xAC00, 0xD7AF]] +}]; +/** + * Given a codepoint, return the name of the script or script family + * it is from, or null if it is not part of a known block + */ + +function scriptFromCodepoint(codepoint) { + for (var i = 0; i < scriptData.length; i++) { + var script = scriptData[i]; + + for (var _i = 0; _i < script.blocks.length; _i++) { + var block = script.blocks[_i]; + + if (codepoint >= block[0] && codepoint <= block[1]) { + return script.name; + } + } + } + + return null; +} +/** + * A flattened version of all the supported blocks in a single array. + * This is an optimization to make supportedCodepoint() fast. + */ + +var allBlocks = []; +scriptData.forEach(s => s.blocks.forEach(b => allBlocks.push(...b))); +/** + * Given a codepoint, return true if it falls within one of the + * scripts or script families defined above and false otherwise. + * + * Micro benchmarks shows that this is faster than + * /[\u3000-\u30FF\u4E00-\u9FAF\uFF00-\uFF60\uAC00-\uD7AF\u0900-\u109F]/.test() + * in Firefox, Chrome and Node. + */ + +function supportedCodepoint(codepoint) { + for (var i = 0; i < allBlocks.length; i += 2) { + if (codepoint >= allBlocks[i] && codepoint <= allBlocks[i + 1]) { + return true; + } + } + + return false; +} + +/** + * This file provides support to domTree.js and delimiter.js. + * It's a storehouse of path geometry for SVG images. + */ +// In all paths below, the viewBox-to-em scale is 1000:1. +var hLinePad = 80; // padding above a sqrt viniculum. Prevents image cropping. +// The viniculum of a \sqrt can be made thicker by a KaTeX rendering option. +// Think of variable extraViniculum as two detours in the SVG path. +// The detour begins at the lower left of the area labeled extraViniculum below. +// The detour proceeds one extraViniculum distance up and slightly to the right, +// displacing the radiused corner between surd and viniculum. The radius is +// traversed as usual, then the detour resumes. It goes right, to the end of +// the very long viniculumn, then down one extraViniculum distance, +// after which it resumes regular path geometry for the radical. + +/* viniculum + / + /▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒←extraViniculum + / █████████████████████←0.04em (40 unit) std viniculum thickness + / / + / / + / /\ + / / surd +*/ + +var sqrtMain = function sqrtMain(extraViniculum, hLinePad) { + // sqrtMain path geometry is from glyph U221A in the font KaTeX Main + return "M95," + (622 + extraViniculum + hLinePad) + "\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl" + extraViniculum / 2.075 + " -" + extraViniculum + "\nc5.3,-9.3,12,-14,20,-14\nH400000v" + (40 + extraViniculum) + "H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM" + (834 + extraViniculum) + " " + hLinePad + "h400000v" + (40 + extraViniculum) + "h-400000z"; +}; + +var sqrtSize1 = function sqrtSize1(extraViniculum, hLinePad) { + // size1 is from glyph U221A in the font KaTeX_Size1-Regular + return "M263," + (601 + extraViniculum + hLinePad) + "c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl" + extraViniculum / 2.084 + " -" + extraViniculum + "\nc4.7,-7.3,11,-11,19,-11\nH40000v" + (40 + extraViniculum) + "H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM" + (1001 + extraViniculum) + " " + hLinePad + "h400000v" + (40 + extraViniculum) + "h-400000z"; +}; + +var sqrtSize2 = function sqrtSize2(extraViniculum, hLinePad) { + // size2 is from glyph U221A in the font KaTeX_Size2-Regular + return "M983 " + (10 + extraViniculum + hLinePad) + "\nl" + extraViniculum / 3.13 + " -" + extraViniculum + "\nc4,-6.7,10,-10,18,-10 H400000v" + (40 + extraViniculum) + "\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM" + (1001 + extraViniculum) + " " + hLinePad + "h400000v" + (40 + extraViniculum) + "h-400000z"; +}; + +var sqrtSize3 = function sqrtSize3(extraViniculum, hLinePad) { + // size3 is from glyph U221A in the font KaTeX_Size3-Regular + return "M424," + (2398 + extraViniculum + hLinePad) + "\nc-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514\nc0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20\ns-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121\ns209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081\nl" + extraViniculum / 4.223 + " -" + extraViniculum + "c4,-6.7,10,-10,18,-10 H400000\nv" + (40 + extraViniculum) + "H1014.6\ns-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185\nc-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2z M" + (1001 + extraViniculum) + " " + hLinePad + "\nh400000v" + (40 + extraViniculum) + "h-400000z"; +}; + +var sqrtSize4 = function sqrtSize4(extraViniculum, hLinePad) { + // size4 is from glyph U221A in the font KaTeX_Size4-Regular + return "M473," + (2713 + extraViniculum + hLinePad) + "\nc339.3,-1799.3,509.3,-2700,510,-2702 l" + extraViniculum / 5.298 + " -" + extraViniculum + "\nc3.3,-7.3,9.3,-11,18,-11 H400000v" + (40 + extraViniculum) + "H1017.7\ns-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200\nc0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26\ns76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,\n606zM" + (1001 + extraViniculum) + " " + hLinePad + "h400000v" + (40 + extraViniculum) + "H1017.7z"; +}; + +var phasePath = function phasePath(y) { + var x = y / 2; // x coordinate at top of angle + + return "M400000 " + y + " H0 L" + x + " 0 l65 45 L145 " + (y - 80) + " H400000z"; +}; + +var sqrtTall = function sqrtTall(extraViniculum, hLinePad, viewBoxHeight) { + // sqrtTall is from glyph U23B7 in the font KaTeX_Size4-Regular + // One path edge has a variable length. It runs vertically from the viniculumn + // to a point near (14 units) the bottom of the surd. The viniculum + // is normally 40 units thick. So the length of the line in question is: + var vertSegment = viewBoxHeight - 54 - hLinePad - extraViniculum; + return "M702 " + (extraViniculum + hLinePad) + "H400000" + (40 + extraViniculum) + "\nH742v" + vertSegment + "l-4 4-4 4c-.667.7 -2 1.5-4 2.5s-4.167 1.833-6.5 2.5-5.5 1-9.5 1\nh-12l-28-84c-16.667-52-96.667 -294.333-240-727l-212 -643 -85 170\nc-4-3.333-8.333-7.667-13 -13l-13-13l77-155 77-156c66 199.333 139 419.667\n219 661 l218 661zM702 " + hLinePad + "H400000v" + (40 + extraViniculum) + "H742z"; +}; + +var sqrtPath = function sqrtPath(size, extraViniculum, viewBoxHeight) { + extraViniculum = 1000 * extraViniculum; // Convert from document ems to viewBox. + + var path = ""; + + switch (size) { + case "sqrtMain": + path = sqrtMain(extraViniculum, hLinePad); + break; + + case "sqrtSize1": + path = sqrtSize1(extraViniculum, hLinePad); + break; + + case "sqrtSize2": + path = sqrtSize2(extraViniculum, hLinePad); + break; + + case "sqrtSize3": + path = sqrtSize3(extraViniculum, hLinePad); + break; + + case "sqrtSize4": + path = sqrtSize4(extraViniculum, hLinePad); + break; + + case "sqrtTall": + path = sqrtTall(extraViniculum, hLinePad, viewBoxHeight); + } + + return path; +}; +var innerPath = function innerPath(name, height) { + // The inner part of stretchy tall delimiters + switch (name) { + case "\u239c": + return "M291 0 H417 V" + height + " H291z M291 0 H417 V" + height + " H291z"; + + case "\u2223": + return "M145 0 H188 V" + height + " H145z M145 0 H188 V" + height + " H145z"; + + case "\u2225": + return "M145 0 H188 V" + height + " H145z M145 0 H188 V" + height + " H145z" + ("M367 0 H410 V" + height + " H367z M367 0 H410 V" + height + " H367z"); + + case "\u239f": + return "M457 0 H583 V" + height + " H457z M457 0 H583 V" + height + " H457z"; + + case "\u23a2": + return "M319 0 H403 V" + height + " H319z M319 0 H403 V" + height + " H319z"; + + case "\u23a5": + return "M263 0 H347 V" + height + " H263z M263 0 H347 V" + height + " H263z"; + + case "\u23aa": + return "M384 0 H504 V" + height + " H384z M384 0 H504 V" + height + " H384z"; + + case "\u23d0": + return "M312 0 H355 V" + height + " H312z M312 0 H355 V" + height + " H312z"; + + case "\u2016": + return "M257 0 H300 V" + height + " H257z M257 0 H300 V" + height + " H257z" + ("M478 0 H521 V" + height + " H478z M478 0 H521 V" + height + " H478z"); + + default: + return ""; + } +}; +var path = { + // The doubleleftarrow geometry is from glyph U+21D0 in the font KaTeX Main + doubleleftarrow: "M262 157\nl10-10c34-36 62.7-77 86-123 3.3-8 5-13.3 5-16 0-5.3-6.7-8-20-8-7.3\n 0-12.2.5-14.5 1.5-2.3 1-4.8 4.5-7.5 10.5-49.3 97.3-121.7 169.3-217 216-28\n 14-57.3 25-88 33-6.7 2-11 3.8-13 5.5-2 1.7-3 4.2-3 7.5s1 5.8 3 7.5\nc2 1.7 6.3 3.5 13 5.5 68 17.3 128.2 47.8 180.5 91.5 52.3 43.7 93.8 96.2 124.5\n 157.5 9.3 8 15.3 12.3 18 13h6c12-.7 18-4 18-10 0-2-1.7-7-5-15-23.3-46-52-87\n-86-123l-10-10h399738v-40H218c328 0 0 0 0 0l-10-8c-26.7-20-65.7-43-117-69 2.7\n-2 6-3.7 10-5 36.7-16 72.3-37.3 107-64l10-8h399782v-40z\nm8 0v40h399730v-40zm0 194v40h399730v-40z", + // doublerightarrow is from glyph U+21D2 in font KaTeX Main + doublerightarrow: "M399738 392l\n-10 10c-34 36-62.7 77-86 123-3.3 8-5 13.3-5 16 0 5.3 6.7 8 20 8 7.3 0 12.2-.5\n 14.5-1.5 2.3-1 4.8-4.5 7.5-10.5 49.3-97.3 121.7-169.3 217-216 28-14 57.3-25 88\n-33 6.7-2 11-3.8 13-5.5 2-1.7 3-4.2 3-7.5s-1-5.8-3-7.5c-2-1.7-6.3-3.5-13-5.5-68\n-17.3-128.2-47.8-180.5-91.5-52.3-43.7-93.8-96.2-124.5-157.5-9.3-8-15.3-12.3-18\n-13h-6c-12 .7-18 4-18 10 0 2 1.7 7 5 15 23.3 46 52 87 86 123l10 10H0v40h399782\nc-328 0 0 0 0 0l10 8c26.7 20 65.7 43 117 69-2.7 2-6 3.7-10 5-36.7 16-72.3 37.3\n-107 64l-10 8H0v40zM0 157v40h399730v-40zm0 194v40h399730v-40z", + // leftarrow is from glyph U+2190 in font KaTeX Main + leftarrow: "M400000 241H110l3-3c68.7-52.7 113.7-120\n 135-202 4-14.7 6-23 6-25 0-7.3-7-11-21-11-8 0-13.2.8-15.5 2.5-2.3 1.7-4.2 5.8\n-5.5 12.5-1.3 4.7-2.7 10.3-4 17-12 48.7-34.8 92-68.5 130S65.3 228.3 18 247\nc-10 4-16 7.7-18 11 0 8.7 6 14.3 18 17 47.3 18.7 87.8 47 121.5 85S196 441.3 208\n 490c.7 2 1.3 5 2 9s1.2 6.7 1.5 8c.3 1.3 1 3.3 2 6s2.2 4.5 3.5 5.5c1.3 1 3.3\n 1.8 6 2.5s6 1 10 1c14 0 21-3.7 21-11 0-2-2-10.3-6-25-20-79.3-65-146.7-135-202\n l-3-3h399890zM100 241v40h399900v-40z", + // overbrace is from glyphs U+23A9/23A8/23A7 in font KaTeX_Size4-Regular + leftbrace: "M6 548l-6-6v-35l6-11c56-104 135.3-181.3 238-232 57.3-28.7 117\n-45 179-50h399577v120H403c-43.3 7-81 15-113 26-100.7 33-179.7 91-237 174-2.7\n 5-6 9-10 13-.7 1-7.3 1-20 1H6z", + leftbraceunder: "M0 6l6-6h17c12.688 0 19.313.3 20 1 4 4 7.313 8.3 10 13\n 35.313 51.3 80.813 93.8 136.5 127.5 55.688 33.7 117.188 55.8 184.5 66.5.688\n 0 2 .3 4 1 18.688 2.7 76 4.3 172 5h399450v120H429l-6-1c-124.688-8-235-61.7\n-331-161C60.687 138.7 32.312 99.3 7 54L0 41V6z", + // overgroup is from the MnSymbol package (public domain) + leftgroup: "M400000 80\nH435C64 80 168.3 229.4 21 260c-5.9 1.2-18 0-18 0-2 0-3-1-3-3v-38C76 61 257 0\n 435 0h399565z", + leftgroupunder: "M400000 262\nH435C64 262 168.3 112.6 21 82c-5.9-1.2-18 0-18 0-2 0-3 1-3 3v38c76 158 257 219\n 435 219h399565z", + // Harpoons are from glyph U+21BD in font KaTeX Main + leftharpoon: "M0 267c.7 5.3 3 10 7 14h399993v-40H93c3.3\n-3.3 10.2-9.5 20.5-18.5s17.8-15.8 22.5-20.5c50.7-52 88-110.3 112-175 4-11.3 5\n-18.3 3-21-1.3-4-7.3-6-18-6-8 0-13 .7-15 2s-4.7 6.7-8 16c-42 98.7-107.3 174.7\n-196 228-6.7 4.7-10.7 8-12 10-1.3 2-2 5.7-2 11zm100-26v40h399900v-40z", + leftharpoonplus: "M0 267c.7 5.3 3 10 7 14h399993v-40H93c3.3-3.3 10.2-9.5\n 20.5-18.5s17.8-15.8 22.5-20.5c50.7-52 88-110.3 112-175 4-11.3 5-18.3 3-21-1.3\n-4-7.3-6-18-6-8 0-13 .7-15 2s-4.7 6.7-8 16c-42 98.7-107.3 174.7-196 228-6.7 4.7\n-10.7 8-12 10-1.3 2-2 5.7-2 11zm100-26v40h399900v-40zM0 435v40h400000v-40z\nm0 0v40h400000v-40z", + leftharpoondown: "M7 241c-4 4-6.333 8.667-7 14 0 5.333.667 9 2 11s5.333\n 5.333 12 10c90.667 54 156 130 196 228 3.333 10.667 6.333 16.333 9 17 2 .667 5\n 1 9 1h5c10.667 0 16.667-2 18-6 2-2.667 1-9.667-3-21-32-87.333-82.667-157.667\n-152-211l-3-3h399907v-40zM93 281 H400000 v-40L7 241z", + leftharpoondownplus: "M7 435c-4 4-6.3 8.7-7 14 0 5.3.7 9 2 11s5.3 5.3 12\n 10c90.7 54 156 130 196 228 3.3 10.7 6.3 16.3 9 17 2 .7 5 1 9 1h5c10.7 0 16.7\n-2 18-6 2-2.7 1-9.7-3-21-32-87.3-82.7-157.7-152-211l-3-3h399907v-40H7zm93 0\nv40h399900v-40zM0 241v40h399900v-40zm0 0v40h399900v-40z", + // hook is from glyph U+21A9 in font KaTeX Main + lefthook: "M400000 281 H103s-33-11.2-61-33.5S0 197.3 0 164s14.2-61.2 42.5\n-83.5C70.8 58.2 104 47 142 47 c16.7 0 25 6.7 25 20 0 12-8.7 18.7-26 20-40 3.3\n-68.7 15.7-86 37-10 12-15 25.3-15 40 0 22.7 9.8 40.7 29.5 54 19.7 13.3 43.5 21\n 71.5 23h399859zM103 281v-40h399897v40z", + leftlinesegment: "M40 281 V428 H0 V94 H40 V241 H400000 v40z\nM40 281 V428 H0 V94 H40 V241 H400000 v40z", + leftmapsto: "M40 281 V448H0V74H40V241H400000v40z\nM40 281 V448H0V74H40V241H400000v40z", + // tofrom is from glyph U+21C4 in font KaTeX AMS Regular + leftToFrom: "M0 147h400000v40H0zm0 214c68 40 115.7 95.7 143 167h22c15.3 0 23\n-.3 23-1 0-1.3-5.3-13.7-16-37-18-35.3-41.3-69-70-101l-7-8h399905v-40H95l7-8\nc28.7-32 52-65.7 70-101 10.7-23.3 16-35.7 16-37 0-.7-7.7-1-23-1h-22C115.7 265.3\n 68 321 0 361zm0-174v-40h399900v40zm100 154v40h399900v-40z", + longequal: "M0 50 h400000 v40H0z m0 194h40000v40H0z\nM0 50 h400000 v40H0z m0 194h40000v40H0z", + midbrace: "M200428 334\nc-100.7-8.3-195.3-44-280-108-55.3-42-101.7-93-139-153l-9-14c-2.7 4-5.7 8.7-9 14\n-53.3 86.7-123.7 153-211 199-66.7 36-137.3 56.3-212 62H0V214h199568c178.3-11.7\n 311.7-78.3 403-201 6-8 9.7-12 11-12 .7-.7 6.7-1 18-1s17.3.3 18 1c1.3 0 5 4 11\n 12 44.7 59.3 101.3 106.3 170 141s145.3 54.3 229 60h199572v120z", + midbraceunder: "M199572 214\nc100.7 8.3 195.3 44 280 108 55.3 42 101.7 93 139 153l9 14c2.7-4 5.7-8.7 9-14\n 53.3-86.7 123.7-153 211-199 66.7-36 137.3-56.3 212-62h199568v120H200432c-178.3\n 11.7-311.7 78.3-403 201-6 8-9.7 12-11 12-.7.7-6.7 1-18 1s-17.3-.3-18-1c-1.3 0\n-5-4-11-12-44.7-59.3-101.3-106.3-170-141s-145.3-54.3-229-60H0V214z", + oiintSize1: "M512.6 71.6c272.6 0 320.3 106.8 320.3 178.2 0 70.8-47.7 177.6\n-320.3 177.6S193.1 320.6 193.1 249.8c0-71.4 46.9-178.2 319.5-178.2z\nm368.1 178.2c0-86.4-60.9-215.4-368.1-215.4-306.4 0-367.3 129-367.3 215.4 0 85.8\n60.9 214.8 367.3 214.8 307.2 0 368.1-129 368.1-214.8z", + oiintSize2: "M757.8 100.1c384.7 0 451.1 137.6 451.1 230 0 91.3-66.4 228.8\n-451.1 228.8-386.3 0-452.7-137.5-452.7-228.8 0-92.4 66.4-230 452.7-230z\nm502.4 230c0-111.2-82.4-277.2-502.4-277.2s-504 166-504 277.2\nc0 110 84 276 504 276s502.4-166 502.4-276z", + oiiintSize1: "M681.4 71.6c408.9 0 480.5 106.8 480.5 178.2 0 70.8-71.6 177.6\n-480.5 177.6S202.1 320.6 202.1 249.8c0-71.4 70.5-178.2 479.3-178.2z\nm525.8 178.2c0-86.4-86.8-215.4-525.7-215.4-437.9 0-524.7 129-524.7 215.4 0\n85.8 86.8 214.8 524.7 214.8 438.9 0 525.7-129 525.7-214.8z", + oiiintSize2: "M1021.2 53c603.6 0 707.8 165.8 707.8 277.2 0 110-104.2 275.8\n-707.8 275.8-606 0-710.2-165.8-710.2-275.8C311 218.8 415.2 53 1021.2 53z\nm770.4 277.1c0-131.2-126.4-327.6-770.5-327.6S248.4 198.9 248.4 330.1\nc0 130 128.8 326.4 772.7 326.4s770.5-196.4 770.5-326.4z", + rightarrow: "M0 241v40h399891c-47.3 35.3-84 78-110 128\n-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20\n 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7\n 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85\n-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n 151.7 139 205zm0 0v40h399900v-40z", + rightbrace: "M400000 542l\n-6 6h-17c-12.7 0-19.3-.3-20-1-4-4-7.3-8.3-10-13-35.3-51.3-80.8-93.8-136.5-127.5\ns-117.2-55.8-184.5-66.5c-.7 0-2-.3-4-1-18.7-2.7-76-4.3-172-5H0V214h399571l6 1\nc124.7 8 235 61.7 331 161 31.3 33.3 59.7 72.7 85 118l7 13v35z", + rightbraceunder: "M399994 0l6 6v35l-6 11c-56 104-135.3 181.3-238 232-57.3\n 28.7-117 45-179 50H-300V214h399897c43.3-7 81-15 113-26 100.7-33 179.7-91 237\n-174 2.7-5 6-9 10-13 .7-1 7.3-1 20-1h17z", + rightgroup: "M0 80h399565c371 0 266.7 149.4 414 180 5.9 1.2 18 0 18 0 2 0\n 3-1 3-3v-38c-76-158-257-219-435-219H0z", + rightgroupunder: "M0 262h399565c371 0 266.7-149.4 414-180 5.9-1.2 18 0 18\n 0 2 0 3 1 3 3v38c-76 158-257 219-435 219H0z", + rightharpoon: "M0 241v40h399993c4.7-4.7 7-9.3 7-14 0-9.3\n-3.7-15.3-11-18-92.7-56.7-159-133.7-199-231-3.3-9.3-6-14.7-8-16-2-1.3-7-2-15-2\n-10.7 0-16.7 2-18 6-2 2.7-1 9.7 3 21 15.3 42 36.7 81.8 64 119.5 27.3 37.7 58\n 69.2 92 94.5zm0 0v40h399900v-40z", + rightharpoonplus: "M0 241v40h399993c4.7-4.7 7-9.3 7-14 0-9.3-3.7-15.3-11\n-18-92.7-56.7-159-133.7-199-231-3.3-9.3-6-14.7-8-16-2-1.3-7-2-15-2-10.7 0-16.7\n 2-18 6-2 2.7-1 9.7 3 21 15.3 42 36.7 81.8 64 119.5 27.3 37.7 58 69.2 92 94.5z\nm0 0v40h399900v-40z m100 194v40h399900v-40zm0 0v40h399900v-40z", + rightharpoondown: "M399747 511c0 7.3 6.7 11 20 11 8 0 13-.8 15-2.5s4.7-6.8\n 8-15.5c40-94 99.3-166.3 178-217 13.3-8 20.3-12.3 21-13 5.3-3.3 8.5-5.8 9.5\n-7.5 1-1.7 1.5-5.2 1.5-10.5s-2.3-10.3-7-15H0v40h399908c-34 25.3-64.7 57-92 95\n-27.3 38-48.7 77.7-64 119-3.3 8.7-5 14-5 16zM0 241v40h399900v-40z", + rightharpoondownplus: "M399747 705c0 7.3 6.7 11 20 11 8 0 13-.8\n 15-2.5s4.7-6.8 8-15.5c40-94 99.3-166.3 178-217 13.3-8 20.3-12.3 21-13 5.3-3.3\n 8.5-5.8 9.5-7.5 1-1.7 1.5-5.2 1.5-10.5s-2.3-10.3-7-15H0v40h399908c-34 25.3\n-64.7 57-92 95-27.3 38-48.7 77.7-64 119-3.3 8.7-5 14-5 16zM0 435v40h399900v-40z\nm0-194v40h400000v-40zm0 0v40h400000v-40z", + righthook: "M399859 241c-764 0 0 0 0 0 40-3.3 68.7-15.7 86-37 10-12 15-25.3\n 15-40 0-22.7-9.8-40.7-29.5-54-19.7-13.3-43.5-21-71.5-23-17.3-1.3-26-8-26-20 0\n-13.3 8.7-20 26-20 38 0 71 11.2 99 33.5 0 0 7 5.6 21 16.7 14 11.2 21 33.5 21\n 66.8s-14 61.2-42 83.5c-28 22.3-61 33.5-99 33.5L0 241z M0 281v-40h399859v40z", + rightlinesegment: "M399960 241 V94 h40 V428 h-40 V281 H0 v-40z\nM399960 241 V94 h40 V428 h-40 V281 H0 v-40z", + rightToFrom: "M400000 167c-70.7-42-118-97.7-142-167h-23c-15.3 0-23 .3-23\n 1 0 1.3 5.3 13.7 16 37 18 35.3 41.3 69 70 101l7 8H0v40h399905l-7 8c-28.7 32\n-52 65.7-70 101-10.7 23.3-16 35.7-16 37 0 .7 7.7 1 23 1h23c24-69.3 71.3-125 142\n-167z M100 147v40h399900v-40zM0 341v40h399900v-40z", + // twoheadleftarrow is from glyph U+219E in font KaTeX AMS Regular + twoheadleftarrow: "M0 167c68 40\n 115.7 95.7 143 167h22c15.3 0 23-.3 23-1 0-1.3-5.3-13.7-16-37-18-35.3-41.3-69\n-70-101l-7-8h125l9 7c50.7 39.3 85 86 103 140h46c0-4.7-6.3-18.7-19-42-18-35.3\n-40-67.3-66-96l-9-9h399716v-40H284l9-9c26-28.7 48-60.7 66-96 12.7-23.333 19\n-37.333 19-42h-46c-18 54-52.3 100.7-103 140l-9 7H95l7-8c28.7-32 52-65.7 70-101\n 10.7-23.333 16-35.7 16-37 0-.7-7.7-1-23-1h-22C115.7 71.3 68 127 0 167z", + twoheadrightarrow: "M400000 167\nc-68-40-115.7-95.7-143-167h-22c-15.3 0-23 .3-23 1 0 1.3 5.3 13.7 16 37 18 35.3\n 41.3 69 70 101l7 8h-125l-9-7c-50.7-39.3-85-86-103-140h-46c0 4.7 6.3 18.7 19 42\n 18 35.3 40 67.3 66 96l9 9H0v40h399716l-9 9c-26 28.7-48 60.7-66 96-12.7 23.333\n-19 37.333-19 42h46c18-54 52.3-100.7 103-140l9-7h125l-7 8c-28.7 32-52 65.7-70\n 101-10.7 23.333-16 35.7-16 37 0 .7 7.7 1 23 1h22c27.3-71.3 75-127 143-167z", + // tilde1 is a modified version of a glyph from the MnSymbol package + tilde1: "M200 55.538c-77 0-168 73.953-177 73.953-3 0-7\n-2.175-9-5.437L2 97c-1-2-2-4-2-6 0-4 2-7 5-9l20-12C116 12 171 0 207 0c86 0\n 114 68 191 68 78 0 168-68 177-68 4 0 7 2 9 5l12 19c1 2.175 2 4.35 2 6.525 0\n 4.35-2 7.613-5 9.788l-19 13.05c-92 63.077-116.937 75.308-183 76.128\n-68.267.847-113-73.952-191-73.952z", + // ditto tilde2, tilde3, & tilde4 + tilde2: "M344 55.266c-142 0-300.638 81.316-311.5 86.418\n-8.01 3.762-22.5 10.91-23.5 5.562L1 120c-1-2-1-3-1-4 0-5 3-9 8-10l18.4-9C160.9\n 31.9 283 0 358 0c148 0 188 122 331 122s314-97 326-97c4 0 8 2 10 7l7 21.114\nc1 2.14 1 3.21 1 4.28 0 5.347-3 9.626-7 10.696l-22.3 12.622C852.6 158.372 751\n 181.476 676 181.476c-149 0-189-126.21-332-126.21z", + tilde3: "M786 59C457 59 32 175.242 13 175.242c-6 0-10-3.457\n-11-10.37L.15 138c-1-7 3-12 10-13l19.2-6.4C378.4 40.7 634.3 0 804.3 0c337 0\n 411.8 157 746.8 157 328 0 754-112 773-112 5 0 10 3 11 9l1 14.075c1 8.066-.697\n 16.595-6.697 17.492l-21.052 7.31c-367.9 98.146-609.15 122.696-778.15 122.696\n -338 0-409-156.573-744-156.573z", + tilde4: "M786 58C457 58 32 177.487 13 177.487c-6 0-10-3.345\n-11-10.035L.15 143c-1-7 3-12 10-13l22-6.7C381.2 35 637.15 0 807.15 0c337 0 409\n 177 744 177 328 0 754-127 773-127 5 0 10 3 11 9l1 14.794c1 7.805-3 13.38-9\n 14.495l-20.7 5.574c-366.85 99.79-607.3 139.372-776.3 139.372-338 0-409\n -175.236-744-175.236z", + // vec is from glyph U+20D7 in font KaTeX Main + vec: "M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z", + // widehat1 is a modified version of a glyph from the MnSymbol package + widehat1: "M529 0h5l519 115c5 1 9 5 9 10 0 1-1 2-1 3l-4 22\nc-1 5-5 9-11 9h-2L532 67 19 159h-2c-5 0-9-4-11-9l-5-22c-1-6 2-12 8-13z", + // ditto widehat2, widehat3, & widehat4 + widehat2: "M1181 0h2l1171 176c6 0 10 5 10 11l-2 23c-1 6-5 10\n-11 10h-1L1182 67 15 220h-1c-6 0-10-4-11-10l-2-23c-1-6 4-11 10-11z", + widehat3: "M1181 0h2l1171 236c6 0 10 5 10 11l-2 23c-1 6-5 10\n-11 10h-1L1182 67 15 280h-1c-6 0-10-4-11-10l-2-23c-1-6 4-11 10-11z", + widehat4: "M1181 0h2l1171 296c6 0 10 5 10 11l-2 23c-1 6-5 10\n-11 10h-1L1182 67 15 340h-1c-6 0-10-4-11-10l-2-23c-1-6 4-11 10-11z", + // widecheck paths are all inverted versions of widehat + widecheck1: "M529,159h5l519,-115c5,-1,9,-5,9,-10c0,-1,-1,-2,-1,-3l-4,-22c-1,\n-5,-5,-9,-11,-9h-2l-512,92l-513,-92h-2c-5,0,-9,4,-11,9l-5,22c-1,6,2,12,8,13z", + widecheck2: "M1181,220h2l1171,-176c6,0,10,-5,10,-11l-2,-23c-1,-6,-5,-10,\n-11,-10h-1l-1168,153l-1167,-153h-1c-6,0,-10,4,-11,10l-2,23c-1,6,4,11,10,11z", + widecheck3: "M1181,280h2l1171,-236c6,0,10,-5,10,-11l-2,-23c-1,-6,-5,-10,\n-11,-10h-1l-1168,213l-1167,-213h-1c-6,0,-10,4,-11,10l-2,23c-1,6,4,11,10,11z", + widecheck4: "M1181,340h2l1171,-296c6,0,10,-5,10,-11l-2,-23c-1,-6,-5,-10,\n-11,-10h-1l-1168,273l-1167,-273h-1c-6,0,-10,4,-11,10l-2,23c-1,6,4,11,10,11z", + // The next ten paths support reaction arrows from the mhchem package. + // Arrows for \ce{<-->} are offset from xAxis by 0.22ex, per mhchem in LaTeX + // baraboveleftarrow is mostly from from glyph U+2190 in font KaTeX Main + baraboveleftarrow: "M400000 620h-399890l3 -3c68.7 -52.7 113.7 -120 135 -202\nc4 -14.7 6 -23 6 -25c0 -7.3 -7 -11 -21 -11c-8 0 -13.2 0.8 -15.5 2.5\nc-2.3 1.7 -4.2 5.8 -5.5 12.5c-1.3 4.7 -2.7 10.3 -4 17c-12 48.7 -34.8 92 -68.5 130\ns-74.2 66.3 -121.5 85c-10 4 -16 7.7 -18 11c0 8.7 6 14.3 18 17c47.3 18.7 87.8 47\n121.5 85s56.5 81.3 68.5 130c0.7 2 1.3 5 2 9s1.2 6.7 1.5 8c0.3 1.3 1 3.3 2 6\ns2.2 4.5 3.5 5.5c1.3 1 3.3 1.8 6 2.5s6 1 10 1c14 0 21 -3.7 21 -11\nc0 -2 -2 -10.3 -6 -25c-20 -79.3 -65 -146.7 -135 -202l-3 -3h399890z\nM100 620v40h399900v-40z M0 241v40h399900v-40zM0 241v40h399900v-40z", + // rightarrowabovebar is mostly from glyph U+2192, KaTeX Main + rightarrowabovebar: "M0 241v40h399891c-47.3 35.3-84 78-110 128-16.7 32\n-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0\n13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39\n-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5\n-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n151.7 139 205zm96 379h399894v40H0zm0 0h399904v40H0z", + // The short left harpoon has 0.5em (i.e. 500 units) kern on the left end. + // Ref from mhchem.sty: \rlap{\raisebox{-.22ex}{$\kern0.5em + baraboveshortleftharpoon: "M507,435c-4,4,-6.3,8.7,-7,14c0,5.3,0.7,9,2,11\nc1.3,2,5.3,5.3,12,10c90.7,54,156,130,196,228c3.3,10.7,6.3,16.3,9,17\nc2,0.7,5,1,9,1c0,0,5,0,5,0c10.7,0,16.7,-2,18,-6c2,-2.7,1,-9.7,-3,-21\nc-32,-87.3,-82.7,-157.7,-152,-211c0,0,-3,-3,-3,-3l399351,0l0,-40\nc-398570,0,-399437,0,-399437,0z M593 435 v40 H399500 v-40z\nM0 281 v-40 H399908 v40z M0 281 v-40 H399908 v40z", + rightharpoonaboveshortbar: "M0,241 l0,40c399126,0,399993,0,399993,0\nc4.7,-4.7,7,-9.3,7,-14c0,-9.3,-3.7,-15.3,-11,-18c-92.7,-56.7,-159,-133.7,-199,\n-231c-3.3,-9.3,-6,-14.7,-8,-16c-2,-1.3,-7,-2,-15,-2c-10.7,0,-16.7,2,-18,6\nc-2,2.7,-1,9.7,3,21c15.3,42,36.7,81.8,64,119.5c27.3,37.7,58,69.2,92,94.5z\nM0 241 v40 H399908 v-40z M0 475 v-40 H399500 v40z M0 475 v-40 H399500 v40z", + shortbaraboveleftharpoon: "M7,435c-4,4,-6.3,8.7,-7,14c0,5.3,0.7,9,2,11\nc1.3,2,5.3,5.3,12,10c90.7,54,156,130,196,228c3.3,10.7,6.3,16.3,9,17c2,0.7,5,1,9,\n1c0,0,5,0,5,0c10.7,0,16.7,-2,18,-6c2,-2.7,1,-9.7,-3,-21c-32,-87.3,-82.7,-157.7,\n-152,-211c0,0,-3,-3,-3,-3l399907,0l0,-40c-399126,0,-399993,0,-399993,0z\nM93 435 v40 H400000 v-40z M500 241 v40 H400000 v-40z M500 241 v40 H400000 v-40z", + shortrightharpoonabovebar: "M53,241l0,40c398570,0,399437,0,399437,0\nc4.7,-4.7,7,-9.3,7,-14c0,-9.3,-3.7,-15.3,-11,-18c-92.7,-56.7,-159,-133.7,-199,\n-231c-3.3,-9.3,-6,-14.7,-8,-16c-2,-1.3,-7,-2,-15,-2c-10.7,0,-16.7,2,-18,6\nc-2,2.7,-1,9.7,3,21c15.3,42,36.7,81.8,64,119.5c27.3,37.7,58,69.2,92,94.5z\nM500 241 v40 H399408 v-40z M500 435 v40 H400000 v-40z" +}; + +/** + * This node represents a document fragment, which contains elements, but when + * placed into the DOM doesn't have any representation itself. It only contains + * children and doesn't have any DOM node properties. + */ +class DocumentFragment { + // HtmlDomNode + // Never used; needed for satisfying interface. + constructor(children) { + this.children = void 0; + this.classes = void 0; + this.height = void 0; + this.depth = void 0; + this.maxFontSize = void 0; + this.style = void 0; + this.children = children; + this.classes = []; + this.height = 0; + this.depth = 0; + this.maxFontSize = 0; + this.style = {}; + } + + hasClass(className) { + return utils.contains(this.classes, className); + } + /** Convert the fragment into a node. */ + + + toNode() { + var frag = document.createDocumentFragment(); + + for (var i = 0; i < this.children.length; i++) { + frag.appendChild(this.children[i].toNode()); + } + + return frag; + } + /** Convert the fragment into HTML markup. */ + + + toMarkup() { + var markup = ""; // Simply concatenate the markup for the children together. + + for (var i = 0; i < this.children.length; i++) { + markup += this.children[i].toMarkup(); + } + + return markup; + } + /** + * Converts the math node into a string, similar to innerText. Applies to + * MathDomNode's only. + */ + + + toText() { + // To avoid this, we would subclass documentFragment separately for + // MathML, but polyfills for subclassing is expensive per PR 1469. + // $FlowFixMe: Only works for ChildType = MathDomNode. + var toText = child => child.toText(); + + return this.children.map(toText).join(""); + } + +} + +/** + * These objects store the data about the DOM nodes we create, as well as some + * extra data. They can then be transformed into real DOM nodes with the + * `toNode` function or HTML markup using `toMarkup`. They are useful for both + * storing extra properties on the nodes, as well as providing a way to easily + * work with the DOM. + * + * Similar functions for working with MathML nodes exist in mathMLTree.js. + * + * TODO: refactor `span` and `anchor` into common superclass when + * target environments support class inheritance + */ + +/** + * Create an HTML className based on a list of classes. In addition to joining + * with spaces, we also remove empty classes. + */ +var createClass = function createClass(classes) { + return classes.filter(cls => cls).join(" "); +}; + +var initNode = function initNode(classes, options, style) { + this.classes = classes || []; + this.attributes = {}; + this.height = 0; + this.depth = 0; + this.maxFontSize = 0; + this.style = style || {}; + + if (options) { + if (options.style.isTight()) { + this.classes.push("mtight"); + } + + var color = options.getColor(); + + if (color) { + this.style.color = color; + } + } +}; +/** + * Convert into an HTML node + */ + + +var toNode = function toNode(tagName) { + var node = document.createElement(tagName); // Apply the class + + node.className = createClass(this.classes); // Apply inline styles + + for (var style in this.style) { + if (this.style.hasOwnProperty(style)) { + // $FlowFixMe Flow doesn't seem to understand span.style's type. + node.style[style] = this.style[style]; + } + } // Apply attributes + + + for (var attr in this.attributes) { + if (this.attributes.hasOwnProperty(attr)) { + node.setAttribute(attr, this.attributes[attr]); + } + } // Append the children, also as HTML nodes + + + for (var i = 0; i < this.children.length; i++) { + node.appendChild(this.children[i].toNode()); + } + + return node; +}; +/** + * Convert into an HTML markup string + */ + + +var toMarkup = function toMarkup(tagName) { + var markup = "<" + tagName; // Add the class + + if (this.classes.length) { + markup += " class=\"" + utils.escape(createClass(this.classes)) + "\""; + } + + var styles = ""; // Add the styles, after hyphenation + + for (var style in this.style) { + if (this.style.hasOwnProperty(style)) { + styles += utils.hyphenate(style) + ":" + this.style[style] + ";"; + } + } + + if (styles) { + markup += " style=\"" + utils.escape(styles) + "\""; + } // Add the attributes + + + for (var attr in this.attributes) { + if (this.attributes.hasOwnProperty(attr)) { + markup += " " + attr + "=\"" + utils.escape(this.attributes[attr]) + "\""; + } + } + + markup += ">"; // Add the markup of the children, also as markup + + for (var i = 0; i < this.children.length; i++) { + markup += this.children[i].toMarkup(); + } + + markup += ""; + return markup; +}; // Making the type below exact with all optional fields doesn't work due to +// - https://github.com/facebook/flow/issues/4582 +// - https://github.com/facebook/flow/issues/5688 +// However, since *all* fields are optional, $Shape<> works as suggested in 5688 +// above. +// This type does not include all CSS properties. Additional properties should +// be added as needed. + + +/** + * This node represents a span node, with a className, a list of children, and + * an inline style. It also contains information about its height, depth, and + * maxFontSize. + * + * Represents two types with different uses: SvgSpan to wrap an SVG and DomSpan + * otherwise. This typesafety is important when HTML builders access a span's + * children. + */ +class Span { + constructor(classes, children, options, style) { + this.children = void 0; + this.attributes = void 0; + this.classes = void 0; + this.height = void 0; + this.depth = void 0; + this.width = void 0; + this.maxFontSize = void 0; + this.style = void 0; + initNode.call(this, classes, options, style); + this.children = children || []; + } + /** + * Sets an arbitrary attribute on the span. Warning: use this wisely. Not + * all browsers support attributes the same, and having too many custom + * attributes is probably bad. + */ + + + setAttribute(attribute, value) { + this.attributes[attribute] = value; + } + + hasClass(className) { + return utils.contains(this.classes, className); + } + + toNode() { + return toNode.call(this, "span"); + } + + toMarkup() { + return toMarkup.call(this, "span"); + } + +} +/** + * This node represents an anchor () element with a hyperlink. See `span` + * for further details. + */ + +class Anchor { + constructor(href, classes, children, options) { + this.children = void 0; + this.attributes = void 0; + this.classes = void 0; + this.height = void 0; + this.depth = void 0; + this.maxFontSize = void 0; + this.style = void 0; + initNode.call(this, classes, options); + this.children = children || []; + this.setAttribute('href', href); + } + + setAttribute(attribute, value) { + this.attributes[attribute] = value; + } + + hasClass(className) { + return utils.contains(this.classes, className); + } + + toNode() { + return toNode.call(this, "a"); + } + + toMarkup() { + return toMarkup.call(this, "a"); + } + +} +/** + * This node represents an image embed () element. + */ + +class Img { + constructor(src, alt, style) { + this.src = void 0; + this.alt = void 0; + this.classes = void 0; + this.height = void 0; + this.depth = void 0; + this.maxFontSize = void 0; + this.style = void 0; + this.alt = alt; + this.src = src; + this.classes = ["mord"]; + this.style = style; + } + + hasClass(className) { + return utils.contains(this.classes, className); + } + + toNode() { + var node = document.createElement("img"); + node.src = this.src; + node.alt = this.alt; + node.className = "mord"; // Apply inline styles + + for (var style in this.style) { + if (this.style.hasOwnProperty(style)) { + // $FlowFixMe + node.style[style] = this.style[style]; + } + } + + return node; + } + + toMarkup() { + var markup = "" + this.alt + " 0) { + span = document.createElement("span"); + span.style.marginRight = this.italic + "em"; + } + + if (this.classes.length > 0) { + span = span || document.createElement("span"); + span.className = createClass(this.classes); + } + + for (var style in this.style) { + if (this.style.hasOwnProperty(style)) { + span = span || document.createElement("span"); // $FlowFixMe Flow doesn't seem to understand span.style's type. + + span.style[style] = this.style[style]; + } + } + + if (span) { + span.appendChild(node); + return span; + } else { + return node; + } + } + /** + * Creates markup for a symbol node. + */ + + + toMarkup() { + // TODO(alpert): More duplication than I'd like from + // span.prototype.toMarkup and symbolNode.prototype.toNode... + var needsSpan = false; + var markup = " 0) { + styles += "margin-right:" + this.italic + "em;"; + } + + for (var style in this.style) { + if (this.style.hasOwnProperty(style)) { + styles += utils.hyphenate(style) + ":" + this.style[style] + ";"; + } + } + + if (styles) { + needsSpan = true; + markup += " style=\"" + utils.escape(styles) + "\""; + } + + var escaped = utils.escape(this.text); + + if (needsSpan) { + markup += ">"; + markup += escaped; + markup += ""; + return markup; + } else { + return escaped; + } + } + +} +/** + * SVG nodes are used to render stretchy wide elements. + */ + +class SvgNode { + constructor(children, attributes) { + this.children = void 0; + this.attributes = void 0; + this.children = children || []; + this.attributes = attributes || {}; + } + + toNode() { + var svgNS = "http://www.w3.org/2000/svg"; + var node = document.createElementNS(svgNS, "svg"); // Apply attributes + + for (var attr in this.attributes) { + if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) { + node.setAttribute(attr, this.attributes[attr]); + } + } + + for (var i = 0; i < this.children.length; i++) { + node.appendChild(this.children[i].toNode()); + } + + return node; + } + + toMarkup() { + var markup = ""; + } else { + return ""; + } + } + +} +class LineNode { + constructor(attributes) { + this.attributes = void 0; + this.attributes = attributes || {}; + } + + toNode() { + var svgNS = "http://www.w3.org/2000/svg"; + var node = document.createElementNS(svgNS, "line"); // Apply attributes + + for (var attr in this.attributes) { + if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) { + node.setAttribute(attr, this.attributes[attr]); + } + } + + return node; + } + + toMarkup() { + var markup = " but got " + String(group) + "."); + } +} + +// This file is GENERATED by buildMetrics.sh. 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0, 0, 0.45], + "57683": [0, 0.12, 0, 0, 0.45] + }, + "Typewriter-Regular": { + "32": [0, 0, 0, 0, 0.525], + "33": [0, 0.61111, 0, 0, 0.525], + "34": [0, 0.61111, 0, 0, 0.525], + "35": [0, 0.61111, 0, 0, 0.525], + "36": [0.08333, 0.69444, 0, 0, 0.525], + "37": [0.08333, 0.69444, 0, 0, 0.525], + "38": [0, 0.61111, 0, 0, 0.525], + "39": [0, 0.61111, 0, 0, 0.525], + "40": [0.08333, 0.69444, 0, 0, 0.525], + "41": [0.08333, 0.69444, 0, 0, 0.525], + "42": [0, 0.52083, 0, 0, 0.525], + "43": [-0.08056, 0.53055, 0, 0, 0.525], + "44": [0.13889, 0.125, 0, 0, 0.525], + "45": [-0.08056, 0.53055, 0, 0, 0.525], + "46": [0, 0.125, 0, 0, 0.525], + "47": [0.08333, 0.69444, 0, 0, 0.525], + "48": [0, 0.61111, 0, 0, 0.525], + "49": [0, 0.61111, 0, 0, 0.525], + "50": [0, 0.61111, 0, 0, 0.525], + "51": [0, 0.61111, 0, 0, 0.525], + "52": [0, 0.61111, 0, 0, 0.525], + "53": [0, 0.61111, 0, 0, 0.525], + "54": [0, 0.61111, 0, 0, 0.525], + "55": [0, 0.61111, 0, 0, 0.525], + "56": [0, 0.61111, 0, 0, 0.525], + "57": 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0.525], + "770": [0, 0.61111, 0, 0, 0.525], + "771": [0, 0.61111, 0, 0, 0.525], + "776": [0, 0.61111, 0, 0, 0.525], + "915": [0, 0.61111, 0, 0, 0.525], + "916": [0, 0.61111, 0, 0, 0.525], + "920": [0, 0.61111, 0, 0, 0.525], + "923": [0, 0.61111, 0, 0, 0.525], + "926": [0, 0.61111, 0, 0, 0.525], + "928": [0, 0.61111, 0, 0, 0.525], + "931": [0, 0.61111, 0, 0, 0.525], + "933": [0, 0.61111, 0, 0, 0.525], + "934": [0, 0.61111, 0, 0, 0.525], + "936": [0, 0.61111, 0, 0, 0.525], + "937": [0, 0.61111, 0, 0, 0.525], + "8216": [0, 0.61111, 0, 0, 0.525], + "8217": [0, 0.61111, 0, 0, 0.525], + "8242": [0, 0.61111, 0, 0, 0.525], + "9251": [0.11111, 0.21944, 0, 0, 0.525] + } +}; + +/** + * This file contains metrics regarding fonts and individual symbols. The sigma + * and xi variables, as well as the metricMap map contain data extracted from + * TeX, TeX font metrics, and the TTF files. These data are then exposed via the + * `metrics` variable and the getCharacterMetrics function. + */ +// In TeX, there are actually three sets of dimensions, one for each of +// textstyle (size index 5 and higher: >=9pt), scriptstyle (size index 3 and 4: +// 7-8pt), and scriptscriptstyle (size index 1 and 2: 5-6pt). These are +// provided in the the arrays below, in that order. +// +// The font metrics are stored in fonts cmsy10, cmsy7, and cmsy5 respsectively. +// This was determined by running the following script: +// +// latex -interaction=nonstopmode \ +// '\documentclass{article}\usepackage{amsmath}\begin{document}' \ +// '$a$ \expandafter\show\the\textfont2' \ +// '\expandafter\show\the\scriptfont2' \ +// '\expandafter\show\the\scriptscriptfont2' \ +// '\stop' +// +// The metrics themselves were retreived using the following commands: +// +// tftopl cmsy10 +// tftopl cmsy7 +// tftopl cmsy5 +// +// The output of each of these commands is quite lengthy. The only part we +// care about is the FONTDIMEN section. Each value is measured in EMs. +var sigmasAndXis = { + slant: [0.250, 0.250, 0.250], + // sigma1 + space: [0.000, 0.000, 0.000], + // sigma2 + stretch: [0.000, 0.000, 0.000], + // sigma3 + shrink: [0.000, 0.000, 0.000], + // sigma4 + xHeight: [0.431, 0.431, 0.431], + // sigma5 + quad: [1.000, 1.171, 1.472], + // sigma6 + extraSpace: [0.000, 0.000, 0.000], + // sigma7 + num1: [0.677, 0.732, 0.925], + // sigma8 + num2: [0.394, 0.384, 0.387], + // sigma9 + num3: [0.444, 0.471, 0.504], + // sigma10 + denom1: [0.686, 0.752, 1.025], + // sigma11 + denom2: [0.345, 0.344, 0.532], + // sigma12 + sup1: [0.413, 0.503, 0.504], + // sigma13 + sup2: [0.363, 0.431, 0.404], + // sigma14 + sup3: [0.289, 0.286, 0.294], + // sigma15 + sub1: [0.150, 0.143, 0.200], + // sigma16 + sub2: [0.247, 0.286, 0.400], + // sigma17 + supDrop: [0.386, 0.353, 0.494], + // sigma18 + subDrop: [0.050, 0.071, 0.100], + // sigma19 + delim1: [2.390, 1.700, 1.980], + // sigma20 + delim2: [1.010, 1.157, 1.420], + // sigma21 + axisHeight: [0.250, 0.250, 0.250], + // sigma22 + // These font metrics are extracted from TeX by using tftopl on cmex10.tfm; + // they correspond to the font parameters of the extension fonts (family 3). + // See the TeXbook, page 441. In AMSTeX, the extension fonts scale; to + // match cmex7, we'd use cmex7.tfm values for script and scriptscript + // values. + defaultRuleThickness: [0.04, 0.049, 0.049], + // xi8; cmex7: 0.049 + bigOpSpacing1: [0.111, 0.111, 0.111], + // xi9 + bigOpSpacing2: [0.166, 0.166, 0.166], + // xi10 + bigOpSpacing3: [0.2, 0.2, 0.2], + // xi11 + bigOpSpacing4: [0.6, 0.611, 0.611], + // xi12; cmex7: 0.611 + bigOpSpacing5: [0.1, 0.143, 0.143], + // xi13; cmex7: 0.143 + // The \sqrt rule width is taken from the height of the surd character. + // Since we use the same font at all sizes, this thickness doesn't scale. + sqrtRuleThickness: [0.04, 0.04, 0.04], + // This value determines how large a pt is, for metrics which are defined + // in terms of pts. + // This value is also used in katex.less; if you change it make sure the + // values match. + ptPerEm: [10.0, 10.0, 10.0], + // The space between adjacent `|` columns in an array definition. From + // `\showthe\doublerulesep` in LaTeX. Equals 2.0 / ptPerEm. + doubleRuleSep: [0.2, 0.2, 0.2], + // The width of separator lines in {array} environments. From + // `\showthe\arrayrulewidth` in LaTeX. Equals 0.4 / ptPerEm. + arrayRuleWidth: [0.04, 0.04, 0.04], + // Two values from LaTeX source2e: + fboxsep: [0.3, 0.3, 0.3], + // 3 pt / ptPerEm + fboxrule: [0.04, 0.04, 0.04] // 0.4 pt / ptPerEm + +}; // This map contains a mapping from font name and character code to character +// should have Latin-1 and Cyrillic characters, but may not depending on the +// operating system. The metrics do not account for extra height from the +// accents. In the case of Cyrillic characters which have both ascenders and +// descenders we prefer approximations with ascenders, primarily to prevent +// the fraction bar or root line from intersecting the glyph. +// TODO(kevinb) allow union of multiple glyph metrics for better accuracy. + +var extraCharacterMap = { + // Latin-1 + 'Å': 'A', + 'Ð': 'D', + 'Þ': 'o', + 'å': 'a', + 'ð': 'd', + 'þ': 'o', + // Cyrillic + 'А': 'A', + 'Б': 'B', + 'В': 'B', + 'Г': 'F', + 'Д': 'A', + 'Е': 'E', + 'Ж': 'K', + 'З': '3', + 'И': 'N', + 'Й': 'N', + 'К': 'K', + 'Л': 'N', + 'М': 'M', + 'Н': 'H', + 'О': 'O', + 'П': 'N', + 'Р': 'P', + 'С': 'C', + 'Т': 'T', + 'У': 'y', + 'Ф': 'O', + 'Х': 'X', + 'Ц': 'U', + 'Ч': 'h', + 'Ш': 'W', + 'Щ': 'W', + 'Ъ': 'B', + 'Ы': 'X', + 'Ь': 'B', + 'Э': '3', + 'Ю': 'X', + 'Я': 'R', + 'а': 'a', + 'б': 'b', + 'в': 'a', + 'г': 'r', + 'д': 'y', + 'е': 'e', + 'ж': 'm', + 'з': 'e', + 'и': 'n', + 'й': 'n', + 'к': 'n', + 'л': 'n', + 'м': 'm', + 'н': 'n', + 'о': 'o', + 'п': 'n', + 'р': 'p', + 'с': 'c', + 'т': 'o', + 'у': 'y', + 'ф': 'b', + 'х': 'x', + 'ц': 'n', + 'ч': 'n', + 'ш': 'w', + 'щ': 'w', + 'ъ': 'a', + 'ы': 'm', + 'ь': 'a', + 'э': 'e', + 'ю': 'm', + 'я': 'r' +}; + +/** + * This function adds new font metrics to default metricMap + * It can also override existing metrics + */ +function setFontMetrics(fontName, metrics) { + fontMetricsData[fontName] = metrics; +} +/** + * This function is a convenience function for looking up information in the + * metricMap table. It takes a character as a string, and a font. + * + * Note: the `width` property may be undefined if fontMetricsData.js wasn't + * built using `Make extended_metrics`. + */ + +function getCharacterMetrics(character, font, mode) { + if (!fontMetricsData[font]) { + throw new Error("Font metrics not found for font: " + font + "."); + } + + var ch = character.charCodeAt(0); + var metrics = fontMetricsData[font][ch]; + + if (!metrics && character[0] in extraCharacterMap) { + ch = extraCharacterMap[character[0]].charCodeAt(0); + metrics = fontMetricsData[font][ch]; + } + + if (!metrics && mode === 'text') { + // We don't typically have font metrics for Asian scripts. + // But since we support them in text mode, we need to return + // some sort of metrics. + // So if the character is in a script we support but we + // don't have metrics for it, just use the metrics for + // the Latin capital letter M. This is close enough because + // we (currently) only care about the height of the glpyh + // not its width. + if (supportedCodepoint(ch)) { + metrics = fontMetricsData[font][77]; // 77 is the charcode for 'M' + } + } + + if (metrics) { + return { + depth: metrics[0], + height: metrics[1], + italic: metrics[2], + skew: metrics[3], + width: metrics[4] + }; + } +} +var fontMetricsBySizeIndex = {}; +/** + * Get the font metrics for a given size. + */ + +function getGlobalMetrics(size) { + var sizeIndex; + + if (size >= 5) { + sizeIndex = 0; + } else if (size >= 3) { + sizeIndex = 1; + } else { + sizeIndex = 2; + } + + if (!fontMetricsBySizeIndex[sizeIndex]) { + var metrics = fontMetricsBySizeIndex[sizeIndex] = { + cssEmPerMu: sigmasAndXis.quad[sizeIndex] / 18 + }; + + for (var key in sigmasAndXis) { + if (sigmasAndXis.hasOwnProperty(key)) { + metrics[key] = sigmasAndXis[key][sizeIndex]; + } + } + } + + return fontMetricsBySizeIndex[sizeIndex]; +} + +/** + * This file holds a list of all no-argument functions and single-character + * symbols (like 'a' or ';'). + * + * For each of the symbols, there are three properties they can have: + * - font (required): the font to be used for this symbol. Either "main" (the + normal font), or "ams" (the ams fonts). + * - group (required): the ParseNode group type the symbol should have (i.e. + "textord", "mathord", etc). + See https://github.com/KaTeX/KaTeX/wiki/Examining-TeX#group-types + * - replace: the character that this symbol or function should be + * replaced with (i.e. "\phi" has a replace value of "\u03d5", the phi + * character in the main font). + * + * The outermost map in the table indicates what mode the symbols should be + * accepted in (e.g. "math" or "text"). + */ +// Some of these have a "-token" suffix since these are also used as `ParseNode` +// types for raw text tokens, and we want to avoid conflicts with higher-level +// `ParseNode` types. These `ParseNode`s are constructed within `Parser` by +// looking up the `symbols` map. +var ATOMS = { + "bin": 1, + "close": 1, + "inner": 1, + "open": 1, + "punct": 1, + "rel": 1 +}; +var NON_ATOMS = { + "accent-token": 1, + "mathord": 1, + "op-token": 1, + "spacing": 1, + "textord": 1 +}; +var symbols = { + "math": {}, + "text": {} +}; +/** `acceptUnicodeChar = true` is only applicable if `replace` is set. */ + +function defineSymbol(mode, font, group, replace, name, acceptUnicodeChar) { + symbols[mode][name] = { + font, + group, + replace + }; + + if (acceptUnicodeChar && replace) { + symbols[mode][replace] = symbols[mode][name]; + } +} // Some abbreviations for commonly used strings. +// This helps minify the code, and also spotting typos using jshint. +// modes: + +var math = "math"; +var text = "text"; // fonts: + +var main = "main"; +var ams = "ams"; // groups: + +var accent = "accent-token"; +var bin = "bin"; +var close = "close"; +var inner = "inner"; +var mathord = "mathord"; +var op = "op-token"; +var open = "open"; +var punct = "punct"; +var rel = "rel"; +var spacing = "spacing"; +var textord = "textord"; // Now comes the symbol table +// Relation Symbols + +defineSymbol(math, main, rel, "\u2261", "\\equiv", true); +defineSymbol(math, main, rel, "\u227a", "\\prec", true); +defineSymbol(math, main, rel, "\u227b", "\\succ", true); +defineSymbol(math, main, rel, "\u223c", "\\sim", true); +defineSymbol(math, main, rel, "\u22a5", "\\perp"); +defineSymbol(math, main, rel, "\u2aaf", "\\preceq", true); +defineSymbol(math, main, rel, "\u2ab0", "\\succeq", true); +defineSymbol(math, main, rel, "\u2243", "\\simeq", true); +defineSymbol(math, main, rel, "\u2223", "\\mid", true); +defineSymbol(math, main, rel, "\u226a", "\\ll", true); +defineSymbol(math, main, rel, "\u226b", "\\gg", true); +defineSymbol(math, main, rel, "\u224d", "\\asymp", true); +defineSymbol(math, main, rel, "\u2225", "\\parallel"); +defineSymbol(math, main, rel, "\u22c8", "\\bowtie", true); +defineSymbol(math, main, rel, "\u2323", "\\smile", true); +defineSymbol(math, main, rel, "\u2291", "\\sqsubseteq", true); +defineSymbol(math, main, rel, "\u2292", "\\sqsupseteq", true); +defineSymbol(math, main, rel, "\u2250", "\\doteq", true); +defineSymbol(math, main, rel, "\u2322", "\\frown", true); +defineSymbol(math, main, rel, "\u220b", "\\ni", true); +defineSymbol(math, main, rel, "\u221d", "\\propto", true); +defineSymbol(math, main, rel, "\u22a2", "\\vdash", true); +defineSymbol(math, main, rel, "\u22a3", "\\dashv", true); +defineSymbol(math, main, rel, "\u220b", "\\owns"); // Punctuation + +defineSymbol(math, main, punct, "\u002e", "\\ldotp"); +defineSymbol(math, main, punct, "\u22c5", "\\cdotp"); // Misc Symbols + +defineSymbol(math, main, textord, "\u0023", "\\#"); +defineSymbol(text, main, textord, "\u0023", "\\#"); +defineSymbol(math, main, textord, "\u0026", "\\&"); +defineSymbol(text, main, textord, "\u0026", "\\&"); +defineSymbol(math, main, textord, "\u2135", "\\aleph", true); +defineSymbol(math, main, textord, "\u2200", "\\forall", true); +defineSymbol(math, main, textord, "\u210f", "\\hbar", true); +defineSymbol(math, main, textord, "\u2203", "\\exists", true); +defineSymbol(math, main, textord, "\u2207", "\\nabla", true); +defineSymbol(math, main, textord, "\u266d", "\\flat", true); +defineSymbol(math, main, textord, "\u2113", "\\ell", true); +defineSymbol(math, main, textord, "\u266e", "\\natural", true); +defineSymbol(math, main, textord, "\u2663", "\\clubsuit", true); +defineSymbol(math, main, textord, "\u2118", "\\wp", true); +defineSymbol(math, main, textord, "\u266f", "\\sharp", true); +defineSymbol(math, main, textord, "\u2662", "\\diamondsuit", true); +defineSymbol(math, main, textord, "\u211c", "\\Re", true); +defineSymbol(math, main, textord, "\u2661", "\\heartsuit", true); +defineSymbol(math, main, textord, "\u2111", "\\Im", true); +defineSymbol(math, main, textord, "\u2660", "\\spadesuit", true); +defineSymbol(math, main, textord, "\u00a7", "\\S", true); +defineSymbol(text, main, textord, "\u00a7", "\\S"); +defineSymbol(math, main, textord, "\u00b6", "\\P", true); +defineSymbol(text, main, textord, "\u00b6", "\\P"); // Math and Text + +defineSymbol(math, main, textord, "\u2020", "\\dag"); +defineSymbol(text, main, textord, "\u2020", "\\dag"); +defineSymbol(text, main, textord, "\u2020", "\\textdagger"); +defineSymbol(math, main, textord, "\u2021", "\\ddag"); +defineSymbol(text, main, textord, "\u2021", "\\ddag"); +defineSymbol(text, main, textord, "\u2021", "\\textdaggerdbl"); // Large Delimiters + +defineSymbol(math, main, close, "\u23b1", "\\rmoustache", true); +defineSymbol(math, main, open, "\u23b0", "\\lmoustache", true); +defineSymbol(math, main, close, "\u27ef", "\\rgroup", true); +defineSymbol(math, main, open, "\u27ee", "\\lgroup", true); // Binary Operators + +defineSymbol(math, main, bin, "\u2213", "\\mp", true); +defineSymbol(math, main, bin, "\u2296", "\\ominus", true); +defineSymbol(math, main, bin, "\u228e", "\\uplus", true); +defineSymbol(math, main, bin, "\u2293", "\\sqcap", true); +defineSymbol(math, main, bin, "\u2217", "\\ast"); +defineSymbol(math, main, bin, "\u2294", "\\sqcup", true); +defineSymbol(math, main, bin, "\u25ef", "\\bigcirc", true); +defineSymbol(math, main, bin, "\u2219", "\\bullet"); +defineSymbol(math, main, bin, "\u2021", "\\ddagger"); +defineSymbol(math, main, bin, "\u2240", "\\wr", true); +defineSymbol(math, main, bin, "\u2a3f", "\\amalg"); +defineSymbol(math, main, bin, "\u0026", "\\And"); // from amsmath +// Arrow Symbols + +defineSymbol(math, main, rel, "\u27f5", "\\longleftarrow", true); +defineSymbol(math, main, rel, "\u21d0", "\\Leftarrow", true); +defineSymbol(math, main, rel, "\u27f8", "\\Longleftarrow", true); +defineSymbol(math, main, rel, "\u27f6", "\\longrightarrow", true); +defineSymbol(math, main, rel, "\u21d2", "\\Rightarrow", true); +defineSymbol(math, main, rel, "\u27f9", "\\Longrightarrow", true); +defineSymbol(math, main, rel, "\u2194", "\\leftrightarrow", true); +defineSymbol(math, main, rel, "\u27f7", "\\longleftrightarrow", true); +defineSymbol(math, main, rel, "\u21d4", "\\Leftrightarrow", true); +defineSymbol(math, main, rel, "\u27fa", "\\Longleftrightarrow", true); +defineSymbol(math, main, rel, "\u21a6", "\\mapsto", true); +defineSymbol(math, main, rel, "\u27fc", "\\longmapsto", true); +defineSymbol(math, main, rel, "\u2197", "\\nearrow", true); +defineSymbol(math, main, rel, "\u21a9", "\\hookleftarrow", true); +defineSymbol(math, main, rel, "\u21aa", "\\hookrightarrow", true); +defineSymbol(math, main, rel, "\u2198", "\\searrow", true); +defineSymbol(math, main, rel, "\u21bc", "\\leftharpoonup", true); +defineSymbol(math, main, rel, "\u21c0", "\\rightharpoonup", true); +defineSymbol(math, main, rel, "\u2199", "\\swarrow", true); +defineSymbol(math, main, rel, "\u21bd", "\\leftharpoondown", true); +defineSymbol(math, main, rel, "\u21c1", "\\rightharpoondown", true); +defineSymbol(math, main, rel, "\u2196", "\\nwarrow", true); +defineSymbol(math, main, rel, "\u21cc", "\\rightleftharpoons", true); // AMS Negated Binary Relations + +defineSymbol(math, ams, rel, "\u226e", "\\nless", true); // Symbol names preceeded by "@" each have a corresponding macro. + +defineSymbol(math, ams, rel, "\ue010", "\\@nleqslant"); +defineSymbol(math, ams, rel, "\ue011", "\\@nleqq"); +defineSymbol(math, ams, rel, "\u2a87", "\\lneq", true); +defineSymbol(math, ams, rel, "\u2268", "\\lneqq", true); +defineSymbol(math, ams, rel, "\ue00c", "\\@lvertneqq"); +defineSymbol(math, ams, rel, "\u22e6", "\\lnsim", true); +defineSymbol(math, ams, rel, "\u2a89", "\\lnapprox", true); +defineSymbol(math, ams, rel, "\u2280", "\\nprec", true); // unicode-math maps \u22e0 to \npreccurlyeq. We'll use the AMS synonym. + +defineSymbol(math, ams, rel, "\u22e0", "\\npreceq", true); +defineSymbol(math, ams, rel, "\u22e8", "\\precnsim", true); +defineSymbol(math, ams, rel, "\u2ab9", "\\precnapprox", true); +defineSymbol(math, ams, rel, "\u2241", "\\nsim", true); +defineSymbol(math, ams, rel, "\ue006", "\\@nshortmid"); +defineSymbol(math, ams, rel, "\u2224", "\\nmid", true); +defineSymbol(math, ams, rel, "\u22ac", "\\nvdash", true); +defineSymbol(math, ams, rel, "\u22ad", "\\nvDash", true); +defineSymbol(math, ams, rel, "\u22ea", "\\ntriangleleft"); +defineSymbol(math, ams, rel, "\u22ec", "\\ntrianglelefteq", true); +defineSymbol(math, ams, rel, "\u228a", "\\subsetneq", true); +defineSymbol(math, ams, rel, "\ue01a", "\\@varsubsetneq"); +defineSymbol(math, ams, rel, "\u2acb", "\\subsetneqq", true); +defineSymbol(math, ams, rel, "\ue017", "\\@varsubsetneqq"); +defineSymbol(math, ams, rel, "\u226f", "\\ngtr", true); +defineSymbol(math, ams, rel, "\ue00f", "\\@ngeqslant"); +defineSymbol(math, ams, rel, "\ue00e", "\\@ngeqq"); +defineSymbol(math, ams, rel, "\u2a88", "\\gneq", true); +defineSymbol(math, ams, rel, "\u2269", "\\gneqq", true); +defineSymbol(math, ams, rel, "\ue00d", "\\@gvertneqq"); +defineSymbol(math, ams, rel, "\u22e7", "\\gnsim", true); +defineSymbol(math, ams, rel, "\u2a8a", "\\gnapprox", true); +defineSymbol(math, ams, rel, "\u2281", "\\nsucc", true); // unicode-math maps \u22e1 to \nsucccurlyeq. We'll use the AMS synonym. + +defineSymbol(math, ams, rel, "\u22e1", "\\nsucceq", true); +defineSymbol(math, ams, rel, "\u22e9", "\\succnsim", true); +defineSymbol(math, ams, rel, "\u2aba", "\\succnapprox", true); // unicode-math maps \u2246 to \simneqq. We'll use the AMS synonym. + +defineSymbol(math, ams, rel, "\u2246", "\\ncong", true); +defineSymbol(math, ams, rel, "\ue007", "\\@nshortparallel"); +defineSymbol(math, ams, rel, "\u2226", "\\nparallel", true); +defineSymbol(math, ams, rel, "\u22af", "\\nVDash", true); +defineSymbol(math, ams, rel, "\u22eb", "\\ntriangleright"); +defineSymbol(math, ams, rel, "\u22ed", "\\ntrianglerighteq", true); +defineSymbol(math, ams, rel, "\ue018", "\\@nsupseteqq"); +defineSymbol(math, ams, rel, "\u228b", "\\supsetneq", true); +defineSymbol(math, ams, rel, "\ue01b", "\\@varsupsetneq"); +defineSymbol(math, ams, rel, "\u2acc", "\\supsetneqq", true); +defineSymbol(math, ams, rel, "\ue019", "\\@varsupsetneqq"); +defineSymbol(math, ams, rel, "\u22ae", "\\nVdash", true); +defineSymbol(math, ams, rel, "\u2ab5", "\\precneqq", true); +defineSymbol(math, ams, rel, "\u2ab6", "\\succneqq", true); +defineSymbol(math, ams, rel, "\ue016", "\\@nsubseteqq"); +defineSymbol(math, ams, bin, "\u22b4", "\\unlhd"); +defineSymbol(math, ams, bin, "\u22b5", "\\unrhd"); // AMS Negated Arrows + +defineSymbol(math, ams, rel, "\u219a", "\\nleftarrow", true); +defineSymbol(math, ams, rel, "\u219b", "\\nrightarrow", true); +defineSymbol(math, ams, rel, "\u21cd", "\\nLeftarrow", true); +defineSymbol(math, ams, rel, "\u21cf", "\\nRightarrow", true); +defineSymbol(math, ams, rel, "\u21ae", "\\nleftrightarrow", true); +defineSymbol(math, ams, rel, "\u21ce", "\\nLeftrightarrow", true); // AMS Misc + +defineSymbol(math, ams, rel, "\u25b3", "\\vartriangle"); +defineSymbol(math, ams, textord, "\u210f", "\\hslash"); +defineSymbol(math, ams, textord, "\u25bd", "\\triangledown"); +defineSymbol(math, ams, textord, "\u25ca", "\\lozenge"); +defineSymbol(math, ams, textord, "\u24c8", "\\circledS"); +defineSymbol(math, ams, textord, "\u00ae", "\\circledR"); +defineSymbol(text, ams, textord, "\u00ae", "\\circledR"); +defineSymbol(math, ams, textord, "\u2221", "\\measuredangle", true); +defineSymbol(math, ams, textord, "\u2204", "\\nexists"); +defineSymbol(math, ams, textord, "\u2127", "\\mho"); +defineSymbol(math, ams, textord, "\u2132", "\\Finv", true); +defineSymbol(math, ams, textord, "\u2141", "\\Game", true); +defineSymbol(math, ams, textord, "\u2035", "\\backprime"); +defineSymbol(math, ams, textord, "\u25b2", "\\blacktriangle"); +defineSymbol(math, ams, textord, "\u25bc", "\\blacktriangledown"); +defineSymbol(math, ams, textord, "\u25a0", "\\blacksquare"); +defineSymbol(math, ams, textord, "\u29eb", "\\blacklozenge"); +defineSymbol(math, ams, textord, "\u2605", "\\bigstar"); +defineSymbol(math, ams, textord, "\u2222", "\\sphericalangle", true); +defineSymbol(math, ams, textord, "\u2201", "\\complement", true); // unicode-math maps U+F0 to \matheth. We map to AMS function \eth + +defineSymbol(math, ams, textord, "\u00f0", "\\eth", true); +defineSymbol(text, main, textord, "\u00f0", "\u00f0"); +defineSymbol(math, ams, textord, "\u2571", "\\diagup"); +defineSymbol(math, ams, textord, "\u2572", "\\diagdown"); +defineSymbol(math, ams, textord, "\u25a1", "\\square"); +defineSymbol(math, ams, textord, "\u25a1", "\\Box"); +defineSymbol(math, ams, textord, "\u25ca", "\\Diamond"); // unicode-math maps U+A5 to \mathyen. We map to AMS function \yen + +defineSymbol(math, ams, textord, "\u00a5", "\\yen", true); +defineSymbol(text, ams, textord, "\u00a5", "\\yen", true); +defineSymbol(math, ams, textord, "\u2713", "\\checkmark", true); +defineSymbol(text, ams, textord, "\u2713", "\\checkmark"); // AMS Hebrew + +defineSymbol(math, ams, textord, "\u2136", "\\beth", true); +defineSymbol(math, ams, textord, "\u2138", "\\daleth", true); +defineSymbol(math, ams, textord, "\u2137", "\\gimel", true); // AMS Greek + +defineSymbol(math, ams, textord, "\u03dd", "\\digamma", true); +defineSymbol(math, ams, textord, "\u03f0", "\\varkappa"); // AMS Delimiters + +defineSymbol(math, ams, open, "\u250c", "\\@ulcorner", true); +defineSymbol(math, ams, close, "\u2510", "\\@urcorner", true); +defineSymbol(math, ams, open, "\u2514", "\\@llcorner", true); +defineSymbol(math, ams, close, "\u2518", "\\@lrcorner", true); // AMS Binary Relations + +defineSymbol(math, ams, rel, "\u2266", "\\leqq", true); +defineSymbol(math, ams, rel, "\u2a7d", "\\leqslant", true); +defineSymbol(math, ams, rel, "\u2a95", "\\eqslantless", true); +defineSymbol(math, ams, rel, "\u2272", "\\lesssim", true); +defineSymbol(math, ams, rel, "\u2a85", "\\lessapprox", true); +defineSymbol(math, ams, rel, "\u224a", "\\approxeq", true); +defineSymbol(math, ams, bin, "\u22d6", "\\lessdot"); +defineSymbol(math, ams, rel, "\u22d8", "\\lll", true); +defineSymbol(math, ams, rel, "\u2276", "\\lessgtr", true); +defineSymbol(math, ams, rel, "\u22da", "\\lesseqgtr", true); +defineSymbol(math, ams, rel, "\u2a8b", "\\lesseqqgtr", true); +defineSymbol(math, ams, rel, "\u2251", "\\doteqdot"); +defineSymbol(math, ams, rel, "\u2253", "\\risingdotseq", true); +defineSymbol(math, ams, rel, "\u2252", "\\fallingdotseq", true); +defineSymbol(math, ams, rel, "\u223d", "\\backsim", true); +defineSymbol(math, ams, rel, "\u22cd", "\\backsimeq", true); +defineSymbol(math, ams, rel, "\u2ac5", "\\subseteqq", true); +defineSymbol(math, ams, rel, "\u22d0", "\\Subset", true); +defineSymbol(math, ams, rel, "\u228f", "\\sqsubset", true); +defineSymbol(math, ams, rel, "\u227c", "\\preccurlyeq", true); +defineSymbol(math, ams, rel, "\u22de", "\\curlyeqprec", true); +defineSymbol(math, ams, rel, "\u227e", "\\precsim", true); +defineSymbol(math, ams, rel, "\u2ab7", "\\precapprox", true); +defineSymbol(math, ams, rel, "\u22b2", "\\vartriangleleft"); +defineSymbol(math, ams, rel, "\u22b4", "\\trianglelefteq"); +defineSymbol(math, ams, rel, "\u22a8", "\\vDash", true); +defineSymbol(math, ams, rel, "\u22aa", "\\Vvdash", true); +defineSymbol(math, ams, rel, "\u2323", "\\smallsmile"); +defineSymbol(math, ams, rel, "\u2322", "\\smallfrown"); +defineSymbol(math, ams, rel, "\u224f", "\\bumpeq", true); +defineSymbol(math, ams, rel, "\u224e", "\\Bumpeq", true); +defineSymbol(math, ams, rel, "\u2267", "\\geqq", true); +defineSymbol(math, ams, rel, "\u2a7e", "\\geqslant", true); +defineSymbol(math, ams, rel, "\u2a96", "\\eqslantgtr", true); +defineSymbol(math, ams, rel, "\u2273", "\\gtrsim", true); +defineSymbol(math, ams, rel, "\u2a86", "\\gtrapprox", true); +defineSymbol(math, ams, bin, "\u22d7", "\\gtrdot"); +defineSymbol(math, ams, rel, "\u22d9", "\\ggg", true); +defineSymbol(math, ams, rel, "\u2277", "\\gtrless", true); +defineSymbol(math, ams, rel, "\u22db", "\\gtreqless", true); +defineSymbol(math, ams, rel, "\u2a8c", "\\gtreqqless", true); +defineSymbol(math, ams, rel, "\u2256", "\\eqcirc", true); +defineSymbol(math, ams, rel, "\u2257", "\\circeq", true); +defineSymbol(math, ams, rel, "\u225c", "\\triangleq", true); +defineSymbol(math, ams, rel, "\u223c", "\\thicksim"); +defineSymbol(math, ams, rel, "\u2248", "\\thickapprox"); +defineSymbol(math, ams, rel, "\u2ac6", "\\supseteqq", true); +defineSymbol(math, ams, rel, "\u22d1", "\\Supset", true); +defineSymbol(math, ams, rel, "\u2290", "\\sqsupset", true); +defineSymbol(math, ams, rel, "\u227d", "\\succcurlyeq", true); +defineSymbol(math, ams, rel, "\u22df", "\\curlyeqsucc", true); +defineSymbol(math, ams, rel, "\u227f", "\\succsim", true); +defineSymbol(math, ams, rel, "\u2ab8", "\\succapprox", true); +defineSymbol(math, ams, rel, "\u22b3", "\\vartriangleright"); +defineSymbol(math, ams, rel, "\u22b5", "\\trianglerighteq"); +defineSymbol(math, ams, rel, "\u22a9", "\\Vdash", true); +defineSymbol(math, ams, rel, "\u2223", "\\shortmid"); +defineSymbol(math, ams, rel, "\u2225", "\\shortparallel"); +defineSymbol(math, ams, rel, "\u226c", "\\between", true); +defineSymbol(math, ams, rel, "\u22d4", "\\pitchfork", true); +defineSymbol(math, ams, rel, "\u221d", "\\varpropto"); +defineSymbol(math, ams, rel, "\u25c0", "\\blacktriangleleft"); // unicode-math says that \therefore is a mathord atom. +// We kept the amssymb atom type, which is rel. + +defineSymbol(math, ams, rel, "\u2234", "\\therefore", true); +defineSymbol(math, ams, rel, "\u220d", "\\backepsilon"); +defineSymbol(math, ams, rel, "\u25b6", "\\blacktriangleright"); // unicode-math says that \because is a mathord atom. +// We kept the amssymb atom type, which is rel. + +defineSymbol(math, ams, rel, "\u2235", "\\because", true); +defineSymbol(math, ams, rel, "\u22d8", "\\llless"); +defineSymbol(math, ams, rel, "\u22d9", "\\gggtr"); +defineSymbol(math, ams, bin, "\u22b2", "\\lhd"); +defineSymbol(math, ams, bin, "\u22b3", "\\rhd"); +defineSymbol(math, ams, rel, "\u2242", "\\eqsim", true); +defineSymbol(math, main, rel, "\u22c8", "\\Join"); +defineSymbol(math, ams, rel, "\u2251", "\\Doteq", true); // AMS Binary Operators + +defineSymbol(math, ams, bin, "\u2214", "\\dotplus", true); +defineSymbol(math, ams, bin, "\u2216", "\\smallsetminus"); +defineSymbol(math, ams, bin, "\u22d2", "\\Cap", true); +defineSymbol(math, ams, bin, "\u22d3", "\\Cup", true); +defineSymbol(math, ams, bin, "\u2a5e", "\\doublebarwedge", true); +defineSymbol(math, ams, bin, "\u229f", "\\boxminus", true); +defineSymbol(math, ams, bin, "\u229e", "\\boxplus", true); +defineSymbol(math, ams, bin, "\u22c7", "\\divideontimes", true); +defineSymbol(math, ams, bin, "\u22c9", "\\ltimes", true); +defineSymbol(math, ams, bin, "\u22ca", "\\rtimes", true); +defineSymbol(math, ams, bin, "\u22cb", "\\leftthreetimes", true); +defineSymbol(math, ams, bin, "\u22cc", "\\rightthreetimes", true); +defineSymbol(math, ams, bin, "\u22cf", "\\curlywedge", true); +defineSymbol(math, ams, bin, "\u22ce", "\\curlyvee", true); +defineSymbol(math, ams, bin, "\u229d", "\\circleddash", true); +defineSymbol(math, ams, bin, "\u229b", "\\circledast", true); +defineSymbol(math, ams, bin, "\u22c5", "\\centerdot"); +defineSymbol(math, ams, bin, "\u22ba", "\\intercal", true); +defineSymbol(math, ams, bin, "\u22d2", "\\doublecap"); +defineSymbol(math, ams, bin, "\u22d3", "\\doublecup"); +defineSymbol(math, ams, bin, "\u22a0", "\\boxtimes", true); // AMS Arrows +// Note: unicode-math maps \u21e2 to their own function \rightdasharrow. +// We'll map it to AMS function \dashrightarrow. It produces the same atom. + +defineSymbol(math, ams, rel, "\u21e2", "\\dashrightarrow", true); // unicode-math maps \u21e0 to \leftdasharrow. We'll use the AMS synonym. + +defineSymbol(math, ams, rel, "\u21e0", "\\dashleftarrow", true); +defineSymbol(math, ams, rel, "\u21c7", "\\leftleftarrows", true); +defineSymbol(math, ams, rel, "\u21c6", "\\leftrightarrows", true); +defineSymbol(math, ams, rel, "\u21da", "\\Lleftarrow", true); +defineSymbol(math, ams, rel, "\u219e", "\\twoheadleftarrow", true); +defineSymbol(math, ams, rel, "\u21a2", "\\leftarrowtail", true); +defineSymbol(math, ams, rel, "\u21ab", "\\looparrowleft", true); +defineSymbol(math, ams, rel, "\u21cb", "\\leftrightharpoons", true); +defineSymbol(math, ams, rel, "\u21b6", "\\curvearrowleft", true); // unicode-math maps \u21ba to \acwopencirclearrow. We'll use the AMS synonym. + +defineSymbol(math, ams, rel, "\u21ba", "\\circlearrowleft", true); +defineSymbol(math, ams, rel, "\u21b0", "\\Lsh", true); +defineSymbol(math, ams, rel, "\u21c8", "\\upuparrows", true); +defineSymbol(math, ams, rel, "\u21bf", "\\upharpoonleft", true); +defineSymbol(math, ams, rel, "\u21c3", "\\downharpoonleft", true); +defineSymbol(math, main, rel, "\u22b6", "\\origof", true); // not in font + +defineSymbol(math, main, rel, "\u22b7", "\\imageof", true); // not in font + +defineSymbol(math, ams, rel, "\u22b8", "\\multimap", true); +defineSymbol(math, ams, rel, "\u21ad", "\\leftrightsquigarrow", true); +defineSymbol(math, ams, rel, "\u21c9", "\\rightrightarrows", true); +defineSymbol(math, ams, rel, "\u21c4", "\\rightleftarrows", true); +defineSymbol(math, ams, rel, "\u21a0", "\\twoheadrightarrow", true); +defineSymbol(math, ams, rel, "\u21a3", "\\rightarrowtail", true); +defineSymbol(math, ams, rel, "\u21ac", "\\looparrowright", true); +defineSymbol(math, ams, rel, "\u21b7", "\\curvearrowright", true); // unicode-math maps \u21bb to \cwopencirclearrow. We'll use the AMS synonym. + +defineSymbol(math, ams, rel, "\u21bb", "\\circlearrowright", true); +defineSymbol(math, ams, rel, "\u21b1", "\\Rsh", true); +defineSymbol(math, ams, rel, "\u21ca", "\\downdownarrows", true); +defineSymbol(math, ams, rel, "\u21be", "\\upharpoonright", true); +defineSymbol(math, ams, rel, "\u21c2", "\\downharpoonright", true); +defineSymbol(math, ams, rel, "\u21dd", "\\rightsquigarrow", true); +defineSymbol(math, ams, rel, "\u21dd", "\\leadsto"); +defineSymbol(math, ams, rel, "\u21db", "\\Rrightarrow", true); +defineSymbol(math, ams, rel, "\u21be", "\\restriction"); +defineSymbol(math, main, textord, "\u2018", "`"); +defineSymbol(math, main, textord, "$", "\\$"); +defineSymbol(text, main, textord, "$", "\\$"); +defineSymbol(text, main, textord, "$", "\\textdollar"); +defineSymbol(math, main, textord, "%", "\\%"); +defineSymbol(text, main, textord, "%", "\\%"); +defineSymbol(math, main, textord, "_", "\\_"); +defineSymbol(text, main, textord, "_", "\\_"); +defineSymbol(text, main, textord, "_", "\\textunderscore"); +defineSymbol(math, main, textord, "\u2220", "\\angle", true); +defineSymbol(math, main, textord, "\u221e", "\\infty", true); +defineSymbol(math, main, textord, "\u2032", "\\prime"); +defineSymbol(math, main, textord, "\u25b3", "\\triangle"); +defineSymbol(math, main, textord, "\u0393", "\\Gamma", true); +defineSymbol(math, main, textord, "\u0394", "\\Delta", true); +defineSymbol(math, main, textord, "\u0398", "\\Theta", true); +defineSymbol(math, main, textord, "\u039b", "\\Lambda", true); +defineSymbol(math, main, textord, "\u039e", "\\Xi", true); +defineSymbol(math, main, textord, "\u03a0", "\\Pi", true); +defineSymbol(math, main, textord, "\u03a3", "\\Sigma", true); +defineSymbol(math, main, textord, "\u03a5", "\\Upsilon", true); +defineSymbol(math, main, textord, "\u03a6", "\\Phi", true); +defineSymbol(math, main, textord, "\u03a8", "\\Psi", true); +defineSymbol(math, main, textord, "\u03a9", "\\Omega", true); +defineSymbol(math, main, textord, "A", "\u0391"); +defineSymbol(math, main, textord, "B", "\u0392"); +defineSymbol(math, main, textord, "E", "\u0395"); +defineSymbol(math, main, textord, "Z", "\u0396"); +defineSymbol(math, main, textord, "H", "\u0397"); +defineSymbol(math, main, textord, "I", "\u0399"); +defineSymbol(math, main, textord, "K", "\u039A"); +defineSymbol(math, main, textord, "M", "\u039C"); +defineSymbol(math, main, textord, "N", "\u039D"); +defineSymbol(math, main, textord, "O", "\u039F"); +defineSymbol(math, main, textord, "P", "\u03A1"); +defineSymbol(math, main, textord, "T", "\u03A4"); +defineSymbol(math, main, textord, "X", "\u03A7"); +defineSymbol(math, main, textord, "\u00ac", "\\neg", true); +defineSymbol(math, main, textord, "\u00ac", "\\lnot"); +defineSymbol(math, main, textord, "\u22a4", "\\top"); +defineSymbol(math, main, textord, "\u22a5", "\\bot"); +defineSymbol(math, main, textord, "\u2205", "\\emptyset"); +defineSymbol(math, ams, textord, "\u2205", "\\varnothing"); +defineSymbol(math, main, mathord, "\u03b1", "\\alpha", true); +defineSymbol(math, main, mathord, "\u03b2", "\\beta", true); +defineSymbol(math, main, mathord, "\u03b3", "\\gamma", true); +defineSymbol(math, main, mathord, "\u03b4", "\\delta", true); +defineSymbol(math, main, mathord, "\u03f5", "\\epsilon", true); +defineSymbol(math, main, mathord, "\u03b6", "\\zeta", true); +defineSymbol(math, main, mathord, "\u03b7", "\\eta", true); +defineSymbol(math, main, mathord, "\u03b8", "\\theta", true); +defineSymbol(math, main, mathord, "\u03b9", "\\iota", true); +defineSymbol(math, main, mathord, "\u03ba", "\\kappa", true); +defineSymbol(math, main, mathord, "\u03bb", "\\lambda", true); +defineSymbol(math, main, mathord, "\u03bc", "\\mu", true); +defineSymbol(math, main, mathord, "\u03bd", "\\nu", true); +defineSymbol(math, main, mathord, "\u03be", "\\xi", true); +defineSymbol(math, main, mathord, "\u03bf", "\\omicron", true); +defineSymbol(math, main, mathord, "\u03c0", "\\pi", true); +defineSymbol(math, main, mathord, "\u03c1", "\\rho", true); +defineSymbol(math, main, mathord, "\u03c3", "\\sigma", true); +defineSymbol(math, main, mathord, "\u03c4", "\\tau", true); +defineSymbol(math, main, mathord, "\u03c5", "\\upsilon", true); +defineSymbol(math, main, mathord, "\u03d5", "\\phi", true); +defineSymbol(math, main, mathord, "\u03c7", "\\chi", true); +defineSymbol(math, main, mathord, "\u03c8", "\\psi", true); +defineSymbol(math, main, mathord, "\u03c9", "\\omega", true); +defineSymbol(math, main, mathord, "\u03b5", "\\varepsilon", true); +defineSymbol(math, main, mathord, "\u03d1", "\\vartheta", true); +defineSymbol(math, main, mathord, "\u03d6", "\\varpi", true); +defineSymbol(math, main, mathord, "\u03f1", "\\varrho", true); +defineSymbol(math, main, mathord, "\u03c2", "\\varsigma", true); +defineSymbol(math, main, mathord, "\u03c6", "\\varphi", true); +defineSymbol(math, main, bin, "\u2217", "*", true); +defineSymbol(math, main, bin, "+", "+"); +defineSymbol(math, main, bin, "\u2212", "-", true); +defineSymbol(math, main, bin, "\u22c5", "\\cdot", true); +defineSymbol(math, main, bin, "\u2218", "\\circ"); +defineSymbol(math, main, bin, "\u00f7", "\\div", true); +defineSymbol(math, main, bin, "\u00b1", "\\pm", true); +defineSymbol(math, main, bin, "\u00d7", "\\times", true); +defineSymbol(math, main, bin, "\u2229", "\\cap", true); +defineSymbol(math, main, bin, "\u222a", "\\cup", true); +defineSymbol(math, main, bin, "\u2216", "\\setminus"); +defineSymbol(math, main, bin, "\u2227", "\\land"); +defineSymbol(math, main, bin, "\u2228", "\\lor"); +defineSymbol(math, main, bin, "\u2227", "\\wedge", true); +defineSymbol(math, main, bin, "\u2228", "\\vee", true); +defineSymbol(math, main, textord, "\u221a", "\\surd"); +defineSymbol(math, main, open, "\u27e8", "\\langle", true); +defineSymbol(math, main, open, "\u2223", "\\lvert"); +defineSymbol(math, main, open, "\u2225", "\\lVert"); +defineSymbol(math, main, close, "?", "?"); +defineSymbol(math, main, close, "!", "!"); +defineSymbol(math, main, close, "\u27e9", "\\rangle", true); +defineSymbol(math, main, close, "\u2223", "\\rvert"); +defineSymbol(math, main, close, "\u2225", "\\rVert"); +defineSymbol(math, main, rel, "=", "="); +defineSymbol(math, main, rel, ":", ":"); +defineSymbol(math, main, rel, "\u2248", "\\approx", true); +defineSymbol(math, main, rel, "\u2245", "\\cong", true); +defineSymbol(math, main, rel, "\u2265", "\\ge"); +defineSymbol(math, main, rel, "\u2265", "\\geq", true); +defineSymbol(math, main, rel, "\u2190", "\\gets"); +defineSymbol(math, main, rel, ">", "\\gt", true); +defineSymbol(math, main, rel, "\u2208", "\\in", true); +defineSymbol(math, main, rel, "\ue020", "\\@not"); +defineSymbol(math, main, rel, "\u2282", "\\subset", true); +defineSymbol(math, main, rel, "\u2283", "\\supset", true); +defineSymbol(math, main, rel, "\u2286", "\\subseteq", true); +defineSymbol(math, main, rel, "\u2287", "\\supseteq", true); +defineSymbol(math, ams, rel, "\u2288", "\\nsubseteq", true); +defineSymbol(math, ams, rel, "\u2289", "\\nsupseteq", true); +defineSymbol(math, main, rel, "\u22a8", "\\models"); +defineSymbol(math, main, rel, "\u2190", "\\leftarrow", true); +defineSymbol(math, main, rel, "\u2264", "\\le"); +defineSymbol(math, main, rel, "\u2264", "\\leq", true); +defineSymbol(math, main, rel, "<", "\\lt", true); +defineSymbol(math, main, rel, "\u2192", "\\rightarrow", true); +defineSymbol(math, main, rel, "\u2192", "\\to"); +defineSymbol(math, ams, rel, "\u2271", "\\ngeq", true); +defineSymbol(math, ams, rel, "\u2270", "\\nleq", true); +defineSymbol(math, main, spacing, "\u00a0", "\\ "); +defineSymbol(math, main, spacing, "\u00a0", "\\space"); // Ref: LaTeX Source 2e: \DeclareRobustCommand{\nobreakspace}{% + +defineSymbol(math, main, spacing, "\u00a0", "\\nobreakspace"); +defineSymbol(text, main, spacing, "\u00a0", "\\ "); +defineSymbol(text, main, spacing, "\u00a0", " "); +defineSymbol(text, main, spacing, "\u00a0", "\\space"); +defineSymbol(text, main, spacing, "\u00a0", "\\nobreakspace"); +defineSymbol(math, main, spacing, null, "\\nobreak"); +defineSymbol(math, main, spacing, null, "\\allowbreak"); +defineSymbol(math, main, punct, ",", ","); +defineSymbol(math, main, punct, ";", ";"); +defineSymbol(math, ams, bin, "\u22bc", "\\barwedge", true); +defineSymbol(math, ams, bin, "\u22bb", "\\veebar", true); +defineSymbol(math, main, bin, "\u2299", "\\odot", true); +defineSymbol(math, main, bin, "\u2295", "\\oplus", true); +defineSymbol(math, main, bin, "\u2297", "\\otimes", true); +defineSymbol(math, main, textord, "\u2202", "\\partial", true); +defineSymbol(math, main, bin, "\u2298", "\\oslash", true); +defineSymbol(math, ams, bin, "\u229a", "\\circledcirc", true); +defineSymbol(math, ams, bin, "\u22a1", "\\boxdot", true); +defineSymbol(math, main, bin, "\u25b3", "\\bigtriangleup"); +defineSymbol(math, main, bin, "\u25bd", "\\bigtriangledown"); +defineSymbol(math, main, bin, "\u2020", "\\dagger"); +defineSymbol(math, main, bin, "\u22c4", "\\diamond"); +defineSymbol(math, main, bin, "\u22c6", "\\star"); +defineSymbol(math, main, bin, "\u25c3", "\\triangleleft"); +defineSymbol(math, main, bin, "\u25b9", "\\triangleright"); +defineSymbol(math, main, open, "{", "\\{"); +defineSymbol(text, main, textord, "{", "\\{"); +defineSymbol(text, main, textord, "{", "\\textbraceleft"); +defineSymbol(math, main, close, "}", "\\}"); +defineSymbol(text, main, textord, "}", "\\}"); +defineSymbol(text, main, textord, "}", "\\textbraceright"); +defineSymbol(math, main, open, "{", "\\lbrace"); +defineSymbol(math, main, close, "}", "\\rbrace"); +defineSymbol(math, main, open, "[", "\\lbrack", true); +defineSymbol(text, main, textord, "[", "\\lbrack", true); +defineSymbol(math, main, close, "]", "\\rbrack", true); +defineSymbol(text, main, textord, "]", "\\rbrack", true); +defineSymbol(math, main, open, "(", "\\lparen", true); +defineSymbol(math, main, close, ")", "\\rparen", true); +defineSymbol(text, main, textord, "<", "\\textless", true); // in T1 fontenc + +defineSymbol(text, main, textord, ">", "\\textgreater", true); // in T1 fontenc + +defineSymbol(math, main, open, "\u230a", "\\lfloor", true); +defineSymbol(math, main, close, "\u230b", "\\rfloor", true); +defineSymbol(math, main, open, "\u2308", "\\lceil", true); +defineSymbol(math, main, close, "\u2309", "\\rceil", true); +defineSymbol(math, main, textord, "\\", "\\backslash"); +defineSymbol(math, main, textord, "\u2223", "|"); +defineSymbol(math, main, textord, "\u2223", "\\vert"); +defineSymbol(text, main, textord, "|", "\\textbar", true); // in T1 fontenc + +defineSymbol(math, main, textord, "\u2225", "\\|"); +defineSymbol(math, main, textord, "\u2225", "\\Vert"); +defineSymbol(text, main, textord, "\u2225", "\\textbardbl"); +defineSymbol(text, main, textord, "~", "\\textasciitilde"); +defineSymbol(text, main, textord, "\\", "\\textbackslash"); +defineSymbol(text, main, textord, "^", "\\textasciicircum"); +defineSymbol(math, main, rel, "\u2191", "\\uparrow", true); +defineSymbol(math, main, rel, "\u21d1", "\\Uparrow", true); +defineSymbol(math, main, rel, "\u2193", "\\downarrow", true); +defineSymbol(math, main, rel, "\u21d3", "\\Downarrow", true); +defineSymbol(math, main, rel, "\u2195", "\\updownarrow", true); +defineSymbol(math, main, rel, "\u21d5", "\\Updownarrow", true); +defineSymbol(math, main, op, "\u2210", "\\coprod"); +defineSymbol(math, main, op, "\u22c1", "\\bigvee"); +defineSymbol(math, main, op, "\u22c0", "\\bigwedge"); +defineSymbol(math, main, op, "\u2a04", "\\biguplus"); +defineSymbol(math, main, op, "\u22c2", "\\bigcap"); +defineSymbol(math, main, op, "\u22c3", "\\bigcup"); +defineSymbol(math, main, op, "\u222b", "\\int"); +defineSymbol(math, main, op, "\u222b", "\\intop"); +defineSymbol(math, main, op, "\u222c", "\\iint"); +defineSymbol(math, main, op, "\u222d", "\\iiint"); +defineSymbol(math, main, op, "\u220f", "\\prod"); +defineSymbol(math, main, op, "\u2211", "\\sum"); +defineSymbol(math, main, op, "\u2a02", "\\bigotimes"); +defineSymbol(math, main, op, "\u2a01", "\\bigoplus"); +defineSymbol(math, main, op, "\u2a00", "\\bigodot"); +defineSymbol(math, main, op, "\u222e", "\\oint"); +defineSymbol(math, main, op, "\u222f", "\\oiint"); +defineSymbol(math, main, op, "\u2230", "\\oiiint"); +defineSymbol(math, main, op, "\u2a06", "\\bigsqcup"); +defineSymbol(math, main, op, "\u222b", "\\smallint"); +defineSymbol(text, main, inner, "\u2026", "\\textellipsis"); +defineSymbol(math, main, inner, "\u2026", "\\mathellipsis"); +defineSymbol(text, main, inner, "\u2026", "\\ldots", true); +defineSymbol(math, main, inner, "\u2026", "\\ldots", true); +defineSymbol(math, main, inner, "\u22ef", "\\@cdots", true); +defineSymbol(math, main, inner, "\u22f1", "\\ddots", true); +defineSymbol(math, main, textord, "\u22ee", "\\varvdots"); // \vdots is a macro + +defineSymbol(math, main, accent, "\u02ca", "\\acute"); +defineSymbol(math, main, accent, "\u02cb", "\\grave"); +defineSymbol(math, main, accent, "\u00a8", "\\ddot"); +defineSymbol(math, main, accent, "\u007e", "\\tilde"); +defineSymbol(math, main, accent, "\u02c9", "\\bar"); +defineSymbol(math, main, accent, "\u02d8", "\\breve"); +defineSymbol(math, main, accent, "\u02c7", "\\check"); +defineSymbol(math, main, accent, "\u005e", "\\hat"); +defineSymbol(math, main, accent, "\u20d7", "\\vec"); +defineSymbol(math, main, accent, "\u02d9", "\\dot"); +defineSymbol(math, main, accent, "\u02da", "\\mathring"); // \imath and \jmath should be invariant to \mathrm, \mathbf, etc., so use PUA + +defineSymbol(math, main, mathord, "\ue131", "\\@imath"); +defineSymbol(math, main, mathord, "\ue237", "\\@jmath"); +defineSymbol(math, main, textord, "\u0131", "\u0131"); +defineSymbol(math, main, textord, "\u0237", "\u0237"); +defineSymbol(text, main, textord, "\u0131", "\\i", true); +defineSymbol(text, main, textord, "\u0237", "\\j", true); +defineSymbol(text, main, textord, "\u00df", "\\ss", true); +defineSymbol(text, main, textord, "\u00e6", "\\ae", true); +defineSymbol(text, main, textord, "\u0153", "\\oe", true); +defineSymbol(text, main, textord, "\u00f8", "\\o", true); +defineSymbol(text, main, textord, "\u00c6", "\\AE", true); +defineSymbol(text, main, textord, "\u0152", "\\OE", true); +defineSymbol(text, main, textord, "\u00d8", "\\O", true); +defineSymbol(text, main, accent, "\u02ca", "\\'"); // acute + +defineSymbol(text, main, accent, "\u02cb", "\\`"); // grave + +defineSymbol(text, main, accent, "\u02c6", "\\^"); // circumflex + +defineSymbol(text, main, accent, "\u02dc", "\\~"); // tilde + +defineSymbol(text, main, accent, "\u02c9", "\\="); // macron + +defineSymbol(text, main, accent, "\u02d8", "\\u"); // breve + +defineSymbol(text, main, accent, "\u02d9", "\\."); // dot above + +defineSymbol(text, main, accent, "\u00b8", "\\c"); // cedilla + +defineSymbol(text, main, accent, "\u02da", "\\r"); // ring above + +defineSymbol(text, main, accent, "\u02c7", "\\v"); // caron + +defineSymbol(text, main, accent, "\u00a8", '\\"'); // diaresis + +defineSymbol(text, main, accent, "\u02dd", "\\H"); // double acute + +defineSymbol(text, main, accent, "\u25ef", "\\textcircled"); // \bigcirc glyph +// These ligatures are detected and created in Parser.js's `formLigatures`. + +var ligatures = { + "--": true, + "---": true, + "``": true, + "''": true +}; +defineSymbol(text, main, textord, "\u2013", "--", true); +defineSymbol(text, main, textord, "\u2013", "\\textendash"); +defineSymbol(text, main, textord, "\u2014", "---", true); +defineSymbol(text, main, textord, "\u2014", "\\textemdash"); +defineSymbol(text, main, textord, "\u2018", "`", true); +defineSymbol(text, main, textord, "\u2018", "\\textquoteleft"); +defineSymbol(text, main, textord, "\u2019", "'", true); +defineSymbol(text, main, textord, "\u2019", "\\textquoteright"); +defineSymbol(text, main, textord, "\u201c", "``", true); +defineSymbol(text, main, textord, "\u201c", "\\textquotedblleft"); +defineSymbol(text, main, textord, "\u201d", "''", true); +defineSymbol(text, main, textord, "\u201d", "\\textquotedblright"); // \degree from gensymb package + +defineSymbol(math, main, textord, "\u00b0", "\\degree", true); +defineSymbol(text, main, textord, "\u00b0", "\\degree"); // \textdegree from inputenc package + +defineSymbol(text, main, textord, "\u00b0", "\\textdegree", true); // TODO: In LaTeX, \pounds can generate a different character in text and math +// mode, but among our fonts, only Main-Regular defines this character "163". + +defineSymbol(math, main, textord, "\u00a3", "\\pounds"); +defineSymbol(math, main, textord, "\u00a3", "\\mathsterling", true); +defineSymbol(text, main, textord, "\u00a3", "\\pounds"); +defineSymbol(text, main, textord, "\u00a3", "\\textsterling", true); +defineSymbol(math, ams, textord, "\u2720", "\\maltese"); +defineSymbol(text, ams, textord, "\u2720", "\\maltese"); // There are lots of symbols which are the same, so we add them in afterwards. +// All of these are textords in math mode + +var mathTextSymbols = "0123456789/@.\""; + +for (var i = 0; i < mathTextSymbols.length; i++) { + var ch = mathTextSymbols.charAt(i); + defineSymbol(math, main, textord, ch, ch); +} // All of these are textords in text mode + + +var textSymbols = "0123456789!@*()-=+\";:?/.,"; + +for (var _i = 0; _i < textSymbols.length; _i++) { + var _ch = textSymbols.charAt(_i); + + defineSymbol(text, main, textord, _ch, _ch); +} // All of these are textords in text mode, and mathords in math mode + + +var letters = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"; + +for (var _i2 = 0; _i2 < letters.length; _i2++) { + var _ch2 = letters.charAt(_i2); + + defineSymbol(math, main, mathord, _ch2, _ch2); + defineSymbol(text, main, textord, _ch2, _ch2); +} // Blackboard bold and script letters in Unicode range + + +defineSymbol(math, ams, textord, "C", "\u2102"); // blackboard bold + +defineSymbol(text, ams, textord, "C", "\u2102"); +defineSymbol(math, ams, textord, "H", "\u210D"); +defineSymbol(text, ams, textord, "H", "\u210D"); +defineSymbol(math, ams, textord, "N", "\u2115"); +defineSymbol(text, ams, textord, "N", "\u2115"); +defineSymbol(math, ams, textord, "P", "\u2119"); +defineSymbol(text, ams, textord, "P", "\u2119"); +defineSymbol(math, ams, textord, "Q", "\u211A"); +defineSymbol(text, ams, textord, "Q", "\u211A"); +defineSymbol(math, ams, textord, "R", "\u211D"); +defineSymbol(text, ams, textord, "R", "\u211D"); +defineSymbol(math, ams, textord, "Z", "\u2124"); +defineSymbol(text, ams, textord, "Z", "\u2124"); +defineSymbol(math, main, mathord, "h", "\u210E"); // italic h, Planck constant + +defineSymbol(text, main, mathord, "h", "\u210E"); // The next loop loads wide (surrogate pair) characters. +// We support some letters in the Unicode range U+1D400 to U+1D7FF, +// Mathematical Alphanumeric Symbols. +// Some editors do not deal well with wide characters. So don't write the +// string into this file. Instead, create the string from the surrogate pair. + +var wideChar = ""; + +for (var _i3 = 0; _i3 < letters.length; _i3++) { + var _ch3 = letters.charAt(_i3); // The hex numbers in the next line are a surrogate pair. + // 0xD835 is the high surrogate for all letters in the range we support. + // 0xDC00 is the low surrogate for bold A. + + + wideChar = String.fromCharCode(0xD835, 0xDC00 + _i3); // A-Z a-z bold + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDC34 + _i3); // A-Z a-z italic + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDC68 + _i3); // A-Z a-z bold italic + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDD04 + _i3); // A-Z a-z Fractur + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDDA0 + _i3); // A-Z a-z sans-serif + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDDD4 + _i3); // A-Z a-z sans bold + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDE08 + _i3); // A-Z a-z sans italic + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDE70 + _i3); // A-Z a-z monospace + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(text, main, textord, _ch3, wideChar); + + if (_i3 < 26) { + // KaTeX fonts have only capital letters for blackboard bold and script. + // See exception for k below. + wideChar = String.fromCharCode(0xD835, 0xDD38 + _i3); // A-Z double struck + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(text, main, textord, _ch3, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDC9C + _i3); // A-Z script + + defineSymbol(math, main, mathord, _ch3, wideChar); + defineSymbol(text, main, textord, _ch3, wideChar); + } // TODO: Add bold script when it is supported by a KaTeX font. + +} // "k" is the only double struck lower case letter in the KaTeX fonts. + + +wideChar = String.fromCharCode(0xD835, 0xDD5C); // k double struck + +defineSymbol(math, main, mathord, "k", wideChar); +defineSymbol(text, main, textord, "k", wideChar); // Next, some wide character numerals + +for (var _i4 = 0; _i4 < 10; _i4++) { + var _ch4 = _i4.toString(); + + wideChar = String.fromCharCode(0xD835, 0xDFCE + _i4); // 0-9 bold + + defineSymbol(math, main, mathord, _ch4, wideChar); + defineSymbol(text, main, textord, _ch4, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDFE2 + _i4); // 0-9 sans serif + + defineSymbol(math, main, mathord, _ch4, wideChar); + defineSymbol(text, main, textord, _ch4, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDFEC + _i4); // 0-9 bold sans + + defineSymbol(math, main, mathord, _ch4, wideChar); + defineSymbol(text, main, textord, _ch4, wideChar); + wideChar = String.fromCharCode(0xD835, 0xDFF6 + _i4); // 0-9 monospace + + defineSymbol(math, main, mathord, _ch4, wideChar); + defineSymbol(text, main, textord, _ch4, wideChar); +} // We add these Latin-1 letters as symbols for backwards-compatibility, +// but they are not actually in the font, nor are they supported by the +// Unicode accent mechanism, so they fall back to Times font and look ugly. +// TODO(edemaine): Fix this. + + +var extraLatin = "\u00d0\u00de\u00fe"; + +for (var _i5 = 0; _i5 < extraLatin.length; _i5++) { + var _ch5 = extraLatin.charAt(_i5); + + defineSymbol(math, main, mathord, _ch5, _ch5); + defineSymbol(text, main, textord, _ch5, _ch5); +} + +/** + * This file provides support for Unicode range U+1D400 to U+1D7FF, + * Mathematical Alphanumeric Symbols. + * + * Function wideCharacterFont takes a wide character as input and returns + * the font information necessary to render it properly. + */ +/** + * Data below is from https://www.unicode.org/charts/PDF/U1D400.pdf + * That document sorts characters into groups by font type, say bold or italic. + * + * In the arrays below, each subarray consists three elements: + * * The CSS class of that group when in math mode. + * * The CSS class of that group when in text mode. + * * The font name, so that KaTeX can get font metrics. + */ + +var wideLatinLetterData = [["mathbf", "textbf", "Main-Bold"], // A-Z bold upright +["mathbf", "textbf", "Main-Bold"], // a-z bold upright +["mathnormal", "textit", "Math-Italic"], // A-Z italic +["mathnormal", "textit", "Math-Italic"], // a-z italic +["boldsymbol", "boldsymbol", "Main-BoldItalic"], // A-Z bold italic +["boldsymbol", "boldsymbol", "Main-BoldItalic"], // a-z bold italic +// Map fancy A-Z letters to script, not calligraphic. +// This aligns with unicode-math and math fonts (except Cambria Math). +["mathscr", "textscr", "Script-Regular"], // A-Z script +["", "", ""], // a-z script. No font +["", "", ""], // A-Z bold script. No font +["", "", ""], // a-z bold script. No font +["mathfrak", "textfrak", "Fraktur-Regular"], // A-Z Fraktur +["mathfrak", "textfrak", "Fraktur-Regular"], // a-z Fraktur +["mathbb", "textbb", "AMS-Regular"], // A-Z double-struck +["mathbb", "textbb", "AMS-Regular"], // k double-struck +["", "", ""], // A-Z bold Fraktur No font metrics +["", "", ""], // a-z bold Fraktur. No font. +["mathsf", "textsf", "SansSerif-Regular"], // A-Z sans-serif +["mathsf", "textsf", "SansSerif-Regular"], // a-z sans-serif +["mathboldsf", "textboldsf", "SansSerif-Bold"], // A-Z bold sans-serif +["mathboldsf", "textboldsf", "SansSerif-Bold"], // a-z bold sans-serif +["mathitsf", "textitsf", "SansSerif-Italic"], // A-Z italic sans-serif +["mathitsf", "textitsf", "SansSerif-Italic"], // a-z italic sans-serif +["", "", ""], // A-Z bold italic sans. No font +["", "", ""], // a-z bold italic sans. No font +["mathtt", "texttt", "Typewriter-Regular"], // A-Z monospace +["mathtt", "texttt", "Typewriter-Regular"] // a-z monospace +]; +var wideNumeralData = [["mathbf", "textbf", "Main-Bold"], // 0-9 bold +["", "", ""], // 0-9 double-struck. No KaTeX font. +["mathsf", "textsf", "SansSerif-Regular"], // 0-9 sans-serif +["mathboldsf", "textboldsf", "SansSerif-Bold"], // 0-9 bold sans-serif +["mathtt", "texttt", "Typewriter-Regular"] // 0-9 monospace +]; +var wideCharacterFont = function wideCharacterFont(wideChar, mode) { + // IE doesn't support codePointAt(). So work with the surrogate pair. + var H = wideChar.charCodeAt(0); // high surrogate + + var L = wideChar.charCodeAt(1); // low surrogate + + var codePoint = (H - 0xD800) * 0x400 + (L - 0xDC00) + 0x10000; + var j = mode === "math" ? 0 : 1; // column index for CSS class. + + if (0x1D400 <= codePoint && codePoint < 0x1D6A4) { + // wideLatinLetterData contains exactly 26 chars on each row. + // So we can calculate the relevant row. No traverse necessary. + var i = Math.floor((codePoint - 0x1D400) / 26); + return [wideLatinLetterData[i][2], wideLatinLetterData[i][j]]; + } else if (0x1D7CE <= codePoint && codePoint <= 0x1D7FF) { + // Numerals, ten per row. + var _i = Math.floor((codePoint - 0x1D7CE) / 10); + + return [wideNumeralData[_i][2], wideNumeralData[_i][j]]; + } else if (codePoint === 0x1D6A5 || codePoint === 0x1D6A6) { + // dotless i or j + return [wideLatinLetterData[0][2], wideLatinLetterData[0][j]]; + } else if (0x1D6A6 < codePoint && codePoint < 0x1D7CE) { + // Greek letters. Not supported, yet. + return ["", ""]; + } else { + // We don't support any wide characters outside 1D400–1D7FF. + throw new ParseError("Unsupported character: " + wideChar); + } +}; + +/** + * This file contains information about the options that the Parser carries + * around with it while parsing. Data is held in an `Options` object, and when + * recursing, a new `Options` object can be created with the `.with*` and + * `.reset` functions. + */ +var sizeStyleMap = [// Each element contains [textsize, scriptsize, scriptscriptsize]. +// The size mappings are taken from TeX with \normalsize=10pt. +[1, 1, 1], // size1: [5, 5, 5] \tiny +[2, 1, 1], // size2: [6, 5, 5] +[3, 1, 1], // size3: [7, 5, 5] \scriptsize +[4, 2, 1], // size4: [8, 6, 5] \footnotesize +[5, 2, 1], // size5: [9, 6, 5] \small +[6, 3, 1], // size6: [10, 7, 5] \normalsize +[7, 4, 2], // size7: [12, 8, 6] \large +[8, 6, 3], // size8: [14.4, 10, 7] \Large +[9, 7, 6], // size9: [17.28, 12, 10] \LARGE +[10, 8, 7], // size10: [20.74, 14.4, 12] \huge +[11, 10, 9] // size11: [24.88, 20.74, 17.28] \HUGE +]; +var sizeMultipliers = [// fontMetrics.js:getGlobalMetrics also uses size indexes, so if +// you change size indexes, change that function. +0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.2, 1.44, 1.728, 2.074, 2.488]; + +var sizeAtStyle = function sizeAtStyle(size, style) { + return style.size < 2 ? size : sizeStyleMap[size - 1][style.size - 1]; +}; // In these types, "" (empty string) means "no change". + + +/** + * This is the main options class. It contains the current style, size, color, + * and font. + * + * Options objects should not be modified. To create a new Options with + * different properties, call a `.having*` method. + */ +class Options { + // A font family applies to a group of fonts (i.e. SansSerif), while a font + // represents a specific font (i.e. SansSerif Bold). + // See: https://tex.stackexchange.com/questions/22350/difference-between-textrm-and-mathrm + + /** + * The base size index. + */ + constructor(data) { + this.style = void 0; + this.color = void 0; + this.size = void 0; + this.textSize = void 0; + this.phantom = void 0; + this.font = void 0; + this.fontFamily = void 0; + this.fontWeight = void 0; + this.fontShape = void 0; + this.sizeMultiplier = void 0; + this.maxSize = void 0; + this.minRuleThickness = void 0; + this._fontMetrics = void 0; + this.style = data.style; + this.color = data.color; + this.size = data.size || Options.BASESIZE; + this.textSize = data.textSize || this.size; + this.phantom = !!data.phantom; + this.font = data.font || ""; + this.fontFamily = data.fontFamily || ""; + this.fontWeight = data.fontWeight || ''; + this.fontShape = data.fontShape || ''; + this.sizeMultiplier = sizeMultipliers[this.size - 1]; + this.maxSize = data.maxSize; + this.minRuleThickness = data.minRuleThickness; + this._fontMetrics = undefined; + } + /** + * Returns a new options object with the same properties as "this". Properties + * from "extension" will be copied to the new options object. + */ + + + extend(extension) { + var data = { + style: this.style, + size: this.size, + textSize: this.textSize, + color: this.color, + phantom: this.phantom, + font: this.font, + fontFamily: this.fontFamily, + fontWeight: this.fontWeight, + fontShape: this.fontShape, + maxSize: this.maxSize, + minRuleThickness: this.minRuleThickness + }; + + for (var key in extension) { + if (extension.hasOwnProperty(key)) { + data[key] = extension[key]; + } + } + + return new Options(data); + } + /** + * Return an options object with the given style. If `this.style === style`, + * returns `this`. + */ + + + havingStyle(style) { + if (this.style === style) { + return this; + } else { + return this.extend({ + style: style, + size: sizeAtStyle(this.textSize, style) + }); + } + } + /** + * Return an options object with a cramped version of the current style. If + * the current style is cramped, returns `this`. + */ + + + havingCrampedStyle() { + return this.havingStyle(this.style.cramp()); + } + /** + * Return an options object with the given size and in at least `\textstyle`. + * Returns `this` if appropriate. + */ + + + havingSize(size) { + if (this.size === size && this.textSize === size) { + return this; + } else { + return this.extend({ + style: this.style.text(), + size: size, + textSize: size, + sizeMultiplier: sizeMultipliers[size - 1] + }); + } + } + /** + * Like `this.havingSize(BASESIZE).havingStyle(style)`. If `style` is omitted, + * changes to at least `\textstyle`. + */ + + + havingBaseStyle(style) { + style = style || this.style.text(); + var wantSize = sizeAtStyle(Options.BASESIZE, style); + + if (this.size === wantSize && this.textSize === Options.BASESIZE && this.style === style) { + return this; + } else { + return this.extend({ + style: style, + size: wantSize + }); + } + } + /** + * Remove the effect of sizing changes such as \Huge. + * Keep the effect of the current style, such as \scriptstyle. + */ + + + havingBaseSizing() { + var size; + + switch (this.style.id) { + case 4: + case 5: + size = 3; // normalsize in scriptstyle + + break; + + case 6: + case 7: + size = 1; // normalsize in scriptscriptstyle + + break; + + default: + size = 6; + // normalsize in textstyle or displaystyle + } + + return this.extend({ + style: this.style.text(), + size: size + }); + } + /** + * Create a new options object with the given color. + */ + + + withColor(color) { + return this.extend({ + color: color + }); + } + /** + * Create a new options object with "phantom" set to true. + */ + + + withPhantom() { + return this.extend({ + phantom: true + }); + } + /** + * Creates a new options object with the given math font or old text font. + * @type {[type]} + */ + + + withFont(font) { + return this.extend({ + font + }); + } + /** + * Create a new options objects with the given fontFamily. + */ + + + withTextFontFamily(fontFamily) { + return this.extend({ + fontFamily, + font: "" + }); + } + /** + * Creates a new options object with the given font weight + */ + + + withTextFontWeight(fontWeight) { + return this.extend({ + fontWeight, + font: "" + }); + } + /** + * Creates a new options object with the given font weight + */ + + + withTextFontShape(fontShape) { + return this.extend({ + fontShape, + font: "" + }); + } + /** + * Return the CSS sizing classes required to switch from enclosing options + * `oldOptions` to `this`. Returns an array of classes. + */ + + + sizingClasses(oldOptions) { + if (oldOptions.size !== this.size) { + return ["sizing", "reset-size" + oldOptions.size, "size" + this.size]; + } else { + return []; + } + } + /** + * Return the CSS sizing classes required to switch to the base size. Like + * `this.havingSize(BASESIZE).sizingClasses(this)`. + */ + + + baseSizingClasses() { + if (this.size !== Options.BASESIZE) { + return ["sizing", "reset-size" + this.size, "size" + Options.BASESIZE]; + } else { + return []; + } + } + /** + * Return the font metrics for this size. + */ + + + fontMetrics() { + if (!this._fontMetrics) { + this._fontMetrics = getGlobalMetrics(this.size); + } + + return this._fontMetrics; + } + /** + * Gets the CSS color of the current options object + */ + + + getColor() { + if (this.phantom) { + return "transparent"; + } else { + return this.color; + } + } + +} + +Options.BASESIZE = 6; + +/** + * This file does conversion between units. In particular, it provides + * calculateSize to convert other units into ems. + */ +// Thus, multiplying a length by this number converts the length from units +// into pts. Dividing the result by ptPerEm gives the number of ems +// *assuming* a font size of ptPerEm (normal size, normal style). + +var ptPerUnit = { + // https://en.wikibooks.org/wiki/LaTeX/Lengths and + // https://tex.stackexchange.com/a/8263 + "pt": 1, + // TeX point + "mm": 7227 / 2540, + // millimeter + "cm": 7227 / 254, + // centimeter + "in": 72.27, + // inch + "bp": 803 / 800, + // big (PostScript) points + "pc": 12, + // pica + "dd": 1238 / 1157, + // didot + "cc": 14856 / 1157, + // cicero (12 didot) + "nd": 685 / 642, + // new didot + "nc": 1370 / 107, + // new cicero (12 new didot) + "sp": 1 / 65536, + // scaled point (TeX's internal smallest unit) + // https://tex.stackexchange.com/a/41371 + "px": 803 / 800 // \pdfpxdimen defaults to 1 bp in pdfTeX and LuaTeX + +}; // Dictionary of relative units, for fast validity testing. + +var relativeUnit = { + "ex": true, + "em": true, + "mu": true +}; + +/** + * Determine whether the specified unit (either a string defining the unit + * or a "size" parse node containing a unit field) is valid. + */ +var validUnit = function validUnit(unit) { + if (typeof unit !== "string") { + unit = unit.unit; + } + + return unit in ptPerUnit || unit in relativeUnit || unit === "ex"; +}; +/* + * Convert a "size" parse node (with numeric "number" and string "unit" fields, + * as parsed by functions.js argType "size") into a CSS em value for the + * current style/scale. `options` gives the current options. + */ + +var calculateSize = function calculateSize(sizeValue, options) { + var scale; + + if (sizeValue.unit in ptPerUnit) { + // Absolute units + scale = ptPerUnit[sizeValue.unit] // Convert unit to pt + / options.fontMetrics().ptPerEm // Convert pt to CSS em + / options.sizeMultiplier; // Unscale to make absolute units + } else if (sizeValue.unit === "mu") { + // `mu` units scale with scriptstyle/scriptscriptstyle. + scale = options.fontMetrics().cssEmPerMu; + } else { + // Other relative units always refer to the *textstyle* font + // in the current size. + var unitOptions; + + if (options.style.isTight()) { + // isTight() means current style is script/scriptscript. + unitOptions = options.havingStyle(options.style.text()); + } else { + unitOptions = options; + } // TODO: In TeX these units are relative to the quad of the current + // *text* font, e.g. cmr10. KaTeX instead uses values from the + // comparably-sized *Computer Modern symbol* font. At 10pt, these + // match. At 7pt and 5pt, they differ: cmr7=1.138894, cmsy7=1.170641; + // cmr5=1.361133, cmsy5=1.472241. Consider $\scriptsize a\kern1emb$. + // TeX \showlists shows a kern of 1.13889 * fontsize; + // KaTeX shows a kern of 1.171 * fontsize. + + + if (sizeValue.unit === "ex") { + scale = unitOptions.fontMetrics().xHeight; + } else if (sizeValue.unit === "em") { + scale = unitOptions.fontMetrics().quad; + } else { + throw new ParseError("Invalid unit: '" + sizeValue.unit + "'"); + } + + if (unitOptions !== options) { + scale *= unitOptions.sizeMultiplier / options.sizeMultiplier; + } + } + + return Math.min(sizeValue.number * scale, options.maxSize); +}; + +/* eslint no-console:0 */ + +/** + * Looks up the given symbol in fontMetrics, after applying any symbol + * replacements defined in symbol.js + */ +var lookupSymbol = function lookupSymbol(value, // TODO(#963): Use a union type for this. +fontName, mode) { + // Replace the value with its replaced value from symbol.js + if (symbols[mode][value] && symbols[mode][value].replace) { + value = symbols[mode][value].replace; + } + + return { + value: value, + metrics: getCharacterMetrics(value, fontName, mode) + }; +}; +/** + * Makes a symbolNode after translation via the list of symbols in symbols.js. + * Correctly pulls out metrics for the character, and optionally takes a list of + * classes to be attached to the node. + * + * TODO: make argument order closer to makeSpan + * TODO: add a separate argument for math class (e.g. `mop`, `mbin`), which + * should if present come first in `classes`. + * TODO(#953): Make `options` mandatory and always pass it in. + */ + + +var makeSymbol = function makeSymbol(value, fontName, mode, options, classes) { + var lookup = lookupSymbol(value, fontName, mode); + var metrics = lookup.metrics; + value = lookup.value; + var symbolNode; + + if (metrics) { + var italic = metrics.italic; + + if (mode === "text" || options && options.font === "mathit") { + italic = 0; + } + + symbolNode = new SymbolNode(value, metrics.height, metrics.depth, italic, metrics.skew, metrics.width, classes); + } else { + // TODO(emily): Figure out a good way to only print this in development + typeof console !== "undefined" && console.warn("No character metrics " + ("for '" + value + "' in style '" + fontName + "' and mode '" + mode + "'")); + symbolNode = new SymbolNode(value, 0, 0, 0, 0, 0, classes); + } + + if (options) { + symbolNode.maxFontSize = options.sizeMultiplier; + + if (options.style.isTight()) { + symbolNode.classes.push("mtight"); + } + + var color = options.getColor(); + + if (color) { + symbolNode.style.color = color; + } + } + + return symbolNode; +}; +/** + * Makes a symbol in Main-Regular or AMS-Regular. + * Used for rel, bin, open, close, inner, and punct. + */ + + +var mathsym = function mathsym(value, mode, options, classes) { + if (classes === void 0) { + classes = []; + } + + // Decide what font to render the symbol in by its entry in the symbols + // table. + // Have a special case for when the value = \ because the \ is used as a + // textord in unsupported command errors but cannot be parsed as a regular + // text ordinal and is therefore not present as a symbol in the symbols + // table for text, as well as a special case for boldsymbol because it + // can be used for bold + and - + if (options.font === "boldsymbol" && lookupSymbol(value, "Main-Bold", mode).metrics) { + return makeSymbol(value, "Main-Bold", mode, options, classes.concat(["mathbf"])); + } else if (value === "\\" || symbols[mode][value].font === "main") { + return makeSymbol(value, "Main-Regular", mode, options, classes); + } else { + return makeSymbol(value, "AMS-Regular", mode, options, classes.concat(["amsrm"])); + } +}; +/** + * Determines which of the two font names (Main-Bold and Math-BoldItalic) and + * corresponding style tags (mathbf or boldsymbol) to use for font "boldsymbol", + * depending on the symbol. Use this function instead of fontMap for font + * "boldsymbol". + */ + + +var boldsymbol = function boldsymbol(value, mode, options, classes, type) { + if (type !== "textord" && lookupSymbol(value, "Math-BoldItalic", mode).metrics) { + return { + fontName: "Math-BoldItalic", + fontClass: "boldsymbol" + }; + } else { + // Some glyphs do not exist in Math-BoldItalic so we need to use + // Main-Bold instead. + return { + fontName: "Main-Bold", + fontClass: "mathbf" + }; + } +}; +/** + * Makes either a mathord or textord in the correct font and color. + */ + + +var makeOrd = function makeOrd(group, options, type) { + var mode = group.mode; + var text = group.text; + var classes = ["mord"]; // Math mode or Old font (i.e. \rm) + + var isFont = mode === "math" || mode === "text" && options.font; + var fontOrFamily = isFont ? options.font : options.fontFamily; + + if (text.charCodeAt(0) === 0xD835) { + // surrogate pairs get special treatment + var [wideFontName, wideFontClass] = wideCharacterFont(text, mode); + return makeSymbol(text, wideFontName, mode, options, classes.concat(wideFontClass)); + } else if (fontOrFamily) { + var fontName; + var fontClasses; + + if (fontOrFamily === "boldsymbol") { + var fontData = boldsymbol(text, mode, options, classes, type); + fontName = fontData.fontName; + fontClasses = [fontData.fontClass]; + } else if (isFont) { + fontName = fontMap[fontOrFamily].fontName; + fontClasses = [fontOrFamily]; + } else { + fontName = retrieveTextFontName(fontOrFamily, options.fontWeight, options.fontShape); + fontClasses = [fontOrFamily, options.fontWeight, options.fontShape]; + } + + if (lookupSymbol(text, fontName, mode).metrics) { + return makeSymbol(text, fontName, mode, options, classes.concat(fontClasses)); + } else if (ligatures.hasOwnProperty(text) && fontName.substr(0, 10) === "Typewriter") { + // Deconstruct ligatures in monospace fonts (\texttt, \tt). + var parts = []; + + for (var i = 0; i < text.length; i++) { + parts.push(makeSymbol(text[i], fontName, mode, options, classes.concat(fontClasses))); + } + + return makeFragment(parts); + } + } // Makes a symbol in the default font for mathords and textords. + + + if (type === "mathord") { + return makeSymbol(text, "Math-Italic", mode, options, classes.concat(["mathnormal"])); + } else if (type === "textord") { + var font = symbols[mode][text] && symbols[mode][text].font; + + if (font === "ams") { + var _fontName = retrieveTextFontName("amsrm", options.fontWeight, options.fontShape); + + return makeSymbol(text, _fontName, mode, options, classes.concat("amsrm", options.fontWeight, options.fontShape)); + } else if (font === "main" || !font) { + var _fontName2 = retrieveTextFontName("textrm", options.fontWeight, options.fontShape); + + return makeSymbol(text, _fontName2, mode, options, classes.concat(options.fontWeight, options.fontShape)); + } else { + // fonts added by plugins + var _fontName3 = retrieveTextFontName(font, options.fontWeight, options.fontShape); // We add font name as a css class + + + return makeSymbol(text, _fontName3, mode, options, classes.concat(_fontName3, options.fontWeight, options.fontShape)); + } + } else { + throw new Error("unexpected type: " + type + " in makeOrd"); + } +}; +/** + * Returns true if subsequent symbolNodes have the same classes, skew, maxFont, + * and styles. + */ + + +var canCombine = (prev, next) => { + if (createClass(prev.classes) !== createClass(next.classes) || prev.skew !== next.skew || prev.maxFontSize !== next.maxFontSize) { + return false; + } // If prev and next both are just "mbin"s or "mord"s we don't combine them + // so that the proper spacing can be preserved. + + + if (prev.classes.length === 1) { + var cls = prev.classes[0]; + + if (cls === "mbin" || cls === "mord") { + return false; + } + } + + for (var style in prev.style) { + if (prev.style.hasOwnProperty(style) && prev.style[style] !== next.style[style]) { + return false; + } + } + + for (var _style in next.style) { + if (next.style.hasOwnProperty(_style) && prev.style[_style] !== next.style[_style]) { + return false; + } + } + + return true; +}; +/** + * Combine consecutive domTree.symbolNodes into a single symbolNode. + * Note: this function mutates the argument. + */ + + +var tryCombineChars = chars => { + for (var i = 0; i < chars.length - 1; i++) { + var prev = chars[i]; + var next = chars[i + 1]; + + if (prev instanceof SymbolNode && next instanceof SymbolNode && canCombine(prev, next)) { + prev.text += next.text; + prev.height = Math.max(prev.height, next.height); + prev.depth = Math.max(prev.depth, next.depth); // Use the last character's italic correction since we use + // it to add padding to the right of the span created from + // the combined characters. + + prev.italic = next.italic; + chars.splice(i + 1, 1); + i--; + } + } + + return chars; +}; +/** + * Calculate the height, depth, and maxFontSize of an element based on its + * children. + */ + + +var sizeElementFromChildren = function sizeElementFromChildren(elem) { + var height = 0; + var depth = 0; + var maxFontSize = 0; + + for (var i = 0; i < elem.children.length; i++) { + var child = elem.children[i]; + + if (child.height > height) { + height = child.height; + } + + if (child.depth > depth) { + depth = child.depth; + } + + if (child.maxFontSize > maxFontSize) { + maxFontSize = child.maxFontSize; + } + } + + elem.height = height; + elem.depth = depth; + elem.maxFontSize = maxFontSize; +}; +/** + * Makes a span with the given list of classes, list of children, and options. + * + * TODO(#953): Ensure that `options` is always provided (currently some call + * sites don't pass it) and make the type below mandatory. + * TODO: add a separate argument for math class (e.g. `mop`, `mbin`), which + * should if present come first in `classes`. + */ + + +var makeSpan$2 = function makeSpan(classes, children, options, style) { + var span = new Span(classes, children, options, style); + sizeElementFromChildren(span); + return span; +}; // SVG one is simpler -- doesn't require height, depth, max-font setting. +// This is also a separate method for typesafety. + + +var makeSvgSpan = (classes, children, options, style) => new Span(classes, children, options, style); + +var makeLineSpan = function makeLineSpan(className, options, thickness) { + var line = makeSpan$2([className], [], options); + line.height = Math.max(thickness || options.fontMetrics().defaultRuleThickness, options.minRuleThickness); + line.style.borderBottomWidth = line.height + "em"; + line.maxFontSize = 1.0; + return line; +}; +/** + * Makes an anchor with the given href, list of classes, list of children, + * and options. + */ + + +var makeAnchor = function makeAnchor(href, classes, children, options) { + var anchor = new Anchor(href, classes, children, options); + sizeElementFromChildren(anchor); + return anchor; +}; +/** + * Makes a document fragment with the given list of children. + */ + + +var makeFragment = function makeFragment(children) { + var fragment = new DocumentFragment(children); + sizeElementFromChildren(fragment); + return fragment; +}; +/** + * Wraps group in a span if it's a document fragment, allowing to apply classes + * and styles + */ + + +var wrapFragment = function wrapFragment(group, options) { + if (group instanceof DocumentFragment) { + return makeSpan$2([], [group], options); + } + + return group; +}; // These are exact object types to catch typos in the names of the optional fields. + + +// Computes the updated `children` list and the overall depth. +// +// This helper function for makeVList makes it easier to enforce type safety by +// allowing early exits (returns) in the logic. +var getVListChildrenAndDepth = function getVListChildrenAndDepth(params) { + if (params.positionType === "individualShift") { + var oldChildren = params.children; + var children = [oldChildren[0]]; // Add in kerns to the list of params.children to get each element to be + // shifted to the correct specified shift + + var _depth = -oldChildren[0].shift - oldChildren[0].elem.depth; + + var currPos = _depth; + + for (var i = 1; i < oldChildren.length; i++) { + var diff = -oldChildren[i].shift - currPos - oldChildren[i].elem.depth; + var size = diff - (oldChildren[i - 1].elem.height + oldChildren[i - 1].elem.depth); + currPos = currPos + diff; + children.push({ + type: "kern", + size + }); + children.push(oldChildren[i]); + } + + return { + children, + depth: _depth + }; + } + + var depth; + + if (params.positionType === "top") { + // We always start at the bottom, so calculate the bottom by adding up + // all the sizes + var bottom = params.positionData; + + for (var _i = 0; _i < params.children.length; _i++) { + var child = params.children[_i]; + bottom -= child.type === "kern" ? child.size : child.elem.height + child.elem.depth; + } + + depth = bottom; + } else if (params.positionType === "bottom") { + depth = -params.positionData; + } else { + var firstChild = params.children[0]; + + if (firstChild.type !== "elem") { + throw new Error('First child must have type "elem".'); + } + + if (params.positionType === "shift") { + depth = -firstChild.elem.depth - params.positionData; + } else if (params.positionType === "firstBaseline") { + depth = -firstChild.elem.depth; + } else { + throw new Error("Invalid positionType " + params.positionType + "."); + } + } + + return { + children: params.children, + depth + }; +}; +/** + * Makes a vertical list by stacking elements and kerns on top of each other. + * Allows for many different ways of specifying the positioning method. + * + * See VListParam documentation above. + */ + + +var makeVList = function makeVList(params, options) { + var { + children, + depth + } = getVListChildrenAndDepth(params); // Create a strut that is taller than any list item. The strut is added to + // each item, where it will determine the item's baseline. Since it has + // `overflow:hidden`, the strut's top edge will sit on the item's line box's + // top edge and the strut's bottom edge will sit on the item's baseline, + // with no additional line-height spacing. This allows the item baseline to + // be positioned precisely without worrying about font ascent and + // line-height. + + var pstrutSize = 0; + + for (var i = 0; i < children.length; i++) { + var child = children[i]; + + if (child.type === "elem") { + var elem = child.elem; + pstrutSize = Math.max(pstrutSize, elem.maxFontSize, elem.height); + } + } + + pstrutSize += 2; + var pstrut = makeSpan$2(["pstrut"], []); + pstrut.style.height = pstrutSize + "em"; // Create a new list of actual children at the correct offsets + + var realChildren = []; + var minPos = depth; + var maxPos = depth; + var currPos = depth; + + for (var _i2 = 0; _i2 < children.length; _i2++) { + var _child = children[_i2]; + + if (_child.type === "kern") { + currPos += _child.size; + } else { + var _elem = _child.elem; + var classes = _child.wrapperClasses || []; + var style = _child.wrapperStyle || {}; + var childWrap = makeSpan$2(classes, [pstrut, _elem], undefined, style); + childWrap.style.top = -pstrutSize - currPos - _elem.depth + "em"; + + if (_child.marginLeft) { + childWrap.style.marginLeft = _child.marginLeft; + } + + if (_child.marginRight) { + childWrap.style.marginRight = _child.marginRight; + } + + realChildren.push(childWrap); + currPos += _elem.height + _elem.depth; + } + + minPos = Math.min(minPos, currPos); + maxPos = Math.max(maxPos, currPos); + } // The vlist contents go in a table-cell with `vertical-align:bottom`. + // This cell's bottom edge will determine the containing table's baseline + // without overly expanding the containing line-box. + + + var vlist = makeSpan$2(["vlist"], realChildren); + vlist.style.height = maxPos + "em"; // A second row is used if necessary to represent the vlist's depth. + + var rows; + + if (minPos < 0) { + // We will define depth in an empty span with display: table-cell. + // It should render with the height that we define. But Chrome, in + // contenteditable mode only, treats that span as if it contains some + // text content. And that min-height over-rides our desired height. + // So we put another empty span inside the depth strut span. + var emptySpan = makeSpan$2([], []); + var depthStrut = makeSpan$2(["vlist"], [emptySpan]); + depthStrut.style.height = -minPos + "em"; // Safari wants the first row to have inline content; otherwise it + // puts the bottom of the *second* row on the baseline. + + var topStrut = makeSpan$2(["vlist-s"], [new SymbolNode("\u200b")]); + rows = [makeSpan$2(["vlist-r"], [vlist, topStrut]), makeSpan$2(["vlist-r"], [depthStrut])]; + } else { + rows = [makeSpan$2(["vlist-r"], [vlist])]; + } + + var vtable = makeSpan$2(["vlist-t"], rows); + + if (rows.length === 2) { + vtable.classes.push("vlist-t2"); + } + + vtable.height = maxPos; + vtable.depth = -minPos; + return vtable; +}; // Glue is a concept from TeX which is a flexible space between elements in +// either a vertical or horizontal list. In KaTeX, at least for now, it's +// static space between elements in a horizontal layout. + + +var makeGlue = (measurement, options) => { + // Make an empty span for the space + var rule = makeSpan$2(["mspace"], [], options); + var size = calculateSize(measurement, options); + rule.style.marginRight = size + "em"; + return rule; +}; // Takes font options, and returns the appropriate fontLookup name + + +var retrieveTextFontName = function retrieveTextFontName(fontFamily, fontWeight, fontShape) { + var baseFontName = ""; + + switch (fontFamily) { + case "amsrm": + baseFontName = "AMS"; + break; + + case "textrm": + baseFontName = "Main"; + break; + + case "textsf": + baseFontName = "SansSerif"; + break; + + case "texttt": + baseFontName = "Typewriter"; + break; + + default: + baseFontName = fontFamily; + // use fonts added by a plugin + } + + var fontStylesName; + + if (fontWeight === "textbf" && fontShape === "textit") { + fontStylesName = "BoldItalic"; + } else if (fontWeight === "textbf") { + fontStylesName = "Bold"; + } else if (fontWeight === "textit") { + fontStylesName = "Italic"; + } else { + fontStylesName = "Regular"; + } + + return baseFontName + "-" + fontStylesName; +}; +/** + * Maps TeX font commands to objects containing: + * - variant: string used for "mathvariant" attribute in buildMathML.js + * - fontName: the "style" parameter to fontMetrics.getCharacterMetrics + */ +// A map between tex font commands an MathML mathvariant attribute values + + +var fontMap = { + // styles + "mathbf": { + variant: "bold", + fontName: "Main-Bold" + }, + "mathrm": { + variant: "normal", + fontName: "Main-Regular" + }, + "textit": { + variant: "italic", + fontName: "Main-Italic" + }, + "mathit": { + variant: "italic", + fontName: "Main-Italic" + }, + "mathnormal": { + variant: "italic", + fontName: "Math-Italic" + }, + // "boldsymbol" is missing because they require the use of multiple fonts: + // Math-BoldItalic and Main-Bold. This is handled by a special case in + // makeOrd which ends up calling boldsymbol. + // families + "mathbb": { + variant: "double-struck", + fontName: "AMS-Regular" + }, + "mathcal": { + variant: "script", + fontName: "Caligraphic-Regular" + }, + "mathfrak": { + variant: "fraktur", + fontName: "Fraktur-Regular" + }, + "mathscr": { + variant: "script", + fontName: "Script-Regular" + }, + "mathsf": { + variant: "sans-serif", + fontName: "SansSerif-Regular" + }, + "mathtt": { + variant: "monospace", + fontName: "Typewriter-Regular" + } +}; +var svgData = { + // path, width, height + vec: ["vec", 0.471, 0.714], + // values from the font glyph + oiintSize1: ["oiintSize1", 0.957, 0.499], + // oval to overlay the integrand + oiintSize2: ["oiintSize2", 1.472, 0.659], + oiiintSize1: ["oiiintSize1", 1.304, 0.499], + oiiintSize2: ["oiiintSize2", 1.98, 0.659] +}; + +var staticSvg = function staticSvg(value, options) { + // Create a span with inline SVG for the element. + var [pathName, width, height] = svgData[value]; + var path = new PathNode(pathName); + var svgNode = new SvgNode([path], { + "width": width + "em", + "height": height + "em", + // Override CSS rule `.katex svg { width: 100% }` + "style": "width:" + width + "em", + "viewBox": "0 0 " + 1000 * width + " " + 1000 * height, + "preserveAspectRatio": "xMinYMin" + }); + var span = makeSvgSpan(["overlay"], [svgNode], options); + span.height = height; + span.style.height = height + "em"; + span.style.width = width + "em"; + return span; +}; + +var buildCommon = { + fontMap, + makeSymbol, + mathsym, + makeSpan: makeSpan$2, + makeSvgSpan, + makeLineSpan, + makeAnchor, + makeFragment, + wrapFragment, + makeVList, + makeOrd, + makeGlue, + staticSvg, + svgData, + tryCombineChars +}; + +/** + * Describes spaces between different classes of atoms. + */ +var thinspace = { + number: 3, + unit: "mu" +}; +var mediumspace = { + number: 4, + unit: "mu" +}; +var thickspace = { + number: 5, + unit: "mu" +}; // Making the type below exact with all optional fields doesn't work due to +// - https://github.com/facebook/flow/issues/4582 +// - https://github.com/facebook/flow/issues/5688 +// However, since *all* fields are optional, $Shape<> works as suggested in 5688 +// above. + +// Spacing relationships for display and text styles +var spacings = { + mord: { + mop: thinspace, + mbin: mediumspace, + mrel: thickspace, + minner: thinspace + }, + mop: { + mord: thinspace, + mop: thinspace, + mrel: thickspace, + minner: thinspace + }, + mbin: { + mord: mediumspace, + mop: mediumspace, + mopen: mediumspace, + minner: mediumspace + }, + mrel: { + mord: thickspace, + mop: thickspace, + mopen: thickspace, + minner: thickspace + }, + mopen: {}, + mclose: { + mop: thinspace, + mbin: mediumspace, + mrel: thickspace, + minner: thinspace + }, + mpunct: { + mord: thinspace, + mop: thinspace, + mrel: thickspace, + mopen: thinspace, + mclose: thinspace, + mpunct: thinspace, + minner: thinspace + }, + minner: { + mord: thinspace, + mop: thinspace, + mbin: mediumspace, + mrel: thickspace, + mopen: thinspace, + mpunct: thinspace, + minner: thinspace + } +}; // Spacing relationships for script and scriptscript styles + +var tightSpacings = { + mord: { + mop: thinspace + }, + mop: { + mord: thinspace, + mop: thinspace + }, + mbin: {}, + mrel: {}, + mopen: {}, + mclose: { + mop: thinspace + }, + mpunct: {}, + minner: { + mop: thinspace + } +}; + +/** Context provided to function handlers for error messages. */ +// Note: reverse the order of the return type union will cause a flow error. +// See https://github.com/facebook/flow/issues/3663. +// More general version of `HtmlBuilder` for nodes (e.g. \sum, accent types) +// whose presence impacts super/subscripting. In this case, ParseNode<"supsub"> +// delegates its HTML building to the HtmlBuilder corresponding to these nodes. + +/** + * Final function spec for use at parse time. + * This is almost identical to `FunctionPropSpec`, except it + * 1. includes the function handler, and + * 2. requires all arguments except argTypes. + * It is generated by `defineFunction()` below. + */ + +/** + * All registered functions. + * `functions.js` just exports this same dictionary again and makes it public. + * `Parser.js` requires this dictionary. + */ +var _functions = {}; +/** + * All HTML builders. Should be only used in the `define*` and the `build*ML` + * functions. + */ + +var _htmlGroupBuilders = {}; +/** + * All MathML builders. Should be only used in the `define*` and the `build*ML` + * functions. + */ + +var _mathmlGroupBuilders = {}; +function defineFunction(_ref) { + var { + type, + names, + props, + handler, + htmlBuilder, + mathmlBuilder + } = _ref; + // Set default values of functions + var data = { + type, + numArgs: props.numArgs, + argTypes: props.argTypes, + allowedInArgument: !!props.allowedInArgument, + allowedInText: !!props.allowedInText, + allowedInMath: props.allowedInMath === undefined ? true : props.allowedInMath, + numOptionalArgs: props.numOptionalArgs || 0, + infix: !!props.infix, + primitive: !!props.primitive, + handler: handler + }; + + for (var i = 0; i < names.length; ++i) { + _functions[names[i]] = data; + } + + if (type) { + if (htmlBuilder) { + _htmlGroupBuilders[type] = htmlBuilder; + } + + if (mathmlBuilder) { + _mathmlGroupBuilders[type] = mathmlBuilder; + } + } +} +/** + * Use this to register only the HTML and MathML builders for a function (e.g. + * if the function's ParseNode is generated in Parser.js rather than via a + * stand-alone handler provided to `defineFunction`). + */ + +function defineFunctionBuilders(_ref2) { + var { + type, + htmlBuilder, + mathmlBuilder + } = _ref2; + defineFunction({ + type, + names: [], + props: { + numArgs: 0 + }, + + handler() { + throw new Error('Should never be called.'); + }, + + htmlBuilder, + mathmlBuilder + }); +} +var normalizeArgument = function normalizeArgument(arg) { + return arg.type === "ordgroup" && arg.body.length === 1 ? arg.body[0] : arg; +}; // Since the corresponding buildHTML/buildMathML function expects a +// list of elements, we normalize for different kinds of arguments + +var ordargument = function ordargument(arg) { + return arg.type === "ordgroup" ? arg.body : [arg]; +}; + +/** + * This file does the main work of building a domTree structure from a parse + * tree. The entry point is the `buildHTML` function, which takes a parse tree. + * Then, the buildExpression, buildGroup, and various groupBuilders functions + * are called, to produce a final HTML tree. + */ +var makeSpan$1 = buildCommon.makeSpan; // Binary atoms (first class `mbin`) change into ordinary atoms (`mord`) +// depending on their surroundings. See TeXbook pg. 442-446, Rules 5 and 6, +// and the text before Rule 19. + +var binLeftCanceller = ["leftmost", "mbin", "mopen", "mrel", "mop", "mpunct"]; +var binRightCanceller = ["rightmost", "mrel", "mclose", "mpunct"]; +var styleMap$1 = { + "display": Style$1.DISPLAY, + "text": Style$1.TEXT, + "script": Style$1.SCRIPT, + "scriptscript": Style$1.SCRIPTSCRIPT +}; +var DomEnum = { + mord: "mord", + mop: "mop", + mbin: "mbin", + mrel: "mrel", + mopen: "mopen", + mclose: "mclose", + mpunct: "mpunct", + minner: "minner" +}; + +/** + * Take a list of nodes, build them in order, and return a list of the built + * nodes. documentFragments are flattened into their contents, so the + * returned list contains no fragments. `isRealGroup` is true if `expression` + * is a real group (no atoms will be added on either side), as opposed to + * a partial group (e.g. one created by \color). `surrounding` is an array + * consisting type of nodes that will be added to the left and right. + */ +var buildExpression$1 = function buildExpression(expression, options, isRealGroup, surrounding) { + if (surrounding === void 0) { + surrounding = [null, null]; + } + + // Parse expressions into `groups`. + var groups = []; + + for (var i = 0; i < expression.length; i++) { + var output = buildGroup$1(expression[i], options); + + if (output instanceof DocumentFragment) { + var children = output.children; + groups.push(...children); + } else { + groups.push(output); + } + } // Combine consecutive domTree.symbolNodes into a single symbolNode. + + + buildCommon.tryCombineChars(groups); // If `expression` is a partial group, let the parent handle spacings + // to avoid processing groups multiple times. + + if (!isRealGroup) { + return groups; + } + + var glueOptions = options; + + if (expression.length === 1) { + var node = expression[0]; + + if (node.type === "sizing") { + glueOptions = options.havingSize(node.size); + } else if (node.type === "styling") { + glueOptions = options.havingStyle(styleMap$1[node.style]); + } + } // Dummy spans for determining spacings between surrounding atoms. + // If `expression` has no atoms on the left or right, class "leftmost" + // or "rightmost", respectively, is used to indicate it. + + + var dummyPrev = makeSpan$1([surrounding[0] || "leftmost"], [], options); + var dummyNext = makeSpan$1([surrounding[1] || "rightmost"], [], options); // TODO: These code assumes that a node's math class is the first element + // of its `classes` array. A later cleanup should ensure this, for + // instance by changing the signature of `makeSpan`. + // Before determining what spaces to insert, perform bin cancellation. + // Binary operators change to ordinary symbols in some contexts. + + var isRoot = isRealGroup === "root"; + traverseNonSpaceNodes(groups, (node, prev) => { + var prevType = prev.classes[0]; + var type = node.classes[0]; + + if (prevType === "mbin" && utils.contains(binRightCanceller, type)) { + prev.classes[0] = "mord"; + } else if (type === "mbin" && utils.contains(binLeftCanceller, prevType)) { + node.classes[0] = "mord"; + } + }, { + node: dummyPrev + }, dummyNext, isRoot); + traverseNonSpaceNodes(groups, (node, prev) => { + var prevType = getTypeOfDomTree(prev); + var type = getTypeOfDomTree(node); // 'mtight' indicates that the node is script or scriptscript style. + + var space = prevType && type ? node.hasClass("mtight") ? tightSpacings[prevType][type] : spacings[prevType][type] : null; + + if (space) { + // Insert glue (spacing) after the `prev`. + return buildCommon.makeGlue(space, glueOptions); + } + }, { + node: dummyPrev + }, dummyNext, isRoot); + return groups; +}; // Depth-first traverse non-space `nodes`, calling `callback` with the current and +// previous node as arguments, optionally returning a node to insert after the +// previous node. `prev` is an object with the previous node and `insertAfter` +// function to insert after it. `next` is a node that will be added to the right. +// Used for bin cancellation and inserting spacings. + +var traverseNonSpaceNodes = function traverseNonSpaceNodes(nodes, callback, prev, next, isRoot) { + if (next) { + // temporarily append the right node, if exists + nodes.push(next); + } + + var i = 0; + + for (; i < nodes.length; i++) { + var node = nodes[i]; + var partialGroup = checkPartialGroup(node); + + if (partialGroup) { + // Recursive DFS + // $FlowFixMe: make nodes a $ReadOnlyArray by returning a new array + traverseNonSpaceNodes(partialGroup.children, callback, prev, null, isRoot); + continue; + } // Ignore explicit spaces (e.g., \;, \,) when determining what implicit + // spacing should go between atoms of different classes + + + var nonspace = !node.hasClass("mspace"); + + if (nonspace) { + var result = callback(node, prev.node); + + if (result) { + if (prev.insertAfter) { + prev.insertAfter(result); + } else { + // insert at front + nodes.unshift(result); + i++; + } + } + } + + if (nonspace) { + prev.node = node; + } else if (isRoot && node.hasClass("newline")) { + prev.node = makeSpan$1(["leftmost"]); // treat like beginning of line + } + + prev.insertAfter = (index => n => { + nodes.splice(index + 1, 0, n); + i++; + })(i); + } + + if (next) { + nodes.pop(); + } +}; // Check if given node is a partial group, i.e., does not affect spacing around. + + +var checkPartialGroup = function checkPartialGroup(node) { + if (node instanceof DocumentFragment || node instanceof Anchor || node instanceof Span && node.hasClass("enclosing")) { + return node; + } + + return null; +}; // Return the outermost node of a domTree. + + +var getOutermostNode = function getOutermostNode(node, side) { + var partialGroup = checkPartialGroup(node); + + if (partialGroup) { + var children = partialGroup.children; + + if (children.length) { + if (side === "right") { + return getOutermostNode(children[children.length - 1], "right"); + } else if (side === "left") { + return getOutermostNode(children[0], "left"); + } + } + } + + return node; +}; // Return math atom class (mclass) of a domTree. +// If `side` is given, it will get the type of the outermost node at given side. + + +var getTypeOfDomTree = function getTypeOfDomTree(node, side) { + if (!node) { + return null; + } + + if (side) { + node = getOutermostNode(node, side); + } // This makes a lot of assumptions as to where the type of atom + // appears. We should do a better job of enforcing this. + + + return DomEnum[node.classes[0]] || null; +}; +var makeNullDelimiter = function makeNullDelimiter(options, classes) { + var moreClasses = ["nulldelimiter"].concat(options.baseSizingClasses()); + return makeSpan$1(classes.concat(moreClasses)); +}; +/** + * buildGroup is the function that takes a group and calls the correct groupType + * function for it. It also handles the interaction of size and style changes + * between parents and children. + */ + +var buildGroup$1 = function buildGroup(group, options, baseOptions) { + if (!group) { + return makeSpan$1(); + } + + if (_htmlGroupBuilders[group.type]) { + // Call the groupBuilders function + // $FlowFixMe + var groupNode = _htmlGroupBuilders[group.type](group, options); // If the size changed between the parent and the current group, account + // for that size difference. + + if (baseOptions && options.size !== baseOptions.size) { + groupNode = makeSpan$1(options.sizingClasses(baseOptions), [groupNode], options); + var multiplier = options.sizeMultiplier / baseOptions.sizeMultiplier; + groupNode.height *= multiplier; + groupNode.depth *= multiplier; + } + + return groupNode; + } else { + throw new ParseError("Got group of unknown type: '" + group.type + "'"); + } +}; +/** + * Combine an array of HTML DOM nodes (e.g., the output of `buildExpression`) + * into an unbreakable HTML node of class .base, with proper struts to + * guarantee correct vertical extent. `buildHTML` calls this repeatedly to + * make up the entire expression as a sequence of unbreakable units. + */ + +function buildHTMLUnbreakable(children, options) { + // Compute height and depth of this chunk. + var body = makeSpan$1(["base"], children, options); // Add strut, which ensures that the top of the HTML element falls at + // the height of the expression, and the bottom of the HTML element + // falls at the depth of the expression. + + var strut = makeSpan$1(["strut"]); + strut.style.height = body.height + body.depth + "em"; + strut.style.verticalAlign = -body.depth + "em"; + body.children.unshift(strut); + return body; +} +/** + * Take an entire parse tree, and build it into an appropriate set of HTML + * nodes. + */ + + +function buildHTML(tree, options) { + // Strip off outer tag wrapper for processing below. + var tag = null; + + if (tree.length === 1 && tree[0].type === "tag") { + tag = tree[0].tag; + tree = tree[0].body; + } // Build the expression contained in the tree + + + var expression = buildExpression$1(tree, options, "root"); + var eqnNum; + + if (expression.length === 2 && expression[1].hasClass("tag")) { + // An environment with automatic equation numbers, e.g. {gather}. + eqnNum = expression.pop(); + } + + var children = []; // Create one base node for each chunk between potential line breaks. + // The TeXBook [p.173] says "A formula will be broken only after a + // relation symbol like $=$ or $<$ or $\rightarrow$, or after a binary + // operation symbol like $+$ or $-$ or $\times$, where the relation or + // binary operation is on the ``outer level'' of the formula (i.e., not + // enclosed in {...} and not part of an \over construction)." + + var parts = []; + + for (var i = 0; i < expression.length; i++) { + parts.push(expression[i]); + + if (expression[i].hasClass("mbin") || expression[i].hasClass("mrel") || expression[i].hasClass("allowbreak")) { + // Put any post-operator glue on same line as operator. + // Watch for \nobreak along the way, and stop at \newline. + var nobreak = false; + + while (i < expression.length - 1 && expression[i + 1].hasClass("mspace") && !expression[i + 1].hasClass("newline")) { + i++; + parts.push(expression[i]); + + if (expression[i].hasClass("nobreak")) { + nobreak = true; + } + } // Don't allow break if \nobreak among the post-operator glue. + + + if (!nobreak) { + children.push(buildHTMLUnbreakable(parts, options)); + parts = []; + } + } else if (expression[i].hasClass("newline")) { + // Write the line except the newline + parts.pop(); + + if (parts.length > 0) { + children.push(buildHTMLUnbreakable(parts, options)); + parts = []; + } // Put the newline at the top level + + + children.push(expression[i]); + } + } + + if (parts.length > 0) { + children.push(buildHTMLUnbreakable(parts, options)); + } // Now, if there was a tag, build it too and append it as a final child. + + + var tagChild; + + if (tag) { + tagChild = buildHTMLUnbreakable(buildExpression$1(tag, options, true)); + tagChild.classes = ["tag"]; + children.push(tagChild); + } else if (eqnNum) { + children.push(eqnNum); + } + + var htmlNode = makeSpan$1(["katex-html"], children); + htmlNode.setAttribute("aria-hidden", "true"); // Adjust the strut of the tag to be the maximum height of all children + // (the height of the enclosing htmlNode) for proper vertical alignment. + + if (tagChild) { + var strut = tagChild.children[0]; + strut.style.height = htmlNode.height + htmlNode.depth + "em"; + strut.style.verticalAlign = -htmlNode.depth + "em"; + } + + return htmlNode; +} + +/** + * These objects store data about MathML nodes. This is the MathML equivalent + * of the types in domTree.js. Since MathML handles its own rendering, and + * since we're mainly using MathML to improve accessibility, we don't manage + * any of the styling state that the plain DOM nodes do. + * + * The `toNode` and `toMarkup` functions work simlarly to how they do in + * domTree.js, creating namespaced DOM nodes and HTML text markup respectively. + */ +function newDocumentFragment(children) { + return new DocumentFragment(children); +} +/** + * This node represents a general purpose MathML node of any type. The + * constructor requires the type of node to create (for example, `"mo"` or + * `"mspace"`, corresponding to `` and `` tags). + */ + +class MathNode { + constructor(type, children, classes) { + this.type = void 0; + this.attributes = void 0; + this.children = void 0; + this.classes = void 0; + this.type = type; + this.attributes = {}; + this.children = children || []; + this.classes = classes || []; + } + /** + * Sets an attribute on a MathML node. MathML depends on attributes to convey a + * semantic content, so this is used heavily. + */ + + + setAttribute(name, value) { + this.attributes[name] = value; + } + /** + * Gets an attribute on a MathML node. + */ + + + getAttribute(name) { + return this.attributes[name]; + } + /** + * Converts the math node into a MathML-namespaced DOM element. + */ + + + toNode() { + var node = document.createElementNS("http://www.w3.org/1998/Math/MathML", this.type); + + for (var attr in this.attributes) { + if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) { + node.setAttribute(attr, this.attributes[attr]); + } + } + + if (this.classes.length > 0) { + node.className = createClass(this.classes); + } + + for (var i = 0; i < this.children.length; i++) { + node.appendChild(this.children[i].toNode()); + } + + return node; + } + /** + * Converts the math node into an HTML markup string. + */ + + + toMarkup() { + var markup = "<" + this.type; // Add the attributes + + for (var attr in this.attributes) { + if (Object.prototype.hasOwnProperty.call(this.attributes, attr)) { + markup += " " + attr + "=\""; + markup += utils.escape(this.attributes[attr]); + markup += "\""; + } + } + + if (this.classes.length > 0) { + markup += " class =\"" + utils.escape(createClass(this.classes)) + "\""; + } + + markup += ">"; + + for (var i = 0; i < this.children.length; i++) { + markup += this.children[i].toMarkup(); + } + + markup += ""; + return markup; + } + /** + * Converts the math node into a string, similar to innerText, but escaped. + */ + + + toText() { + return this.children.map(child => child.toText()).join(""); + } + +} +/** + * This node represents a piece of text. + */ + +class TextNode { + constructor(text) { + this.text = void 0; + this.text = text; + } + /** + * Converts the text node into a DOM text node. + */ + + + toNode() { + return document.createTextNode(this.text); + } + /** + * Converts the text node into escaped HTML markup + * (representing the text itself). + */ + + + toMarkup() { + return utils.escape(this.toText()); + } + /** + * Converts the text node into a string + * (representing the text iteself). + */ + + + toText() { + return this.text; + } + +} +/** + * This node represents a space, but may render as or as text, + * depending on the width. + */ + +class SpaceNode { + /** + * Create a Space node with width given in CSS ems. + */ + constructor(width) { + this.width = void 0; + this.character = void 0; + this.width = width; // See https://www.w3.org/TR/2000/WD-MathML2-20000328/chapter6.html + // for a table of space-like characters. We use Unicode + // representations instead of &LongNames; as it's not clear how to + // make the latter via document.createTextNode. + + if (width >= 0.05555 && width <= 0.05556) { + this.character = "\u200a"; //   + } else if (width >= 0.1666 && width <= 0.1667) { + this.character = "\u2009"; //   + } else if (width >= 0.2222 && width <= 0.2223) { + this.character = "\u2005"; //   + } else if (width >= 0.2777 && width <= 0.2778) { + this.character = "\u2005\u200a"; //    + } else if (width >= -0.05556 && width <= -0.05555) { + this.character = "\u200a\u2063"; // ​ + } else if (width >= -0.1667 && width <= -0.1666) { + this.character = "\u2009\u2063"; // ​ + } else if (width >= -0.2223 && width <= -0.2222) { + this.character = "\u205f\u2063"; // ​ + } else if (width >= -0.2778 && width <= -0.2777) { + this.character = "\u2005\u2063"; // ​ + } else { + this.character = null; + } + } + /** + * Converts the math node into a MathML-namespaced DOM element. + */ + + + toNode() { + if (this.character) { + return document.createTextNode(this.character); + } else { + var node = document.createElementNS("http://www.w3.org/1998/Math/MathML", "mspace"); + node.setAttribute("width", this.width + "em"); + return node; + } + } + /** + * Converts the math node into an HTML markup string. + */ + + + toMarkup() { + if (this.character) { + return "" + this.character + ""; + } else { + return ""; + } + } + /** + * Converts the math node into a string, similar to innerText. + */ + + + toText() { + if (this.character) { + return this.character; + } else { + return " "; + } + } + +} + +var mathMLTree = { + MathNode, + TextNode, + SpaceNode, + newDocumentFragment +}; + +/** + * This file converts a parse tree into a cooresponding MathML tree. The main + * entry point is the `buildMathML` function, which takes a parse tree from the + * parser. + */ + +/** + * Takes a symbol and converts it into a MathML text node after performing + * optional replacement from symbols.js. + */ +var makeText = function makeText(text, mode, options) { + if (symbols[mode][text] && symbols[mode][text].replace && text.charCodeAt(0) !== 0xD835 && !(ligatures.hasOwnProperty(text) && options && (options.fontFamily && options.fontFamily.substr(4, 2) === "tt" || options.font && options.font.substr(4, 2) === "tt"))) { + text = symbols[mode][text].replace; + } + + return new mathMLTree.TextNode(text); +}; +/** + * Wrap the given array of nodes in an node if needed, i.e., + * unless the array has length 1. Always returns a single node. + */ + +var makeRow = function makeRow(body) { + if (body.length === 1) { + return body[0]; + } else { + return new mathMLTree.MathNode("mrow", body); + } +}; +/** + * Returns the math variant as a string or null if none is required. + */ + +var getVariant = function getVariant(group, options) { + // Handle \text... font specifiers as best we can. + // MathML has a limited list of allowable mathvariant specifiers; see + // https://www.w3.org/TR/MathML3/chapter3.html#presm.commatt + if (options.fontFamily === "texttt") { + return "monospace"; + } else if (options.fontFamily === "textsf") { + if (options.fontShape === "textit" && options.fontWeight === "textbf") { + return "sans-serif-bold-italic"; + } else if (options.fontShape === "textit") { + return "sans-serif-italic"; + } else if (options.fontWeight === "textbf") { + return "bold-sans-serif"; + } else { + return "sans-serif"; + } + } else if (options.fontShape === "textit" && options.fontWeight === "textbf") { + return "bold-italic"; + } else if (options.fontShape === "textit") { + return "italic"; + } else if (options.fontWeight === "textbf") { + return "bold"; + } + + var font = options.font; + + if (!font || font === "mathnormal") { + return null; + } + + var mode = group.mode; + + if (font === "mathit") { + return "italic"; + } else if (font === "boldsymbol") { + return group.type === "textord" ? "bold" : "bold-italic"; + } else if (font === "mathbf") { + return "bold"; + } else if (font === "mathbb") { + return "double-struck"; + } else if (font === "mathfrak") { + return "fraktur"; + } else if (font === "mathscr" || font === "mathcal") { + // MathML makes no distinction between script and caligrahpic + return "script"; + } else if (font === "mathsf") { + return "sans-serif"; + } else if (font === "mathtt") { + return "monospace"; + } + + var text = group.text; + + if (utils.contains(["\\imath", "\\jmath"], text)) { + return null; + } + + if (symbols[mode][text] && symbols[mode][text].replace) { + text = symbols[mode][text].replace; + } + + var fontName = buildCommon.fontMap[font].fontName; + + if (getCharacterMetrics(text, fontName, mode)) { + return buildCommon.fontMap[font].variant; + } + + return null; +}; +/** + * Takes a list of nodes, builds them, and returns a list of the generated + * MathML nodes. Also combine consecutive outputs into a single + * tag. + */ + +var buildExpression = function buildExpression(expression, options, isOrdgroup) { + if (expression.length === 1) { + var group = buildGroup(expression[0], options); + + if (isOrdgroup && group instanceof MathNode && group.type === "mo") { + // When TeX writers want to suppress spacing on an operator, + // they often put the operator by itself inside braces. + group.setAttribute("lspace", "0em"); + group.setAttribute("rspace", "0em"); + } + + return [group]; + } + + var groups = []; + var lastGroup; + + for (var i = 0; i < expression.length; i++) { + var _group = buildGroup(expression[i], options); + + if (_group instanceof MathNode && lastGroup instanceof MathNode) { + // Concatenate adjacent s + if (_group.type === 'mtext' && lastGroup.type === 'mtext' && _group.getAttribute('mathvariant') === lastGroup.getAttribute('mathvariant')) { + lastGroup.children.push(..._group.children); + continue; // Concatenate adjacent s + } else if (_group.type === 'mn' && lastGroup.type === 'mn') { + lastGroup.children.push(..._group.children); + continue; // Concatenate ... followed by . + } else if (_group.type === 'mi' && _group.children.length === 1 && lastGroup.type === 'mn') { + var child = _group.children[0]; + + if (child instanceof TextNode && child.text === '.') { + lastGroup.children.push(..._group.children); + continue; + } + } else if (lastGroup.type === 'mi' && lastGroup.children.length === 1) { + var lastChild = lastGroup.children[0]; + + if (lastChild instanceof TextNode && lastChild.text === '\u0338' && (_group.type === 'mo' || _group.type === 'mi' || _group.type === 'mn')) { + var _child = _group.children[0]; + + if (_child instanceof TextNode && _child.text.length > 0) { + // Overlay with combining character long solidus + _child.text = _child.text.slice(0, 1) + "\u0338" + _child.text.slice(1); + groups.pop(); + } + } + } + } + + groups.push(_group); + lastGroup = _group; + } + + return groups; +}; +/** + * Equivalent to buildExpression, but wraps the elements in an + * if there's more than one. Returns a single node instead of an array. + */ + +var buildExpressionRow = function buildExpressionRow(expression, options, isOrdgroup) { + return makeRow(buildExpression(expression, options, isOrdgroup)); +}; +/** + * Takes a group from the parser and calls the appropriate groupBuilders function + * on it to produce a MathML node. + */ + +var buildGroup = function buildGroup(group, options) { + if (!group) { + return new mathMLTree.MathNode("mrow"); + } + + if (_mathmlGroupBuilders[group.type]) { + // Call the groupBuilders function + // $FlowFixMe + var result = _mathmlGroupBuilders[group.type](group, options); // $FlowFixMe + + return result; + } else { + throw new ParseError("Got group of unknown type: '" + group.type + "'"); + } +}; +/** + * Takes a full parse tree and settings and builds a MathML representation of + * it. In particular, we put the elements from building the parse tree into a + * tag so we can also include that TeX source as an annotation. + * + * Note that we actually return a domTree element with a `` inside it so + * we can do appropriate styling. + */ + +function buildMathML(tree, texExpression, options, isDisplayMode, forMathmlOnly) { + var expression = buildExpression(tree, options); // TODO: Make a pass thru the MathML similar to buildHTML.traverseNonSpaceNodes + // and add spacing nodes. This is necessary only adjacent to math operators + // like \sin or \lim or to subsup elements that contain math operators. + // MathML takes care of the other spacing issues. + // Wrap up the expression in an mrow so it is presented in the semantics + // tag correctly, unless it's a single or . + + var wrapper; + + if (expression.length === 1 && expression[0] instanceof MathNode && utils.contains(["mrow", "mtable"], expression[0].type)) { + wrapper = expression[0]; + } else { + wrapper = new mathMLTree.MathNode("mrow", expression); + } // Build a TeX annotation of the source + + + var annotation = new mathMLTree.MathNode("annotation", [new mathMLTree.TextNode(texExpression)]); + annotation.setAttribute("encoding", "application/x-tex"); + var semantics = new mathMLTree.MathNode("semantics", [wrapper, annotation]); + var math = new mathMLTree.MathNode("math", [semantics]); + math.setAttribute("xmlns", "http://www.w3.org/1998/Math/MathML"); + + if (isDisplayMode) { + math.setAttribute("display", "block"); + } // You can't style nodes, so we wrap the node in a span. + // NOTE: The span class is not typed to have nodes as children, and + // we don't want to make the children type more generic since the children + // of span are expected to have more fields in `buildHtml` contexts. + + + var wrapperClass = forMathmlOnly ? "katex" : "katex-mathml"; // $FlowFixMe + + return buildCommon.makeSpan([wrapperClass], [math]); +} + +var optionsFromSettings = function optionsFromSettings(settings) { + return new Options({ + style: settings.displayMode ? Style$1.DISPLAY : Style$1.TEXT, + maxSize: settings.maxSize, + minRuleThickness: settings.minRuleThickness + }); +}; + +var displayWrap = function displayWrap(node, settings) { + if (settings.displayMode) { + var classes = ["katex-display"]; + + if (settings.leqno) { + classes.push("leqno"); + } + + if (settings.fleqn) { + classes.push("fleqn"); + } + + node = buildCommon.makeSpan(classes, [node]); + } + + return node; +}; + +var buildTree = function buildTree(tree, expression, settings) { + var options = optionsFromSettings(settings); + var katexNode; + + if (settings.output === "mathml") { + return buildMathML(tree, expression, options, settings.displayMode, true); + } else if (settings.output === "html") { + var htmlNode = buildHTML(tree, options); + katexNode = buildCommon.makeSpan(["katex"], [htmlNode]); + } else { + var mathMLNode = buildMathML(tree, expression, options, settings.displayMode, false); + + var _htmlNode = buildHTML(tree, options); + + katexNode = buildCommon.makeSpan(["katex"], [mathMLNode, _htmlNode]); + } + + return displayWrap(katexNode, settings); +}; +var buildHTMLTree = function buildHTMLTree(tree, expression, settings) { + var options = optionsFromSettings(settings); + var htmlNode = buildHTML(tree, options); + var katexNode = buildCommon.makeSpan(["katex"], [htmlNode]); + return displayWrap(katexNode, settings); +}; + +/** + * This file provides support to buildMathML.js and buildHTML.js + * for stretchy wide elements rendered from SVG files + * and other CSS trickery. + */ +var stretchyCodePoint = { + widehat: "^", + widecheck: "ˇ", + widetilde: "~", + utilde: "~", + overleftarrow: "\u2190", + underleftarrow: "\u2190", + xleftarrow: "\u2190", + overrightarrow: "\u2192", + underrightarrow: "\u2192", + xrightarrow: "\u2192", + underbrace: "\u23df", + overbrace: "\u23de", + overgroup: "\u23e0", + undergroup: "\u23e1", + overleftrightarrow: "\u2194", + underleftrightarrow: "\u2194", + xleftrightarrow: "\u2194", + Overrightarrow: "\u21d2", + xRightarrow: "\u21d2", + overleftharpoon: "\u21bc", + xleftharpoonup: "\u21bc", + overrightharpoon: "\u21c0", + xrightharpoonup: "\u21c0", + xLeftarrow: "\u21d0", + xLeftrightarrow: "\u21d4", + xhookleftarrow: "\u21a9", + xhookrightarrow: "\u21aa", + xmapsto: "\u21a6", + xrightharpoondown: "\u21c1", + xleftharpoondown: "\u21bd", + xrightleftharpoons: "\u21cc", + xleftrightharpoons: "\u21cb", + xtwoheadleftarrow: "\u219e", + xtwoheadrightarrow: "\u21a0", + xlongequal: "=", + xtofrom: "\u21c4", + xrightleftarrows: "\u21c4", + xrightequilibrium: "\u21cc", + // Not a perfect match. + xleftequilibrium: "\u21cb", + // None better available. + "\\cdrightarrow": "\u2192", + "\\cdleftarrow": "\u2190", + "\\cdlongequal": "=" +}; + +var mathMLnode = function mathMLnode(label) { + var node = new mathMLTree.MathNode("mo", [new mathMLTree.TextNode(stretchyCodePoint[label.replace(/^\\/, '')])]); + node.setAttribute("stretchy", "true"); + return node; +}; // Many of the KaTeX SVG images have been adapted from glyphs in KaTeX fonts. +// Copyright (c) 2009-2010, Design Science, Inc. () +// Copyright (c) 2014-2017 Khan Academy () +// Licensed under the SIL Open Font License, Version 1.1. +// See \nhttp://scripts.sil.org/OFL +// Very Long SVGs +// Many of the KaTeX stretchy wide elements use a long SVG image and an +// overflow: hidden tactic to achieve a stretchy image while avoiding +// distortion of arrowheads or brace corners. +// The SVG typically contains a very long (400 em) arrow. +// The SVG is in a container span that has overflow: hidden, so the span +// acts like a window that exposes only part of the SVG. +// The SVG always has a longer, thinner aspect ratio than the container span. +// After the SVG fills 100% of the height of the container span, +// there is a long arrow shaft left over. That left-over shaft is not shown. +// Instead, it is sliced off because the span's CSS has overflow: hidden. +// Thus, the reader sees an arrow that matches the subject matter width +// without distortion. +// Some functions, such as \cancel, need to vary their aspect ratio. These +// functions do not get the overflow SVG treatment. +// Second Brush Stroke +// Low resolution monitors struggle to display images in fine detail. +// So browsers apply anti-aliasing. A long straight arrow shaft therefore +// will sometimes appear as if it has a blurred edge. +// To mitigate this, these SVG files contain a second "brush-stroke" on the +// arrow shafts. That is, a second long thin rectangular SVG path has been +// written directly on top of each arrow shaft. This reinforcement causes +// some of the screen pixels to display as black instead of the anti-aliased +// gray pixel that a single path would generate. So we get arrow shafts +// whose edges appear to be sharper. +// In the katexImagesData object just below, the dimensions all +// correspond to path geometry inside the relevant SVG. +// For example, \overrightarrow uses the same arrowhead as glyph U+2192 +// from the KaTeX Main font. The scaling factor is 1000. +// That is, inside the font, that arrowhead is 522 units tall, which +// corresponds to 0.522 em inside the document. + + +var katexImagesData = { + // path(s), minWidth, height, align + overrightarrow: [["rightarrow"], 0.888, 522, "xMaxYMin"], + overleftarrow: [["leftarrow"], 0.888, 522, "xMinYMin"], + underrightarrow: [["rightarrow"], 0.888, 522, "xMaxYMin"], + underleftarrow: [["leftarrow"], 0.888, 522, "xMinYMin"], + xrightarrow: [["rightarrow"], 1.469, 522, "xMaxYMin"], + "\\cdrightarrow": [["rightarrow"], 3.0, 522, "xMaxYMin"], + // CD minwwidth2.5pc + xleftarrow: [["leftarrow"], 1.469, 522, "xMinYMin"], + "\\cdleftarrow": [["leftarrow"], 3.0, 522, "xMinYMin"], + Overrightarrow: [["doublerightarrow"], 0.888, 560, "xMaxYMin"], + xRightarrow: [["doublerightarrow"], 1.526, 560, "xMaxYMin"], + xLeftarrow: [["doubleleftarrow"], 1.526, 560, "xMinYMin"], + overleftharpoon: [["leftharpoon"], 0.888, 522, "xMinYMin"], + xleftharpoonup: [["leftharpoon"], 0.888, 522, "xMinYMin"], + xleftharpoondown: [["leftharpoondown"], 0.888, 522, "xMinYMin"], + overrightharpoon: [["rightharpoon"], 0.888, 522, "xMaxYMin"], + xrightharpoonup: [["rightharpoon"], 0.888, 522, "xMaxYMin"], + xrightharpoondown: [["rightharpoondown"], 0.888, 522, "xMaxYMin"], + xlongequal: [["longequal"], 0.888, 334, "xMinYMin"], + "\\cdlongequal": [["longequal"], 3.0, 334, "xMinYMin"], + xtwoheadleftarrow: [["twoheadleftarrow"], 0.888, 334, "xMinYMin"], + xtwoheadrightarrow: [["twoheadrightarrow"], 0.888, 334, "xMaxYMin"], + overleftrightarrow: [["leftarrow", "rightarrow"], 0.888, 522], + overbrace: [["leftbrace", "midbrace", "rightbrace"], 1.6, 548], + underbrace: [["leftbraceunder", "midbraceunder", "rightbraceunder"], 1.6, 548], + underleftrightarrow: [["leftarrow", "rightarrow"], 0.888, 522], + xleftrightarrow: [["leftarrow", "rightarrow"], 1.75, 522], + xLeftrightarrow: [["doubleleftarrow", "doublerightarrow"], 1.75, 560], + xrightleftharpoons: [["leftharpoondownplus", "rightharpoonplus"], 1.75, 716], + xleftrightharpoons: [["leftharpoonplus", "rightharpoondownplus"], 1.75, 716], + xhookleftarrow: [["leftarrow", "righthook"], 1.08, 522], + xhookrightarrow: [["lefthook", "rightarrow"], 1.08, 522], + overlinesegment: [["leftlinesegment", "rightlinesegment"], 0.888, 522], + underlinesegment: [["leftlinesegment", "rightlinesegment"], 0.888, 522], + overgroup: [["leftgroup", "rightgroup"], 0.888, 342], + undergroup: [["leftgroupunder", "rightgroupunder"], 0.888, 342], + xmapsto: [["leftmapsto", "rightarrow"], 1.5, 522], + xtofrom: [["leftToFrom", "rightToFrom"], 1.75, 528], + // The next three arrows are from the mhchem package. + // In mhchem.sty, min-length is 2.0em. But these arrows might appear in the + // document as \xrightarrow or \xrightleftharpoons. Those have + // min-length = 1.75em, so we set min-length on these next three to match. + xrightleftarrows: [["baraboveleftarrow", "rightarrowabovebar"], 1.75, 901], + xrightequilibrium: [["baraboveshortleftharpoon", "rightharpoonaboveshortbar"], 1.75, 716], + xleftequilibrium: [["shortbaraboveleftharpoon", "shortrightharpoonabovebar"], 1.75, 716] +}; + +var groupLength = function groupLength(arg) { + if (arg.type === "ordgroup") { + return arg.body.length; + } else { + return 1; + } +}; + +var svgSpan = function svgSpan(group, options) { + // Create a span with inline SVG for the element. + function buildSvgSpan_() { + var viewBoxWidth = 400000; // default + + var label = group.label.substr(1); + + if (utils.contains(["widehat", "widecheck", "widetilde", "utilde"], label)) { + // Each type in the `if` statement corresponds to one of the ParseNode + // types below. This narrowing is required to access `grp.base`. + // $FlowFixMe + var grp = group; // There are four SVG images available for each function. + // Choose a taller image when there are more characters. + + var numChars = groupLength(grp.base); + var viewBoxHeight; + var pathName; + + var _height; + + if (numChars > 5) { + if (label === "widehat" || label === "widecheck") { + viewBoxHeight = 420; + viewBoxWidth = 2364; + _height = 0.42; + pathName = label + "4"; + } else { + viewBoxHeight = 312; + viewBoxWidth = 2340; + _height = 0.34; + pathName = "tilde4"; + } + } else { + var imgIndex = [1, 1, 2, 2, 3, 3][numChars]; + + if (label === "widehat" || label === "widecheck") { + viewBoxWidth = [0, 1062, 2364, 2364, 2364][imgIndex]; + viewBoxHeight = [0, 239, 300, 360, 420][imgIndex]; + _height = [0, 0.24, 0.3, 0.3, 0.36, 0.42][imgIndex]; + pathName = label + imgIndex; + } else { + viewBoxWidth = [0, 600, 1033, 2339, 2340][imgIndex]; + viewBoxHeight = [0, 260, 286, 306, 312][imgIndex]; + _height = [0, 0.26, 0.286, 0.3, 0.306, 0.34][imgIndex]; + pathName = "tilde" + imgIndex; + } + } + + var path = new PathNode(pathName); + var svgNode = new SvgNode([path], { + "width": "100%", + "height": _height + "em", + "viewBox": "0 0 " + viewBoxWidth + " " + viewBoxHeight, + "preserveAspectRatio": "none" + }); + return { + span: buildCommon.makeSvgSpan([], [svgNode], options), + minWidth: 0, + height: _height + }; + } else { + var spans = []; + var data = katexImagesData[label]; + var [paths, _minWidth, _viewBoxHeight] = data; + + var _height2 = _viewBoxHeight / 1000; + + var numSvgChildren = paths.length; + var widthClasses; + var aligns; + + if (numSvgChildren === 1) { + // $FlowFixMe: All these cases must be of the 4-tuple type. + var align1 = data[3]; + widthClasses = ["hide-tail"]; + aligns = [align1]; + } else if (numSvgChildren === 2) { + widthClasses = ["halfarrow-left", "halfarrow-right"]; + aligns = ["xMinYMin", "xMaxYMin"]; + } else if (numSvgChildren === 3) { + widthClasses = ["brace-left", "brace-center", "brace-right"]; + aligns = ["xMinYMin", "xMidYMin", "xMaxYMin"]; + } else { + throw new Error("Correct katexImagesData or update code here to support\n " + numSvgChildren + " children."); + } + + for (var i = 0; i < numSvgChildren; i++) { + var _path = new PathNode(paths[i]); + + var _svgNode = new SvgNode([_path], { + "width": "400em", + "height": _height2 + "em", + "viewBox": "0 0 " + viewBoxWidth + " " + _viewBoxHeight, + "preserveAspectRatio": aligns[i] + " slice" + }); + + var _span = buildCommon.makeSvgSpan([widthClasses[i]], [_svgNode], options); + + if (numSvgChildren === 1) { + return { + span: _span, + minWidth: _minWidth, + height: _height2 + }; + } else { + _span.style.height = _height2 + "em"; + spans.push(_span); + } + } + + return { + span: buildCommon.makeSpan(["stretchy"], spans, options), + minWidth: _minWidth, + height: _height2 + }; + } + } // buildSvgSpan_() + + + var { + span, + minWidth, + height + } = buildSvgSpan_(); // Note that we are returning span.depth = 0. + // Any adjustments relative to the baseline must be done in buildHTML. + + span.height = height; + span.style.height = height + "em"; + + if (minWidth > 0) { + span.style.minWidth = minWidth + "em"; + } + + return span; +}; + +var encloseSpan = function encloseSpan(inner, label, topPad, bottomPad, options) { + // Return an image span for \cancel, \bcancel, \xcancel, \fbox, or \angl + var img; + var totalHeight = inner.height + inner.depth + topPad + bottomPad; + + if (/fbox|color|angl/.test(label)) { + img = buildCommon.makeSpan(["stretchy", label], [], options); + + if (label === "fbox") { + var color = options.color && options.getColor(); + + if (color) { + img.style.borderColor = color; + } + } + } else { + // \cancel, \bcancel, or \xcancel + // Since \cancel's SVG is inline and it omits the viewBox attribute, + // its stroke-width will not vary with span area. + var lines = []; + + if (/^[bx]cancel$/.test(label)) { + lines.push(new LineNode({ + "x1": "0", + "y1": "0", + "x2": "100%", + "y2": "100%", + "stroke-width": "0.046em" + })); + } + + if (/^x?cancel$/.test(label)) { + lines.push(new LineNode({ + "x1": "0", + "y1": "100%", + "x2": "100%", + "y2": "0", + "stroke-width": "0.046em" + })); + } + + var svgNode = new SvgNode(lines, { + "width": "100%", + "height": totalHeight + "em" + }); + img = buildCommon.makeSvgSpan([], [svgNode], options); + } + + img.height = totalHeight; + img.style.height = totalHeight + "em"; + return img; +}; + +var stretchy = { + encloseSpan, + mathMLnode, + svgSpan +}; + +/** + * Asserts that the node is of the given type and returns it with stricter + * typing. Throws if the node's type does not match. + */ +function assertNodeType(node, type) { + if (!node || node.type !== type) { + throw new Error("Expected node of type " + type + ", but got " + (node ? "node of type " + node.type : String(node))); + } // $FlowFixMe, >=0.125 + + + return node; +} +/** + * Returns the node more strictly typed iff it is of the given type. Otherwise, + * returns null. + */ + +function assertSymbolNodeType(node) { + var typedNode = checkSymbolNodeType(node); + + if (!typedNode) { + throw new Error("Expected node of symbol group type, but got " + (node ? "node of type " + node.type : String(node))); + } + + return typedNode; +} +/** + * Returns the node more strictly typed iff it is of the given type. Otherwise, + * returns null. + */ + +function checkSymbolNodeType(node) { + if (node && (node.type === "atom" || NON_ATOMS.hasOwnProperty(node.type))) { + // $FlowFixMe + return node; + } + + return null; +} + +// NOTE: Unlike most `htmlBuilder`s, this one handles not only "accent", but +// also "supsub" since an accent can affect super/subscripting. +var htmlBuilder$a = (grp, options) => { + // Accents are handled in the TeXbook pg. 443, rule 12. + var base; + var group; + var supSubGroup; + + if (grp && grp.type === "supsub") { + // If our base is a character box, and we have superscripts and + // subscripts, the supsub will defer to us. In particular, we want + // to attach the superscripts and subscripts to the inner body (so + // that the position of the superscripts and subscripts won't be + // affected by the height of the accent). We accomplish this by + // sticking the base of the accent into the base of the supsub, and + // rendering that, while keeping track of where the accent is. + // The real accent group is the base of the supsub group + group = assertNodeType(grp.base, "accent"); // The character box is the base of the accent group + + base = group.base; // Stick the character box into the base of the supsub group + + grp.base = base; // Rerender the supsub group with its new base, and store that + // result. + + supSubGroup = assertSpan(buildGroup$1(grp, options)); // reset original base + + grp.base = group; + } else { + group = assertNodeType(grp, "accent"); + base = group.base; + } // Build the base group + + + var body = buildGroup$1(base, options.havingCrampedStyle()); // Does the accent need to shift for the skew of a character? + + var mustShift = group.isShifty && utils.isCharacterBox(base); // Calculate the skew of the accent. This is based on the line "If the + // nucleus is not a single character, let s = 0; otherwise set s to the + // kern amount for the nucleus followed by the \skewchar of its font." + // Note that our skew metrics are just the kern between each character + // and the skewchar. + + var skew = 0; + + if (mustShift) { + // If the base is a character box, then we want the skew of the + // innermost character. To do that, we find the innermost character: + var baseChar = utils.getBaseElem(base); // Then, we render its group to get the symbol inside it + + var baseGroup = buildGroup$1(baseChar, options.havingCrampedStyle()); // Finally, we pull the skew off of the symbol. + + skew = assertSymbolDomNode(baseGroup).skew; // Note that we now throw away baseGroup, because the layers we + // removed with getBaseElem might contain things like \color which + // we can't get rid of. + // TODO(emily): Find a better way to get the skew + } + + var accentBelow = group.label === "\\c"; // calculate the amount of space between the body and the accent + + var clearance = accentBelow ? body.height + body.depth : Math.min(body.height, options.fontMetrics().xHeight); // Build the accent + + var accentBody; + + if (!group.isStretchy) { + var accent; + var width; + + if (group.label === "\\vec") { + // Before version 0.9, \vec used the combining font glyph U+20D7. + // But browsers, especially Safari, are not consistent in how they + // render combining characters when not preceded by a character. + // So now we use an SVG. + // If Safari reforms, we should consider reverting to the glyph. + accent = buildCommon.staticSvg("vec", options); + width = buildCommon.svgData.vec[1]; + } else { + accent = buildCommon.makeOrd({ + mode: group.mode, + text: group.label + }, options, "textord"); + accent = assertSymbolDomNode(accent); // Remove the italic correction of the accent, because it only serves to + // shift the accent over to a place we don't want. + + accent.italic = 0; + width = accent.width; + + if (accentBelow) { + clearance += accent.depth; + } + } + + accentBody = buildCommon.makeSpan(["accent-body"], [accent]); // "Full" accents expand the width of the resulting symbol to be + // at least the width of the accent, and overlap directly onto the + // character without any vertical offset. + + var accentFull = group.label === "\\textcircled"; + + if (accentFull) { + accentBody.classes.push('accent-full'); + clearance = body.height; + } // Shift the accent over by the skew. + + + var left = skew; // CSS defines `.katex .accent .accent-body:not(.accent-full) { width: 0 }` + // so that the accent doesn't contribute to the bounding box. + // We need to shift the character by its width (effectively half + // its width) to compensate. + + if (!accentFull) { + left -= width / 2; + } + + accentBody.style.left = left + "em"; // \textcircled uses the \bigcirc glyph, so it needs some + // vertical adjustment to match LaTeX. + + if (group.label === "\\textcircled") { + accentBody.style.top = ".2em"; + } + + accentBody = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: body + }, { + type: "kern", + size: -clearance + }, { + type: "elem", + elem: accentBody + }] + }, options); + } else { + accentBody = stretchy.svgSpan(group, options); + accentBody = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: body + }, { + type: "elem", + elem: accentBody, + wrapperClasses: ["svg-align"], + wrapperStyle: skew > 0 ? { + width: "calc(100% - " + 2 * skew + "em)", + marginLeft: 2 * skew + "em" + } : undefined + }] + }, options); + } + + var accentWrap = buildCommon.makeSpan(["mord", "accent"], [accentBody], options); + + if (supSubGroup) { + // Here, we replace the "base" child of the supsub with our newly + // generated accent. + supSubGroup.children[0] = accentWrap; // Since we don't rerun the height calculation after replacing the + // accent, we manually recalculate height. + + supSubGroup.height = Math.max(accentWrap.height, supSubGroup.height); // Accents should always be ords, even when their innards are not. + + supSubGroup.classes[0] = "mord"; + return supSubGroup; + } else { + return accentWrap; + } +}; + +var mathmlBuilder$9 = (group, options) => { + var accentNode = group.isStretchy ? stretchy.mathMLnode(group.label) : new mathMLTree.MathNode("mo", [makeText(group.label, group.mode)]); + var node = new mathMLTree.MathNode("mover", [buildGroup(group.base, options), accentNode]); + node.setAttribute("accent", "true"); + return node; +}; + +var NON_STRETCHY_ACCENT_REGEX = new RegExp(["\\acute", "\\grave", "\\ddot", "\\tilde", "\\bar", "\\breve", "\\check", "\\hat", "\\vec", "\\dot", "\\mathring"].map(accent => "\\" + accent).join("|")); // Accents + +defineFunction({ + type: "accent", + names: ["\\acute", "\\grave", "\\ddot", "\\tilde", "\\bar", "\\breve", "\\check", "\\hat", "\\vec", "\\dot", "\\mathring", "\\widecheck", "\\widehat", "\\widetilde", "\\overrightarrow", "\\overleftarrow", "\\Overrightarrow", "\\overleftrightarrow", "\\overgroup", "\\overlinesegment", "\\overleftharpoon", "\\overrightharpoon"], + props: { + numArgs: 1 + }, + handler: (context, args) => { + var base = normalizeArgument(args[0]); + var isStretchy = !NON_STRETCHY_ACCENT_REGEX.test(context.funcName); + var isShifty = !isStretchy || context.funcName === "\\widehat" || context.funcName === "\\widetilde" || context.funcName === "\\widecheck"; + return { + type: "accent", + mode: context.parser.mode, + label: context.funcName, + isStretchy: isStretchy, + isShifty: isShifty, + base: base + }; + }, + htmlBuilder: htmlBuilder$a, + mathmlBuilder: mathmlBuilder$9 +}); // Text-mode accents + +defineFunction({ + type: "accent", + names: ["\\'", "\\`", "\\^", "\\~", "\\=", "\\u", "\\.", '\\"', "\\c", "\\r", "\\H", "\\v", "\\textcircled"], + props: { + numArgs: 1, + allowedInText: true, + allowedInMath: true, + // unless in strict mode + argTypes: ["primitive"] + }, + handler: (context, args) => { + var base = args[0]; + var mode = context.parser.mode; + + if (mode === "math") { + context.parser.settings.reportNonstrict("mathVsTextAccents", "LaTeX's accent " + context.funcName + " works only in text mode"); + mode = "text"; + } + + return { + type: "accent", + mode: mode, + label: context.funcName, + isStretchy: false, + isShifty: true, + base: base + }; + }, + htmlBuilder: htmlBuilder$a, + mathmlBuilder: mathmlBuilder$9 +}); + +// Horizontal overlap functions +defineFunction({ + type: "accentUnder", + names: ["\\underleftarrow", "\\underrightarrow", "\\underleftrightarrow", "\\undergroup", "\\underlinesegment", "\\utilde"], + props: { + numArgs: 1 + }, + handler: (_ref, args) => { + var { + parser, + funcName + } = _ref; + var base = args[0]; + return { + type: "accentUnder", + mode: parser.mode, + label: funcName, + base: base + }; + }, + htmlBuilder: (group, options) => { + // Treat under accents much like underlines. + var innerGroup = buildGroup$1(group.base, options); + var accentBody = stretchy.svgSpan(group, options); + var kern = group.label === "\\utilde" ? 0.12 : 0; // Generate the vlist, with the appropriate kerns + + var vlist = buildCommon.makeVList({ + positionType: "top", + positionData: innerGroup.height, + children: [{ + type: "elem", + elem: accentBody, + wrapperClasses: ["svg-align"] + }, { + type: "kern", + size: kern + }, { + type: "elem", + elem: innerGroup + }] + }, options); + return buildCommon.makeSpan(["mord", "accentunder"], [vlist], options); + }, + mathmlBuilder: (group, options) => { + var accentNode = stretchy.mathMLnode(group.label); + var node = new mathMLTree.MathNode("munder", [buildGroup(group.base, options), accentNode]); + node.setAttribute("accentunder", "true"); + return node; + } +}); + +// Helper function +var paddedNode = group => { + var node = new mathMLTree.MathNode("mpadded", group ? [group] : []); + node.setAttribute("width", "+0.6em"); + node.setAttribute("lspace", "0.3em"); + return node; +}; // Stretchy arrows with an optional argument + + +defineFunction({ + type: "xArrow", + names: ["\\xleftarrow", "\\xrightarrow", "\\xLeftarrow", "\\xRightarrow", "\\xleftrightarrow", "\\xLeftrightarrow", "\\xhookleftarrow", "\\xhookrightarrow", "\\xmapsto", "\\xrightharpoondown", "\\xrightharpoonup", "\\xleftharpoondown", "\\xleftharpoonup", "\\xrightleftharpoons", "\\xleftrightharpoons", "\\xlongequal", "\\xtwoheadrightarrow", "\\xtwoheadleftarrow", "\\xtofrom", // The next 3 functions are here to support the mhchem extension. + // Direct use of these functions is discouraged and may break someday. + "\\xrightleftarrows", "\\xrightequilibrium", "\\xleftequilibrium", // The next 3 functions are here only to support the {CD} environment. + "\\\\cdrightarrow", "\\\\cdleftarrow", "\\\\cdlongequal"], + props: { + numArgs: 1, + numOptionalArgs: 1 + }, + + handler(_ref, args, optArgs) { + var { + parser, + funcName + } = _ref; + return { + type: "xArrow", + mode: parser.mode, + label: funcName, + body: args[0], + below: optArgs[0] + }; + }, + + // Flow is unable to correctly infer the type of `group`, even though it's + // unamibiguously determined from the passed-in `type` above. + htmlBuilder(group, options) { + var style = options.style; // Build the argument groups in the appropriate style. + // Ref: amsmath.dtx: \hbox{$\scriptstyle\mkern#3mu{#6}\mkern#4mu$}% + // Some groups can return document fragments. Handle those by wrapping + // them in a span. + + var newOptions = options.havingStyle(style.sup()); + var upperGroup = buildCommon.wrapFragment(buildGroup$1(group.body, newOptions, options), options); + var arrowPrefix = group.label.slice(0, 2) === "\\x" ? "x" : "cd"; + upperGroup.classes.push(arrowPrefix + "-arrow-pad"); + var lowerGroup; + + if (group.below) { + // Build the lower group + newOptions = options.havingStyle(style.sub()); + lowerGroup = buildCommon.wrapFragment(buildGroup$1(group.below, newOptions, options), options); + lowerGroup.classes.push(arrowPrefix + "-arrow-pad"); + } + + var arrowBody = stretchy.svgSpan(group, options); // Re shift: Note that stretchy.svgSpan returned arrowBody.depth = 0. + // The point we want on the math axis is at 0.5 * arrowBody.height. + + var arrowShift = -options.fontMetrics().axisHeight + 0.5 * arrowBody.height; // 2 mu kern. Ref: amsmath.dtx: #7\if0#2\else\mkern#2mu\fi + + var upperShift = -options.fontMetrics().axisHeight - 0.5 * arrowBody.height - 0.111; // 0.111 em = 2 mu + + if (upperGroup.depth > 0.25 || group.label === "\\xleftequilibrium") { + upperShift -= upperGroup.depth; // shift up if depth encroaches + } // Generate the vlist + + + var vlist; + + if (lowerGroup) { + var lowerShift = -options.fontMetrics().axisHeight + lowerGroup.height + 0.5 * arrowBody.height + 0.111; + vlist = buildCommon.makeVList({ + positionType: "individualShift", + children: [{ + type: "elem", + elem: upperGroup, + shift: upperShift + }, { + type: "elem", + elem: arrowBody, + shift: arrowShift + }, { + type: "elem", + elem: lowerGroup, + shift: lowerShift + }] + }, options); + } else { + vlist = buildCommon.makeVList({ + positionType: "individualShift", + children: [{ + type: "elem", + elem: upperGroup, + shift: upperShift + }, { + type: "elem", + elem: arrowBody, + shift: arrowShift + }] + }, options); + } // $FlowFixMe: Replace this with passing "svg-align" into makeVList. + + + vlist.children[0].children[0].children[1].classes.push("svg-align"); + return buildCommon.makeSpan(["mrel", "x-arrow"], [vlist], options); + }, + + mathmlBuilder(group, options) { + var arrowNode = stretchy.mathMLnode(group.label); + arrowNode.setAttribute("minsize", group.label.charAt(0) === "x" ? "1.75em" : "3.0em"); + var node; + + if (group.body) { + var upperNode = paddedNode(buildGroup(group.body, options)); + + if (group.below) { + var lowerNode = paddedNode(buildGroup(group.below, options)); + node = new mathMLTree.MathNode("munderover", [arrowNode, lowerNode, upperNode]); + } else { + node = new mathMLTree.MathNode("mover", [arrowNode, upperNode]); + } + } else if (group.below) { + var _lowerNode = paddedNode(buildGroup(group.below, options)); + + node = new mathMLTree.MathNode("munder", [arrowNode, _lowerNode]); + } else { + // This should never happen. + // Parser.js throws an error if there is no argument. + node = paddedNode(); + node = new mathMLTree.MathNode("mover", [arrowNode, node]); + } + + return node; + } + +}); + +var cdArrowFunctionName = { + ">": "\\\\cdrightarrow", + "<": "\\\\cdleftarrow", + "=": "\\\\cdlongequal", + "A": "\\uparrow", + "V": "\\downarrow", + "|": "\\Vert", + ".": "no arrow" +}; + +var newCell = () => { + // Create an empty cell, to be filled below with parse nodes. + // The parseTree from this module must be constructed like the + // one created by parseArray(), so an empty CD cell must + // be a ParseNode<"styling">. And CD is always displaystyle. + // So these values are fixed and flow can do implicit typing. + return { + type: "styling", + body: [], + mode: "math", + style: "display" + }; +}; + +var isStartOfArrow = node => { + return node.type === "textord" && node.text === "@"; +}; + +var isLabelEnd = (node, endChar) => { + return (node.type === "mathord" || node.type === "atom") && node.text === endChar; +}; + +function cdArrow(arrowChar, labels, parser) { + // Return a parse tree of an arrow and its labels. + // This acts in a way similar to a macro expansion. + var funcName = cdArrowFunctionName[arrowChar]; + + switch (funcName) { + case "\\\\cdrightarrow": + case "\\\\cdleftarrow": + return parser.callFunction(funcName, [labels[0]], [labels[1]]); + + case "\\uparrow": + case "\\downarrow": + { + var leftLabel = parser.callFunction("\\\\cdleft", [labels[0]], []); + var bareArrow = { + type: "atom", + text: funcName, + mode: "math", + family: "rel" + }; + var sizedArrow = parser.callFunction("\\Big", [bareArrow], []); + var rightLabel = parser.callFunction("\\\\cdright", [labels[1]], []); + var arrowGroup = { + type: "ordgroup", + mode: "math", + body: [leftLabel, sizedArrow, rightLabel] + }; + return parser.callFunction("\\\\cdparent", [arrowGroup], []); + } + + case "\\\\cdlongequal": + return parser.callFunction("\\\\cdlongequal", [], []); + + case "\\Vert": + { + var arrow = { + type: "textord", + text: "\\Vert", + mode: "math" + }; + return parser.callFunction("\\Big", [arrow], []); + } + + default: + return { + type: "textord", + text: " ", + mode: "math" + }; + } +} + +function parseCD(parser) { + // Get the array's parse nodes with \\ temporarily mapped to \cr. + var parsedRows = []; + parser.gullet.beginGroup(); + parser.gullet.macros.set("\\cr", "\\\\\\relax"); + parser.gullet.beginGroup(); + + while (true) { + // eslint-disable-line no-constant-condition + // Get the parse nodes for the next row. + parsedRows.push(parser.parseExpression(false, "\\\\")); + parser.gullet.endGroup(); + parser.gullet.beginGroup(); + var next = parser.fetch().text; + + if (next === "&" || next === "\\\\") { + parser.consume(); + } else if (next === "\\end") { + if (parsedRows[parsedRows.length - 1].length === 0) { + parsedRows.pop(); // final row ended in \\ + } + + break; + } else { + throw new ParseError("Expected \\\\ or \\cr or \\end", parser.nextToken); + } + } + + var row = []; + var body = [row]; // Loop thru the parse nodes. Collect them into cells and arrows. + + for (var i = 0; i < parsedRows.length; i++) { + // Start a new row. + var rowNodes = parsedRows[i]; // Create the first cell. + + var cell = newCell(); + + for (var j = 0; j < rowNodes.length; j++) { + if (!isStartOfArrow(rowNodes[j])) { + // If a parseNode is not an arrow, it goes into a cell. + cell.body.push(rowNodes[j]); + } else { + // Parse node j is an "@", the start of an arrow. + // Before starting on the arrow, push the cell into `row`. + row.push(cell); // Now collect parseNodes into an arrow. + // The character after "@" defines the arrow type. + + j += 1; + var arrowChar = assertSymbolNodeType(rowNodes[j]).text; // Create two empty label nodes. We may or may not use them. + + var labels = new Array(2); + labels[0] = { + type: "ordgroup", + mode: "math", + body: [] + }; + labels[1] = { + type: "ordgroup", + mode: "math", + body: [] + }; // Process the arrow. + + if ("=|.".indexOf(arrowChar) > -1) ; else if ("<>AV".indexOf(arrowChar) > -1) { + // Four arrows, `@>>>`, `@<<<`, `@AAA`, and `@VVV`, each take + // two optional labels. E.g. the right-point arrow syntax is + // really: @>{optional label}>{optional label}> + // Collect parseNodes into labels. + for (var labelNum = 0; labelNum < 2; labelNum++) { + var inLabel = true; + + for (var k = j + 1; k < rowNodes.length; k++) { + if (isLabelEnd(rowNodes[k], arrowChar)) { + inLabel = false; + j = k; + break; + } + + if (isStartOfArrow(rowNodes[k])) { + throw new ParseError("Missing a " + arrowChar + " character to complete a CD arrow.", rowNodes[k]); + } + + labels[labelNum].body.push(rowNodes[k]); + } + + if (inLabel) { + // isLabelEnd never returned a true. + throw new ParseError("Missing a " + arrowChar + " character to complete a CD arrow.", rowNodes[j]); + } + } + } else { + throw new ParseError("Expected one of \"<>AV=|.\" after @", rowNodes[j]); + } // Now join the arrow to its labels. + + + var arrow = cdArrow(arrowChar, labels, parser); // Wrap the arrow in ParseNode<"styling">. + // This is done to match parseArray() behavior. + + var wrappedArrow = { + type: "styling", + body: [arrow], + mode: "math", + style: "display" // CD is always displaystyle. + + }; + row.push(wrappedArrow); // In CD's syntax, cells are implicit. That is, everything that + // is not an arrow gets collected into a cell. So create an empty + // cell now. It will collect upcoming parseNodes. + + cell = newCell(); + } + } + + if (i % 2 === 0) { + // Even-numbered rows consist of: cell, arrow, cell, arrow, ... cell + // The last cell is not yet pushed into `row`, so: + row.push(cell); + } else { + // Odd-numbered rows consist of: vert arrow, empty cell, ... vert arrow + // Remove the empty cell that was placed at the beginning of `row`. + row.shift(); + } + + row = []; + body.push(row); + } // End row group + + + parser.gullet.endGroup(); // End array group defining \\ + + parser.gullet.endGroup(); // define column separation. + + var cols = new Array(body[0].length).fill({ + type: "align", + align: "c", + pregap: 0.25, + // CD package sets \enskip between columns. + postgap: 0.25 // So pre and post each get half an \enskip, i.e. 0.25em. + + }); + return { + type: "array", + mode: "math", + body, + arraystretch: 1, + addJot: true, + rowGaps: [null], + cols, + colSeparationType: "CD", + hLinesBeforeRow: new Array(body.length + 1).fill([]) + }; +} // The functions below are not available for general use. +// They are here only for internal use by the {CD} environment in placing labels +// next to vertical arrows. +// We don't need any such functions for horizontal arrows because we can reuse +// the functionality that already exists for extensible arrows. + +defineFunction({ + type: "cdlabel", + names: ["\\\\cdleft", "\\\\cdright"], + props: { + numArgs: 1 + }, + + handler(_ref, args) { + var { + parser, + funcName + } = _ref; + return { + type: "cdlabel", + mode: parser.mode, + side: funcName.slice(4), + label: args[0] + }; + }, + + htmlBuilder(group, options) { + var newOptions = options.havingStyle(options.style.sup()); + var label = buildCommon.wrapFragment(buildGroup$1(group.label, newOptions, options), options); + label.classes.push("cd-label-" + group.side); + label.style.bottom = 0.8 - label.depth + "em"; // Zero out label height & depth, so vertical align of arrow is set + // by the arrow height, not by the label. + + label.height = 0; + label.depth = 0; + return label; + }, + + mathmlBuilder(group, options) { + var label = new mathMLTree.MathNode("mrow", [buildGroup(group.label, options)]); + label = new mathMLTree.MathNode("mpadded", [label]); + label.setAttribute("width", "0"); + + if (group.side === "left") { + label.setAttribute("lspace", "-1width"); + } // We have to guess at vertical alignment. We know the arrow is 1.8em tall, + // But we don't know the height or depth of the label. + + + label.setAttribute("voffset", "0.7em"); + label = new mathMLTree.MathNode("mstyle", [label]); + label.setAttribute("displaystyle", "false"); + label.setAttribute("scriptlevel", "1"); + return label; + } + +}); +defineFunction({ + type: "cdlabelparent", + names: ["\\\\cdparent"], + props: { + numArgs: 1 + }, + + handler(_ref2, args) { + var { + parser + } = _ref2; + return { + type: "cdlabelparent", + mode: parser.mode, + fragment: args[0] + }; + }, + + htmlBuilder(group, options) { + // Wrap the vertical arrow and its labels. + // The parent gets position: relative. The child gets position: absolute. + // So CSS can locate the label correctly. + var parent = buildCommon.wrapFragment(buildGroup$1(group.fragment, options), options); + parent.classes.push("cd-vert-arrow"); + return parent; + }, + + mathmlBuilder(group, options) { + return new mathMLTree.MathNode("mrow", [buildGroup(group.fragment, options)]); + } + +}); + +// {123} and converts into symbol with code 123. It is used by the *macro* +// \char defined in macros.js. + +defineFunction({ + type: "textord", + names: ["\\@char"], + props: { + numArgs: 1, + allowedInText: true + }, + + handler(_ref, args) { + var { + parser + } = _ref; + var arg = assertNodeType(args[0], "ordgroup"); + var group = arg.body; + var number = ""; + + for (var i = 0; i < group.length; i++) { + var node = assertNodeType(group[i], "textord"); + number += node.text; + } + + var code = parseInt(number); + var text; + + if (isNaN(code)) { + throw new ParseError("\\@char has non-numeric argument " + number); // If we drop IE support, the following code could be replaced with + // text = String.fromCodePoint(code) + } else if (code < 0 || code >= 0x10ffff) { + throw new ParseError("\\@char with invalid code point " + number); + } else if (code <= 0xffff) { + text = String.fromCharCode(code); + } else { + // Astral code point; split into surrogate halves + code -= 0x10000; + text = String.fromCharCode((code >> 10) + 0xd800, (code & 0x3ff) + 0xdc00); + } + + return { + type: "textord", + mode: parser.mode, + text: text + }; + } + +}); + +var htmlBuilder$9 = (group, options) => { + var elements = buildExpression$1(group.body, options.withColor(group.color), false); // \color isn't supposed to affect the type of the elements it contains. + // To accomplish this, we wrap the results in a fragment, so the inner + // elements will be able to directly interact with their neighbors. For + // example, `\color{red}{2 +} 3` has the same spacing as `2 + 3` + + return buildCommon.makeFragment(elements); +}; + +var mathmlBuilder$8 = (group, options) => { + var inner = buildExpression(group.body, options.withColor(group.color)); + var node = new mathMLTree.MathNode("mstyle", inner); + node.setAttribute("mathcolor", group.color); + return node; +}; + +defineFunction({ + type: "color", + names: ["\\textcolor"], + props: { + numArgs: 2, + allowedInText: true, + argTypes: ["color", "original"] + }, + + handler(_ref, args) { + var { + parser + } = _ref; + var color = assertNodeType(args[0], "color-token").color; + var body = args[1]; + return { + type: "color", + mode: parser.mode, + color, + body: ordargument(body) + }; + }, + + htmlBuilder: htmlBuilder$9, + mathmlBuilder: mathmlBuilder$8 +}); +defineFunction({ + type: "color", + names: ["\\color"], + props: { + numArgs: 1, + allowedInText: true, + argTypes: ["color"] + }, + + handler(_ref2, args) { + var { + parser, + breakOnTokenText + } = _ref2; + var color = assertNodeType(args[0], "color-token").color; // Set macro \current@color in current namespace to store the current + // color, mimicking the behavior of color.sty. + // This is currently used just to correctly color a \right + // that follows a \color command. + + parser.gullet.macros.set("\\current@color", color); // Parse out the implicit body that should be colored. + + var body = parser.parseExpression(true, breakOnTokenText); + return { + type: "color", + mode: parser.mode, + color, + body + }; + }, + + htmlBuilder: htmlBuilder$9, + mathmlBuilder: mathmlBuilder$8 +}); + +// Row breaks within tabular environments, and line breaks at top level + +defineFunction({ + type: "cr", + names: ["\\\\"], + props: { + numArgs: 0, + numOptionalArgs: 1, + argTypes: ["size"], + allowedInText: true + }, + + handler(_ref, args, optArgs) { + var { + parser + } = _ref; + var size = optArgs[0]; + var newLine = !parser.settings.displayMode || !parser.settings.useStrictBehavior("newLineInDisplayMode", "In LaTeX, \\\\ or \\newline " + "does nothing in display mode"); + return { + type: "cr", + mode: parser.mode, + newLine, + size: size && assertNodeType(size, "size").value + }; + }, + + // The following builders are called only at the top level, + // not within tabular/array environments. + htmlBuilder(group, options) { + var span = buildCommon.makeSpan(["mspace"], [], options); + + if (group.newLine) { + span.classes.push("newline"); + + if (group.size) { + span.style.marginTop = calculateSize(group.size, options) + "em"; + } + } + + return span; + }, + + mathmlBuilder(group, options) { + var node = new mathMLTree.MathNode("mspace"); + + if (group.newLine) { + node.setAttribute("linebreak", "newline"); + + if (group.size) { + node.setAttribute("height", calculateSize(group.size, options) + "em"); + } + } + + return node; + } + +}); + +var globalMap = { + "\\global": "\\global", + "\\long": "\\\\globallong", + "\\\\globallong": "\\\\globallong", + "\\def": "\\gdef", + "\\gdef": "\\gdef", + "\\edef": "\\xdef", + "\\xdef": "\\xdef", + "\\let": "\\\\globallet", + "\\futurelet": "\\\\globalfuture" +}; + +var checkControlSequence = tok => { + var name = tok.text; + + if (/^(?:[\\{}$&#^_]|EOF)$/.test(name)) { + throw new ParseError("Expected a control sequence", tok); + } + + return name; +}; + +var getRHS = parser => { + var tok = parser.gullet.popToken(); + + if (tok.text === "=") { + // consume optional equals + tok = parser.gullet.popToken(); + + if (tok.text === " ") { + // consume one optional space + tok = parser.gullet.popToken(); + } + } + + return tok; +}; + +var letCommand = (parser, name, tok, global) => { + var macro = parser.gullet.macros.get(tok.text); + + if (macro == null) { + // don't expand it later even if a macro with the same name is defined + // e.g., \let\foo=\frac \def\frac{\relax} \frac12 + tok.noexpand = true; + macro = { + tokens: [tok], + numArgs: 0, + // reproduce the same behavior in expansion + unexpandable: !parser.gullet.isExpandable(tok.text) + }; + } + + parser.gullet.macros.set(name, macro, global); +}; // -> | +// -> |\global +// -> | +// -> \global|\long|\outer + + +defineFunction({ + type: "internal", + names: ["\\global", "\\long", "\\\\globallong" // can’t be entered directly + ], + props: { + numArgs: 0, + allowedInText: true + }, + + handler(_ref) { + var { + parser, + funcName + } = _ref; + parser.consumeSpaces(); + var token = parser.fetch(); + + if (globalMap[token.text]) { + // KaTeX doesn't have \par, so ignore \long + if (funcName === "\\global" || funcName === "\\\\globallong") { + token.text = globalMap[token.text]; + } + + return assertNodeType(parser.parseFunction(), "internal"); + } + + throw new ParseError("Invalid token after macro prefix", token); + } + +}); // Basic support for macro definitions: \def, \gdef, \edef, \xdef +// -> +// -> \def|\gdef|\edef|\xdef +// -> + +defineFunction({ + type: "internal", + names: ["\\def", "\\gdef", "\\edef", "\\xdef"], + props: { + numArgs: 0, + allowedInText: true, + primitive: true + }, + + handler(_ref2) { + var { + parser, + funcName + } = _ref2; + var tok = parser.gullet.popToken(); + var name = tok.text; + + if (/^(?:[\\{}$&#^_]|EOF)$/.test(name)) { + throw new ParseError("Expected a control sequence", tok); + } + + var numArgs = 0; + var insert; + var delimiters = [[]]; // contains no braces + + while (parser.gullet.future().text !== "{") { + tok = parser.gullet.popToken(); + + if (tok.text === "#") { + // If the very last character of the is #, so that + // this # is immediately followed by {, TeX will behave as if the { + // had been inserted at the right end of both the parameter text + // and the replacement text. + if (parser.gullet.future().text === "{") { + insert = parser.gullet.future(); + delimiters[numArgs].push("{"); + break; + } // A parameter, the first appearance of # must be followed by 1, + // the next by 2, and so on; up to nine #’s are allowed + + + tok = parser.gullet.popToken(); + + if (!/^[1-9]$/.test(tok.text)) { + throw new ParseError("Invalid argument number \"" + tok.text + "\""); + } + + if (parseInt(tok.text) !== numArgs + 1) { + throw new ParseError("Argument number \"" + tok.text + "\" out of order"); + } + + numArgs++; + delimiters.push([]); + } else if (tok.text === "EOF") { + throw new ParseError("Expected a macro definition"); + } else { + delimiters[numArgs].push(tok.text); + } + } // replacement text, enclosed in '{' and '}' and properly nested + + + var { + tokens + } = parser.gullet.consumeArg(); + + if (insert) { + tokens.unshift(insert); + } + + if (funcName === "\\edef" || funcName === "\\xdef") { + tokens = parser.gullet.expandTokens(tokens); + tokens.reverse(); // to fit in with stack order + } // Final arg is the expansion of the macro + + + parser.gullet.macros.set(name, { + tokens, + numArgs, + delimiters + }, funcName === globalMap[funcName]); + return { + type: "internal", + mode: parser.mode + }; + } + +}); // -> +// -> \futurelet +// | \let +// -> |= + +defineFunction({ + type: "internal", + names: ["\\let", "\\\\globallet" // can’t be entered directly + ], + props: { + numArgs: 0, + allowedInText: true, + primitive: true + }, + + handler(_ref3) { + var { + parser, + funcName + } = _ref3; + var name = checkControlSequence(parser.gullet.popToken()); + parser.gullet.consumeSpaces(); + var tok = getRHS(parser); + letCommand(parser, name, tok, funcName === "\\\\globallet"); + return { + type: "internal", + mode: parser.mode + }; + } + +}); // ref: https://www.tug.org/TUGboat/tb09-3/tb22bechtolsheim.pdf + +defineFunction({ + type: "internal", + names: ["\\futurelet", "\\\\globalfuture" // can’t be entered directly + ], + props: { + numArgs: 0, + allowedInText: true, + primitive: true + }, + + handler(_ref4) { + var { + parser, + funcName + } = _ref4; + var name = checkControlSequence(parser.gullet.popToken()); + var middle = parser.gullet.popToken(); + var tok = parser.gullet.popToken(); + letCommand(parser, name, tok, funcName === "\\\\globalfuture"); + parser.gullet.pushToken(tok); + parser.gullet.pushToken(middle); + return { + type: "internal", + mode: parser.mode + }; + } + +}); + +/** + * This file deals with creating delimiters of various sizes. The TeXbook + * discusses these routines on page 441-442, in the "Another subroutine sets box + * x to a specified variable delimiter" paragraph. + * + * There are three main routines here. `makeSmallDelim` makes a delimiter in the + * normal font, but in either text, script, or scriptscript style. + * `makeLargeDelim` makes a delimiter in textstyle, but in one of the Size1, + * Size2, Size3, or Size4 fonts. `makeStackedDelim` makes a delimiter out of + * smaller pieces that are stacked on top of one another. + * + * The functions take a parameter `center`, which determines if the delimiter + * should be centered around the axis. + * + * Then, there are three exposed functions. `sizedDelim` makes a delimiter in + * one of the given sizes. This is used for things like `\bigl`. + * `customSizedDelim` makes a delimiter with a given total height+depth. It is + * called in places like `\sqrt`. `leftRightDelim` makes an appropriate + * delimiter which surrounds an expression of a given height an depth. It is + * used in `\left` and `\right`. + */ + +/** + * Get the metrics for a given symbol and font, after transformation (i.e. + * after following replacement from symbols.js) + */ +var getMetrics = function getMetrics(symbol, font, mode) { + var replace = symbols.math[symbol] && symbols.math[symbol].replace; + var metrics = getCharacterMetrics(replace || symbol, font, mode); + + if (!metrics) { + throw new Error("Unsupported symbol " + symbol + " and font size " + font + "."); + } + + return metrics; +}; +/** + * Puts a delimiter span in a given style, and adds appropriate height, depth, + * and maxFontSizes. + */ + + +var styleWrap = function styleWrap(delim, toStyle, options, classes) { + var newOptions = options.havingBaseStyle(toStyle); + var span = buildCommon.makeSpan(classes.concat(newOptions.sizingClasses(options)), [delim], options); + var delimSizeMultiplier = newOptions.sizeMultiplier / options.sizeMultiplier; + span.height *= delimSizeMultiplier; + span.depth *= delimSizeMultiplier; + span.maxFontSize = newOptions.sizeMultiplier; + return span; +}; + +var centerSpan = function centerSpan(span, options, style) { + var newOptions = options.havingBaseStyle(style); + var shift = (1 - options.sizeMultiplier / newOptions.sizeMultiplier) * options.fontMetrics().axisHeight; + span.classes.push("delimcenter"); + span.style.top = shift + "em"; + span.height -= shift; + span.depth += shift; +}; +/** + * Makes a small delimiter. This is a delimiter that comes in the Main-Regular + * font, but is restyled to either be in textstyle, scriptstyle, or + * scriptscriptstyle. + */ + + +var makeSmallDelim = function makeSmallDelim(delim, style, center, options, mode, classes) { + var text = buildCommon.makeSymbol(delim, "Main-Regular", mode, options); + var span = styleWrap(text, style, options, classes); + + if (center) { + centerSpan(span, options, style); + } + + return span; +}; +/** + * Builds a symbol in the given font size (note size is an integer) + */ + + +var mathrmSize = function mathrmSize(value, size, mode, options) { + return buildCommon.makeSymbol(value, "Size" + size + "-Regular", mode, options); +}; +/** + * Makes a large delimiter. This is a delimiter that comes in the Size1, Size2, + * Size3, or Size4 fonts. It is always rendered in textstyle. + */ + + +var makeLargeDelim = function makeLargeDelim(delim, size, center, options, mode, classes) { + var inner = mathrmSize(delim, size, mode, options); + var span = styleWrap(buildCommon.makeSpan(["delimsizing", "size" + size], [inner], options), Style$1.TEXT, options, classes); + + if (center) { + centerSpan(span, options, Style$1.TEXT); + } + + return span; +}; +/** + * Make a span from a font glyph with the given offset and in the given font. + * This is used in makeStackedDelim to make the stacking pieces for the delimiter. + */ + + +var makeGlyphSpan = function makeGlyphSpan(symbol, font, mode) { + var sizeClass; // Apply the correct CSS class to choose the right font. + + if (font === "Size1-Regular") { + sizeClass = "delim-size1"; + } else + /* if (font === "Size4-Regular") */ + { + sizeClass = "delim-size4"; + } + + var corner = buildCommon.makeSpan(["delimsizinginner", sizeClass], [buildCommon.makeSpan([], [buildCommon.makeSymbol(symbol, font, mode)])]); // Since this will be passed into `makeVList` in the end, wrap the element + // in the appropriate tag that VList uses. + + return { + type: "elem", + elem: corner + }; +}; + +var makeInner = function makeInner(ch, height, options) { + // Create a span with inline SVG for the inner part of a tall stacked delimiter. + var width = fontMetricsData['Size4-Regular'][ch.charCodeAt(0)] ? fontMetricsData['Size4-Regular'][ch.charCodeAt(0)][4].toFixed(3) : fontMetricsData['Size1-Regular'][ch.charCodeAt(0)][4].toFixed(3); + var path = new PathNode("inner", innerPath(ch, Math.round(1000 * height))); + var svgNode = new SvgNode([path], { + "width": width + "em", + "height": height + "em", + // Override CSS rule `.katex svg { width: 100% }` + "style": "width:" + width + "em", + "viewBox": "0 0 " + 1000 * width + " " + Math.round(1000 * height), + "preserveAspectRatio": "xMinYMin" + }); + var span = buildCommon.makeSvgSpan([], [svgNode], options); + span.height = height; + span.style.height = height + "em"; + span.style.width = width + "em"; + return { + type: "elem", + elem: span + }; +}; // Helpers for makeStackedDelim + + +var lapInEms = 0.008; +var lap = { + type: "kern", + size: -1 * lapInEms +}; +var verts = ["|", "\\lvert", "\\rvert", "\\vert"]; +var doubleVerts = ["\\|", "\\lVert", "\\rVert", "\\Vert"]; +/** + * Make a stacked delimiter out of a given delimiter, with the total height at + * least `heightTotal`. This routine is mentioned on page 442 of the TeXbook. + */ + +var makeStackedDelim = function makeStackedDelim(delim, heightTotal, center, options, mode, classes) { + // There are four parts, the top, an optional middle, a repeated part, and a + // bottom. + var top; + var middle; + var repeat; + var bottom; + top = repeat = bottom = delim; + middle = null; // Also keep track of what font the delimiters are in + + var font = "Size1-Regular"; // We set the parts and font based on the symbol. Note that we use + // '\u23d0' instead of '|' and '\u2016' instead of '\\|' for the + // repeats of the arrows + + if (delim === "\\uparrow") { + repeat = bottom = "\u23d0"; + } else if (delim === "\\Uparrow") { + repeat = bottom = "\u2016"; + } else if (delim === "\\downarrow") { + top = repeat = "\u23d0"; + } else if (delim === "\\Downarrow") { + top = repeat = "\u2016"; + } else if (delim === "\\updownarrow") { + top = "\\uparrow"; + repeat = "\u23d0"; + bottom = "\\downarrow"; + } else if (delim === "\\Updownarrow") { + top = "\\Uparrow"; + repeat = "\u2016"; + bottom = "\\Downarrow"; + } else if (utils.contains(verts, delim)) { + repeat = "\u2223"; + } else if (utils.contains(doubleVerts, delim)) { + repeat = "\u2225"; + } else if (delim === "[" || delim === "\\lbrack") { + top = "\u23a1"; + repeat = "\u23a2"; + bottom = "\u23a3"; + font = "Size4-Regular"; + } else if (delim === "]" || delim === "\\rbrack") { + top = "\u23a4"; + repeat = "\u23a5"; + bottom = "\u23a6"; + font = "Size4-Regular"; + } else if (delim === "\\lfloor" || delim === "\u230a") { + repeat = top = "\u23a2"; + bottom = "\u23a3"; + font = "Size4-Regular"; + } else if (delim === "\\lceil" || delim === "\u2308") { + top = "\u23a1"; + repeat = bottom = "\u23a2"; + font = "Size4-Regular"; + } else if (delim === "\\rfloor" || delim === "\u230b") { + repeat = top = "\u23a5"; + bottom = "\u23a6"; + font = "Size4-Regular"; + } else if (delim === "\\rceil" || delim === "\u2309") { + top = "\u23a4"; + repeat = bottom = "\u23a5"; + font = "Size4-Regular"; + } else if (delim === "(" || delim === "\\lparen") { + top = "\u239b"; + repeat = "\u239c"; + bottom = "\u239d"; + font = "Size4-Regular"; + } else if (delim === ")" || delim === "\\rparen") { + top = "\u239e"; + repeat = "\u239f"; + bottom = "\u23a0"; + font = "Size4-Regular"; + } else if (delim === "\\{" || delim === "\\lbrace") { + top = "\u23a7"; + middle = "\u23a8"; + bottom = "\u23a9"; + repeat = "\u23aa"; + font = "Size4-Regular"; + } else if (delim === "\\}" || delim === "\\rbrace") { + top = "\u23ab"; + middle = "\u23ac"; + bottom = "\u23ad"; + repeat = "\u23aa"; + font = "Size4-Regular"; + } else if (delim === "\\lgroup" || delim === "\u27ee") { + top = "\u23a7"; + bottom = "\u23a9"; + repeat = "\u23aa"; + font = "Size4-Regular"; + } else if (delim === "\\rgroup" || delim === "\u27ef") { + top = "\u23ab"; + bottom = "\u23ad"; + repeat = "\u23aa"; + font = "Size4-Regular"; + } else if (delim === "\\lmoustache" || delim === "\u23b0") { + top = "\u23a7"; + bottom = "\u23ad"; + repeat = "\u23aa"; + font = "Size4-Regular"; + } else if (delim === "\\rmoustache" || delim === "\u23b1") { + top = "\u23ab"; + bottom = "\u23a9"; + repeat = "\u23aa"; + font = "Size4-Regular"; + } // Get the metrics of the four sections + + + var topMetrics = getMetrics(top, font, mode); + var topHeightTotal = topMetrics.height + topMetrics.depth; + var repeatMetrics = getMetrics(repeat, font, mode); + var repeatHeightTotal = repeatMetrics.height + repeatMetrics.depth; + var bottomMetrics = getMetrics(bottom, font, mode); + var bottomHeightTotal = bottomMetrics.height + bottomMetrics.depth; + var middleHeightTotal = 0; + var middleFactor = 1; + + if (middle !== null) { + var middleMetrics = getMetrics(middle, font, mode); + middleHeightTotal = middleMetrics.height + middleMetrics.depth; + middleFactor = 2; // repeat symmetrically above and below middle + } // Calcuate the minimal height that the delimiter can have. + // It is at least the size of the top, bottom, and optional middle combined. + + + var minHeight = topHeightTotal + bottomHeightTotal + middleHeightTotal; // Compute the number of copies of the repeat symbol we will need + + var repeatCount = Math.max(0, Math.ceil((heightTotal - minHeight) / (middleFactor * repeatHeightTotal))); // Compute the total height of the delimiter including all the symbols + + var realHeightTotal = minHeight + repeatCount * middleFactor * repeatHeightTotal; // The center of the delimiter is placed at the center of the axis. Note + // that in this context, "center" means that the delimiter should be + // centered around the axis in the current style, while normally it is + // centered around the axis in textstyle. + + var axisHeight = options.fontMetrics().axisHeight; + + if (center) { + axisHeight *= options.sizeMultiplier; + } // Calculate the depth + + + var depth = realHeightTotal / 2 - axisHeight; // Now, we start building the pieces that will go into the vlist + // Keep a list of the pieces of the stacked delimiter + + var stack = []; // Add the bottom symbol + + stack.push(makeGlyphSpan(bottom, font, mode)); + stack.push(lap); // overlap + + if (middle === null) { + // The middle section will be an SVG. Make it an extra 0.016em tall. + // We'll overlap by 0.008em at top and bottom. + var innerHeight = realHeightTotal - topHeightTotal - bottomHeightTotal + 2 * lapInEms; + stack.push(makeInner(repeat, innerHeight, options)); + } else { + // When there is a middle bit, we need the middle part and two repeated + // sections + var _innerHeight = (realHeightTotal - topHeightTotal - bottomHeightTotal - middleHeightTotal) / 2 + 2 * lapInEms; + + stack.push(makeInner(repeat, _innerHeight, options)); // Now insert the middle of the brace. + + stack.push(lap); + stack.push(makeGlyphSpan(middle, font, mode)); + stack.push(lap); + stack.push(makeInner(repeat, _innerHeight, options)); + } // Add the top symbol + + + stack.push(lap); + stack.push(makeGlyphSpan(top, font, mode)); // Finally, build the vlist + + var newOptions = options.havingBaseStyle(Style$1.TEXT); + var inner = buildCommon.makeVList({ + positionType: "bottom", + positionData: depth, + children: stack + }, newOptions); + return styleWrap(buildCommon.makeSpan(["delimsizing", "mult"], [inner], newOptions), Style$1.TEXT, options, classes); +}; // All surds have 0.08em padding above the viniculum inside the SVG. +// That keeps browser span height rounding error from pinching the line. + + +var vbPad = 80; // padding above the surd, measured inside the viewBox. + +var emPad = 0.08; // padding, in ems, measured in the document. + +var sqrtSvg = function sqrtSvg(sqrtName, height, viewBoxHeight, extraViniculum, options) { + var path = sqrtPath(sqrtName, extraViniculum, viewBoxHeight); + var pathNode = new PathNode(sqrtName, path); + var svg = new SvgNode([pathNode], { + // Note: 1000:1 ratio of viewBox to document em width. + "width": "400em", + "height": height + "em", + "viewBox": "0 0 400000 " + viewBoxHeight, + "preserveAspectRatio": "xMinYMin slice" + }); + return buildCommon.makeSvgSpan(["hide-tail"], [svg], options); +}; +/** + * Make a sqrt image of the given height, + */ + + +var makeSqrtImage = function makeSqrtImage(height, options) { + // Define a newOptions that removes the effect of size changes such as \Huge. + // We don't pick different a height surd for \Huge. For it, we scale up. + var newOptions = options.havingBaseSizing(); // Pick the desired surd glyph from a sequence of surds. + + var delim = traverseSequence("\\surd", height * newOptions.sizeMultiplier, stackLargeDelimiterSequence, newOptions); + var sizeMultiplier = newOptions.sizeMultiplier; // default + // The standard sqrt SVGs each have a 0.04em thick viniculum. + // If Settings.minRuleThickness is larger than that, we add extraViniculum. + + var extraViniculum = Math.max(0, options.minRuleThickness - options.fontMetrics().sqrtRuleThickness); // Create a span containing an SVG image of a sqrt symbol. + + var span; + var spanHeight = 0; + var texHeight = 0; + var viewBoxHeight = 0; + var advanceWidth; // We create viewBoxes with 80 units of "padding" above each surd. + // Then browser rounding error on the parent span height will not + // encroach on the ink of the viniculum. But that padding is not + // included in the TeX-like `height` used for calculation of + // vertical alignment. So texHeight = span.height < span.style.height. + + if (delim.type === "small") { + // Get an SVG that is derived from glyph U+221A in font KaTeX-Main. + // 1000 unit normal glyph height. + viewBoxHeight = 1000 + 1000 * extraViniculum + vbPad; + + if (height < 1.0) { + sizeMultiplier = 1.0; // mimic a \textfont radical + } else if (height < 1.4) { + sizeMultiplier = 0.7; // mimic a \scriptfont radical + } + + spanHeight = (1.0 + extraViniculum + emPad) / sizeMultiplier; + texHeight = (1.00 + extraViniculum) / sizeMultiplier; + span = sqrtSvg("sqrtMain", spanHeight, viewBoxHeight, extraViniculum, options); + span.style.minWidth = "0.853em"; + advanceWidth = 0.833 / sizeMultiplier; // from the font. + } else if (delim.type === "large") { + // These SVGs come from fonts: KaTeX_Size1, _Size2, etc. + viewBoxHeight = (1000 + vbPad) * sizeToMaxHeight[delim.size]; + texHeight = (sizeToMaxHeight[delim.size] + extraViniculum) / sizeMultiplier; + spanHeight = (sizeToMaxHeight[delim.size] + extraViniculum + emPad) / sizeMultiplier; + span = sqrtSvg("sqrtSize" + delim.size, spanHeight, viewBoxHeight, extraViniculum, options); + span.style.minWidth = "1.02em"; + advanceWidth = 1.0 / sizeMultiplier; // 1.0 from the font. + } else { + // Tall sqrt. In TeX, this would be stacked using multiple glyphs. + // We'll use a single SVG to accomplish the same thing. + spanHeight = height + extraViniculum + emPad; + texHeight = height + extraViniculum; + viewBoxHeight = Math.floor(1000 * height + extraViniculum) + vbPad; + span = sqrtSvg("sqrtTall", spanHeight, viewBoxHeight, extraViniculum, options); + span.style.minWidth = "0.742em"; + advanceWidth = 1.056; + } + + span.height = texHeight; + span.style.height = spanHeight + "em"; + return { + span, + advanceWidth, + // Calculate the actual line width. + // This actually should depend on the chosen font -- e.g. \boldmath + // should use the thicker surd symbols from e.g. KaTeX_Main-Bold, and + // have thicker rules. + ruleWidth: (options.fontMetrics().sqrtRuleThickness + extraViniculum) * sizeMultiplier + }; +}; // There are three kinds of delimiters, delimiters that stack when they become +// too large + + +var stackLargeDelimiters = ["(", "\\lparen", ")", "\\rparen", "[", "\\lbrack", "]", "\\rbrack", "\\{", "\\lbrace", "\\}", "\\rbrace", "\\lfloor", "\\rfloor", "\u230a", "\u230b", "\\lceil", "\\rceil", "\u2308", "\u2309", "\\surd"]; // delimiters that always stack + +var stackAlwaysDelimiters = ["\\uparrow", "\\downarrow", "\\updownarrow", "\\Uparrow", "\\Downarrow", "\\Updownarrow", "|", "\\|", "\\vert", "\\Vert", "\\lvert", "\\rvert", "\\lVert", "\\rVert", "\\lgroup", "\\rgroup", "\u27ee", "\u27ef", "\\lmoustache", "\\rmoustache", "\u23b0", "\u23b1"]; // and delimiters that never stack + +var stackNeverDelimiters = ["<", ">", "\\langle", "\\rangle", "/", "\\backslash", "\\lt", "\\gt"]; // Metrics of the different sizes. Found by looking at TeX's output of +// $\bigl| // \Bigl| \biggl| \Biggl| \showlists$ +// Used to create stacked delimiters of appropriate sizes in makeSizedDelim. + +var sizeToMaxHeight = [0, 1.2, 1.8, 2.4, 3.0]; +/** + * Used to create a delimiter of a specific size, where `size` is 1, 2, 3, or 4. + */ + +var makeSizedDelim = function makeSizedDelim(delim, size, options, mode, classes) { + // < and > turn into \langle and \rangle in delimiters + if (delim === "<" || delim === "\\lt" || delim === "\u27e8") { + delim = "\\langle"; + } else if (delim === ">" || delim === "\\gt" || delim === "\u27e9") { + delim = "\\rangle"; + } // Sized delimiters are never centered. + + + if (utils.contains(stackLargeDelimiters, delim) || utils.contains(stackNeverDelimiters, delim)) { + return makeLargeDelim(delim, size, false, options, mode, classes); + } else if (utils.contains(stackAlwaysDelimiters, delim)) { + return makeStackedDelim(delim, sizeToMaxHeight[size], false, options, mode, classes); + } else { + throw new ParseError("Illegal delimiter: '" + delim + "'"); + } +}; +/** + * There are three different sequences of delimiter sizes that the delimiters + * follow depending on the kind of delimiter. This is used when creating custom + * sized delimiters to decide whether to create a small, large, or stacked + * delimiter. + * + * In real TeX, these sequences aren't explicitly defined, but are instead + * defined inside the font metrics. Since there are only three sequences that + * are possible for the delimiters that TeX defines, it is easier to just encode + * them explicitly here. + */ + + +// Delimiters that never stack try small delimiters and large delimiters only +var stackNeverDelimiterSequence = [{ + type: "small", + style: Style$1.SCRIPTSCRIPT +}, { + type: "small", + style: Style$1.SCRIPT +}, { + type: "small", + style: Style$1.TEXT +}, { + type: "large", + size: 1 +}, { + type: "large", + size: 2 +}, { + type: "large", + size: 3 +}, { + type: "large", + size: 4 +}]; // Delimiters that always stack try the small delimiters first, then stack + +var stackAlwaysDelimiterSequence = [{ + type: "small", + style: Style$1.SCRIPTSCRIPT +}, { + type: "small", + style: Style$1.SCRIPT +}, { + type: "small", + style: Style$1.TEXT +}, { + type: "stack" +}]; // Delimiters that stack when large try the small and then large delimiters, and +// stack afterwards + +var stackLargeDelimiterSequence = [{ + type: "small", + style: Style$1.SCRIPTSCRIPT +}, { + type: "small", + style: Style$1.SCRIPT +}, { + type: "small", + style: Style$1.TEXT +}, { + type: "large", + size: 1 +}, { + type: "large", + size: 2 +}, { + type: "large", + size: 3 +}, { + type: "large", + size: 4 +}, { + type: "stack" +}]; +/** + * Get the font used in a delimiter based on what kind of delimiter it is. + * TODO(#963) Use more specific font family return type once that is introduced. + */ + +var delimTypeToFont = function delimTypeToFont(type) { + if (type.type === "small") { + return "Main-Regular"; + } else if (type.type === "large") { + return "Size" + type.size + "-Regular"; + } else if (type.type === "stack") { + return "Size4-Regular"; + } else { + throw new Error("Add support for delim type '" + type.type + "' here."); + } +}; +/** + * Traverse a sequence of types of delimiters to decide what kind of delimiter + * should be used to create a delimiter of the given height+depth. + */ + + +var traverseSequence = function traverseSequence(delim, height, sequence, options) { + // Here, we choose the index we should start at in the sequences. In smaller + // sizes (which correspond to larger numbers in style.size) we start earlier + // in the sequence. Thus, scriptscript starts at index 3-3=0, script starts + // at index 3-2=1, text starts at 3-1=2, and display starts at min(2,3-0)=2 + var start = Math.min(2, 3 - options.style.size); + + for (var i = start; i < sequence.length; i++) { + if (sequence[i].type === "stack") { + // This is always the last delimiter, so we just break the loop now. + break; + } + + var metrics = getMetrics(delim, delimTypeToFont(sequence[i]), "math"); + var heightDepth = metrics.height + metrics.depth; // Small delimiters are scaled down versions of the same font, so we + // account for the style change size. + + if (sequence[i].type === "small") { + var newOptions = options.havingBaseStyle(sequence[i].style); + heightDepth *= newOptions.sizeMultiplier; + } // Check if the delimiter at this size works for the given height. + + + if (heightDepth > height) { + return sequence[i]; + } + } // If we reached the end of the sequence, return the last sequence element. + + + return sequence[sequence.length - 1]; +}; +/** + * Make a delimiter of a given height+depth, with optional centering. Here, we + * traverse the sequences, and create a delimiter that the sequence tells us to. + */ + + +var makeCustomSizedDelim = function makeCustomSizedDelim(delim, height, center, options, mode, classes) { + if (delim === "<" || delim === "\\lt" || delim === "\u27e8") { + delim = "\\langle"; + } else if (delim === ">" || delim === "\\gt" || delim === "\u27e9") { + delim = "\\rangle"; + } // Decide what sequence to use + + + var sequence; + + if (utils.contains(stackNeverDelimiters, delim)) { + sequence = stackNeverDelimiterSequence; + } else if (utils.contains(stackLargeDelimiters, delim)) { + sequence = stackLargeDelimiterSequence; + } else { + sequence = stackAlwaysDelimiterSequence; + } // Look through the sequence + + + var delimType = traverseSequence(delim, height, sequence, options); // Get the delimiter from font glyphs. + // Depending on the sequence element we decided on, call the + // appropriate function. + + if (delimType.type === "small") { + return makeSmallDelim(delim, delimType.style, center, options, mode, classes); + } else if (delimType.type === "large") { + return makeLargeDelim(delim, delimType.size, center, options, mode, classes); + } else + /* if (delimType.type === "stack") */ + { + return makeStackedDelim(delim, height, center, options, mode, classes); + } +}; +/** + * Make a delimiter for use with `\left` and `\right`, given a height and depth + * of an expression that the delimiters surround. + */ + + +var makeLeftRightDelim = function makeLeftRightDelim(delim, height, depth, options, mode, classes) { + // We always center \left/\right delimiters, so the axis is always shifted + var axisHeight = options.fontMetrics().axisHeight * options.sizeMultiplier; // Taken from TeX source, tex.web, function make_left_right + + var delimiterFactor = 901; + var delimiterExtend = 5.0 / options.fontMetrics().ptPerEm; + var maxDistFromAxis = Math.max(height - axisHeight, depth + axisHeight); + var totalHeight = Math.max( // In real TeX, calculations are done using integral values which are + // 65536 per pt, or 655360 per em. So, the division here truncates in + // TeX but doesn't here, producing different results. If we wanted to + // exactly match TeX's calculation, we could do + // Math.floor(655360 * maxDistFromAxis / 500) * + // delimiterFactor / 655360 + // (To see the difference, compare + // x^{x^{\left(\rule{0.1em}{0.68em}\right)}} + // in TeX and KaTeX) + maxDistFromAxis / 500 * delimiterFactor, 2 * maxDistFromAxis - delimiterExtend); // Finally, we defer to `makeCustomSizedDelim` with our calculated total + // height + + return makeCustomSizedDelim(delim, totalHeight, true, options, mode, classes); +}; + +var delimiter = { + sqrtImage: makeSqrtImage, + sizedDelim: makeSizedDelim, + sizeToMaxHeight: sizeToMaxHeight, + customSizedDelim: makeCustomSizedDelim, + leftRightDelim: makeLeftRightDelim +}; + +// Extra data needed for the delimiter handler down below +var delimiterSizes = { + "\\bigl": { + mclass: "mopen", + size: 1 + }, + "\\Bigl": { + mclass: "mopen", + size: 2 + }, + "\\biggl": { + mclass: "mopen", + size: 3 + }, + "\\Biggl": { + mclass: "mopen", + size: 4 + }, + "\\bigr": { + mclass: "mclose", + size: 1 + }, + "\\Bigr": { + mclass: "mclose", + size: 2 + }, + "\\biggr": { + mclass: "mclose", + size: 3 + }, + "\\Biggr": { + mclass: "mclose", + size: 4 + }, + "\\bigm": { + mclass: "mrel", + size: 1 + }, + "\\Bigm": { + mclass: "mrel", + size: 2 + }, + "\\biggm": { + mclass: "mrel", + size: 3 + }, + "\\Biggm": { + mclass: "mrel", + size: 4 + }, + "\\big": { + mclass: "mord", + size: 1 + }, + "\\Big": { + mclass: "mord", + size: 2 + }, + "\\bigg": { + mclass: "mord", + size: 3 + }, + "\\Bigg": { + mclass: "mord", + size: 4 + } +}; +var delimiters = ["(", "\\lparen", ")", "\\rparen", "[", "\\lbrack", "]", "\\rbrack", "\\{", "\\lbrace", "\\}", "\\rbrace", "\\lfloor", "\\rfloor", "\u230a", "\u230b", "\\lceil", "\\rceil", "\u2308", "\u2309", "<", ">", "\\langle", "\u27e8", "\\rangle", "\u27e9", "\\lt", "\\gt", "\\lvert", "\\rvert", "\\lVert", "\\rVert", "\\lgroup", "\\rgroup", "\u27ee", "\u27ef", "\\lmoustache", "\\rmoustache", "\u23b0", "\u23b1", "/", "\\backslash", "|", "\\vert", "\\|", "\\Vert", "\\uparrow", "\\Uparrow", "\\downarrow", "\\Downarrow", "\\updownarrow", "\\Updownarrow", "."]; + +// Delimiter functions +function checkDelimiter(delim, context) { + var symDelim = checkSymbolNodeType(delim); + + if (symDelim && utils.contains(delimiters, symDelim.text)) { + return symDelim; + } else if (symDelim) { + throw new ParseError("Invalid delimiter '" + symDelim.text + "' after '" + context.funcName + "'", delim); + } else { + throw new ParseError("Invalid delimiter type '" + delim.type + "'", delim); + } +} + +defineFunction({ + type: "delimsizing", + names: ["\\bigl", "\\Bigl", "\\biggl", "\\Biggl", "\\bigr", "\\Bigr", "\\biggr", "\\Biggr", "\\bigm", "\\Bigm", "\\biggm", "\\Biggm", "\\big", "\\Big", "\\bigg", "\\Bigg"], + props: { + numArgs: 1, + argTypes: ["primitive"] + }, + handler: (context, args) => { + var delim = checkDelimiter(args[0], context); + return { + type: "delimsizing", + mode: context.parser.mode, + size: delimiterSizes[context.funcName].size, + mclass: delimiterSizes[context.funcName].mclass, + delim: delim.text + }; + }, + htmlBuilder: (group, options) => { + if (group.delim === ".") { + // Empty delimiters still count as elements, even though they don't + // show anything. + return buildCommon.makeSpan([group.mclass]); + } // Use delimiter.sizedDelim to generate the delimiter. + + + return delimiter.sizedDelim(group.delim, group.size, options, group.mode, [group.mclass]); + }, + mathmlBuilder: group => { + var children = []; + + if (group.delim !== ".") { + children.push(makeText(group.delim, group.mode)); + } + + var node = new mathMLTree.MathNode("mo", children); + + if (group.mclass === "mopen" || group.mclass === "mclose") { + // Only some of the delimsizing functions act as fences, and they + // return "mopen" or "mclose" mclass. + node.setAttribute("fence", "true"); + } else { + // Explicitly disable fencing if it's not a fence, to override the + // defaults. + node.setAttribute("fence", "false"); + } + + node.setAttribute("stretchy", "true"); + node.setAttribute("minsize", delimiter.sizeToMaxHeight[group.size] + "em"); + node.setAttribute("maxsize", delimiter.sizeToMaxHeight[group.size] + "em"); + return node; + } +}); + +function assertParsed(group) { + if (!group.body) { + throw new Error("Bug: The leftright ParseNode wasn't fully parsed."); + } +} + +defineFunction({ + type: "leftright-right", + names: ["\\right"], + props: { + numArgs: 1, + primitive: true + }, + handler: (context, args) => { + // \left case below triggers parsing of \right in + // `const right = parser.parseFunction();` + // uses this return value. + var color = context.parser.gullet.macros.get("\\current@color"); + + if (color && typeof color !== "string") { + throw new ParseError("\\current@color set to non-string in \\right"); + } + + return { + type: "leftright-right", + mode: context.parser.mode, + delim: checkDelimiter(args[0], context).text, + color // undefined if not set via \color + + }; + } +}); +defineFunction({ + type: "leftright", + names: ["\\left"], + props: { + numArgs: 1, + primitive: true + }, + handler: (context, args) => { + var delim = checkDelimiter(args[0], context); + var parser = context.parser; // Parse out the implicit body + + ++parser.leftrightDepth; // parseExpression stops before '\\right' + + var body = parser.parseExpression(false); + --parser.leftrightDepth; // Check the next token + + parser.expect("\\right", false); + var right = assertNodeType(parser.parseFunction(), "leftright-right"); + return { + type: "leftright", + mode: parser.mode, + body, + left: delim.text, + right: right.delim, + rightColor: right.color + }; + }, + htmlBuilder: (group, options) => { + assertParsed(group); // Build the inner expression + + var inner = buildExpression$1(group.body, options, true, ["mopen", "mclose"]); + var innerHeight = 0; + var innerDepth = 0; + var hadMiddle = false; // Calculate its height and depth + + for (var i = 0; i < inner.length; i++) { + // Property `isMiddle` not defined on `span`. See comment in + // "middle"'s htmlBuilder. + // $FlowFixMe + if (inner[i].isMiddle) { + hadMiddle = true; + } else { + innerHeight = Math.max(inner[i].height, innerHeight); + innerDepth = Math.max(inner[i].depth, innerDepth); + } + } // The size of delimiters is the same, regardless of what style we are + // in. Thus, to correctly calculate the size of delimiter we need around + // a group, we scale down the inner size based on the size. + + + innerHeight *= options.sizeMultiplier; + innerDepth *= options.sizeMultiplier; + var leftDelim; + + if (group.left === ".") { + // Empty delimiters in \left and \right make null delimiter spaces. + leftDelim = makeNullDelimiter(options, ["mopen"]); + } else { + // Otherwise, use leftRightDelim to generate the correct sized + // delimiter. + leftDelim = delimiter.leftRightDelim(group.left, innerHeight, innerDepth, options, group.mode, ["mopen"]); + } // Add it to the beginning of the expression + + + inner.unshift(leftDelim); // Handle middle delimiters + + if (hadMiddle) { + for (var _i = 1; _i < inner.length; _i++) { + var middleDelim = inner[_i]; // Property `isMiddle` not defined on `span`. See comment in + // "middle"'s htmlBuilder. + // $FlowFixMe + + var isMiddle = middleDelim.isMiddle; + + if (isMiddle) { + // Apply the options that were active when \middle was called + inner[_i] = delimiter.leftRightDelim(isMiddle.delim, innerHeight, innerDepth, isMiddle.options, group.mode, []); + } + } + } + + var rightDelim; // Same for the right delimiter, but using color specified by \color + + if (group.right === ".") { + rightDelim = makeNullDelimiter(options, ["mclose"]); + } else { + var colorOptions = group.rightColor ? options.withColor(group.rightColor) : options; + rightDelim = delimiter.leftRightDelim(group.right, innerHeight, innerDepth, colorOptions, group.mode, ["mclose"]); + } // Add it to the end of the expression. + + + inner.push(rightDelim); + return buildCommon.makeSpan(["minner"], inner, options); + }, + mathmlBuilder: (group, options) => { + assertParsed(group); + var inner = buildExpression(group.body, options); + + if (group.left !== ".") { + var leftNode = new mathMLTree.MathNode("mo", [makeText(group.left, group.mode)]); + leftNode.setAttribute("fence", "true"); + inner.unshift(leftNode); + } + + if (group.right !== ".") { + var rightNode = new mathMLTree.MathNode("mo", [makeText(group.right, group.mode)]); + rightNode.setAttribute("fence", "true"); + + if (group.rightColor) { + rightNode.setAttribute("mathcolor", group.rightColor); + } + + inner.push(rightNode); + } + + return makeRow(inner); + } +}); +defineFunction({ + type: "middle", + names: ["\\middle"], + props: { + numArgs: 1, + primitive: true + }, + handler: (context, args) => { + var delim = checkDelimiter(args[0], context); + + if (!context.parser.leftrightDepth) { + throw new ParseError("\\middle without preceding \\left", delim); + } + + return { + type: "middle", + mode: context.parser.mode, + delim: delim.text + }; + }, + htmlBuilder: (group, options) => { + var middleDelim; + + if (group.delim === ".") { + middleDelim = makeNullDelimiter(options, []); + } else { + middleDelim = delimiter.sizedDelim(group.delim, 1, options, group.mode, []); + var isMiddle = { + delim: group.delim, + options + }; // Property `isMiddle` not defined on `span`. It is only used in + // this file above. + // TODO: Fix this violation of the `span` type and possibly rename + // things since `isMiddle` sounds like a boolean, but is a struct. + // $FlowFixMe + + middleDelim.isMiddle = isMiddle; + } + + return middleDelim; + }, + mathmlBuilder: (group, options) => { + // A Firefox \middle will strech a character vertically only if it + // is in the fence part of the operator dictionary at: + // https://www.w3.org/TR/MathML3/appendixc.html. + // So we need to avoid U+2223 and use plain "|" instead. + var textNode = group.delim === "\\vert" || group.delim === "|" ? makeText("|", "text") : makeText(group.delim, group.mode); + var middleNode = new mathMLTree.MathNode("mo", [textNode]); + middleNode.setAttribute("fence", "true"); // MathML gives 5/18em spacing to each element. + // \middle should get delimiter spacing instead. + + middleNode.setAttribute("lspace", "0.05em"); + middleNode.setAttribute("rspace", "0.05em"); + return middleNode; + } +}); + +var htmlBuilder$8 = (group, options) => { + // \cancel, \bcancel, \xcancel, \sout, \fbox, \colorbox, \fcolorbox, \phase + // Some groups can return document fragments. Handle those by wrapping + // them in a span. + var inner = buildCommon.wrapFragment(buildGroup$1(group.body, options), options); + var label = group.label.substr(1); + var scale = options.sizeMultiplier; + var img; + var imgShift = 0; // In the LaTeX cancel package, line geometry is slightly different + // depending on whether the subject is wider than it is tall, or vice versa. + // We don't know the width of a group, so as a proxy, we test if + // the subject is a single character. This captures most of the + // subjects that should get the "tall" treatment. + + var isSingleChar = utils.isCharacterBox(group.body); + + if (label === "sout") { + img = buildCommon.makeSpan(["stretchy", "sout"]); + img.height = options.fontMetrics().defaultRuleThickness / scale; + imgShift = -0.5 * options.fontMetrics().xHeight; + } else if (label === "phase") { + // Set a couple of dimensions from the steinmetz package. + var lineWeight = calculateSize({ + number: 0.6, + unit: "pt" + }, options); + var clearance = calculateSize({ + number: 0.35, + unit: "ex" + }, options); // Prevent size changes like \Huge from affecting line thickness + + var newOptions = options.havingBaseSizing(); + scale = scale / newOptions.sizeMultiplier; + var angleHeight = inner.height + inner.depth + lineWeight + clearance; // Reserve a left pad for the angle. + + inner.style.paddingLeft = angleHeight / 2 + lineWeight + "em"; // Create an SVG + + var viewBoxHeight = Math.floor(1000 * angleHeight * scale); + var path = phasePath(viewBoxHeight); + var svgNode = new SvgNode([new PathNode("phase", path)], { + "width": "400em", + "height": viewBoxHeight / 1000 + "em", + "viewBox": "0 0 400000 " + viewBoxHeight, + "preserveAspectRatio": "xMinYMin slice" + }); // Wrap it in a span with overflow: hidden. + + img = buildCommon.makeSvgSpan(["hide-tail"], [svgNode], options); + img.style.height = angleHeight + "em"; + imgShift = inner.depth + lineWeight + clearance; + } else { + // Add horizontal padding + if (/cancel/.test(label)) { + if (!isSingleChar) { + inner.classes.push("cancel-pad"); + } + } else if (label === "angl") { + inner.classes.push("anglpad"); + } else { + inner.classes.push("boxpad"); + } // Add vertical padding + + + var topPad = 0; + var bottomPad = 0; + var ruleThickness = 0; // ref: cancel package: \advance\totalheight2\p@ % "+2" + + if (/box/.test(label)) { + ruleThickness = Math.max(options.fontMetrics().fboxrule, // default + options.minRuleThickness // User override. + ); + topPad = options.fontMetrics().fboxsep + (label === "colorbox" ? 0 : ruleThickness); + bottomPad = topPad; + } else if (label === "angl") { + ruleThickness = Math.max(options.fontMetrics().defaultRuleThickness, options.minRuleThickness); + topPad = 4 * ruleThickness; // gap = 3 × line, plus the line itself. + + bottomPad = Math.max(0, 0.25 - inner.depth); + } else { + topPad = isSingleChar ? 0.2 : 0; + bottomPad = topPad; + } + + img = stretchy.encloseSpan(inner, label, topPad, bottomPad, options); + + if (/fbox|boxed|fcolorbox/.test(label)) { + img.style.borderStyle = "solid"; + img.style.borderWidth = ruleThickness + "em"; + } else if (label === "angl" && ruleThickness !== 0.049) { + img.style.borderTopWidth = ruleThickness + "em"; + img.style.borderRightWidth = ruleThickness + "em"; + } + + imgShift = inner.depth + bottomPad; + + if (group.backgroundColor) { + img.style.backgroundColor = group.backgroundColor; + + if (group.borderColor) { + img.style.borderColor = group.borderColor; + } + } + } + + var vlist; + + if (group.backgroundColor) { + vlist = buildCommon.makeVList({ + positionType: "individualShift", + children: [// Put the color background behind inner; + { + type: "elem", + elem: img, + shift: imgShift + }, { + type: "elem", + elem: inner, + shift: 0 + }] + }, options); + } else { + var classes = /cancel|phase/.test(label) ? ["svg-align"] : []; + vlist = buildCommon.makeVList({ + positionType: "individualShift", + children: [// Write the \cancel stroke on top of inner. + { + type: "elem", + elem: inner, + shift: 0 + }, { + type: "elem", + elem: img, + shift: imgShift, + wrapperClasses: classes + }] + }, options); + } + + if (/cancel/.test(label)) { + // The cancel package documentation says that cancel lines add their height + // to the expression, but tests show that isn't how it actually works. + vlist.height = inner.height; + vlist.depth = inner.depth; + } + + if (/cancel/.test(label) && !isSingleChar) { + // cancel does not create horiz space for its line extension. + return buildCommon.makeSpan(["mord", "cancel-lap"], [vlist], options); + } else { + return buildCommon.makeSpan(["mord"], [vlist], options); + } +}; + +var mathmlBuilder$7 = (group, options) => { + var fboxsep = 0; + var node = new mathMLTree.MathNode(group.label.indexOf("colorbox") > -1 ? "mpadded" : "menclose", [buildGroup(group.body, options)]); + + switch (group.label) { + case "\\cancel": + node.setAttribute("notation", "updiagonalstrike"); + break; + + case "\\bcancel": + node.setAttribute("notation", "downdiagonalstrike"); + break; + + case "\\phase": + node.setAttribute("notation", "phasorangle"); + break; + + case "\\sout": + node.setAttribute("notation", "horizontalstrike"); + break; + + case "\\fbox": + node.setAttribute("notation", "box"); + break; + + case "\\angl": + node.setAttribute("notation", "actuarial"); + break; + + case "\\fcolorbox": + case "\\colorbox": + // doesn't have a good notation option. So use + // instead. Set some attributes that come included with . + fboxsep = options.fontMetrics().fboxsep * options.fontMetrics().ptPerEm; + node.setAttribute("width", "+" + 2 * fboxsep + "pt"); + node.setAttribute("height", "+" + 2 * fboxsep + "pt"); + node.setAttribute("lspace", fboxsep + "pt"); // + + node.setAttribute("voffset", fboxsep + "pt"); + + if (group.label === "\\fcolorbox") { + var thk = Math.max(options.fontMetrics().fboxrule, // default + options.minRuleThickness // user override + ); + node.setAttribute("style", "border: " + thk + "em solid " + String(group.borderColor)); + } + + break; + + case "\\xcancel": + node.setAttribute("notation", "updiagonalstrike downdiagonalstrike"); + break; + } + + if (group.backgroundColor) { + node.setAttribute("mathbackground", group.backgroundColor); + } + + return node; +}; + +defineFunction({ + type: "enclose", + names: ["\\colorbox"], + props: { + numArgs: 2, + allowedInText: true, + argTypes: ["color", "text"] + }, + + handler(_ref, args, optArgs) { + var { + parser, + funcName + } = _ref; + var color = assertNodeType(args[0], "color-token").color; + var body = args[1]; + return { + type: "enclose", + mode: parser.mode, + label: funcName, + backgroundColor: color, + body + }; + }, + + htmlBuilder: htmlBuilder$8, + mathmlBuilder: mathmlBuilder$7 +}); +defineFunction({ + type: "enclose", + names: ["\\fcolorbox"], + props: { + numArgs: 3, + allowedInText: true, + argTypes: ["color", "color", "text"] + }, + + handler(_ref2, args, optArgs) { + var { + parser, + funcName + } = _ref2; + var borderColor = assertNodeType(args[0], "color-token").color; + var backgroundColor = assertNodeType(args[1], "color-token").color; + var body = args[2]; + return { + type: "enclose", + mode: parser.mode, + label: funcName, + backgroundColor, + borderColor, + body + }; + }, + + htmlBuilder: htmlBuilder$8, + mathmlBuilder: mathmlBuilder$7 +}); +defineFunction({ + type: "enclose", + names: ["\\fbox"], + props: { + numArgs: 1, + argTypes: ["hbox"], + allowedInText: true + }, + + handler(_ref3, args) { + var { + parser + } = _ref3; + return { + type: "enclose", + mode: parser.mode, + label: "\\fbox", + body: args[0] + }; + } + +}); +defineFunction({ + type: "enclose", + names: ["\\cancel", "\\bcancel", "\\xcancel", "\\sout", "\\phase"], + props: { + numArgs: 1 + }, + + handler(_ref4, args) { + var { + parser, + funcName + } = _ref4; + var body = args[0]; + return { + type: "enclose", + mode: parser.mode, + label: funcName, + body + }; + }, + + htmlBuilder: htmlBuilder$8, + mathmlBuilder: mathmlBuilder$7 +}); +defineFunction({ + type: "enclose", + names: ["\\angl"], + props: { + numArgs: 1, + argTypes: ["hbox"], + allowedInText: false + }, + + handler(_ref5, args) { + var { + parser + } = _ref5; + return { + type: "enclose", + mode: parser.mode, + label: "\\angl", + body: args[0] + }; + } + +}); + +/** + * All registered environments. + * `environments.js` exports this same dictionary again and makes it public. + * `Parser.js` requires this dictionary via `environments.js`. + */ +var _environments = {}; +function defineEnvironment(_ref) { + var { + type, + names, + props, + handler, + htmlBuilder, + mathmlBuilder + } = _ref; + // Set default values of environments. + var data = { + type, + numArgs: props.numArgs || 0, + allowedInText: false, + numOptionalArgs: 0, + handler + }; + + for (var i = 0; i < names.length; ++i) { + // TODO: The value type of _environments should be a type union of all + // possible `EnvSpec<>` possibilities instead of `EnvSpec<*>`, which is + // an existential type. + _environments[names[i]] = data; + } + + if (htmlBuilder) { + _htmlGroupBuilders[type] = htmlBuilder; + } + + if (mathmlBuilder) { + _mathmlGroupBuilders[type] = mathmlBuilder; + } +} + +// Helper functions +function getHLines(parser) { + // Return an array. The array length = number of hlines. + // Each element in the array tells if the line is dashed. + var hlineInfo = []; + parser.consumeSpaces(); + var nxt = parser.fetch().text; + + while (nxt === "\\hline" || nxt === "\\hdashline") { + parser.consume(); + hlineInfo.push(nxt === "\\hdashline"); + parser.consumeSpaces(); + nxt = parser.fetch().text; + } + + return hlineInfo; +} + +var validateAmsEnvironmentContext = context => { + var settings = context.parser.settings; + + if (!settings.displayMode) { + throw new ParseError("{" + context.envName + "} can be used only in" + " display mode."); + } +}; +/** + * Parse the body of the environment, with rows delimited by \\ and + * columns delimited by &, and create a nested list in row-major order + * with one group per cell. If given an optional argument style + * ("text", "display", etc.), then each cell is cast into that style. + */ + + +function parseArray(parser, _ref, style) { + var { + hskipBeforeAndAfter, + addJot, + cols, + arraystretch, + colSeparationType, + addEqnNum, + singleRow, + emptySingleRow, + maxNumCols, + leqno + } = _ref; + parser.gullet.beginGroup(); + + if (!singleRow) { + // \cr is equivalent to \\ without the optional size argument (see below) + // TODO: provide helpful error when \cr is used outside array environment + parser.gullet.macros.set("\\cr", "\\\\\\relax"); + } // Get current arraystretch if it's not set by the environment + + + if (!arraystretch) { + var stretch = parser.gullet.expandMacroAsText("\\arraystretch"); + + if (stretch == null) { + // Default \arraystretch from lttab.dtx + arraystretch = 1; + } else { + arraystretch = parseFloat(stretch); + + if (!arraystretch || arraystretch < 0) { + throw new ParseError("Invalid \\arraystretch: " + stretch); + } + } + } // Start group for first cell + + + parser.gullet.beginGroup(); + var row = []; + var body = [row]; + var rowGaps = []; + var hLinesBeforeRow = []; // Test for \hline at the top of the array. + + hLinesBeforeRow.push(getHLines(parser)); + + while (true) { + // eslint-disable-line no-constant-condition + // Parse each cell in its own group (namespace) + var cell = parser.parseExpression(false, singleRow ? "\\end" : "\\\\"); + parser.gullet.endGroup(); + parser.gullet.beginGroup(); + cell = { + type: "ordgroup", + mode: parser.mode, + body: cell + }; + + if (style) { + cell = { + type: "styling", + mode: parser.mode, + style, + body: [cell] + }; + } + + row.push(cell); + var next = parser.fetch().text; + + if (next === "&") { + if (maxNumCols && row.length === maxNumCols) { + if (singleRow || colSeparationType) { + // {equation} or {split} + throw new ParseError("Too many tab characters: &", parser.nextToken); + } else { + // {array} environment + parser.settings.reportNonstrict("textEnv", "Too few columns " + "specified in the {array} column argument."); + } + } + + parser.consume(); + } else if (next === "\\end") { + // Arrays terminate newlines with `\crcr` which consumes a `\cr` if + // the last line is empty. However, AMS environments keep the + // empty row if it's the only one. + // NOTE: Currently, `cell` is the last item added into `row`. + if (row.length === 1 && cell.type === "styling" && cell.body[0].body.length === 0 && (body.length > 1 || !emptySingleRow)) { + body.pop(); + } + + if (hLinesBeforeRow.length < body.length + 1) { + hLinesBeforeRow.push([]); + } + + break; + } else if (next === "\\\\") { + parser.consume(); + var size = void 0; // \def\Let@{\let\\\math@cr} + // \def\math@cr{...\math@cr@} + // \def\math@cr@{\new@ifnextchar[\math@cr@@{\math@cr@@[\z@]}} + // \def\math@cr@@[#1]{...\math@cr@@@...} + // \def\math@cr@@@{\cr} + + if (parser.gullet.future().text !== " ") { + size = parser.parseSizeGroup(true); + } + + rowGaps.push(size ? size.value : null); // check for \hline(s) following the row separator + + hLinesBeforeRow.push(getHLines(parser)); + row = []; + body.push(row); + } else { + throw new ParseError("Expected & or \\\\ or \\cr or \\end", parser.nextToken); + } + } // End cell group + + + parser.gullet.endGroup(); // End array group defining \cr + + parser.gullet.endGroup(); + return { + type: "array", + mode: parser.mode, + addJot, + arraystretch, + body, + cols, + rowGaps, + hskipBeforeAndAfter, + hLinesBeforeRow, + colSeparationType, + addEqnNum, + leqno + }; +} // Decides on a style for cells in an array according to whether the given +// environment name starts with the letter 'd'. + + +function dCellStyle(envName) { + if (envName.substr(0, 1) === "d") { + return "display"; + } else { + return "text"; + } +} + +var htmlBuilder$7 = function htmlBuilder(group, options) { + var r; + var c; + var nr = group.body.length; + var hLinesBeforeRow = group.hLinesBeforeRow; + var nc = 0; + var body = new Array(nr); + var hlines = []; + var ruleThickness = Math.max( // From LaTeX \showthe\arrayrulewidth. Equals 0.04 em. + options.fontMetrics().arrayRuleWidth, options.minRuleThickness // User override. + ); // Horizontal spacing + + var pt = 1 / options.fontMetrics().ptPerEm; + var arraycolsep = 5 * pt; // default value, i.e. \arraycolsep in article.cls + + if (group.colSeparationType && group.colSeparationType === "small") { + // We're in a {smallmatrix}. Default column space is \thickspace, + // i.e. 5/18em = 0.2778em, per amsmath.dtx for {smallmatrix}. + // But that needs adjustment because LaTeX applies \scriptstyle to the + // entire array, including the colspace, but this function applies + // \scriptstyle only inside each element. + var localMultiplier = options.havingStyle(Style$1.SCRIPT).sizeMultiplier; + arraycolsep = 0.2778 * (localMultiplier / options.sizeMultiplier); + } // Vertical spacing + + + var baselineskip = group.colSeparationType === "CD" ? calculateSize({ + number: 3, + unit: "ex" + }, options) : 12 * pt; // see size10.clo + // Default \jot from ltmath.dtx + // TODO(edemaine): allow overriding \jot via \setlength (#687) + + var jot = 3 * pt; + var arrayskip = group.arraystretch * baselineskip; + var arstrutHeight = 0.7 * arrayskip; // \strutbox in ltfsstrc.dtx and + + var arstrutDepth = 0.3 * arrayskip; // \@arstrutbox in lttab.dtx + + var totalHeight = 0; // Set a position for \hline(s) at the top of the array, if any. + + function setHLinePos(hlinesInGap) { + for (var i = 0; i < hlinesInGap.length; ++i) { + if (i > 0) { + totalHeight += 0.25; + } + + hlines.push({ + pos: totalHeight, + isDashed: hlinesInGap[i] + }); + } + } + + setHLinePos(hLinesBeforeRow[0]); + + for (r = 0; r < group.body.length; ++r) { + var inrow = group.body[r]; + var height = arstrutHeight; // \@array adds an \@arstrut + + var depth = arstrutDepth; // to each tow (via the template) + + if (nc < inrow.length) { + nc = inrow.length; + } + + var outrow = new Array(inrow.length); + + for (c = 0; c < inrow.length; ++c) { + var elt = buildGroup$1(inrow[c], options); + + if (depth < elt.depth) { + depth = elt.depth; + } + + if (height < elt.height) { + height = elt.height; + } + + outrow[c] = elt; + } + + var rowGap = group.rowGaps[r]; + var gap = 0; + + if (rowGap) { + gap = calculateSize(rowGap, options); + + if (gap > 0) { + // \@argarraycr + gap += arstrutDepth; + + if (depth < gap) { + depth = gap; // \@xargarraycr + } + + gap = 0; + } + } // In AMS multiline environments such as aligned and gathered, rows + // correspond to lines that have additional \jot added to the + // \baselineskip via \openup. + + + if (group.addJot) { + depth += jot; + } + + outrow.height = height; + outrow.depth = depth; + totalHeight += height; + outrow.pos = totalHeight; + totalHeight += depth + gap; // \@yargarraycr + + body[r] = outrow; // Set a position for \hline(s), if any. + + setHLinePos(hLinesBeforeRow[r + 1]); + } + + var offset = totalHeight / 2 + options.fontMetrics().axisHeight; + var colDescriptions = group.cols || []; + var cols = []; + var colSep; + var colDescrNum; + var eqnNumSpans = []; + + if (group.addEqnNum) { + // An environment with automatic equation numbers. + // Create node(s) that will trigger CSS counter increment. + for (r = 0; r < nr; ++r) { + var rw = body[r]; + var shift = rw.pos - offset; + var eqnTag = buildCommon.makeSpan(["eqn-num"], [], options); + eqnTag.depth = rw.depth; + eqnTag.height = rw.height; + eqnNumSpans.push({ + type: "elem", + elem: eqnTag, + shift + }); + } + } + + for (c = 0, colDescrNum = 0; // Continue while either there are more columns or more column + // descriptions, so trailing separators don't get lost. + c < nc || colDescrNum < colDescriptions.length; ++c, ++colDescrNum) { + var colDescr = colDescriptions[colDescrNum] || {}; + var firstSeparator = true; + + while (colDescr.type === "separator") { + // If there is more than one separator in a row, add a space + // between them. + if (!firstSeparator) { + colSep = buildCommon.makeSpan(["arraycolsep"], []); + colSep.style.width = options.fontMetrics().doubleRuleSep + "em"; + cols.push(colSep); + } + + if (colDescr.separator === "|" || colDescr.separator === ":") { + var lineType = colDescr.separator === "|" ? "solid" : "dashed"; + var separator = buildCommon.makeSpan(["vertical-separator"], [], options); + separator.style.height = totalHeight + "em"; + separator.style.borderRightWidth = ruleThickness + "em"; + separator.style.borderRightStyle = lineType; + separator.style.margin = "0 -" + ruleThickness / 2 + "em"; + separator.style.verticalAlign = -(totalHeight - offset) + "em"; + cols.push(separator); + } else { + throw new ParseError("Invalid separator type: " + colDescr.separator); + } + + colDescrNum++; + colDescr = colDescriptions[colDescrNum] || {}; + firstSeparator = false; + } + + if (c >= nc) { + continue; + } + + var sepwidth = void 0; + + if (c > 0 || group.hskipBeforeAndAfter) { + sepwidth = utils.deflt(colDescr.pregap, arraycolsep); + + if (sepwidth !== 0) { + colSep = buildCommon.makeSpan(["arraycolsep"], []); + colSep.style.width = sepwidth + "em"; + cols.push(colSep); + } + } + + var col = []; + + for (r = 0; r < nr; ++r) { + var row = body[r]; + var elem = row[c]; + + if (!elem) { + continue; + } + + var _shift = row.pos - offset; + + elem.depth = row.depth; + elem.height = row.height; + col.push({ + type: "elem", + elem: elem, + shift: _shift + }); + } + + col = buildCommon.makeVList({ + positionType: "individualShift", + children: col + }, options); + col = buildCommon.makeSpan(["col-align-" + (colDescr.align || "c")], [col]); + cols.push(col); + + if (c < nc - 1 || group.hskipBeforeAndAfter) { + sepwidth = utils.deflt(colDescr.postgap, arraycolsep); + + if (sepwidth !== 0) { + colSep = buildCommon.makeSpan(["arraycolsep"], []); + colSep.style.width = sepwidth + "em"; + cols.push(colSep); + } + } + } + + body = buildCommon.makeSpan(["mtable"], cols); // Add \hline(s), if any. + + if (hlines.length > 0) { + var line = buildCommon.makeLineSpan("hline", options, ruleThickness); + var dashes = buildCommon.makeLineSpan("hdashline", options, ruleThickness); + var vListElems = [{ + type: "elem", + elem: body, + shift: 0 + }]; + + while (hlines.length > 0) { + var hline = hlines.pop(); + var lineShift = hline.pos - offset; + + if (hline.isDashed) { + vListElems.push({ + type: "elem", + elem: dashes, + shift: lineShift + }); + } else { + vListElems.push({ + type: "elem", + elem: line, + shift: lineShift + }); + } + } + + body = buildCommon.makeVList({ + positionType: "individualShift", + children: vListElems + }, options); + } + + if (!group.addEqnNum) { + return buildCommon.makeSpan(["mord"], [body], options); + } else { + var eqnNumCol = buildCommon.makeVList({ + positionType: "individualShift", + children: eqnNumSpans + }, options); + eqnNumCol = buildCommon.makeSpan(["tag"], [eqnNumCol], options); + return buildCommon.makeFragment([body, eqnNumCol]); + } +}; + +var alignMap = { + c: "center ", + l: "left ", + r: "right " +}; + +var mathmlBuilder$6 = function mathmlBuilder(group, options) { + var tbl = []; + var glue = new mathMLTree.MathNode("mtd", [], ["mtr-glue"]); + var tag = new mathMLTree.MathNode("mtd", [], ["mml-eqn-num"]); + + for (var i = 0; i < group.body.length; i++) { + var rw = group.body[i]; + var row = []; + + for (var j = 0; j < rw.length; j++) { + row.push(new mathMLTree.MathNode("mtd", [buildGroup(rw[j], options)])); + } + + if (group.addEqnNum) { + row.unshift(glue); + row.push(glue); + + if (group.leqno) { + row.unshift(tag); + } else { + row.push(tag); + } + } + + tbl.push(new mathMLTree.MathNode("mtr", row)); + } + + var table = new mathMLTree.MathNode("mtable", tbl); // Set column alignment, row spacing, column spacing, and + // array lines by setting attributes on the table element. + // Set the row spacing. In MathML, we specify a gap distance. + // We do not use rowGap[] because MathML automatically increases + // cell height with the height/depth of the element content. + // LaTeX \arraystretch multiplies the row baseline-to-baseline distance. + // We simulate this by adding (arraystretch - 1)em to the gap. This + // does a reasonable job of adjusting arrays containing 1 em tall content. + // The 0.16 and 0.09 values are found emprically. They produce an array + // similar to LaTeX and in which content does not interfere with \hines. + + var gap = group.arraystretch === 0.5 ? 0.1 // {smallmatrix}, {subarray} + : 0.16 + group.arraystretch - 1 + (group.addJot ? 0.09 : 0); + table.setAttribute("rowspacing", gap.toFixed(4) + "em"); // MathML table lines go only between cells. + // To place a line on an edge we'll use , if necessary. + + var menclose = ""; + var align = ""; + + if (group.cols && group.cols.length > 0) { + // Find column alignment, column spacing, and vertical lines. + var cols = group.cols; + var columnLines = ""; + var prevTypeWasAlign = false; + var iStart = 0; + var iEnd = cols.length; + + if (cols[0].type === "separator") { + menclose += "top "; + iStart = 1; + } + + if (cols[cols.length - 1].type === "separator") { + menclose += "bottom "; + iEnd -= 1; + } + + for (var _i = iStart; _i < iEnd; _i++) { + if (cols[_i].type === "align") { + align += alignMap[cols[_i].align]; + + if (prevTypeWasAlign) { + columnLines += "none "; + } + + prevTypeWasAlign = true; + } else if (cols[_i].type === "separator") { + // MathML accepts only single lines between cells. + // So we read only the first of consecutive separators. + if (prevTypeWasAlign) { + columnLines += cols[_i].separator === "|" ? "solid " : "dashed "; + prevTypeWasAlign = false; + } + } + } + + table.setAttribute("columnalign", align.trim()); + + if (/[sd]/.test(columnLines)) { + table.setAttribute("columnlines", columnLines.trim()); + } + } // Set column spacing. + + + if (group.colSeparationType === "align") { + var _cols = group.cols || []; + + var spacing = ""; + + for (var _i2 = 1; _i2 < _cols.length; _i2++) { + spacing += _i2 % 2 ? "0em " : "1em "; + } + + table.setAttribute("columnspacing", spacing.trim()); + } else if (group.colSeparationType === "alignat" || group.colSeparationType === "gather") { + table.setAttribute("columnspacing", "0em"); + } else if (group.colSeparationType === "small") { + table.setAttribute("columnspacing", "0.2778em"); + } else if (group.colSeparationType === "CD") { + table.setAttribute("columnspacing", "0.5em"); + } else { + table.setAttribute("columnspacing", "1em"); + } // Address \hline and \hdashline + + + var rowLines = ""; + var hlines = group.hLinesBeforeRow; + menclose += hlines[0].length > 0 ? "left " : ""; + menclose += hlines[hlines.length - 1].length > 0 ? "right " : ""; + + for (var _i3 = 1; _i3 < hlines.length - 1; _i3++) { + rowLines += hlines[_i3].length === 0 ? "none " // MathML accepts only a single line between rows. Read one element. + : hlines[_i3][0] ? "dashed " : "solid "; + } + + if (/[sd]/.test(rowLines)) { + table.setAttribute("rowlines", rowLines.trim()); + } + + if (menclose !== "") { + table = new mathMLTree.MathNode("menclose", [table]); + table.setAttribute("notation", menclose.trim()); + } + + if (group.arraystretch && group.arraystretch < 1) { + // A small array. Wrap in scriptstyle so row gap is not too large. + table = new mathMLTree.MathNode("mstyle", [table]); + table.setAttribute("scriptlevel", "1"); + } + + return table; +}; // Convenience function for align, align*, aligned, alignat, alignat*, alignedat. + + +var alignedHandler = function alignedHandler(context, args) { + if (context.envName.indexOf("ed") === -1) { + validateAmsEnvironmentContext(context); + } + + var cols = []; + var separationType = context.envName.indexOf("at") > -1 ? "alignat" : "align"; + var res = parseArray(context.parser, { + cols, + addJot: true, + addEqnNum: context.envName === "align" || context.envName === "alignat", + emptySingleRow: true, + colSeparationType: separationType, + maxNumCols: context.envName === "split" ? 2 : undefined, + leqno: context.parser.settings.leqno + }, "display"); // Determining number of columns. + // 1. If the first argument is given, we use it as a number of columns, + // and makes sure that each row doesn't exceed that number. + // 2. Otherwise, just count number of columns = maximum number + // of cells in each row ("aligned" mode -- isAligned will be true). + // + // At the same time, prepend empty group {} at beginning of every second + // cell in each row (starting with second cell) so that operators become + // binary. This behavior is implemented in amsmath's \start@aligned. + + var numMaths; + var numCols = 0; + var emptyGroup = { + type: "ordgroup", + mode: context.mode, + body: [] + }; + + if (args[0] && args[0].type === "ordgroup") { + var arg0 = ""; + + for (var i = 0; i < args[0].body.length; i++) { + var textord = assertNodeType(args[0].body[i], "textord"); + arg0 += textord.text; + } + + numMaths = Number(arg0); + numCols = numMaths * 2; + } + + var isAligned = !numCols; + res.body.forEach(function (row) { + for (var _i4 = 1; _i4 < row.length; _i4 += 2) { + // Modify ordgroup node within styling node + var styling = assertNodeType(row[_i4], "styling"); + var ordgroup = assertNodeType(styling.body[0], "ordgroup"); + ordgroup.body.unshift(emptyGroup); + } + + if (!isAligned) { + // Case 1 + var curMaths = row.length / 2; + + if (numMaths < curMaths) { + throw new ParseError("Too many math in a row: " + ("expected " + numMaths + ", but got " + curMaths), row[0]); + } + } else if (numCols < row.length) { + // Case 2 + numCols = row.length; + } + }); // Adjusting alignment. + // In aligned mode, we add one \qquad between columns; + // otherwise we add nothing. + + for (var _i5 = 0; _i5 < numCols; ++_i5) { + var align = "r"; + var pregap = 0; + + if (_i5 % 2 === 1) { + align = "l"; + } else if (_i5 > 0 && isAligned) { + // "aligned" mode. + pregap = 1; // add one \quad + } + + cols[_i5] = { + type: "align", + align: align, + pregap: pregap, + postgap: 0 + }; + } + + res.colSeparationType = isAligned ? "align" : "alignat"; + return res; +}; // Arrays are part of LaTeX, defined in lttab.dtx so its documentation +// is part of the source2e.pdf file of LaTeX2e source documentation. +// {darray} is an {array} environment where cells are set in \displaystyle, +// as defined in nccmath.sty. + + +defineEnvironment({ + type: "array", + names: ["array", "darray"], + props: { + numArgs: 1 + }, + + handler(context, args) { + // Since no types are specified above, the two possibilities are + // - The argument is wrapped in {} or [], in which case Parser's + // parseGroup() returns an "ordgroup" wrapping some symbol node. + // - The argument is a bare symbol node. + var symNode = checkSymbolNodeType(args[0]); + var colalign = symNode ? [args[0]] : assertNodeType(args[0], "ordgroup").body; + var cols = colalign.map(function (nde) { + var node = assertSymbolNodeType(nde); + var ca = node.text; + + if ("lcr".indexOf(ca) !== -1) { + return { + type: "align", + align: ca + }; + } else if (ca === "|") { + return { + type: "separator", + separator: "|" + }; + } else if (ca === ":") { + return { + type: "separator", + separator: ":" + }; + } + + throw new ParseError("Unknown column alignment: " + ca, nde); + }); + var res = { + cols, + hskipBeforeAndAfter: true, + // \@preamble in lttab.dtx + maxNumCols: cols.length + }; + return parseArray(context.parser, res, dCellStyle(context.envName)); + }, + + htmlBuilder: htmlBuilder$7, + mathmlBuilder: mathmlBuilder$6 +}); // The matrix environments of amsmath builds on the array environment +// of LaTeX, which is discussed above. +// The mathtools package adds starred versions of the same environments. +// These have an optional argument to choose left|center|right justification. + +defineEnvironment({ + type: "array", + names: ["matrix", "pmatrix", "bmatrix", "Bmatrix", "vmatrix", "Vmatrix", "matrix*", "pmatrix*", "bmatrix*", "Bmatrix*", "vmatrix*", "Vmatrix*"], + props: { + numArgs: 0 + }, + + handler(context) { + var delimiters = { + "matrix": null, + "pmatrix": ["(", ")"], + "bmatrix": ["[", "]"], + "Bmatrix": ["\\{", "\\}"], + "vmatrix": ["|", "|"], + "Vmatrix": ["\\Vert", "\\Vert"] + }[context.envName.replace("*", "")]; // \hskip -\arraycolsep in amsmath + + var colAlign = "c"; + var payload = { + hskipBeforeAndAfter: false, + cols: [{ + type: "align", + align: colAlign + }] + }; + + if (context.envName.charAt(context.envName.length - 1) === "*") { + // It's one of the mathtools starred functions. + // Parse the optional alignment argument. + var parser = context.parser; + parser.consumeSpaces(); + + if (parser.fetch().text === "[") { + parser.consume(); + parser.consumeSpaces(); + colAlign = parser.fetch().text; + + if ("lcr".indexOf(colAlign) === -1) { + throw new ParseError("Expected l or c or r", parser.nextToken); + } + + parser.consume(); + parser.consumeSpaces(); + parser.expect("]"); + parser.consume(); + payload.cols = [{ + type: "align", + align: colAlign + }]; + } + } + + var res = parseArray(context.parser, payload, dCellStyle(context.envName)); // Populate cols with the correct number of column alignment specs. + + var numCols = Math.max(0, ...res.body.map(row => row.length)); + res.cols = new Array(numCols).fill({ + type: "align", + align: colAlign + }); + return delimiters ? { + type: "leftright", + mode: context.mode, + body: [res], + left: delimiters[0], + right: delimiters[1], + rightColor: undefined // \right uninfluenced by \color in array + + } : res; + }, + + htmlBuilder: htmlBuilder$7, + mathmlBuilder: mathmlBuilder$6 +}); +defineEnvironment({ + type: "array", + names: ["smallmatrix"], + props: { + numArgs: 0 + }, + + handler(context) { + var payload = { + arraystretch: 0.5 + }; + var res = parseArray(context.parser, payload, "script"); + res.colSeparationType = "small"; + return res; + }, + + htmlBuilder: htmlBuilder$7, + mathmlBuilder: mathmlBuilder$6 +}); +defineEnvironment({ + type: "array", + names: ["subarray"], + props: { + numArgs: 1 + }, + + handler(context, args) { + // Parsing of {subarray} is similar to {array} + var symNode = checkSymbolNodeType(args[0]); + var colalign = symNode ? [args[0]] : assertNodeType(args[0], "ordgroup").body; + var cols = colalign.map(function (nde) { + var node = assertSymbolNodeType(nde); + var ca = node.text; // {subarray} only recognizes "l" & "c" + + if ("lc".indexOf(ca) !== -1) { + return { + type: "align", + align: ca + }; + } + + throw new ParseError("Unknown column alignment: " + ca, nde); + }); + + if (cols.length > 1) { + throw new ParseError("{subarray} can contain only one column"); + } + + var res = { + cols, + hskipBeforeAndAfter: false, + arraystretch: 0.5 + }; + res = parseArray(context.parser, res, "script"); + + if (res.body.length > 0 && res.body[0].length > 1) { + throw new ParseError("{subarray} can contain only one column"); + } + + return res; + }, + + htmlBuilder: htmlBuilder$7, + mathmlBuilder: mathmlBuilder$6 +}); // A cases environment (in amsmath.sty) is almost equivalent to +// \def\arraystretch{1.2}% +// \left\{\begin{array}{@{}l@{\quad}l@{}} … \end{array}\right. +// {dcases} is a {cases} environment where cells are set in \displaystyle, +// as defined in mathtools.sty. +// {rcases} is another mathtools environment. It's brace is on the right side. + +defineEnvironment({ + type: "array", + names: ["cases", "dcases", "rcases", "drcases"], + props: { + numArgs: 0 + }, + + handler(context) { + var payload = { + arraystretch: 1.2, + cols: [{ + type: "align", + align: "l", + pregap: 0, + // TODO(kevinb) get the current style. + // For now we use the metrics for TEXT style which is what we were + // doing before. Before attempting to get the current style we + // should look at TeX's behavior especially for \over and matrices. + postgap: 1.0 + /* 1em quad */ + + }, { + type: "align", + align: "l", + pregap: 0, + postgap: 0 + }] + }; + var res = parseArray(context.parser, payload, dCellStyle(context.envName)); + return { + type: "leftright", + mode: context.mode, + body: [res], + left: context.envName.indexOf("r") > -1 ? "." : "\\{", + right: context.envName.indexOf("r") > -1 ? "\\}" : ".", + rightColor: undefined + }; + }, + + htmlBuilder: htmlBuilder$7, + mathmlBuilder: mathmlBuilder$6 +}); // In the align environment, one uses ampersands, &, to specify number of +// columns in each row, and to locate spacing between each column. +// align gets automatic numbering. align* and aligned do not. +// The alignedat environment can be used in math mode. +// Note that we assume \nomallineskiplimit to be zero, +// so that \strut@ is the same as \strut. + +defineEnvironment({ + type: "array", + names: ["align", "align*", "aligned", "split"], + props: { + numArgs: 0 + }, + handler: alignedHandler, + htmlBuilder: htmlBuilder$7, + mathmlBuilder: mathmlBuilder$6 +}); // A gathered environment is like an array environment with one centered +// column, but where rows are considered lines so get \jot line spacing +// and contents are set in \displaystyle. + +defineEnvironment({ + type: "array", + names: ["gathered", "gather", "gather*"], + props: { + numArgs: 0 + }, + + handler(context) { + if (utils.contains(["gather", "gather*"], context.envName)) { + validateAmsEnvironmentContext(context); + } + + var res = { + cols: [{ + type: "align", + align: "c" + }], + addJot: true, + colSeparationType: "gather", + addEqnNum: context.envName === "gather", + emptySingleRow: true, + leqno: context.parser.settings.leqno + }; + return parseArray(context.parser, res, "display"); + }, + + htmlBuilder: htmlBuilder$7, + mathmlBuilder: mathmlBuilder$6 +}); // alignat environment is like an align environment, but one must explicitly +// specify maximum number of columns in each row, and can adjust spacing between +// each columns. + +defineEnvironment({ + type: "array", + names: ["alignat", "alignat*", "alignedat"], + props: { + numArgs: 1 + }, + handler: alignedHandler, + htmlBuilder: htmlBuilder$7, + mathmlBuilder: mathmlBuilder$6 +}); +defineEnvironment({ + type: "array", + names: ["equation", "equation*"], + props: { + numArgs: 0 + }, + + handler(context) { + validateAmsEnvironmentContext(context); + var res = { + addEqnNum: context.envName === "equation", + emptySingleRow: true, + singleRow: true, + maxNumCols: 1, + leqno: context.parser.settings.leqno + }; + return parseArray(context.parser, res, "display"); + }, + + htmlBuilder: htmlBuilder$7, + mathmlBuilder: mathmlBuilder$6 +}); +defineEnvironment({ + type: "array", + names: ["CD"], + props: { + numArgs: 0 + }, + + handler(context) { + validateAmsEnvironmentContext(context); + return parseCD(context.parser); + }, + + htmlBuilder: htmlBuilder$7, + mathmlBuilder: mathmlBuilder$6 +}); // Catch \hline outside array environment + +defineFunction({ + type: "text", + // Doesn't matter what this is. + names: ["\\hline", "\\hdashline"], + props: { + numArgs: 0, + allowedInText: true, + allowedInMath: true + }, + + handler(context, args) { + throw new ParseError(context.funcName + " valid only within array environment"); + } + +}); + +var environments = _environments; + +// defineEnvironment definitions. + +defineFunction({ + type: "environment", + names: ["\\begin", "\\end"], + props: { + numArgs: 1, + argTypes: ["text"] + }, + + handler(_ref, args) { + var { + parser, + funcName + } = _ref; + var nameGroup = args[0]; + + if (nameGroup.type !== "ordgroup") { + throw new ParseError("Invalid environment name", nameGroup); + } + + var envName = ""; + + for (var i = 0; i < nameGroup.body.length; ++i) { + envName += assertNodeType(nameGroup.body[i], "textord").text; + } + + if (funcName === "\\begin") { + // begin...end is similar to left...right + if (!environments.hasOwnProperty(envName)) { + throw new ParseError("No such environment: " + envName, nameGroup); + } // Build the environment object. Arguments and other information will + // be made available to the begin and end methods using properties. + + + var env = environments[envName]; + var { + args: _args, + optArgs + } = parser.parseArguments("\\begin{" + envName + "}", env); + var context = { + mode: parser.mode, + envName, + parser + }; + var result = env.handler(context, _args, optArgs); + parser.expect("\\end", false); + var endNameToken = parser.nextToken; + var end = assertNodeType(parser.parseFunction(), "environment"); + + if (end.name !== envName) { + throw new ParseError("Mismatch: \\begin{" + envName + "} matched by \\end{" + end.name + "}", endNameToken); + } // $FlowFixMe, "environment" handler returns an environment ParseNode + + + return result; + } + + return { + type: "environment", + mode: parser.mode, + name: envName, + nameGroup + }; + } + +}); + +var makeSpan = buildCommon.makeSpan; + +function htmlBuilder$6(group, options) { + var elements = buildExpression$1(group.body, options, true); + return makeSpan([group.mclass], elements, options); +} + +function mathmlBuilder$5(group, options) { + var node; + var inner = buildExpression(group.body, options); + + if (group.mclass === "minner") { + return mathMLTree.newDocumentFragment(inner); + } else if (group.mclass === "mord") { + if (group.isCharacterBox) { + node = inner[0]; + node.type = "mi"; + } else { + node = new mathMLTree.MathNode("mi", inner); + } + } else { + if (group.isCharacterBox) { + node = inner[0]; + node.type = "mo"; + } else { + node = new mathMLTree.MathNode("mo", inner); + } // Set spacing based on what is the most likely adjacent atom type. + // See TeXbook p170. + + + if (group.mclass === "mbin") { + node.attributes.lspace = "0.22em"; // medium space + + node.attributes.rspace = "0.22em"; + } else if (group.mclass === "mpunct") { + node.attributes.lspace = "0em"; + node.attributes.rspace = "0.17em"; // thinspace + } else if (group.mclass === "mopen" || group.mclass === "mclose") { + node.attributes.lspace = "0em"; + node.attributes.rspace = "0em"; + } // MathML default space is 5/18 em, so needs no action. + // Ref: https://developer.mozilla.org/en-US/docs/Web/MathML/Element/mo + + } + + return node; +} // Math class commands except \mathop + + +defineFunction({ + type: "mclass", + names: ["\\mathord", "\\mathbin", "\\mathrel", "\\mathopen", "\\mathclose", "\\mathpunct", "\\mathinner"], + props: { + numArgs: 1, + primitive: true + }, + + handler(_ref, args) { + var { + parser, + funcName + } = _ref; + var body = args[0]; + return { + type: "mclass", + mode: parser.mode, + mclass: "m" + funcName.substr(5), + // TODO(kevinb): don't prefix with 'm' + body: ordargument(body), + isCharacterBox: utils.isCharacterBox(body) + }; + }, + + htmlBuilder: htmlBuilder$6, + mathmlBuilder: mathmlBuilder$5 +}); +var binrelClass = arg => { + // \binrel@ spacing varies with (bin|rel|ord) of the atom in the argument. + // (by rendering separately and with {}s before and after, and measuring + // the change in spacing). We'll do roughly the same by detecting the + // atom type directly. + var atom = arg.type === "ordgroup" && arg.body.length ? arg.body[0] : arg; + + if (atom.type === "atom" && (atom.family === "bin" || atom.family === "rel")) { + return "m" + atom.family; + } else { + return "mord"; + } +}; // \@binrel{x}{y} renders like y but as mbin/mrel/mord if x is mbin/mrel/mord. +// This is equivalent to \binrel@{x}\binrel@@{y} in AMSTeX. + +defineFunction({ + type: "mclass", + names: ["\\@binrel"], + props: { + numArgs: 2 + }, + + handler(_ref2, args) { + var { + parser + } = _ref2; + return { + type: "mclass", + mode: parser.mode, + mclass: binrelClass(args[0]), + body: ordargument(args[1]), + isCharacterBox: utils.isCharacterBox(args[1]) + }; + } + +}); // Build a relation or stacked op by placing one symbol on top of another + +defineFunction({ + type: "mclass", + names: ["\\stackrel", "\\overset", "\\underset"], + props: { + numArgs: 2 + }, + + handler(_ref3, args) { + var { + parser, + funcName + } = _ref3; + var baseArg = args[1]; + var shiftedArg = args[0]; + var mclass; + + if (funcName !== "\\stackrel") { + // LaTeX applies \binrel spacing to \overset and \underset. + mclass = binrelClass(baseArg); + } else { + mclass = "mrel"; // for \stackrel + } + + var baseOp = { + type: "op", + mode: baseArg.mode, + limits: true, + alwaysHandleSupSub: true, + parentIsSupSub: false, + symbol: false, + suppressBaseShift: funcName !== "\\stackrel", + body: ordargument(baseArg) + }; + var supsub = { + type: "supsub", + mode: shiftedArg.mode, + base: baseOp, + sup: funcName === "\\underset" ? null : shiftedArg, + sub: funcName === "\\underset" ? shiftedArg : null + }; + return { + type: "mclass", + mode: parser.mode, + mclass, + body: [supsub], + isCharacterBox: utils.isCharacterBox(supsub) + }; + }, + + htmlBuilder: htmlBuilder$6, + mathmlBuilder: mathmlBuilder$5 +}); + +// TODO(kevinb): implement \\sl and \\sc + +var htmlBuilder$5 = (group, options) => { + var font = group.font; + var newOptions = options.withFont(font); + return buildGroup$1(group.body, newOptions); +}; + +var mathmlBuilder$4 = (group, options) => { + var font = group.font; + var newOptions = options.withFont(font); + return buildGroup(group.body, newOptions); +}; + +var fontAliases = { + "\\Bbb": "\\mathbb", + "\\bold": "\\mathbf", + "\\frak": "\\mathfrak", + "\\bm": "\\boldsymbol" +}; +defineFunction({ + type: "font", + names: [// styles, except \boldsymbol defined below + "\\mathrm", "\\mathit", "\\mathbf", "\\mathnormal", // families + "\\mathbb", "\\mathcal", "\\mathfrak", "\\mathscr", "\\mathsf", "\\mathtt", // aliases, except \bm defined below + "\\Bbb", "\\bold", "\\frak"], + props: { + numArgs: 1, + allowedInArgument: true + }, + handler: (_ref, args) => { + var { + parser, + funcName + } = _ref; + var body = normalizeArgument(args[0]); + var func = funcName; + + if (func in fontAliases) { + func = fontAliases[func]; + } + + return { + type: "font", + mode: parser.mode, + font: func.slice(1), + body + }; + }, + htmlBuilder: htmlBuilder$5, + mathmlBuilder: mathmlBuilder$4 +}); +defineFunction({ + type: "mclass", + names: ["\\boldsymbol", "\\bm"], + props: { + numArgs: 1 + }, + handler: (_ref2, args) => { + var { + parser + } = _ref2; + var body = args[0]; + var isCharacterBox = utils.isCharacterBox(body); // amsbsy.sty's \boldsymbol uses \binrel spacing to inherit the + // argument's bin|rel|ord status + + return { + type: "mclass", + mode: parser.mode, + mclass: binrelClass(body), + body: [{ + type: "font", + mode: parser.mode, + font: "boldsymbol", + body + }], + isCharacterBox: isCharacterBox + }; + } +}); // Old font changing functions + +defineFunction({ + type: "font", + names: ["\\rm", "\\sf", "\\tt", "\\bf", "\\it", "\\cal"], + props: { + numArgs: 0, + allowedInText: true + }, + handler: (_ref3, args) => { + var { + parser, + funcName, + breakOnTokenText + } = _ref3; + var { + mode + } = parser; + var body = parser.parseExpression(true, breakOnTokenText); + var style = "math" + funcName.slice(1); + return { + type: "font", + mode: mode, + font: style, + body: { + type: "ordgroup", + mode: parser.mode, + body + } + }; + }, + htmlBuilder: htmlBuilder$5, + mathmlBuilder: mathmlBuilder$4 +}); + +var adjustStyle = (size, originalStyle) => { + // Figure out what style this fraction should be in based on the + // function used + var style = originalStyle; + + if (size === "display") { + // Get display style as a default. + // If incoming style is sub/sup, use style.text() to get correct size. + style = style.id >= Style$1.SCRIPT.id ? style.text() : Style$1.DISPLAY; + } else if (size === "text" && style.size === Style$1.DISPLAY.size) { + // We're in a \tfrac but incoming style is displaystyle, so: + style = Style$1.TEXT; + } else if (size === "script") { + style = Style$1.SCRIPT; + } else if (size === "scriptscript") { + style = Style$1.SCRIPTSCRIPT; + } + + return style; +}; + +var htmlBuilder$4 = (group, options) => { + // Fractions are handled in the TeXbook on pages 444-445, rules 15(a-e). + var style = adjustStyle(group.size, options.style); + var nstyle = style.fracNum(); + var dstyle = style.fracDen(); + var newOptions; + newOptions = options.havingStyle(nstyle); + var numerm = buildGroup$1(group.numer, newOptions, options); + + if (group.continued) { + // \cfrac inserts a \strut into the numerator. + // Get \strut dimensions from TeXbook page 353. + var hStrut = 8.5 / options.fontMetrics().ptPerEm; + var dStrut = 3.5 / options.fontMetrics().ptPerEm; + numerm.height = numerm.height < hStrut ? hStrut : numerm.height; + numerm.depth = numerm.depth < dStrut ? dStrut : numerm.depth; + } + + newOptions = options.havingStyle(dstyle); + var denomm = buildGroup$1(group.denom, newOptions, options); + var rule; + var ruleWidth; + var ruleSpacing; + + if (group.hasBarLine) { + if (group.barSize) { + ruleWidth = calculateSize(group.barSize, options); + rule = buildCommon.makeLineSpan("frac-line", options, ruleWidth); + } else { + rule = buildCommon.makeLineSpan("frac-line", options); + } + + ruleWidth = rule.height; + ruleSpacing = rule.height; + } else { + rule = null; + ruleWidth = 0; + ruleSpacing = options.fontMetrics().defaultRuleThickness; + } // Rule 15b + + + var numShift; + var clearance; + var denomShift; + + if (style.size === Style$1.DISPLAY.size || group.size === "display") { + numShift = options.fontMetrics().num1; + + if (ruleWidth > 0) { + clearance = 3 * ruleSpacing; + } else { + clearance = 7 * ruleSpacing; + } + + denomShift = options.fontMetrics().denom1; + } else { + if (ruleWidth > 0) { + numShift = options.fontMetrics().num2; + clearance = ruleSpacing; + } else { + numShift = options.fontMetrics().num3; + clearance = 3 * ruleSpacing; + } + + denomShift = options.fontMetrics().denom2; + } + + var frac; + + if (!rule) { + // Rule 15c + var candidateClearance = numShift - numerm.depth - (denomm.height - denomShift); + + if (candidateClearance < clearance) { + numShift += 0.5 * (clearance - candidateClearance); + denomShift += 0.5 * (clearance - candidateClearance); + } + + frac = buildCommon.makeVList({ + positionType: "individualShift", + children: [{ + type: "elem", + elem: denomm, + shift: denomShift + }, { + type: "elem", + elem: numerm, + shift: -numShift + }] + }, options); + } else { + // Rule 15d + var axisHeight = options.fontMetrics().axisHeight; + + if (numShift - numerm.depth - (axisHeight + 0.5 * ruleWidth) < clearance) { + numShift += clearance - (numShift - numerm.depth - (axisHeight + 0.5 * ruleWidth)); + } + + if (axisHeight - 0.5 * ruleWidth - (denomm.height - denomShift) < clearance) { + denomShift += clearance - (axisHeight - 0.5 * ruleWidth - (denomm.height - denomShift)); + } + + var midShift = -(axisHeight - 0.5 * ruleWidth); + frac = buildCommon.makeVList({ + positionType: "individualShift", + children: [{ + type: "elem", + elem: denomm, + shift: denomShift + }, { + type: "elem", + elem: rule, + shift: midShift + }, { + type: "elem", + elem: numerm, + shift: -numShift + }] + }, options); + } // Since we manually change the style sometimes (with \dfrac or \tfrac), + // account for the possible size change here. + + + newOptions = options.havingStyle(style); + frac.height *= newOptions.sizeMultiplier / options.sizeMultiplier; + frac.depth *= newOptions.sizeMultiplier / options.sizeMultiplier; // Rule 15e + + var delimSize; + + if (style.size === Style$1.DISPLAY.size) { + delimSize = options.fontMetrics().delim1; + } else if (style.size === Style$1.SCRIPTSCRIPT.size) { + delimSize = options.havingStyle(Style$1.SCRIPT).fontMetrics().delim2; + } else { + delimSize = options.fontMetrics().delim2; + } + + var leftDelim; + var rightDelim; + + if (group.leftDelim == null) { + leftDelim = makeNullDelimiter(options, ["mopen"]); + } else { + leftDelim = delimiter.customSizedDelim(group.leftDelim, delimSize, true, options.havingStyle(style), group.mode, ["mopen"]); + } + + if (group.continued) { + rightDelim = buildCommon.makeSpan([]); // zero width for \cfrac + } else if (group.rightDelim == null) { + rightDelim = makeNullDelimiter(options, ["mclose"]); + } else { + rightDelim = delimiter.customSizedDelim(group.rightDelim, delimSize, true, options.havingStyle(style), group.mode, ["mclose"]); + } + + return buildCommon.makeSpan(["mord"].concat(newOptions.sizingClasses(options)), [leftDelim, buildCommon.makeSpan(["mfrac"], [frac]), rightDelim], options); +}; + +var mathmlBuilder$3 = (group, options) => { + var node = new mathMLTree.MathNode("mfrac", [buildGroup(group.numer, options), buildGroup(group.denom, options)]); + + if (!group.hasBarLine) { + node.setAttribute("linethickness", "0px"); + } else if (group.barSize) { + var ruleWidth = calculateSize(group.barSize, options); + node.setAttribute("linethickness", ruleWidth + "em"); + } + + var style = adjustStyle(group.size, options.style); + + if (style.size !== options.style.size) { + node = new mathMLTree.MathNode("mstyle", [node]); + var isDisplay = style.size === Style$1.DISPLAY.size ? "true" : "false"; + node.setAttribute("displaystyle", isDisplay); + node.setAttribute("scriptlevel", "0"); + } + + if (group.leftDelim != null || group.rightDelim != null) { + var withDelims = []; + + if (group.leftDelim != null) { + var leftOp = new mathMLTree.MathNode("mo", [new mathMLTree.TextNode(group.leftDelim.replace("\\", ""))]); + leftOp.setAttribute("fence", "true"); + withDelims.push(leftOp); + } + + withDelims.push(node); + + if (group.rightDelim != null) { + var rightOp = new mathMLTree.MathNode("mo", [new mathMLTree.TextNode(group.rightDelim.replace("\\", ""))]); + rightOp.setAttribute("fence", "true"); + withDelims.push(rightOp); + } + + return makeRow(withDelims); + } + + return node; +}; + +defineFunction({ + type: "genfrac", + names: ["\\dfrac", "\\frac", "\\tfrac", "\\dbinom", "\\binom", "\\tbinom", "\\\\atopfrac", // can’t be entered directly + "\\\\bracefrac", "\\\\brackfrac" // ditto + ], + props: { + numArgs: 2, + allowedInArgument: true + }, + handler: (_ref, args) => { + var { + parser, + funcName + } = _ref; + var numer = args[0]; + var denom = args[1]; + var hasBarLine; + var leftDelim = null; + var rightDelim = null; + var size = "auto"; + + switch (funcName) { + case "\\dfrac": + case "\\frac": + case "\\tfrac": + hasBarLine = true; + break; + + case "\\\\atopfrac": + hasBarLine = false; + break; + + case "\\dbinom": + case "\\binom": + case "\\tbinom": + hasBarLine = false; + leftDelim = "("; + rightDelim = ")"; + break; + + case "\\\\bracefrac": + hasBarLine = false; + leftDelim = "\\{"; + rightDelim = "\\}"; + break; + + case "\\\\brackfrac": + hasBarLine = false; + leftDelim = "["; + rightDelim = "]"; + break; + + default: + throw new Error("Unrecognized genfrac command"); + } + + switch (funcName) { + case "\\dfrac": + case "\\dbinom": + size = "display"; + break; + + case "\\tfrac": + case "\\tbinom": + size = "text"; + break; + } + + return { + type: "genfrac", + mode: parser.mode, + continued: false, + numer, + denom, + hasBarLine, + leftDelim, + rightDelim, + size, + barSize: null + }; + }, + htmlBuilder: htmlBuilder$4, + mathmlBuilder: mathmlBuilder$3 +}); +defineFunction({ + type: "genfrac", + names: ["\\cfrac"], + props: { + numArgs: 2 + }, + handler: (_ref2, args) => { + var { + parser, + funcName + } = _ref2; + var numer = args[0]; + var denom = args[1]; + return { + type: "genfrac", + mode: parser.mode, + continued: true, + numer, + denom, + hasBarLine: true, + leftDelim: null, + rightDelim: null, + size: "display", + barSize: null + }; + } +}); // Infix generalized fractions -- these are not rendered directly, but replaced +// immediately by one of the variants above. + +defineFunction({ + type: "infix", + names: ["\\over", "\\choose", "\\atop", "\\brace", "\\brack"], + props: { + numArgs: 0, + infix: true + }, + + handler(_ref3) { + var { + parser, + funcName, + token + } = _ref3; + var replaceWith; + + switch (funcName) { + case "\\over": + replaceWith = "\\frac"; + break; + + case "\\choose": + replaceWith = "\\binom"; + break; + + case "\\atop": + replaceWith = "\\\\atopfrac"; + break; + + case "\\brace": + replaceWith = "\\\\bracefrac"; + break; + + case "\\brack": + replaceWith = "\\\\brackfrac"; + break; + + default: + throw new Error("Unrecognized infix genfrac command"); + } + + return { + type: "infix", + mode: parser.mode, + replaceWith, + token + }; + } + +}); +var stylArray = ["display", "text", "script", "scriptscript"]; + +var delimFromValue = function delimFromValue(delimString) { + var delim = null; + + if (delimString.length > 0) { + delim = delimString; + delim = delim === "." ? null : delim; + } + + return delim; +}; + +defineFunction({ + type: "genfrac", + names: ["\\genfrac"], + props: { + numArgs: 6, + allowedInArgument: true, + argTypes: ["math", "math", "size", "text", "math", "math"] + }, + + handler(_ref4, args) { + var { + parser + } = _ref4; + var numer = args[4]; + var denom = args[5]; // Look into the parse nodes to get the desired delimiters. + + var leftNode = normalizeArgument(args[0]); + var leftDelim = leftNode.type === "atom" && leftNode.family === "open" ? delimFromValue(leftNode.text) : null; + var rightNode = normalizeArgument(args[1]); + var rightDelim = rightNode.type === "atom" && rightNode.family === "close" ? delimFromValue(rightNode.text) : null; + var barNode = assertNodeType(args[2], "size"); + var hasBarLine; + var barSize = null; + + if (barNode.isBlank) { + // \genfrac acts differently than \above. + // \genfrac treats an empty size group as a signal to use a + // standard bar size. \above would see size = 0 and omit the bar. + hasBarLine = true; + } else { + barSize = barNode.value; + hasBarLine = barSize.number > 0; + } // Find out if we want displaystyle, textstyle, etc. + + + var size = "auto"; + var styl = args[3]; + + if (styl.type === "ordgroup") { + if (styl.body.length > 0) { + var textOrd = assertNodeType(styl.body[0], "textord"); + size = stylArray[Number(textOrd.text)]; + } + } else { + styl = assertNodeType(styl, "textord"); + size = stylArray[Number(styl.text)]; + } + + return { + type: "genfrac", + mode: parser.mode, + numer, + denom, + continued: false, + hasBarLine, + barSize, + leftDelim, + rightDelim, + size + }; + }, + + htmlBuilder: htmlBuilder$4, + mathmlBuilder: mathmlBuilder$3 +}); // \above is an infix fraction that also defines a fraction bar size. + +defineFunction({ + type: "infix", + names: ["\\above"], + props: { + numArgs: 1, + argTypes: ["size"], + infix: true + }, + + handler(_ref5, args) { + var { + parser, + funcName, + token + } = _ref5; + return { + type: "infix", + mode: parser.mode, + replaceWith: "\\\\abovefrac", + size: assertNodeType(args[0], "size").value, + token + }; + } + +}); +defineFunction({ + type: "genfrac", + names: ["\\\\abovefrac"], + props: { + numArgs: 3, + argTypes: ["math", "size", "math"] + }, + handler: (_ref6, args) => { + var { + parser, + funcName + } = _ref6; + var numer = args[0]; + var barSize = assert(assertNodeType(args[1], "infix").size); + var denom = args[2]; + var hasBarLine = barSize.number > 0; + return { + type: "genfrac", + mode: parser.mode, + numer, + denom, + continued: false, + hasBarLine, + barSize, + leftDelim: null, + rightDelim: null, + size: "auto" + }; + }, + htmlBuilder: htmlBuilder$4, + mathmlBuilder: mathmlBuilder$3 +}); + +// NOTE: Unlike most `htmlBuilder`s, this one handles not only "horizBrace", but +// also "supsub" since an over/underbrace can affect super/subscripting. +var htmlBuilder$3 = (grp, options) => { + var style = options.style; // Pull out the `ParseNode<"horizBrace">` if `grp` is a "supsub" node. + + var supSubGroup; + var group; + + if (grp.type === "supsub") { + // Ref: LaTeX source2e: }}}}\limits} + // i.e. LaTeX treats the brace similar to an op and passes it + // with \limits, so we need to assign supsub style. + supSubGroup = grp.sup ? buildGroup$1(grp.sup, options.havingStyle(style.sup()), options) : buildGroup$1(grp.sub, options.havingStyle(style.sub()), options); + group = assertNodeType(grp.base, "horizBrace"); + } else { + group = assertNodeType(grp, "horizBrace"); + } // Build the base group + + + var body = buildGroup$1(group.base, options.havingBaseStyle(Style$1.DISPLAY)); // Create the stretchy element + + var braceBody = stretchy.svgSpan(group, options); // Generate the vlist, with the appropriate kerns ┏━━━━━━━━┓ + // This first vlist contains the content and the brace: equation + + var vlist; + + if (group.isOver) { + vlist = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: body + }, { + type: "kern", + size: 0.1 + }, { + type: "elem", + elem: braceBody + }] + }, options); // $FlowFixMe: Replace this with passing "svg-align" into makeVList. + + vlist.children[0].children[0].children[1].classes.push("svg-align"); + } else { + vlist = buildCommon.makeVList({ + positionType: "bottom", + positionData: body.depth + 0.1 + braceBody.height, + children: [{ + type: "elem", + elem: braceBody + }, { + type: "kern", + size: 0.1 + }, { + type: "elem", + elem: body + }] + }, options); // $FlowFixMe: Replace this with passing "svg-align" into makeVList. + + vlist.children[0].children[0].children[0].classes.push("svg-align"); + } + + if (supSubGroup) { + // To write the supsub, wrap the first vlist in another vlist: + // They can't all go in the same vlist, because the note might be + // wider than the equation. We want the equation to control the + // brace width. + // note long note long note + // ┏━━━━━━━━┓ or ┏━━━┓ not ┏━━━━━━━━━┓ + // equation eqn eqn + var vSpan = buildCommon.makeSpan(["mord", group.isOver ? "mover" : "munder"], [vlist], options); + + if (group.isOver) { + vlist = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: vSpan + }, { + type: "kern", + size: 0.2 + }, { + type: "elem", + elem: supSubGroup + }] + }, options); + } else { + vlist = buildCommon.makeVList({ + positionType: "bottom", + positionData: vSpan.depth + 0.2 + supSubGroup.height + supSubGroup.depth, + children: [{ + type: "elem", + elem: supSubGroup + }, { + type: "kern", + size: 0.2 + }, { + type: "elem", + elem: vSpan + }] + }, options); + } + } + + return buildCommon.makeSpan(["mord", group.isOver ? "mover" : "munder"], [vlist], options); +}; + +var mathmlBuilder$2 = (group, options) => { + var accentNode = stretchy.mathMLnode(group.label); + return new mathMLTree.MathNode(group.isOver ? "mover" : "munder", [buildGroup(group.base, options), accentNode]); +}; // Horizontal stretchy braces + + +defineFunction({ + type: "horizBrace", + names: ["\\overbrace", "\\underbrace"], + props: { + numArgs: 1 + }, + + handler(_ref, args) { + var { + parser, + funcName + } = _ref; + return { + type: "horizBrace", + mode: parser.mode, + label: funcName, + isOver: /^\\over/.test(funcName), + base: args[0] + }; + }, + + htmlBuilder: htmlBuilder$3, + mathmlBuilder: mathmlBuilder$2 +}); + +defineFunction({ + type: "href", + names: ["\\href"], + props: { + numArgs: 2, + argTypes: ["url", "original"], + allowedInText: true + }, + handler: (_ref, args) => { + var { + parser + } = _ref; + var body = args[1]; + var href = assertNodeType(args[0], "url").url; + + if (!parser.settings.isTrusted({ + command: "\\href", + url: href + })) { + return parser.formatUnsupportedCmd("\\href"); + } + + return { + type: "href", + mode: parser.mode, + href, + body: ordargument(body) + }; + }, + htmlBuilder: (group, options) => { + var elements = buildExpression$1(group.body, options, false); + return buildCommon.makeAnchor(group.href, [], elements, options); + }, + mathmlBuilder: (group, options) => { + var math = buildExpressionRow(group.body, options); + + if (!(math instanceof MathNode)) { + math = new MathNode("mrow", [math]); + } + + math.setAttribute("href", group.href); + return math; + } +}); +defineFunction({ + type: "href", + names: ["\\url"], + props: { + numArgs: 1, + argTypes: ["url"], + allowedInText: true + }, + handler: (_ref2, args) => { + var { + parser + } = _ref2; + var href = assertNodeType(args[0], "url").url; + + if (!parser.settings.isTrusted({ + command: "\\url", + url: href + })) { + return parser.formatUnsupportedCmd("\\url"); + } + + var chars = []; + + for (var i = 0; i < href.length; i++) { + var c = href[i]; + + if (c === "~") { + c = "\\textasciitilde"; + } + + chars.push({ + type: "textord", + mode: "text", + text: c + }); + } + + var body = { + type: "text", + mode: parser.mode, + font: "\\texttt", + body: chars + }; + return { + type: "href", + mode: parser.mode, + href, + body: ordargument(body) + }; + } +}); + +// In LaTeX, \vcenter can act only on a box, as in +// \vcenter{\hbox{$\frac{a+b}{\dfrac{c}{d}}$}} +// This function by itself doesn't do anything but prevent a soft line break. + +defineFunction({ + type: "hbox", + names: ["\\hbox"], + props: { + numArgs: 1, + argTypes: ["text"], + allowedInText: true, + primitive: true + }, + + handler(_ref, args) { + var { + parser + } = _ref; + return { + type: "hbox", + mode: parser.mode, + body: ordargument(args[0]) + }; + }, + + htmlBuilder(group, options) { + var elements = buildExpression$1(group.body, options, false); + return buildCommon.makeFragment(elements); + }, + + mathmlBuilder(group, options) { + return new mathMLTree.MathNode("mrow", buildExpression(group.body, options)); + } + +}); + +defineFunction({ + type: "html", + names: ["\\htmlClass", "\\htmlId", "\\htmlStyle", "\\htmlData"], + props: { + numArgs: 2, + argTypes: ["raw", "original"], + allowedInText: true + }, + handler: (_ref, args) => { + var { + parser, + funcName, + token + } = _ref; + var value = assertNodeType(args[0], "raw").string; + var body = args[1]; + + if (parser.settings.strict) { + parser.settings.reportNonstrict("htmlExtension", "HTML extension is disabled on strict mode"); + } + + var trustContext; + var attributes = {}; + + switch (funcName) { + case "\\htmlClass": + attributes.class = value; + trustContext = { + command: "\\htmlClass", + class: value + }; + break; + + case "\\htmlId": + attributes.id = value; + trustContext = { + command: "\\htmlId", + id: value + }; + break; + + case "\\htmlStyle": + attributes.style = value; + trustContext = { + command: "\\htmlStyle", + style: value + }; + break; + + case "\\htmlData": + { + var data = value.split(","); + + for (var i = 0; i < data.length; i++) { + var keyVal = data[i].split("="); + + if (keyVal.length !== 2) { + throw new ParseError("Error parsing key-value for \\htmlData"); + } + + attributes["data-" + keyVal[0].trim()] = keyVal[1].trim(); + } + + trustContext = { + command: "\\htmlData", + attributes + }; + break; + } + + default: + throw new Error("Unrecognized html command"); + } + + if (!parser.settings.isTrusted(trustContext)) { + return parser.formatUnsupportedCmd(funcName); + } + + return { + type: "html", + mode: parser.mode, + attributes, + body: ordargument(body) + }; + }, + htmlBuilder: (group, options) => { + var elements = buildExpression$1(group.body, options, false); + var classes = ["enclosing"]; + + if (group.attributes.class) { + classes.push(...group.attributes.class.trim().split(/\s+/)); + } + + var span = buildCommon.makeSpan(classes, elements, options); + + for (var attr in group.attributes) { + if (attr !== "class" && group.attributes.hasOwnProperty(attr)) { + span.setAttribute(attr, group.attributes[attr]); + } + } + + return span; + }, + mathmlBuilder: (group, options) => { + return buildExpressionRow(group.body, options); + } +}); + +defineFunction({ + type: "htmlmathml", + names: ["\\html@mathml"], + props: { + numArgs: 2, + allowedInText: true + }, + handler: (_ref, args) => { + var { + parser + } = _ref; + return { + type: "htmlmathml", + mode: parser.mode, + html: ordargument(args[0]), + mathml: ordargument(args[1]) + }; + }, + htmlBuilder: (group, options) => { + var elements = buildExpression$1(group.html, options, false); + return buildCommon.makeFragment(elements); + }, + mathmlBuilder: (group, options) => { + return buildExpressionRow(group.mathml, options); + } +}); + +var sizeData = function sizeData(str) { + if (/^[-+]? *(\d+(\.\d*)?|\.\d+)$/.test(str)) { + // str is a number with no unit specified. + // default unit is bp, per graphix package. + return { + number: +str, + unit: "bp" + }; + } else { + var match = /([-+]?) *(\d+(?:\.\d*)?|\.\d+) *([a-z]{2})/.exec(str); + + if (!match) { + throw new ParseError("Invalid size: '" + str + "' in \\includegraphics"); + } + + var data = { + number: +(match[1] + match[2]), + // sign + magnitude, cast to number + unit: match[3] + }; + + if (!validUnit(data)) { + throw new ParseError("Invalid unit: '" + data.unit + "' in \\includegraphics."); + } + + return data; + } +}; + +defineFunction({ + type: "includegraphics", + names: ["\\includegraphics"], + props: { + numArgs: 1, + numOptionalArgs: 1, + argTypes: ["raw", "url"], + allowedInText: false + }, + handler: (_ref, args, optArgs) => { + var { + parser + } = _ref; + var width = { + number: 0, + unit: "em" + }; + var height = { + number: 0.9, + unit: "em" + }; // sorta character sized. + + var totalheight = { + number: 0, + unit: "em" + }; + var alt = ""; + + if (optArgs[0]) { + var attributeStr = assertNodeType(optArgs[0], "raw").string; // Parser.js does not parse key/value pairs. We get a string. + + var attributes = attributeStr.split(","); + + for (var i = 0; i < attributes.length; i++) { + var keyVal = attributes[i].split("="); + + if (keyVal.length === 2) { + var str = keyVal[1].trim(); + + switch (keyVal[0].trim()) { + case "alt": + alt = str; + break; + + case "width": + width = sizeData(str); + break; + + case "height": + height = sizeData(str); + break; + + case "totalheight": + totalheight = sizeData(str); + break; + + default: + throw new ParseError("Invalid key: '" + keyVal[0] + "' in \\includegraphics."); + } + } + } + } + + var src = assertNodeType(args[0], "url").url; + + if (alt === "") { + // No alt given. Use the file name. Strip away the path. + alt = src; + alt = alt.replace(/^.*[\\/]/, ''); + alt = alt.substring(0, alt.lastIndexOf('.')); + } + + if (!parser.settings.isTrusted({ + command: "\\includegraphics", + url: src + })) { + return parser.formatUnsupportedCmd("\\includegraphics"); + } + + return { + type: "includegraphics", + mode: parser.mode, + alt: alt, + width: width, + height: height, + totalheight: totalheight, + src: src + }; + }, + htmlBuilder: (group, options) => { + var height = calculateSize(group.height, options); + var depth = 0; + + if (group.totalheight.number > 0) { + depth = calculateSize(group.totalheight, options) - height; + depth = Number(depth.toFixed(2)); + } + + var width = 0; + + if (group.width.number > 0) { + width = calculateSize(group.width, options); + } + + var style = { + height: height + depth + "em" + }; + + if (width > 0) { + style.width = width + "em"; + } + + if (depth > 0) { + style.verticalAlign = -depth + "em"; + } + + var node = new Img(group.src, group.alt, style); + node.height = height; + node.depth = depth; + return node; + }, + mathmlBuilder: (group, options) => { + var node = new mathMLTree.MathNode("mglyph", []); + node.setAttribute("alt", group.alt); + var height = calculateSize(group.height, options); + var depth = 0; + + if (group.totalheight.number > 0) { + depth = calculateSize(group.totalheight, options) - height; + depth = depth.toFixed(2); + node.setAttribute("valign", "-" + depth + "em"); + } + + node.setAttribute("height", height + depth + "em"); + + if (group.width.number > 0) { + var width = calculateSize(group.width, options); + node.setAttribute("width", width + "em"); + } + + node.setAttribute("src", group.src); + return node; + } +}); + +// Horizontal spacing commands + +defineFunction({ + type: "kern", + names: ["\\kern", "\\mkern", "\\hskip", "\\mskip"], + props: { + numArgs: 1, + argTypes: ["size"], + primitive: true, + allowedInText: true + }, + + handler(_ref, args) { + var { + parser, + funcName + } = _ref; + var size = assertNodeType(args[0], "size"); + + if (parser.settings.strict) { + var mathFunction = funcName[1] === 'm'; // \mkern, \mskip + + var muUnit = size.value.unit === 'mu'; + + if (mathFunction) { + if (!muUnit) { + parser.settings.reportNonstrict("mathVsTextUnits", "LaTeX's " + funcName + " supports only mu units, " + ("not " + size.value.unit + " units")); + } + + if (parser.mode !== "math") { + parser.settings.reportNonstrict("mathVsTextUnits", "LaTeX's " + funcName + " works only in math mode"); + } + } else { + // !mathFunction + if (muUnit) { + parser.settings.reportNonstrict("mathVsTextUnits", "LaTeX's " + funcName + " doesn't support mu units"); + } + } + } + + return { + type: "kern", + mode: parser.mode, + dimension: size.value + }; + }, + + htmlBuilder(group, options) { + return buildCommon.makeGlue(group.dimension, options); + }, + + mathmlBuilder(group, options) { + var dimension = calculateSize(group.dimension, options); + return new mathMLTree.SpaceNode(dimension); + } + +}); + +// Horizontal overlap functions +defineFunction({ + type: "lap", + names: ["\\mathllap", "\\mathrlap", "\\mathclap"], + props: { + numArgs: 1, + allowedInText: true + }, + handler: (_ref, args) => { + var { + parser, + funcName + } = _ref; + var body = args[0]; + return { + type: "lap", + mode: parser.mode, + alignment: funcName.slice(5), + body + }; + }, + htmlBuilder: (group, options) => { + // mathllap, mathrlap, mathclap + var inner; + + if (group.alignment === "clap") { + // ref: https://www.math.lsu.edu/~aperlis/publications/mathclap/ + inner = buildCommon.makeSpan([], [buildGroup$1(group.body, options)]); // wrap, since CSS will center a .clap > .inner > span + + inner = buildCommon.makeSpan(["inner"], [inner], options); + } else { + inner = buildCommon.makeSpan(["inner"], [buildGroup$1(group.body, options)]); + } + + var fix = buildCommon.makeSpan(["fix"], []); + var node = buildCommon.makeSpan([group.alignment], [inner, fix], options); // At this point, we have correctly set horizontal alignment of the + // two items involved in the lap. + // Next, use a strut to set the height of the HTML bounding box. + // Otherwise, a tall argument may be misplaced. + // This code resolved issue #1153 + + var strut = buildCommon.makeSpan(["strut"]); + strut.style.height = node.height + node.depth + "em"; + strut.style.verticalAlign = -node.depth + "em"; + node.children.unshift(strut); // Next, prevent vertical misplacement when next to something tall. + // This code resolves issue #1234 + + node = buildCommon.makeSpan(["thinbox"], [node], options); + return buildCommon.makeSpan(["mord", "vbox"], [node], options); + }, + mathmlBuilder: (group, options) => { + // mathllap, mathrlap, mathclap + var node = new mathMLTree.MathNode("mpadded", [buildGroup(group.body, options)]); + + if (group.alignment !== "rlap") { + var offset = group.alignment === "llap" ? "-1" : "-0.5"; + node.setAttribute("lspace", offset + "width"); + } + + node.setAttribute("width", "0px"); + return node; + } +}); + +defineFunction({ + type: "styling", + names: ["\\(", "$"], + props: { + numArgs: 0, + allowedInText: true, + allowedInMath: false + }, + + handler(_ref, args) { + var { + funcName, + parser + } = _ref; + var outerMode = parser.mode; + parser.switchMode("math"); + var close = funcName === "\\(" ? "\\)" : "$"; + var body = parser.parseExpression(false, close); + parser.expect(close); + parser.switchMode(outerMode); + return { + type: "styling", + mode: parser.mode, + style: "text", + body + }; + } + +}); // Check for extra closing math delimiters + +defineFunction({ + type: "text", + // Doesn't matter what this is. + names: ["\\)", "\\]"], + props: { + numArgs: 0, + allowedInText: true, + allowedInMath: false + }, + + handler(context, args) { + throw new ParseError("Mismatched " + context.funcName); + } + +}); + +var chooseMathStyle = (group, options) => { + switch (options.style.size) { + case Style$1.DISPLAY.size: + return group.display; + + case Style$1.TEXT.size: + return group.text; + + case Style$1.SCRIPT.size: + return group.script; + + case Style$1.SCRIPTSCRIPT.size: + return group.scriptscript; + + default: + return group.text; + } +}; + +defineFunction({ + type: "mathchoice", + names: ["\\mathchoice"], + props: { + numArgs: 4, + primitive: true + }, + handler: (_ref, args) => { + var { + parser + } = _ref; + return { + type: "mathchoice", + mode: parser.mode, + display: ordargument(args[0]), + text: ordargument(args[1]), + script: ordargument(args[2]), + scriptscript: ordargument(args[3]) + }; + }, + htmlBuilder: (group, options) => { + var body = chooseMathStyle(group, options); + var elements = buildExpression$1(body, options, false); + return buildCommon.makeFragment(elements); + }, + mathmlBuilder: (group, options) => { + var body = chooseMathStyle(group, options); + return buildExpressionRow(body, options); + } +}); + +// For an operator with limits, assemble the base, sup, and sub into a span. +var assembleSupSub = (base, supGroup, subGroup, options, style, slant, baseShift) => { + base = buildCommon.makeSpan([], [base]); + var subIsSingleCharacter = subGroup && utils.isCharacterBox(subGroup); + var sub; + var sup; // We manually have to handle the superscripts and subscripts. This, + // aside from the kern calculations, is copied from supsub. + + if (supGroup) { + var elem = buildGroup$1(supGroup, options.havingStyle(style.sup()), options); + sup = { + elem, + kern: Math.max(options.fontMetrics().bigOpSpacing1, options.fontMetrics().bigOpSpacing3 - elem.depth) + }; + } + + if (subGroup) { + var _elem = buildGroup$1(subGroup, options.havingStyle(style.sub()), options); + + sub = { + elem: _elem, + kern: Math.max(options.fontMetrics().bigOpSpacing2, options.fontMetrics().bigOpSpacing4 - _elem.height) + }; + } // Build the final group as a vlist of the possible subscript, base, + // and possible superscript. + + + var finalGroup; + + if (sup && sub) { + var bottom = options.fontMetrics().bigOpSpacing5 + sub.elem.height + sub.elem.depth + sub.kern + base.depth + baseShift; + finalGroup = buildCommon.makeVList({ + positionType: "bottom", + positionData: bottom, + children: [{ + type: "kern", + size: options.fontMetrics().bigOpSpacing5 + }, { + type: "elem", + elem: sub.elem, + marginLeft: -slant + "em" + }, { + type: "kern", + size: sub.kern + }, { + type: "elem", + elem: base + }, { + type: "kern", + size: sup.kern + }, { + type: "elem", + elem: sup.elem, + marginLeft: slant + "em" + }, { + type: "kern", + size: options.fontMetrics().bigOpSpacing5 + }] + }, options); + } else if (sub) { + var top = base.height - baseShift; // Shift the limits by the slant of the symbol. Note + // that we are supposed to shift the limits by 1/2 of the slant, + // but since we are centering the limits adding a full slant of + // margin will shift by 1/2 that. + + finalGroup = buildCommon.makeVList({ + positionType: "top", + positionData: top, + children: [{ + type: "kern", + size: options.fontMetrics().bigOpSpacing5 + }, { + type: "elem", + elem: sub.elem, + marginLeft: -slant + "em" + }, { + type: "kern", + size: sub.kern + }, { + type: "elem", + elem: base + }] + }, options); + } else if (sup) { + var _bottom = base.depth + baseShift; + + finalGroup = buildCommon.makeVList({ + positionType: "bottom", + positionData: _bottom, + children: [{ + type: "elem", + elem: base + }, { + type: "kern", + size: sup.kern + }, { + type: "elem", + elem: sup.elem, + marginLeft: slant + "em" + }, { + type: "kern", + size: options.fontMetrics().bigOpSpacing5 + }] + }, options); + } else { + // This case probably shouldn't occur (this would mean the + // supsub was sending us a group with no superscript or + // subscript) but be safe. + return base; + } + + var parts = [finalGroup]; + + if (sub && slant !== 0 && !subIsSingleCharacter) { + // A negative margin-left was applied to the lower limit. + // Avoid an overlap by placing a spacer on the left on the group. + var spacer = buildCommon.makeSpan(["mspace"], [], options); + spacer.style.marginRight = slant + "em"; + parts.unshift(spacer); + } + + return buildCommon.makeSpan(["mop", "op-limits"], parts, options); +}; + +// Limits, symbols +// Most operators have a large successor symbol, but these don't. +var noSuccessor = ["\\smallint"]; // NOTE: Unlike most `htmlBuilder`s, this one handles not only "op", but also +// "supsub" since some of them (like \int) can affect super/subscripting. + +var htmlBuilder$2 = (grp, options) => { + // Operators are handled in the TeXbook pg. 443-444, rule 13(a). + var supGroup; + var subGroup; + var hasLimits = false; + var group; + + if (grp.type === "supsub") { + // If we have limits, supsub will pass us its group to handle. Pull + // out the superscript and subscript and set the group to the op in + // its base. + supGroup = grp.sup; + subGroup = grp.sub; + group = assertNodeType(grp.base, "op"); + hasLimits = true; + } else { + group = assertNodeType(grp, "op"); + } + + var style = options.style; + var large = false; + + if (style.size === Style$1.DISPLAY.size && group.symbol && !utils.contains(noSuccessor, group.name)) { + // Most symbol operators get larger in displaystyle (rule 13) + large = true; + } + + var base; + + if (group.symbol) { + // If this is a symbol, create the symbol. + var fontName = large ? "Size2-Regular" : "Size1-Regular"; + var stash = ""; + + if (group.name === "\\oiint" || group.name === "\\oiiint") { + // No font glyphs yet, so use a glyph w/o the oval. + // TODO: When font glyphs are available, delete this code. + stash = group.name.substr(1); + group.name = stash === "oiint" ? "\\iint" : "\\iiint"; + } + + base = buildCommon.makeSymbol(group.name, fontName, "math", options, ["mop", "op-symbol", large ? "large-op" : "small-op"]); + + if (stash.length > 0) { + // We're in \oiint or \oiiint. Overlay the oval. + // TODO: When font glyphs are available, delete this code. + var italic = base.italic; + var oval = buildCommon.staticSvg(stash + "Size" + (large ? "2" : "1"), options); + base = buildCommon.makeVList({ + positionType: "individualShift", + children: [{ + type: "elem", + elem: base, + shift: 0 + }, { + type: "elem", + elem: oval, + shift: large ? 0.08 : 0 + }] + }, options); + group.name = "\\" + stash; + base.classes.unshift("mop"); // $FlowFixMe + + base.italic = italic; + } + } else if (group.body) { + // If this is a list, compose that list. + var inner = buildExpression$1(group.body, options, true); + + if (inner.length === 1 && inner[0] instanceof SymbolNode) { + base = inner[0]; + base.classes[0] = "mop"; // replace old mclass + } else { + base = buildCommon.makeSpan(["mop"], inner, options); + } + } else { + // Otherwise, this is a text operator. Build the text from the + // operator's name. + var output = []; + + for (var i = 1; i < group.name.length; i++) { + output.push(buildCommon.mathsym(group.name[i], group.mode, options)); + } + + base = buildCommon.makeSpan(["mop"], output, options); + } // If content of op is a single symbol, shift it vertically. + + + var baseShift = 0; + var slant = 0; + + if ((base instanceof SymbolNode || group.name === "\\oiint" || group.name === "\\oiiint") && !group.suppressBaseShift) { + // We suppress the shift of the base of \overset and \underset. Otherwise, + // shift the symbol so its center lies on the axis (rule 13). It + // appears that our fonts have the centers of the symbols already + // almost on the axis, so these numbers are very small. Note we + // don't actually apply this here, but instead it is used either in + // the vlist creation or separately when there are no limits. + baseShift = (base.height - base.depth) / 2 - options.fontMetrics().axisHeight; // The slant of the symbol is just its italic correction. + // $FlowFixMe + + slant = base.italic; + } + + if (hasLimits) { + return assembleSupSub(base, supGroup, subGroup, options, style, slant, baseShift); + } else { + if (baseShift) { + base.style.position = "relative"; + base.style.top = baseShift + "em"; + } + + return base; + } +}; + +var mathmlBuilder$1 = (group, options) => { + var node; + + if (group.symbol) { + // This is a symbol. Just add the symbol. + node = new MathNode("mo", [makeText(group.name, group.mode)]); + + if (utils.contains(noSuccessor, group.name)) { + node.setAttribute("largeop", "false"); + } + } else if (group.body) { + // This is an operator with children. Add them. + node = new MathNode("mo", buildExpression(group.body, options)); + } else { + // This is a text operator. Add all of the characters from the + // operator's name. + node = new MathNode("mi", [new TextNode(group.name.slice(1))]); // Append an ⁡. + // ref: https://www.w3.org/TR/REC-MathML/chap3_2.html#sec3.2.4 + + var operator = new MathNode("mo", [makeText("\u2061", "text")]); + + if (group.parentIsSupSub) { + node = new MathNode("mrow", [node, operator]); + } else { + node = newDocumentFragment([node, operator]); + } + } + + return node; +}; + +var singleCharBigOps = { + "\u220F": "\\prod", + "\u2210": "\\coprod", + "\u2211": "\\sum", + "\u22c0": "\\bigwedge", + "\u22c1": "\\bigvee", + "\u22c2": "\\bigcap", + "\u22c3": "\\bigcup", + "\u2a00": "\\bigodot", + "\u2a01": "\\bigoplus", + "\u2a02": "\\bigotimes", + "\u2a04": "\\biguplus", + "\u2a06": "\\bigsqcup" +}; +defineFunction({ + type: "op", + names: ["\\coprod", "\\bigvee", "\\bigwedge", "\\biguplus", "\\bigcap", "\\bigcup", "\\intop", "\\prod", "\\sum", "\\bigotimes", "\\bigoplus", "\\bigodot", "\\bigsqcup", "\\smallint", "\u220F", "\u2210", "\u2211", "\u22c0", "\u22c1", "\u22c2", "\u22c3", "\u2a00", "\u2a01", "\u2a02", "\u2a04", "\u2a06"], + props: { + numArgs: 0 + }, + handler: (_ref, args) => { + var { + parser, + funcName + } = _ref; + var fName = funcName; + + if (fName.length === 1) { + fName = singleCharBigOps[fName]; + } + + return { + type: "op", + mode: parser.mode, + limits: true, + parentIsSupSub: false, + symbol: true, + name: fName + }; + }, + htmlBuilder: htmlBuilder$2, + mathmlBuilder: mathmlBuilder$1 +}); // Note: calling defineFunction with a type that's already been defined only +// works because the same htmlBuilder and mathmlBuilder are being used. + +defineFunction({ + type: "op", + names: ["\\mathop"], + props: { + numArgs: 1, + primitive: true + }, + handler: (_ref2, args) => { + var { + parser + } = _ref2; + var body = args[0]; + return { + type: "op", + mode: parser.mode, + limits: false, + parentIsSupSub: false, + symbol: false, + body: ordargument(body) + }; + }, + htmlBuilder: htmlBuilder$2, + mathmlBuilder: mathmlBuilder$1 +}); // There are 2 flags for operators; whether they produce limits in +// displaystyle, and whether they are symbols and should grow in +// displaystyle. These four groups cover the four possible choices. + +var singleCharIntegrals = { + "\u222b": "\\int", + "\u222c": "\\iint", + "\u222d": "\\iiint", + "\u222e": "\\oint", + "\u222f": "\\oiint", + "\u2230": "\\oiiint" +}; // No limits, not symbols + +defineFunction({ + type: "op", + names: ["\\arcsin", "\\arccos", "\\arctan", "\\arctg", "\\arcctg", "\\arg", "\\ch", "\\cos", "\\cosec", "\\cosh", "\\cot", "\\cotg", "\\coth", "\\csc", "\\ctg", "\\cth", "\\deg", "\\dim", "\\exp", "\\hom", "\\ker", "\\lg", "\\ln", "\\log", "\\sec", "\\sin", "\\sinh", "\\sh", "\\tan", "\\tanh", "\\tg", "\\th"], + props: { + numArgs: 0 + }, + + handler(_ref3) { + var { + parser, + funcName + } = _ref3; + return { + type: "op", + mode: parser.mode, + limits: false, + parentIsSupSub: false, + symbol: false, + name: funcName + }; + }, + + htmlBuilder: htmlBuilder$2, + mathmlBuilder: mathmlBuilder$1 +}); // Limits, not symbols + +defineFunction({ + type: "op", + names: ["\\det", "\\gcd", "\\inf", "\\lim", "\\max", "\\min", "\\Pr", "\\sup"], + props: { + numArgs: 0 + }, + + handler(_ref4) { + var { + parser, + funcName + } = _ref4; + return { + type: "op", + mode: parser.mode, + limits: true, + parentIsSupSub: false, + symbol: false, + name: funcName + }; + }, + + htmlBuilder: htmlBuilder$2, + mathmlBuilder: mathmlBuilder$1 +}); // No limits, symbols + +defineFunction({ + type: "op", + names: ["\\int", "\\iint", "\\iiint", "\\oint", "\\oiint", "\\oiiint", "\u222b", "\u222c", "\u222d", "\u222e", "\u222f", "\u2230"], + props: { + numArgs: 0 + }, + + handler(_ref5) { + var { + parser, + funcName + } = _ref5; + var fName = funcName; + + if (fName.length === 1) { + fName = singleCharIntegrals[fName]; + } + + return { + type: "op", + mode: parser.mode, + limits: false, + parentIsSupSub: false, + symbol: true, + name: fName + }; + }, + + htmlBuilder: htmlBuilder$2, + mathmlBuilder: mathmlBuilder$1 +}); + +/** + * All registered global/built-in macros. + * `macros.js` exports this same dictionary again and makes it public. + * `Parser.js` requires this dictionary via `macros.js`. + */ +var _macros = {}; // This function might one day accept an additional argument and do more things. + +function defineMacro(name, body) { + _macros[name] = body; +} + +// NOTE: Unlike most `htmlBuilder`s, this one handles not only +// "operatorname", but also "supsub" since \operatorname* can +// affect super/subscripting. +var htmlBuilder$1 = (grp, options) => { + // Operators are handled in the TeXbook pg. 443-444, rule 13(a). + var supGroup; + var subGroup; + var hasLimits = false; + var group; + + if (grp.type === "supsub") { + // If we have limits, supsub will pass us its group to handle. Pull + // out the superscript and subscript and set the group to the op in + // its base. + supGroup = grp.sup; + subGroup = grp.sub; + group = assertNodeType(grp.base, "operatorname"); + hasLimits = true; + } else { + group = assertNodeType(grp, "operatorname"); + } + + var base; + + if (group.body.length > 0) { + var body = group.body.map(child => { + // $FlowFixMe: Check if the node has a string `text` property. + var childText = child.text; + + if (typeof childText === "string") { + return { + type: "textord", + mode: child.mode, + text: childText + }; + } else { + return child; + } + }); // Consolidate function names into symbol characters. + + var expression = buildExpression$1(body, options.withFont("mathrm"), true); + + for (var i = 0; i < expression.length; i++) { + var child = expression[i]; + + if (child instanceof SymbolNode) { + // Per amsopn package, + // change minus to hyphen and \ast to asterisk + child.text = child.text.replace(/\u2212/, "-").replace(/\u2217/, "*"); + } + } + + base = buildCommon.makeSpan(["mop"], expression, options); + } else { + base = buildCommon.makeSpan(["mop"], [], options); + } + + if (hasLimits) { + return assembleSupSub(base, supGroup, subGroup, options, options.style, 0, 0); + } else { + return base; + } +}; + +var mathmlBuilder = (group, options) => { + // The steps taken here are similar to the html version. + var expression = buildExpression(group.body, options.withFont("mathrm")); // Is expression a string or has it something like a fraction? + + var isAllString = true; // default + + for (var i = 0; i < expression.length; i++) { + var node = expression[i]; + + if (node instanceof mathMLTree.SpaceNode) ; else if (node instanceof mathMLTree.MathNode) { + switch (node.type) { + case "mi": + case "mn": + case "ms": + case "mspace": + case "mtext": + break; + // Do nothing yet. + + case "mo": + { + var child = node.children[0]; + + if (node.children.length === 1 && child instanceof mathMLTree.TextNode) { + child.text = child.text.replace(/\u2212/, "-").replace(/\u2217/, "*"); + } else { + isAllString = false; + } + + break; + } + + default: + isAllString = false; + } + } else { + isAllString = false; + } + } + + if (isAllString) { + // Write a single TextNode instead of multiple nested tags. + var word = expression.map(node => node.toText()).join(""); + expression = [new mathMLTree.TextNode(word)]; + } + + var identifier = new mathMLTree.MathNode("mi", expression); + identifier.setAttribute("mathvariant", "normal"); // \u2061 is the same as ⁡ + // ref: https://www.w3schools.com/charsets/ref_html_entities_a.asp + + var operator = new mathMLTree.MathNode("mo", [makeText("\u2061", "text")]); + + if (group.parentIsSupSub) { + return new mathMLTree.MathNode("mrow", [identifier, operator]); + } else { + return mathMLTree.newDocumentFragment([identifier, operator]); + } +}; // \operatorname +// amsopn.dtx: \mathop{#1\kern\z@\operator@font#3}\newmcodes@ + + +defineFunction({ + type: "operatorname", + names: ["\\operatorname@", "\\operatornamewithlimits"], + props: { + numArgs: 1 + }, + handler: (_ref, args) => { + var { + parser, + funcName + } = _ref; + var body = args[0]; + return { + type: "operatorname", + mode: parser.mode, + body: ordargument(body), + alwaysHandleSupSub: funcName === "\\operatornamewithlimits", + limits: false, + parentIsSupSub: false + }; + }, + htmlBuilder: htmlBuilder$1, + mathmlBuilder +}); +defineMacro("\\operatorname", "\\@ifstar\\operatornamewithlimits\\operatorname@"); + +defineFunctionBuilders({ + type: "ordgroup", + + htmlBuilder(group, options) { + if (group.semisimple) { + return buildCommon.makeFragment(buildExpression$1(group.body, options, false)); + } + + return buildCommon.makeSpan(["mord"], buildExpression$1(group.body, options, true), options); + }, + + mathmlBuilder(group, options) { + return buildExpressionRow(group.body, options, true); + } + +}); + +defineFunction({ + type: "overline", + names: ["\\overline"], + props: { + numArgs: 1 + }, + + handler(_ref, args) { + var { + parser + } = _ref; + var body = args[0]; + return { + type: "overline", + mode: parser.mode, + body + }; + }, + + htmlBuilder(group, options) { + // Overlines are handled in the TeXbook pg 443, Rule 9. + // Build the inner group in the cramped style. + var innerGroup = buildGroup$1(group.body, options.havingCrampedStyle()); // Create the line above the body + + var line = buildCommon.makeLineSpan("overline-line", options); // Generate the vlist, with the appropriate kerns + + var defaultRuleThickness = options.fontMetrics().defaultRuleThickness; + var vlist = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: innerGroup + }, { + type: "kern", + size: 3 * defaultRuleThickness + }, { + type: "elem", + elem: line + }, { + type: "kern", + size: defaultRuleThickness + }] + }, options); + return buildCommon.makeSpan(["mord", "overline"], [vlist], options); + }, + + mathmlBuilder(group, options) { + var operator = new mathMLTree.MathNode("mo", [new mathMLTree.TextNode("\u203e")]); + operator.setAttribute("stretchy", "true"); + var node = new mathMLTree.MathNode("mover", [buildGroup(group.body, options), operator]); + node.setAttribute("accent", "true"); + return node; + } + +}); + +defineFunction({ + type: "phantom", + names: ["\\phantom"], + props: { + numArgs: 1, + allowedInText: true + }, + handler: (_ref, args) => { + var { + parser + } = _ref; + var body = args[0]; + return { + type: "phantom", + mode: parser.mode, + body: ordargument(body) + }; + }, + htmlBuilder: (group, options) => { + var elements = buildExpression$1(group.body, options.withPhantom(), false); // \phantom isn't supposed to affect the elements it contains. + // See "color" for more details. + + return buildCommon.makeFragment(elements); + }, + mathmlBuilder: (group, options) => { + var inner = buildExpression(group.body, options); + return new mathMLTree.MathNode("mphantom", inner); + } +}); +defineFunction({ + type: "hphantom", + names: ["\\hphantom"], + props: { + numArgs: 1, + allowedInText: true + }, + handler: (_ref2, args) => { + var { + parser + } = _ref2; + var body = args[0]; + return { + type: "hphantom", + mode: parser.mode, + body + }; + }, + htmlBuilder: (group, options) => { + var node = buildCommon.makeSpan([], [buildGroup$1(group.body, options.withPhantom())]); + node.height = 0; + node.depth = 0; + + if (node.children) { + for (var i = 0; i < node.children.length; i++) { + node.children[i].height = 0; + node.children[i].depth = 0; + } + } // See smash for comment re: use of makeVList + + + node = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: node + }] + }, options); // For spacing, TeX treats \smash as a math group (same spacing as ord). + + return buildCommon.makeSpan(["mord"], [node], options); + }, + mathmlBuilder: (group, options) => { + var inner = buildExpression(ordargument(group.body), options); + var phantom = new mathMLTree.MathNode("mphantom", inner); + var node = new mathMLTree.MathNode("mpadded", [phantom]); + node.setAttribute("height", "0px"); + node.setAttribute("depth", "0px"); + return node; + } +}); +defineFunction({ + type: "vphantom", + names: ["\\vphantom"], + props: { + numArgs: 1, + allowedInText: true + }, + handler: (_ref3, args) => { + var { + parser + } = _ref3; + var body = args[0]; + return { + type: "vphantom", + mode: parser.mode, + body + }; + }, + htmlBuilder: (group, options) => { + var inner = buildCommon.makeSpan(["inner"], [buildGroup$1(group.body, options.withPhantom())]); + var fix = buildCommon.makeSpan(["fix"], []); + return buildCommon.makeSpan(["mord", "rlap"], [inner, fix], options); + }, + mathmlBuilder: (group, options) => { + var inner = buildExpression(ordargument(group.body), options); + var phantom = new mathMLTree.MathNode("mphantom", inner); + var node = new mathMLTree.MathNode("mpadded", [phantom]); + node.setAttribute("width", "0px"); + return node; + } +}); + +defineFunction({ + type: "raisebox", + names: ["\\raisebox"], + props: { + numArgs: 2, + argTypes: ["size", "hbox"], + allowedInText: true + }, + + handler(_ref, args) { + var { + parser + } = _ref; + var amount = assertNodeType(args[0], "size").value; + var body = args[1]; + return { + type: "raisebox", + mode: parser.mode, + dy: amount, + body + }; + }, + + htmlBuilder(group, options) { + var body = buildGroup$1(group.body, options); + var dy = calculateSize(group.dy, options); + return buildCommon.makeVList({ + positionType: "shift", + positionData: -dy, + children: [{ + type: "elem", + elem: body + }] + }, options); + }, + + mathmlBuilder(group, options) { + var node = new mathMLTree.MathNode("mpadded", [buildGroup(group.body, options)]); + var dy = group.dy.number + group.dy.unit; + node.setAttribute("voffset", dy); + return node; + } + +}); + +defineFunction({ + type: "rule", + names: ["\\rule"], + props: { + numArgs: 2, + numOptionalArgs: 1, + argTypes: ["size", "size", "size"] + }, + + handler(_ref, args, optArgs) { + var { + parser + } = _ref; + var shift = optArgs[0]; + var width = assertNodeType(args[0], "size"); + var height = assertNodeType(args[1], "size"); + return { + type: "rule", + mode: parser.mode, + shift: shift && assertNodeType(shift, "size").value, + width: width.value, + height: height.value + }; + }, + + htmlBuilder(group, options) { + // Make an empty span for the rule + var rule = buildCommon.makeSpan(["mord", "rule"], [], options); // Calculate the shift, width, and height of the rule, and account for units + + var width = calculateSize(group.width, options); + var height = calculateSize(group.height, options); + var shift = group.shift ? calculateSize(group.shift, options) : 0; // Style the rule to the right size + + rule.style.borderRightWidth = width + "em"; + rule.style.borderTopWidth = height + "em"; + rule.style.bottom = shift + "em"; // Record the height and width + + rule.width = width; + rule.height = height + shift; + rule.depth = -shift; // Font size is the number large enough that the browser will + // reserve at least `absHeight` space above the baseline. + // The 1.125 factor was empirically determined + + rule.maxFontSize = height * 1.125 * options.sizeMultiplier; + return rule; + }, + + mathmlBuilder(group, options) { + var width = calculateSize(group.width, options); + var height = calculateSize(group.height, options); + var shift = group.shift ? calculateSize(group.shift, options) : 0; + var color = options.color && options.getColor() || "black"; + var rule = new mathMLTree.MathNode("mspace"); + rule.setAttribute("mathbackground", color); + rule.setAttribute("width", width + "em"); + rule.setAttribute("height", height + "em"); + var wrapper = new mathMLTree.MathNode("mpadded", [rule]); + + if (shift >= 0) { + wrapper.setAttribute("height", "+" + shift + "em"); + } else { + wrapper.setAttribute("height", shift + "em"); + wrapper.setAttribute("depth", "+" + -shift + "em"); + } + + wrapper.setAttribute("voffset", shift + "em"); + return wrapper; + } + +}); + +function sizingGroup(value, options, baseOptions) { + var inner = buildExpression$1(value, options, false); + var multiplier = options.sizeMultiplier / baseOptions.sizeMultiplier; // Add size-resetting classes to the inner list and set maxFontSize + // manually. Handle nested size changes. + + for (var i = 0; i < inner.length; i++) { + var pos = inner[i].classes.indexOf("sizing"); + + if (pos < 0) { + Array.prototype.push.apply(inner[i].classes, options.sizingClasses(baseOptions)); + } else if (inner[i].classes[pos + 1] === "reset-size" + options.size) { + // This is a nested size change: e.g., inner[i] is the "b" in + // `\Huge a \small b`. Override the old size (the `reset-` class) + // but not the new size. + inner[i].classes[pos + 1] = "reset-size" + baseOptions.size; + } + + inner[i].height *= multiplier; + inner[i].depth *= multiplier; + } + + return buildCommon.makeFragment(inner); +} +var sizeFuncs = ["\\tiny", "\\sixptsize", "\\scriptsize", "\\footnotesize", "\\small", "\\normalsize", "\\large", "\\Large", "\\LARGE", "\\huge", "\\Huge"]; +var htmlBuilder = (group, options) => { + // Handle sizing operators like \Huge. Real TeX doesn't actually allow + // these functions inside of math expressions, so we do some special + // handling. + var newOptions = options.havingSize(group.size); + return sizingGroup(group.body, newOptions, options); +}; +defineFunction({ + type: "sizing", + names: sizeFuncs, + props: { + numArgs: 0, + allowedInText: true + }, + handler: (_ref, args) => { + var { + breakOnTokenText, + funcName, + parser + } = _ref; + var body = parser.parseExpression(false, breakOnTokenText); + return { + type: "sizing", + mode: parser.mode, + // Figure out what size to use based on the list of functions above + size: sizeFuncs.indexOf(funcName) + 1, + body + }; + }, + htmlBuilder, + mathmlBuilder: (group, options) => { + var newOptions = options.havingSize(group.size); + var inner = buildExpression(group.body, newOptions); + var node = new mathMLTree.MathNode("mstyle", inner); // TODO(emily): This doesn't produce the correct size for nested size + // changes, because we don't keep state of what style we're currently + // in, so we can't reset the size to normal before changing it. Now + // that we're passing an options parameter we should be able to fix + // this. + + node.setAttribute("mathsize", newOptions.sizeMultiplier + "em"); + return node; + } +}); + +// smash, with optional [tb], as in AMS +defineFunction({ + type: "smash", + names: ["\\smash"], + props: { + numArgs: 1, + numOptionalArgs: 1, + allowedInText: true + }, + handler: (_ref, args, optArgs) => { + var { + parser + } = _ref; + var smashHeight = false; + var smashDepth = false; + var tbArg = optArgs[0] && assertNodeType(optArgs[0], "ordgroup"); + + if (tbArg) { + // Optional [tb] argument is engaged. + // ref: amsmath: \renewcommand{\smash}[1][tb]{% + // def\mb@t{\ht}\def\mb@b{\dp}\def\mb@tb{\ht\z@\z@\dp}% + var letter = ""; + + for (var i = 0; i < tbArg.body.length; ++i) { + var node = tbArg.body[i]; // $FlowFixMe: Not every node type has a `text` property. + + letter = node.text; + + if (letter === "t") { + smashHeight = true; + } else if (letter === "b") { + smashDepth = true; + } else { + smashHeight = false; + smashDepth = false; + break; + } + } + } else { + smashHeight = true; + smashDepth = true; + } + + var body = args[0]; + return { + type: "smash", + mode: parser.mode, + body, + smashHeight, + smashDepth + }; + }, + htmlBuilder: (group, options) => { + var node = buildCommon.makeSpan([], [buildGroup$1(group.body, options)]); + + if (!group.smashHeight && !group.smashDepth) { + return node; + } + + if (group.smashHeight) { + node.height = 0; // In order to influence makeVList, we have to reset the children. + + if (node.children) { + for (var i = 0; i < node.children.length; i++) { + node.children[i].height = 0; + } + } + } + + if (group.smashDepth) { + node.depth = 0; + + if (node.children) { + for (var _i = 0; _i < node.children.length; _i++) { + node.children[_i].depth = 0; + } + } + } // At this point, we've reset the TeX-like height and depth values. + // But the span still has an HTML line height. + // makeVList applies "display: table-cell", which prevents the browser + // from acting on that line height. So we'll call makeVList now. + + + var smashedNode = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: node + }] + }, options); // For spacing, TeX treats \hphantom as a math group (same spacing as ord). + + return buildCommon.makeSpan(["mord"], [smashedNode], options); + }, + mathmlBuilder: (group, options) => { + var node = new mathMLTree.MathNode("mpadded", [buildGroup(group.body, options)]); + + if (group.smashHeight) { + node.setAttribute("height", "0px"); + } + + if (group.smashDepth) { + node.setAttribute("depth", "0px"); + } + + return node; + } +}); + +defineFunction({ + type: "sqrt", + names: ["\\sqrt"], + props: { + numArgs: 1, + numOptionalArgs: 1 + }, + + handler(_ref, args, optArgs) { + var { + parser + } = _ref; + var index = optArgs[0]; + var body = args[0]; + return { + type: "sqrt", + mode: parser.mode, + body, + index + }; + }, + + htmlBuilder(group, options) { + // Square roots are handled in the TeXbook pg. 443, Rule 11. + // First, we do the same steps as in overline to build the inner group + // and line + var inner = buildGroup$1(group.body, options.havingCrampedStyle()); + + if (inner.height === 0) { + // Render a small surd. + inner.height = options.fontMetrics().xHeight; + } // Some groups can return document fragments. Handle those by wrapping + // them in a span. + + + inner = buildCommon.wrapFragment(inner, options); // Calculate the minimum size for the \surd delimiter + + var metrics = options.fontMetrics(); + var theta = metrics.defaultRuleThickness; + var phi = theta; + + if (options.style.id < Style$1.TEXT.id) { + phi = options.fontMetrics().xHeight; + } // Calculate the clearance between the body and line + + + var lineClearance = theta + phi / 4; + var minDelimiterHeight = inner.height + inner.depth + lineClearance + theta; // Create a sqrt SVG of the required minimum size + + var { + span: img, + ruleWidth, + advanceWidth + } = delimiter.sqrtImage(minDelimiterHeight, options); + var delimDepth = img.height - ruleWidth; // Adjust the clearance based on the delimiter size + + if (delimDepth > inner.height + inner.depth + lineClearance) { + lineClearance = (lineClearance + delimDepth - inner.height - inner.depth) / 2; + } // Shift the sqrt image + + + var imgShift = img.height - inner.height - lineClearance - ruleWidth; + inner.style.paddingLeft = advanceWidth + "em"; // Overlay the image and the argument. + + var body = buildCommon.makeVList({ + positionType: "firstBaseline", + children: [{ + type: "elem", + elem: inner, + wrapperClasses: ["svg-align"] + }, { + type: "kern", + size: -(inner.height + imgShift) + }, { + type: "elem", + elem: img + }, { + type: "kern", + size: ruleWidth + }] + }, options); + + if (!group.index) { + return buildCommon.makeSpan(["mord", "sqrt"], [body], options); + } else { + // Handle the optional root index + // The index is always in scriptscript style + var newOptions = options.havingStyle(Style$1.SCRIPTSCRIPT); + var rootm = buildGroup$1(group.index, newOptions, options); // The amount the index is shifted by. This is taken from the TeX + // source, in the definition of `\r@@t`. + + var toShift = 0.6 * (body.height - body.depth); // Build a VList with the superscript shifted up correctly + + var rootVList = buildCommon.makeVList({ + positionType: "shift", + positionData: -toShift, + children: [{ + type: "elem", + elem: rootm + }] + }, options); // Add a class surrounding it so we can add on the appropriate + // kerning + + var rootVListWrap = buildCommon.makeSpan(["root"], [rootVList]); + return buildCommon.makeSpan(["mord", "sqrt"], [rootVListWrap, body], options); + } + }, + + mathmlBuilder(group, options) { + var { + body, + index + } = group; + return index ? new mathMLTree.MathNode("mroot", [buildGroup(body, options), buildGroup(index, options)]) : new mathMLTree.MathNode("msqrt", [buildGroup(body, options)]); + } + +}); + +var styleMap = { + "display": Style$1.DISPLAY, + "text": Style$1.TEXT, + "script": Style$1.SCRIPT, + "scriptscript": Style$1.SCRIPTSCRIPT +}; +defineFunction({ + type: "styling", + names: ["\\displaystyle", "\\textstyle", "\\scriptstyle", "\\scriptscriptstyle"], + props: { + numArgs: 0, + allowedInText: true, + primitive: true + }, + + handler(_ref, args) { + var { + breakOnTokenText, + funcName, + parser + } = _ref; + // parse out the implicit body + var body = parser.parseExpression(true, breakOnTokenText); // TODO: Refactor to avoid duplicating styleMap in multiple places (e.g. + // here and in buildHTML and de-dupe the enumeration of all the styles). + // $FlowFixMe: The names above exactly match the styles. + + var style = funcName.slice(1, funcName.length - 5); + return { + type: "styling", + mode: parser.mode, + // Figure out what style to use by pulling out the style from + // the function name + style, + body + }; + }, + + htmlBuilder(group, options) { + // Style changes are handled in the TeXbook on pg. 442, Rule 3. + var newStyle = styleMap[group.style]; + var newOptions = options.havingStyle(newStyle).withFont(''); + return sizingGroup(group.body, newOptions, options); + }, + + mathmlBuilder(group, options) { + // Figure out what style we're changing to. + var newStyle = styleMap[group.style]; + var newOptions = options.havingStyle(newStyle); + var inner = buildExpression(group.body, newOptions); + var node = new mathMLTree.MathNode("mstyle", inner); + var styleAttributes = { + "display": ["0", "true"], + "text": ["0", "false"], + "script": ["1", "false"], + "scriptscript": ["2", "false"] + }; + var attr = styleAttributes[group.style]; + node.setAttribute("scriptlevel", attr[0]); + node.setAttribute("displaystyle", attr[1]); + return node; + } + +}); + +/** + * Sometimes, groups perform special rules when they have superscripts or + * subscripts attached to them. This function lets the `supsub` group know that + * Sometimes, groups perform special rules when they have superscripts or + * its inner element should handle the superscripts and subscripts instead of + * handling them itself. + */ +var htmlBuilderDelegate = function htmlBuilderDelegate(group, options) { + var base = group.base; + + if (!base) { + return null; + } else if (base.type === "op") { + // Operators handle supsubs differently when they have limits + // (e.g. `\displaystyle\sum_2^3`) + var delegate = base.limits && (options.style.size === Style$1.DISPLAY.size || base.alwaysHandleSupSub); + return delegate ? htmlBuilder$2 : null; + } else if (base.type === "operatorname") { + var _delegate = base.alwaysHandleSupSub && (options.style.size === Style$1.DISPLAY.size || base.limits); + + return _delegate ? htmlBuilder$1 : null; + } else if (base.type === "accent") { + return utils.isCharacterBox(base.base) ? htmlBuilder$a : null; + } else if (base.type === "horizBrace") { + var isSup = !group.sub; + return isSup === base.isOver ? htmlBuilder$3 : null; + } else { + return null; + } +}; // Super scripts and subscripts, whose precise placement can depend on other +// functions that precede them. + + +defineFunctionBuilders({ + type: "supsub", + + htmlBuilder(group, options) { + // Superscript and subscripts are handled in the TeXbook on page + // 445-446, rules 18(a-f). + // Here is where we defer to the inner group if it should handle + // superscripts and subscripts itself. + var builderDelegate = htmlBuilderDelegate(group, options); + + if (builderDelegate) { + return builderDelegate(group, options); + } + + var { + base: valueBase, + sup: valueSup, + sub: valueSub + } = group; + var base = buildGroup$1(valueBase, options); + var supm; + var subm; + var metrics = options.fontMetrics(); // Rule 18a + + var supShift = 0; + var subShift = 0; + var isCharacterBox = valueBase && utils.isCharacterBox(valueBase); + + if (valueSup) { + var newOptions = options.havingStyle(options.style.sup()); + supm = buildGroup$1(valueSup, newOptions, options); + + if (!isCharacterBox) { + supShift = base.height - newOptions.fontMetrics().supDrop * newOptions.sizeMultiplier / options.sizeMultiplier; + } + } + + if (valueSub) { + var _newOptions = options.havingStyle(options.style.sub()); + + subm = buildGroup$1(valueSub, _newOptions, options); + + if (!isCharacterBox) { + subShift = base.depth + _newOptions.fontMetrics().subDrop * _newOptions.sizeMultiplier / options.sizeMultiplier; + } + } // Rule 18c + + + var minSupShift; + + if (options.style === Style$1.DISPLAY) { + minSupShift = metrics.sup1; + } else if (options.style.cramped) { + minSupShift = metrics.sup3; + } else { + minSupShift = metrics.sup2; + } // scriptspace is a font-size-independent size, so scale it + // appropriately for use as the marginRight. + + + var multiplier = options.sizeMultiplier; + var marginRight = 0.5 / metrics.ptPerEm / multiplier + "em"; + var marginLeft = null; + + if (subm) { + // Subscripts shouldn't be shifted by the base's italic correction. + // Account for that by shifting the subscript back the appropriate + // amount. Note we only do this when the base is a single symbol. + var isOiint = group.base && group.base.type === "op" && group.base.name && (group.base.name === "\\oiint" || group.base.name === "\\oiiint"); + + if (base instanceof SymbolNode || isOiint) { + // $FlowFixMe + marginLeft = -base.italic + "em"; + } + } + + var supsub; + + if (supm && subm) { + supShift = Math.max(supShift, minSupShift, supm.depth + 0.25 * metrics.xHeight); + subShift = Math.max(subShift, metrics.sub2); + var ruleWidth = metrics.defaultRuleThickness; // Rule 18e + + var maxWidth = 4 * ruleWidth; + + if (supShift - supm.depth - (subm.height - subShift) < maxWidth) { + subShift = maxWidth - (supShift - supm.depth) + subm.height; + var psi = 0.8 * metrics.xHeight - (supShift - supm.depth); + + if (psi > 0) { + supShift += psi; + subShift -= psi; + } + } + + var vlistElem = [{ + type: "elem", + elem: subm, + shift: subShift, + marginRight, + marginLeft + }, { + type: "elem", + elem: supm, + shift: -supShift, + marginRight + }]; + supsub = buildCommon.makeVList({ + positionType: "individualShift", + children: vlistElem + }, options); + } else if (subm) { + // Rule 18b + subShift = Math.max(subShift, metrics.sub1, subm.height - 0.8 * metrics.xHeight); + var _vlistElem = [{ + type: "elem", + elem: subm, + marginLeft, + marginRight + }]; + supsub = buildCommon.makeVList({ + positionType: "shift", + positionData: subShift, + children: _vlistElem + }, options); + } else if (supm) { + // Rule 18c, d + supShift = Math.max(supShift, minSupShift, supm.depth + 0.25 * metrics.xHeight); + supsub = buildCommon.makeVList({ + positionType: "shift", + positionData: -supShift, + children: [{ + type: "elem", + elem: supm, + marginRight + }] + }, options); + } else { + throw new Error("supsub must have either sup or sub."); + } // Wrap the supsub vlist in a span.msupsub to reset text-align. + + + var mclass = getTypeOfDomTree(base, "right") || "mord"; + return buildCommon.makeSpan([mclass], [base, buildCommon.makeSpan(["msupsub"], [supsub])], options); + }, + + mathmlBuilder(group, options) { + // Is the inner group a relevant horizonal brace? + var isBrace = false; + var isOver; + var isSup; + + if (group.base && group.base.type === "horizBrace") { + isSup = !!group.sup; + + if (isSup === group.base.isOver) { + isBrace = true; + isOver = group.base.isOver; + } + } + + if (group.base && (group.base.type === "op" || group.base.type === "operatorname")) { + group.base.parentIsSupSub = true; + } + + var children = [buildGroup(group.base, options)]; + + if (group.sub) { + children.push(buildGroup(group.sub, options)); + } + + if (group.sup) { + children.push(buildGroup(group.sup, options)); + } + + var nodeType; + + if (isBrace) { + nodeType = isOver ? "mover" : "munder"; + } else if (!group.sub) { + var base = group.base; + + if (base && base.type === "op" && base.limits && (options.style === Style$1.DISPLAY || base.alwaysHandleSupSub)) { + nodeType = "mover"; + } else if (base && base.type === "operatorname" && base.alwaysHandleSupSub && (base.limits || options.style === Style$1.DISPLAY)) { + nodeType = "mover"; + } else { + nodeType = "msup"; + } + } else if (!group.sup) { + var _base = group.base; + + if (_base && _base.type === "op" && _base.limits && (options.style === Style$1.DISPLAY || _base.alwaysHandleSupSub)) { + nodeType = "munder"; + } else if (_base && _base.type === "operatorname" && _base.alwaysHandleSupSub && (_base.limits || options.style === Style$1.DISPLAY)) { + nodeType = "munder"; + } else { + nodeType = "msub"; + } + } else { + var _base2 = group.base; + + if (_base2 && _base2.type === "op" && _base2.limits && options.style === Style$1.DISPLAY) { + nodeType = "munderover"; + } else if (_base2 && _base2.type === "operatorname" && _base2.alwaysHandleSupSub && (options.style === Style$1.DISPLAY || _base2.limits)) { + nodeType = "munderover"; + } else { + nodeType = "msubsup"; + } + } + + return new mathMLTree.MathNode(nodeType, children); + } + +}); + +defineFunctionBuilders({ + type: "atom", + + htmlBuilder(group, options) { + return buildCommon.mathsym(group.text, group.mode, options, ["m" + group.family]); + }, + + mathmlBuilder(group, options) { + var node = new mathMLTree.MathNode("mo", [makeText(group.text, group.mode)]); + + if (group.family === "bin") { + var variant = getVariant(group, options); + + if (variant === "bold-italic") { + node.setAttribute("mathvariant", variant); + } + } else if (group.family === "punct") { + node.setAttribute("separator", "true"); + } else if (group.family === "open" || group.family === "close") { + // Delims built here should not stretch vertically. + // See delimsizing.js for stretchy delims. + node.setAttribute("stretchy", "false"); + } + + return node; + } + +}); + +// "mathord" and "textord" ParseNodes created in Parser.js from symbol Groups in +// src/symbols.js. +var defaultVariant = { + "mi": "italic", + "mn": "normal", + "mtext": "normal" +}; +defineFunctionBuilders({ + type: "mathord", + + htmlBuilder(group, options) { + return buildCommon.makeOrd(group, options, "mathord"); + }, + + mathmlBuilder(group, options) { + var node = new mathMLTree.MathNode("mi", [makeText(group.text, group.mode, options)]); + var variant = getVariant(group, options) || "italic"; + + if (variant !== defaultVariant[node.type]) { + node.setAttribute("mathvariant", variant); + } + + return node; + } + +}); +defineFunctionBuilders({ + type: "textord", + + htmlBuilder(group, options) { + return buildCommon.makeOrd(group, options, "textord"); + }, + + mathmlBuilder(group, options) { + var text = makeText(group.text, group.mode, options); + var variant = getVariant(group, options) || "normal"; + var node; + + if (group.mode === 'text') { + node = new mathMLTree.MathNode("mtext", [text]); + } else if (/[0-9]/.test(group.text)) { + node = new mathMLTree.MathNode("mn", [text]); + } else if (group.text === "\\prime") { + node = new mathMLTree.MathNode("mo", [text]); + } else { + node = new mathMLTree.MathNode("mi", [text]); + } + + if (variant !== defaultVariant[node.type]) { + node.setAttribute("mathvariant", variant); + } + + return node; + } + +}); + +var cssSpace = { + "\\nobreak": "nobreak", + "\\allowbreak": "allowbreak" +}; // A lookup table to determine whether a spacing function/symbol should be +// treated like a regular space character. If a symbol or command is a key +// in this table, then it should be a regular space character. Furthermore, +// the associated value may have a `className` specifying an extra CSS class +// to add to the created `span`. + +var regularSpace = { + " ": {}, + "\\ ": {}, + "~": { + className: "nobreak" + }, + "\\space": {}, + "\\nobreakspace": { + className: "nobreak" + } +}; // ParseNode<"spacing"> created in Parser.js from the "spacing" symbol Groups in +// src/symbols.js. + +defineFunctionBuilders({ + type: "spacing", + + htmlBuilder(group, options) { + if (regularSpace.hasOwnProperty(group.text)) { + var className = regularSpace[group.text].className || ""; // Spaces are generated by adding an actual space. Each of these + // things has an entry in the symbols table, so these will be turned + // into appropriate outputs. + + if (group.mode === "text") { + var ord = buildCommon.makeOrd(group, options, "textord"); + ord.classes.push(className); + return ord; + } else { + return buildCommon.makeSpan(["mspace", className], [buildCommon.mathsym(group.text, group.mode, options)], options); + } + } else if (cssSpace.hasOwnProperty(group.text)) { + // Spaces based on just a CSS class. + return buildCommon.makeSpan(["mspace", cssSpace[group.text]], [], options); + } else { + throw new ParseError("Unknown type of space \"" + group.text + "\""); + } + }, + + mathmlBuilder(group, options) { + var node; + + if (regularSpace.hasOwnProperty(group.text)) { + node = new mathMLTree.MathNode("mtext", [new mathMLTree.TextNode("\u00a0")]); + } else if (cssSpace.hasOwnProperty(group.text)) { + // CSS-based MathML spaces (\nobreak, \allowbreak) are ignored + return new mathMLTree.MathNode("mspace"); + } else { + throw new ParseError("Unknown type of space \"" + group.text + "\""); + } + + return node; + } + +}); + +var pad = () => { + var padNode = new mathMLTree.MathNode("mtd", []); + padNode.setAttribute("width", "50%"); + return padNode; +}; + +defineFunctionBuilders({ + type: "tag", + + mathmlBuilder(group, options) { + var table = new mathMLTree.MathNode("mtable", [new mathMLTree.MathNode("mtr", [pad(), new mathMLTree.MathNode("mtd", [buildExpressionRow(group.body, options)]), pad(), new mathMLTree.MathNode("mtd", [buildExpressionRow(group.tag, options)])])]); + table.setAttribute("width", "100%"); + return table; // TODO: Left-aligned tags. + // Currently, the group and options passed here do not contain + // enough info to set tag alignment. `leqno` is in Settings but it is + // not passed to Options. On the HTML side, leqno is + // set by a CSS class applied in buildTree.js. That would have worked + // in MathML if browsers supported . Since they don't, we + // need to rewrite the way this function is called. + } + +}); + +var textFontFamilies = { + "\\text": undefined, + "\\textrm": "textrm", + "\\textsf": "textsf", + "\\texttt": "texttt", + "\\textnormal": "textrm" +}; +var textFontWeights = { + "\\textbf": "textbf", + "\\textmd": "textmd" +}; +var textFontShapes = { + "\\textit": "textit", + "\\textup": "textup" +}; + +var optionsWithFont = (group, options) => { + var font = group.font; // Checks if the argument is a font family or a font style. + + if (!font) { + return options; + } else if (textFontFamilies[font]) { + return options.withTextFontFamily(textFontFamilies[font]); + } else if (textFontWeights[font]) { + return options.withTextFontWeight(textFontWeights[font]); + } else { + return options.withTextFontShape(textFontShapes[font]); + } +}; + +defineFunction({ + type: "text", + names: [// Font families + "\\text", "\\textrm", "\\textsf", "\\texttt", "\\textnormal", // Font weights + "\\textbf", "\\textmd", // Font Shapes + "\\textit", "\\textup"], + props: { + numArgs: 1, + argTypes: ["text"], + allowedInArgument: true, + allowedInText: true + }, + + handler(_ref, args) { + var { + parser, + funcName + } = _ref; + var body = args[0]; + return { + type: "text", + mode: parser.mode, + body: ordargument(body), + font: funcName + }; + }, + + htmlBuilder(group, options) { + var newOptions = optionsWithFont(group, options); + var inner = buildExpression$1(group.body, newOptions, true); + return buildCommon.makeSpan(["mord", "text"], inner, newOptions); + }, + + mathmlBuilder(group, options) { + var newOptions = optionsWithFont(group, options); + return buildExpressionRow(group.body, newOptions); + } + +}); + +defineFunction({ + type: "underline", + names: ["\\underline"], + props: { + numArgs: 1, + allowedInText: true + }, + + handler(_ref, args) { + var { + parser + } = _ref; + return { + type: "underline", + mode: parser.mode, + body: args[0] + }; + }, + + htmlBuilder(group, options) { + // Underlines are handled in the TeXbook pg 443, Rule 10. + // Build the inner group. + var innerGroup = buildGroup$1(group.body, options); // Create the line to go below the body + + var line = buildCommon.makeLineSpan("underline-line", options); // Generate the vlist, with the appropriate kerns + + var defaultRuleThickness = options.fontMetrics().defaultRuleThickness; + var vlist = buildCommon.makeVList({ + positionType: "top", + positionData: innerGroup.height, + children: [{ + type: "kern", + size: defaultRuleThickness + }, { + type: "elem", + elem: line + }, { + type: "kern", + size: 3 * defaultRuleThickness + }, { + type: "elem", + elem: innerGroup + }] + }, options); + return buildCommon.makeSpan(["mord", "underline"], [vlist], options); + }, + + mathmlBuilder(group, options) { + var operator = new mathMLTree.MathNode("mo", [new mathMLTree.TextNode("\u203e")]); + operator.setAttribute("stretchy", "true"); + var node = new mathMLTree.MathNode("munder", [buildGroup(group.body, options), operator]); + node.setAttribute("accentunder", "true"); + return node; + } + +}); + +defineFunction({ + type: "vcenter", + names: ["\\vcenter"], + props: { + numArgs: 1, + argTypes: ["original"], + // In LaTeX, \vcenter can act only on a box. + allowedInText: false + }, + + handler(_ref, args) { + var { + parser + } = _ref; + return { + type: "vcenter", + mode: parser.mode, + body: args[0] + }; + }, + + htmlBuilder(group, options) { + var body = buildGroup$1(group.body, options); + var axisHeight = options.fontMetrics().axisHeight; + var dy = 0.5 * (body.height - axisHeight - (body.depth + axisHeight)); + return buildCommon.makeVList({ + positionType: "shift", + positionData: dy, + children: [{ + type: "elem", + elem: body + }] + }, options); + }, + + mathmlBuilder(group, options) { + // There is no way to do this in MathML. + // Write a class as a breadcrumb in case some post-processor wants + // to perform a vcenter adjustment. + return new mathMLTree.MathNode("mpadded", [buildGroup(group.body, options)], ["vcenter"]); + } + +}); + +defineFunction({ + type: "verb", + names: ["\\verb"], + props: { + numArgs: 0, + allowedInText: true + }, + + handler(context, args, optArgs) { + // \verb and \verb* are dealt with directly in Parser.js. + // If we end up here, it's because of a failure to match the two delimiters + // in the regex in Lexer.js. LaTeX raises the following error when \verb is + // terminated by end of line (or file). + throw new ParseError("\\verb ended by end of line instead of matching delimiter"); + }, + + htmlBuilder(group, options) { + var text = makeVerb(group); + var body = []; // \verb enters text mode and therefore is sized like \textstyle + + var newOptions = options.havingStyle(options.style.text()); + + for (var i = 0; i < text.length; i++) { + var c = text[i]; + + if (c === '~') { + c = '\\textasciitilde'; + } + + body.push(buildCommon.makeSymbol(c, "Typewriter-Regular", group.mode, newOptions, ["mord", "texttt"])); + } + + return buildCommon.makeSpan(["mord", "text"].concat(newOptions.sizingClasses(options)), buildCommon.tryCombineChars(body), newOptions); + }, + + mathmlBuilder(group, options) { + var text = new mathMLTree.TextNode(makeVerb(group)); + var node = new mathMLTree.MathNode("mtext", [text]); + node.setAttribute("mathvariant", "monospace"); + return node; + } + +}); +/** + * Converts verb group into body string. + * + * \verb* replaces each space with an open box \u2423 + * \verb replaces each space with a no-break space \xA0 + */ + +var makeVerb = group => group.body.replace(/ /g, group.star ? '\u2423' : '\xA0'); + +/** Include this to ensure that all functions are defined. */ +var functions = _functions; + +/** + * The Lexer class handles tokenizing the input in various ways. Since our + * parser expects us to be able to backtrack, the lexer allows lexing from any + * given starting point. + * + * Its main exposed function is the `lex` function, which takes a position to + * lex from and a type of token to lex. It defers to the appropriate `_innerLex` + * function. + * + * The various `_innerLex` functions perform the actual lexing of different + * kinds. + */ + +/* The following tokenRegex + * - matches typical whitespace (but not NBSP etc.) using its first group + * - does not match any control character \x00-\x1f except whitespace + * - does not match a bare backslash + * - matches any ASCII character except those just mentioned + * - does not match the BMP private use area \uE000-\uF8FF + * - does not match bare surrogate code units + * - matches any BMP character except for those just described + * - matches any valid Unicode surrogate pair + * - matches a backslash followed by one or more whitespace characters + * - matches a backslash followed by one or more letters then whitespace + * - matches a backslash followed by any BMP character + * Capturing groups: + * [1] regular whitespace + * [2] backslash followed by whitespace + * [3] anything else, which may include: + * [4] left character of \verb* + * [5] left character of \verb + * [6] backslash followed by word, excluding any trailing whitespace + * Just because the Lexer matches something doesn't mean it's valid input: + * If there is no matching function or symbol definition, the Parser will + * still reject the input. + */ +var spaceRegexString = "[ \r\n\t]"; +var controlWordRegexString = "\\\\[a-zA-Z@]+"; +var controlSymbolRegexString = "\\\\[^\uD800-\uDFFF]"; +var controlWordWhitespaceRegexString = "(" + controlWordRegexString + ")" + spaceRegexString + "*"; +var controlSpaceRegexString = "\\\\(\n|[ \r\t]+\n?)[ \r\t]*"; +var combiningDiacriticalMarkString = "[\u0300-\u036f]"; +var combiningDiacriticalMarksEndRegex = new RegExp(combiningDiacriticalMarkString + "+$"); +var tokenRegexString = "(" + spaceRegexString + "+)|" + ( // whitespace +controlSpaceRegexString + "|") + // \whitespace +"([!-\\[\\]-\u2027\u202A-\uD7FF\uF900-\uFFFF]" + ( // single codepoint +combiningDiacriticalMarkString + "*") + // ...plus accents +"|[\uD800-\uDBFF][\uDC00-\uDFFF]" + ( // surrogate pair +combiningDiacriticalMarkString + "*") + // ...plus accents +"|\\\\verb\\*([^]).*?\\4" + // \verb* +"|\\\\verb([^*a-zA-Z]).*?\\5" + ( // \verb unstarred +"|" + controlWordWhitespaceRegexString) + ( // \macroName + spaces +"|" + controlSymbolRegexString + ")"); // \\, \', etc. + +/** Main Lexer class */ + +class Lexer { + // Category codes. The lexer only supports comment characters (14) for now. + // MacroExpander additionally distinguishes active (13). + constructor(input, settings) { + this.input = void 0; + this.settings = void 0; + this.tokenRegex = void 0; + this.catcodes = void 0; + // Separate accents from characters + this.input = input; + this.settings = settings; + this.tokenRegex = new RegExp(tokenRegexString, 'g'); + this.catcodes = { + "%": 14, + // comment character + "~": 13 // active character + + }; + } + + setCatcode(char, code) { + this.catcodes[char] = code; + } + /** + * This function lexes a single token. + */ + + + lex() { + var input = this.input; + var pos = this.tokenRegex.lastIndex; + + if (pos === input.length) { + return new Token("EOF", new SourceLocation(this, pos, pos)); + } + + var match = this.tokenRegex.exec(input); + + if (match === null || match.index !== pos) { + throw new ParseError("Unexpected character: '" + input[pos] + "'", new Token(input[pos], new SourceLocation(this, pos, pos + 1))); + } + + var text = match[6] || match[3] || (match[2] ? "\\ " : " "); + + if (this.catcodes[text] === 14) { + // comment character + var nlIndex = input.indexOf('\n', this.tokenRegex.lastIndex); + + if (nlIndex === -1) { + this.tokenRegex.lastIndex = input.length; // EOF + + this.settings.reportNonstrict("commentAtEnd", "% comment has no terminating newline; LaTeX would " + "fail because of commenting the end of math mode (e.g. $)"); + } else { + this.tokenRegex.lastIndex = nlIndex + 1; + } + + return this.lex(); + } + + return new Token(text, new SourceLocation(this, pos, this.tokenRegex.lastIndex)); + } + +} + +/** + * A `Namespace` refers to a space of nameable things like macros or lengths, + * which can be `set` either globally or local to a nested group, using an + * undo stack similar to how TeX implements this functionality. + * Performance-wise, `get` and local `set` take constant time, while global + * `set` takes time proportional to the depth of group nesting. + */ +class Namespace { + /** + * Both arguments are optional. The first argument is an object of + * built-in mappings which never change. The second argument is an object + * of initial (global-level) mappings, which will constantly change + * according to any global/top-level `set`s done. + */ + constructor(builtins, globalMacros) { + if (builtins === void 0) { + builtins = {}; + } + + if (globalMacros === void 0) { + globalMacros = {}; + } + + this.current = void 0; + this.builtins = void 0; + this.undefStack = void 0; + this.current = globalMacros; + this.builtins = builtins; + this.undefStack = []; + } + /** + * Start a new nested group, affecting future local `set`s. + */ + + + beginGroup() { + this.undefStack.push({}); + } + /** + * End current nested group, restoring values before the group began. + */ + + + endGroup() { + if (this.undefStack.length === 0) { + throw new ParseError("Unbalanced namespace destruction: attempt " + "to pop global namespace; please report this as a bug"); + } + + var undefs = this.undefStack.pop(); + + for (var undef in undefs) { + if (undefs.hasOwnProperty(undef)) { + if (undefs[undef] === undefined) { + delete this.current[undef]; + } else { + this.current[undef] = undefs[undef]; + } + } + } + } + /** + * Ends all currently nested groups (if any), restoring values before the + * groups began. Useful in case of an error in the middle of parsing. + */ + + + endGroups() { + while (this.undefStack.length > 0) { + this.endGroup(); + } + } + /** + * Detect whether `name` has a definition. Equivalent to + * `get(name) != null`. + */ + + + has(name) { + return this.current.hasOwnProperty(name) || this.builtins.hasOwnProperty(name); + } + /** + * Get the current value of a name, or `undefined` if there is no value. + * + * Note: Do not use `if (namespace.get(...))` to detect whether a macro + * is defined, as the definition may be the empty string which evaluates + * to `false` in JavaScript. Use `if (namespace.get(...) != null)` or + * `if (namespace.has(...))`. + */ + + + get(name) { + if (this.current.hasOwnProperty(name)) { + return this.current[name]; + } else { + return this.builtins[name]; + } + } + /** + * Set the current value of a name, and optionally set it globally too. + * Local set() sets the current value and (when appropriate) adds an undo + * operation to the undo stack. Global set() may change the undo + * operation at every level, so takes time linear in their number. + */ + + + set(name, value, global) { + if (global === void 0) { + global = false; + } + + if (global) { + // Global set is equivalent to setting in all groups. Simulate this + // by destroying any undos currently scheduled for this name, + // and adding an undo with the *new* value (in case it later gets + // locally reset within this environment). + for (var i = 0; i < this.undefStack.length; i++) { + delete this.undefStack[i][name]; + } + + if (this.undefStack.length > 0) { + this.undefStack[this.undefStack.length - 1][name] = value; + } + } else { + // Undo this set at end of this group (possibly to `undefined`), + // unless an undo is already in place, in which case that older + // value is the correct one. + var top = this.undefStack[this.undefStack.length - 1]; + + if (top && !top.hasOwnProperty(name)) { + top[name] = this.current[name]; + } + } + + this.current[name] = value; + } + +} + +/** + * Predefined macros for KaTeX. + * This can be used to define some commands in terms of others. + */ +var macros = _macros; +// macro tools + +defineMacro("\\noexpand", function (context) { + // The expansion is the token itself; but that token is interpreted + // as if its meaning were ‘\relax’ if it is a control sequence that + // would ordinarily be expanded by TeX’s expansion rules. + var t = context.popToken(); + + if (context.isExpandable(t.text)) { + t.noexpand = true; + t.treatAsRelax = true; + } + + return { + tokens: [t], + numArgs: 0 + }; +}); +defineMacro("\\expandafter", function (context) { + // TeX first reads the token that comes immediately after \expandafter, + // without expanding it; let’s call this token t. Then TeX reads the + // token that comes after t (and possibly more tokens, if that token + // has an argument), replacing it by its expansion. Finally TeX puts + // t back in front of that expansion. + var t = context.popToken(); + context.expandOnce(true); // expand only an expandable token + + return { + tokens: [t], + numArgs: 0 + }; +}); // LaTeX's \@firstoftwo{#1}{#2} expands to #1, skipping #2 +// TeX source: \long\def\@firstoftwo#1#2{#1} + +defineMacro("\\@firstoftwo", function (context) { + var args = context.consumeArgs(2); + return { + tokens: args[0], + numArgs: 0 + }; +}); // LaTeX's \@secondoftwo{#1}{#2} expands to #2, skipping #1 +// TeX source: \long\def\@secondoftwo#1#2{#2} + +defineMacro("\\@secondoftwo", function (context) { + var args = context.consumeArgs(2); + return { + tokens: args[1], + numArgs: 0 + }; +}); // LaTeX's \@ifnextchar{#1}{#2}{#3} looks ahead to the next (unexpanded) +// symbol that isn't a space, consuming any spaces but not consuming the +// first nonspace character. If that nonspace character matches #1, then +// the macro expands to #2; otherwise, it expands to #3. + +defineMacro("\\@ifnextchar", function (context) { + var args = context.consumeArgs(3); // symbol, if, else + + context.consumeSpaces(); + var nextToken = context.future(); + + if (args[0].length === 1 && args[0][0].text === nextToken.text) { + return { + tokens: args[1], + numArgs: 0 + }; + } else { + return { + tokens: args[2], + numArgs: 0 + }; + } +}); // LaTeX's \@ifstar{#1}{#2} looks ahead to the next (unexpanded) symbol. +// If it is `*`, then it consumes the symbol, and the macro expands to #1; +// otherwise, the macro expands to #2 (without consuming the symbol). +// TeX source: \def\@ifstar#1{\@ifnextchar *{\@firstoftwo{#1}}} + +defineMacro("\\@ifstar", "\\@ifnextchar *{\\@firstoftwo{#1}}"); // LaTeX's \TextOrMath{#1}{#2} expands to #1 in text mode, #2 in math mode + +defineMacro("\\TextOrMath", function (context) { + var args = context.consumeArgs(2); + + if (context.mode === 'text') { + return { + tokens: args[0], + numArgs: 0 + }; + } else { + return { + tokens: args[1], + numArgs: 0 + }; + } +}); // Lookup table for parsing numbers in base 8 through 16 + +var digitToNumber = { + "0": 0, + "1": 1, + "2": 2, + "3": 3, + "4": 4, + "5": 5, + "6": 6, + "7": 7, + "8": 8, + "9": 9, + "a": 10, + "A": 10, + "b": 11, + "B": 11, + "c": 12, + "C": 12, + "d": 13, + "D": 13, + "e": 14, + "E": 14, + "f": 15, + "F": 15 +}; // TeX \char makes a literal character (catcode 12) using the following forms: +// (see The TeXBook, p. 43) +// \char123 -- decimal +// \char'123 -- octal +// \char"123 -- hex +// \char`x -- character that can be written (i.e. isn't active) +// \char`\x -- character that cannot be written (e.g. %) +// These all refer to characters from the font, so we turn them into special +// calls to a function \@char dealt with in the Parser. + +defineMacro("\\char", function (context) { + var token = context.popToken(); + var base; + var number = ''; + + if (token.text === "'") { + base = 8; + token = context.popToken(); + } else if (token.text === '"') { + base = 16; + token = context.popToken(); + } else if (token.text === "`") { + token = context.popToken(); + + if (token.text[0] === "\\") { + number = token.text.charCodeAt(1); + } else if (token.text === "EOF") { + throw new ParseError("\\char` missing argument"); + } else { + number = token.text.charCodeAt(0); + } + } else { + base = 10; + } + + if (base) { + // Parse a number in the given base, starting with first `token`. + number = digitToNumber[token.text]; + + if (number == null || number >= base) { + throw new ParseError("Invalid base-" + base + " digit " + token.text); + } + + var digit; + + while ((digit = digitToNumber[context.future().text]) != null && digit < base) { + number *= base; + number += digit; + context.popToken(); + } + } + + return "\\@char{" + number + "}"; +}); // \newcommand{\macro}[args]{definition} +// \renewcommand{\macro}[args]{definition} +// TODO: Optional arguments: \newcommand{\macro}[args][default]{definition} + +var newcommand = (context, existsOK, nonexistsOK) => { + var arg = context.consumeArg().tokens; + + if (arg.length !== 1) { + throw new ParseError("\\newcommand's first argument must be a macro name"); + } + + var name = arg[0].text; + var exists = context.isDefined(name); + + if (exists && !existsOK) { + throw new ParseError("\\newcommand{" + name + "} attempting to redefine " + (name + "; use \\renewcommand")); + } + + if (!exists && !nonexistsOK) { + throw new ParseError("\\renewcommand{" + name + "} when command " + name + " " + "does not yet exist; use \\newcommand"); + } + + var numArgs = 0; + arg = context.consumeArg().tokens; + + if (arg.length === 1 && arg[0].text === "[") { + var argText = ''; + var token = context.expandNextToken(); + + while (token.text !== "]" && token.text !== "EOF") { + // TODO: Should properly expand arg, e.g., ignore {}s + argText += token.text; + token = context.expandNextToken(); + } + + if (!argText.match(/^\s*[0-9]+\s*$/)) { + throw new ParseError("Invalid number of arguments: " + argText); + } + + numArgs = parseInt(argText); + arg = context.consumeArg().tokens; + } // Final arg is the expansion of the macro + + + context.macros.set(name, { + tokens: arg, + numArgs + }); + return ''; +}; + +defineMacro("\\newcommand", context => newcommand(context, false, true)); +defineMacro("\\renewcommand", context => newcommand(context, true, false)); +defineMacro("\\providecommand", context => newcommand(context, true, true)); // terminal (console) tools + +defineMacro("\\message", context => { + var arg = context.consumeArgs(1)[0]; // eslint-disable-next-line no-console + + console.log(arg.reverse().map(token => token.text).join("")); + return ''; +}); +defineMacro("\\errmessage", context => { + var arg = context.consumeArgs(1)[0]; // eslint-disable-next-line no-console + + console.error(arg.reverse().map(token => token.text).join("")); + return ''; +}); +defineMacro("\\show", context => { + var tok = context.popToken(); + var name = tok.text; // eslint-disable-next-line no-console + + console.log(tok, context.macros.get(name), functions[name], symbols.math[name], symbols.text[name]); + return ''; +}); ////////////////////////////////////////////////////////////////////// +// Grouping +// \let\bgroup={ \let\egroup=} + +defineMacro("\\bgroup", "{"); +defineMacro("\\egroup", "}"); // Symbols from latex.ltx: +// \def~{\nobreakspace{}} +// \def\lq{`} +// \def\rq{'} +// \def \aa {\r a} +// \def \AA {\r A} + +defineMacro("~", "\\nobreakspace"); +defineMacro("\\lq", "`"); +defineMacro("\\rq", "'"); +defineMacro("\\aa", "\\r a"); +defineMacro("\\AA", "\\r A"); // Copyright (C) and registered (R) symbols. Use raw symbol in MathML. +// \DeclareTextCommandDefault{\textcopyright}{\textcircled{c}} +// \DeclareTextCommandDefault{\textregistered}{\textcircled{% +// \check@mathfonts\fontsize\sf@size\z@\math@fontsfalse\selectfont R}} +// \DeclareRobustCommand{\copyright}{% +// \ifmmode{\nfss@text{\textcopyright}}\else\textcopyright\fi} + +defineMacro("\\textcopyright", "\\html@mathml{\\textcircled{c}}{\\char`©}"); +defineMacro("\\copyright", "\\TextOrMath{\\textcopyright}{\\text{\\textcopyright}}"); +defineMacro("\\textregistered", "\\html@mathml{\\textcircled{\\scriptsize R}}{\\char`®}"); // Characters omitted from Unicode range 1D400–1D7FF + +defineMacro("\u212C", "\\mathscr{B}"); // script + +defineMacro("\u2130", "\\mathscr{E}"); +defineMacro("\u2131", "\\mathscr{F}"); +defineMacro("\u210B", "\\mathscr{H}"); +defineMacro("\u2110", "\\mathscr{I}"); +defineMacro("\u2112", "\\mathscr{L}"); +defineMacro("\u2133", "\\mathscr{M}"); +defineMacro("\u211B", "\\mathscr{R}"); +defineMacro("\u212D", "\\mathfrak{C}"); // Fraktur + +defineMacro("\u210C", "\\mathfrak{H}"); +defineMacro("\u2128", "\\mathfrak{Z}"); // Define \Bbbk with a macro that works in both HTML and MathML. + +defineMacro("\\Bbbk", "\\Bbb{k}"); // Unicode middle dot +// The KaTeX fonts do not contain U+00B7. Instead, \cdotp displays +// the dot at U+22C5 and gives it punct spacing. + +defineMacro("\u00b7", "\\cdotp"); // \llap and \rlap render their contents in text mode + +defineMacro("\\llap", "\\mathllap{\\textrm{#1}}"); +defineMacro("\\rlap", "\\mathrlap{\\textrm{#1}}"); +defineMacro("\\clap", "\\mathclap{\\textrm{#1}}"); // \mathstrut from the TeXbook, p 360 + +defineMacro("\\mathstrut", "\\vphantom{(}"); // \underbar from TeXbook p 353 + +defineMacro("\\underbar", "\\underline{\\text{#1}}"); // \not is defined by base/fontmath.ltx via +// \DeclareMathSymbol{\not}{\mathrel}{symbols}{"36} +// It's thus treated like a \mathrel, but defined by a symbol that has zero +// width but extends to the right. We use \rlap to get that spacing. +// For MathML we write U+0338 here. buildMathML.js will then do the overlay. + +defineMacro("\\not", '\\html@mathml{\\mathrel{\\mathrlap\\@not}}{\\char"338}'); // Negated symbols from base/fontmath.ltx: +// \def\neq{\not=} \let\ne=\neq +// \DeclareRobustCommand +// \notin{\mathrel{\m@th\mathpalette\c@ncel\in}} +// \def\c@ncel#1#2{\m@th\ooalign{$\hfil#1\mkern1mu/\hfil$\crcr$#1#2$}} + +defineMacro("\\neq", "\\html@mathml{\\mathrel{\\not=}}{\\mathrel{\\char`≠}}"); +defineMacro("\\ne", "\\neq"); +defineMacro("\u2260", "\\neq"); +defineMacro("\\notin", "\\html@mathml{\\mathrel{{\\in}\\mathllap{/\\mskip1mu}}}" + "{\\mathrel{\\char`∉}}"); +defineMacro("\u2209", "\\notin"); // Unicode stacked relations + +defineMacro("\u2258", "\\html@mathml{" + "\\mathrel{=\\kern{-1em}\\raisebox{0.4em}{$\\scriptsize\\frown$}}" + "}{\\mathrel{\\char`\u2258}}"); +defineMacro("\u2259", "\\html@mathml{\\stackrel{\\tiny\\wedge}{=}}{\\mathrel{\\char`\u2258}}"); +defineMacro("\u225A", "\\html@mathml{\\stackrel{\\tiny\\vee}{=}}{\\mathrel{\\char`\u225A}}"); +defineMacro("\u225B", "\\html@mathml{\\stackrel{\\scriptsize\\star}{=}}" + "{\\mathrel{\\char`\u225B}}"); +defineMacro("\u225D", "\\html@mathml{\\stackrel{\\tiny\\mathrm{def}}{=}}" + "{\\mathrel{\\char`\u225D}}"); +defineMacro("\u225E", "\\html@mathml{\\stackrel{\\tiny\\mathrm{m}}{=}}" + "{\\mathrel{\\char`\u225E}}"); +defineMacro("\u225F", "\\html@mathml{\\stackrel{\\tiny?}{=}}{\\mathrel{\\char`\u225F}}"); // Misc Unicode + +defineMacro("\u27C2", "\\perp"); +defineMacro("\u203C", "\\mathclose{!\\mkern-0.8mu!}"); +defineMacro("\u220C", "\\notni"); +defineMacro("\u231C", "\\ulcorner"); +defineMacro("\u231D", "\\urcorner"); +defineMacro("\u231E", "\\llcorner"); +defineMacro("\u231F", "\\lrcorner"); +defineMacro("\u00A9", "\\copyright"); +defineMacro("\u00AE", "\\textregistered"); +defineMacro("\uFE0F", "\\textregistered"); // The KaTeX fonts have corners at codepoints that don't match Unicode. +// For MathML purposes, use the Unicode code point. + +defineMacro("\\ulcorner", "\\html@mathml{\\@ulcorner}{\\mathop{\\char\"231c}}"); +defineMacro("\\urcorner", "\\html@mathml{\\@urcorner}{\\mathop{\\char\"231d}}"); +defineMacro("\\llcorner", "\\html@mathml{\\@llcorner}{\\mathop{\\char\"231e}}"); +defineMacro("\\lrcorner", "\\html@mathml{\\@lrcorner}{\\mathop{\\char\"231f}}"); ////////////////////////////////////////////////////////////////////// +// LaTeX_2ε +// \vdots{\vbox{\baselineskip4\p@ \lineskiplimit\z@ +// \kern6\p@\hbox{.}\hbox{.}\hbox{.}}} +// We'll call \varvdots, which gets a glyph from symbols.js. +// The zero-width rule gets us an equivalent to the vertical 6pt kern. + +defineMacro("\\vdots", "\\mathord{\\varvdots\\rule{0pt}{15pt}}"); +defineMacro("\u22ee", "\\vdots"); ////////////////////////////////////////////////////////////////////// +// amsmath.sty +// http://mirrors.concertpass.com/tex-archive/macros/latex/required/amsmath/amsmath.pdf +// Italic Greek capital letters. AMS defines these with \DeclareMathSymbol, +// but they are equivalent to \mathit{\Letter}. + +defineMacro("\\varGamma", "\\mathit{\\Gamma}"); +defineMacro("\\varDelta", "\\mathit{\\Delta}"); +defineMacro("\\varTheta", "\\mathit{\\Theta}"); +defineMacro("\\varLambda", "\\mathit{\\Lambda}"); +defineMacro("\\varXi", "\\mathit{\\Xi}"); +defineMacro("\\varPi", "\\mathit{\\Pi}"); +defineMacro("\\varSigma", "\\mathit{\\Sigma}"); +defineMacro("\\varUpsilon", "\\mathit{\\Upsilon}"); +defineMacro("\\varPhi", "\\mathit{\\Phi}"); +defineMacro("\\varPsi", "\\mathit{\\Psi}"); +defineMacro("\\varOmega", "\\mathit{\\Omega}"); //\newcommand{\substack}[1]{\subarray{c}#1\endsubarray} + +defineMacro("\\substack", "\\begin{subarray}{c}#1\\end{subarray}"); // \renewcommand{\colon}{\nobreak\mskip2mu\mathpunct{}\nonscript +// \mkern-\thinmuskip{:}\mskip6muplus1mu\relax} + +defineMacro("\\colon", "\\nobreak\\mskip2mu\\mathpunct{}" + "\\mathchoice{\\mkern-3mu}{\\mkern-3mu}{}{}{:}\\mskip6mu"); // \newcommand{\boxed}[1]{\fbox{\m@th$\displaystyle#1$}} + +defineMacro("\\boxed", "\\fbox{$\\displaystyle{#1}$}"); // \def\iff{\DOTSB\;\Longleftrightarrow\;} +// \def\implies{\DOTSB\;\Longrightarrow\;} +// \def\impliedby{\DOTSB\;\Longleftarrow\;} + +defineMacro("\\iff", "\\DOTSB\\;\\Longleftrightarrow\\;"); +defineMacro("\\implies", "\\DOTSB\\;\\Longrightarrow\\;"); +defineMacro("\\impliedby", "\\DOTSB\\;\\Longleftarrow\\;"); // AMSMath's automatic \dots, based on \mdots@@ macro. + +var dotsByToken = { + ',': '\\dotsc', + '\\not': '\\dotsb', + // \keybin@ checks for the following: + '+': '\\dotsb', + '=': '\\dotsb', + '<': '\\dotsb', + '>': '\\dotsb', + '-': '\\dotsb', + '*': '\\dotsb', + ':': '\\dotsb', + // Symbols whose definition starts with \DOTSB: + '\\DOTSB': '\\dotsb', + '\\coprod': '\\dotsb', + '\\bigvee': '\\dotsb', + '\\bigwedge': '\\dotsb', + '\\biguplus': '\\dotsb', + '\\bigcap': '\\dotsb', + '\\bigcup': '\\dotsb', + '\\prod': '\\dotsb', + '\\sum': '\\dotsb', + '\\bigotimes': '\\dotsb', + '\\bigoplus': '\\dotsb', + '\\bigodot': '\\dotsb', + '\\bigsqcup': '\\dotsb', + '\\And': '\\dotsb', + '\\longrightarrow': '\\dotsb', + '\\Longrightarrow': '\\dotsb', + '\\longleftarrow': '\\dotsb', + '\\Longleftarrow': '\\dotsb', + '\\longleftrightarrow': '\\dotsb', + '\\Longleftrightarrow': '\\dotsb', + '\\mapsto': '\\dotsb', + '\\longmapsto': '\\dotsb', + '\\hookrightarrow': '\\dotsb', + '\\doteq': '\\dotsb', + // Symbols whose definition starts with \mathbin: + '\\mathbin': '\\dotsb', + // Symbols whose definition starts with \mathrel: + '\\mathrel': '\\dotsb', + '\\relbar': '\\dotsb', + '\\Relbar': '\\dotsb', + '\\xrightarrow': '\\dotsb', + '\\xleftarrow': '\\dotsb', + // Symbols whose definition starts with \DOTSI: + '\\DOTSI': '\\dotsi', + '\\int': '\\dotsi', + '\\oint': '\\dotsi', + '\\iint': '\\dotsi', + '\\iiint': '\\dotsi', + '\\iiiint': '\\dotsi', + '\\idotsint': '\\dotsi', + // Symbols whose definition starts with \DOTSX: + '\\DOTSX': '\\dotsx' +}; +defineMacro("\\dots", function (context) { + // TODO: If used in text mode, should expand to \textellipsis. + // However, in KaTeX, \textellipsis and \ldots behave the same + // (in text mode), and it's unlikely we'd see any of the math commands + // that affect the behavior of \dots when in text mode. So fine for now + // (until we support \ifmmode ... \else ... \fi). + var thedots = '\\dotso'; + var next = context.expandAfterFuture().text; + + if (next in dotsByToken) { + thedots = dotsByToken[next]; + } else if (next.substr(0, 4) === '\\not') { + thedots = '\\dotsb'; + } else if (next in symbols.math) { + if (utils.contains(['bin', 'rel'], symbols.math[next].group)) { + thedots = '\\dotsb'; + } + } + + return thedots; +}); +var spaceAfterDots = { + // \rightdelim@ checks for the following: + ')': true, + ']': true, + '\\rbrack': true, + '\\}': true, + '\\rbrace': true, + '\\rangle': true, + '\\rceil': true, + '\\rfloor': true, + '\\rgroup': true, + '\\rmoustache': true, + '\\right': true, + '\\bigr': true, + '\\biggr': true, + '\\Bigr': true, + '\\Biggr': true, + // \extra@ also tests for the following: + '$': true, + // \extrap@ checks for the following: + ';': true, + '.': true, + ',': true +}; +defineMacro("\\dotso", function (context) { + var next = context.future().text; + + if (next in spaceAfterDots) { + return "\\ldots\\,"; + } else { + return "\\ldots"; + } +}); +defineMacro("\\dotsc", function (context) { + var next = context.future().text; // \dotsc uses \extra@ but not \extrap@, instead specially checking for + // ';' and '.', but doesn't check for ','. + + if (next in spaceAfterDots && next !== ',') { + return "\\ldots\\,"; + } else { + return "\\ldots"; + } +}); +defineMacro("\\cdots", function (context) { + var next = context.future().text; + + if (next in spaceAfterDots) { + return "\\@cdots\\,"; + } else { + return "\\@cdots"; + } +}); +defineMacro("\\dotsb", "\\cdots"); +defineMacro("\\dotsm", "\\cdots"); +defineMacro("\\dotsi", "\\!\\cdots"); // amsmath doesn't actually define \dotsx, but \dots followed by a macro +// starting with \DOTSX implies \dotso, and then \extra@ detects this case +// and forces the added `\,`. + +defineMacro("\\dotsx", "\\ldots\\,"); // \let\DOTSI\relax +// \let\DOTSB\relax +// \let\DOTSX\relax + +defineMacro("\\DOTSI", "\\relax"); +defineMacro("\\DOTSB", "\\relax"); +defineMacro("\\DOTSX", "\\relax"); // Spacing, based on amsmath.sty's override of LaTeX defaults +// \DeclareRobustCommand{\tmspace}[3]{% +// \ifmmode\mskip#1#2\else\kern#1#3\fi\relax} + +defineMacro("\\tmspace", "\\TextOrMath{\\kern#1#3}{\\mskip#1#2}\\relax"); // \renewcommand{\,}{\tmspace+\thinmuskip{.1667em}} +// TODO: math mode should use \thinmuskip + +defineMacro("\\,", "\\tmspace+{3mu}{.1667em}"); // \let\thinspace\, + +defineMacro("\\thinspace", "\\,"); // \def\>{\mskip\medmuskip} +// \renewcommand{\:}{\tmspace+\medmuskip{.2222em}} +// TODO: \> and math mode of \: should use \medmuskip = 4mu plus 2mu minus 4mu + +defineMacro("\\>", "\\mskip{4mu}"); +defineMacro("\\:", "\\tmspace+{4mu}{.2222em}"); // \let\medspace\: + +defineMacro("\\medspace", "\\:"); // \renewcommand{\;}{\tmspace+\thickmuskip{.2777em}} +// TODO: math mode should use \thickmuskip = 5mu plus 5mu + +defineMacro("\\;", "\\tmspace+{5mu}{.2777em}"); // \let\thickspace\; + +defineMacro("\\thickspace", "\\;"); // \renewcommand{\!}{\tmspace-\thinmuskip{.1667em}} +// TODO: math mode should use \thinmuskip + +defineMacro("\\!", "\\tmspace-{3mu}{.1667em}"); // \let\negthinspace\! + +defineMacro("\\negthinspace", "\\!"); // \newcommand{\negmedspace}{\tmspace-\medmuskip{.2222em}} +// TODO: math mode should use \medmuskip + +defineMacro("\\negmedspace", "\\tmspace-{4mu}{.2222em}"); // \newcommand{\negthickspace}{\tmspace-\thickmuskip{.2777em}} +// TODO: math mode should use \thickmuskip + +defineMacro("\\negthickspace", "\\tmspace-{5mu}{.277em}"); // \def\enspace{\kern.5em } + +defineMacro("\\enspace", "\\kern.5em "); // \def\enskip{\hskip.5em\relax} + +defineMacro("\\enskip", "\\hskip.5em\\relax"); // \def\quad{\hskip1em\relax} + +defineMacro("\\quad", "\\hskip1em\\relax"); // \def\qquad{\hskip2em\relax} + +defineMacro("\\qquad", "\\hskip2em\\relax"); // \tag@in@display form of \tag + +defineMacro("\\tag", "\\@ifstar\\tag@literal\\tag@paren"); +defineMacro("\\tag@paren", "\\tag@literal{({#1})}"); +defineMacro("\\tag@literal", context => { + if (context.macros.get("\\df@tag")) { + throw new ParseError("Multiple \\tag"); + } + + return "\\gdef\\df@tag{\\text{#1}}"; +}); // \renewcommand{\bmod}{\nonscript\mskip-\medmuskip\mkern5mu\mathbin +// {\operator@font mod}\penalty900 +// \mkern5mu\nonscript\mskip-\medmuskip} +// \newcommand{\pod}[1]{\allowbreak +// \if@display\mkern18mu\else\mkern8mu\fi(#1)} +// \renewcommand{\pmod}[1]{\pod{{\operator@font mod}\mkern6mu#1}} +// \newcommand{\mod}[1]{\allowbreak\if@display\mkern18mu +// \else\mkern12mu\fi{\operator@font mod}\,\,#1} +// TODO: math mode should use \medmuskip = 4mu plus 2mu minus 4mu + +defineMacro("\\bmod", "\\mathchoice{\\mskip1mu}{\\mskip1mu}{\\mskip5mu}{\\mskip5mu}" + "\\mathbin{\\rm mod}" + "\\mathchoice{\\mskip1mu}{\\mskip1mu}{\\mskip5mu}{\\mskip5mu}"); +defineMacro("\\pod", "\\allowbreak" + "\\mathchoice{\\mkern18mu}{\\mkern8mu}{\\mkern8mu}{\\mkern8mu}(#1)"); +defineMacro("\\pmod", "\\pod{{\\rm mod}\\mkern6mu#1}"); +defineMacro("\\mod", "\\allowbreak" + "\\mathchoice{\\mkern18mu}{\\mkern12mu}{\\mkern12mu}{\\mkern12mu}" + "{\\rm mod}\\,\\,#1"); // \pmb -- A simulation of bold. +// The version in ambsy.sty works by typesetting three copies of the argument +// with small offsets. We use two copies. We omit the vertical offset because +// of rendering problems that makeVList encounters in Safari. + +defineMacro("\\pmb", "\\html@mathml{" + "\\@binrel{#1}{\\mathrlap{#1}\\kern0.5px#1}}" + "{\\mathbf{#1}}"); ////////////////////////////////////////////////////////////////////// +// LaTeX source2e +// \expandafter\let\expandafter\@normalcr +// \csname\expandafter\@gobble\string\\ \endcsname +// \DeclareRobustCommand\newline{\@normalcr\relax} + +defineMacro("\\newline", "\\\\\\relax"); // \def\TeX{T\kern-.1667em\lower.5ex\hbox{E}\kern-.125emX\@} +// TODO: Doesn't normally work in math mode because \@ fails. KaTeX doesn't +// support \@ yet, so that's omitted, and we add \text so that the result +// doesn't look funny in math mode. + +defineMacro("\\TeX", "\\textrm{\\html@mathml{" + "T\\kern-.1667em\\raisebox{-.5ex}{E}\\kern-.125emX" + "}{TeX}}"); // \DeclareRobustCommand{\LaTeX}{L\kern-.36em% +// {\sbox\z@ T% +// \vbox to\ht\z@{\hbox{\check@mathfonts +// \fontsize\sf@size\z@ +// \math@fontsfalse\selectfont +// A}% +// \vss}% +// }% +// \kern-.15em% +// \TeX} +// This code aligns the top of the A with the T (from the perspective of TeX's +// boxes, though visually the A appears to extend above slightly). +// We compute the corresponding \raisebox when A is rendered in \normalsize +// \scriptstyle, which has a scale factor of 0.7 (see Options.js). + +var latexRaiseA = fontMetricsData['Main-Regular']["T".charCodeAt(0)][1] - 0.7 * fontMetricsData['Main-Regular']["A".charCodeAt(0)][1] + "em"; +defineMacro("\\LaTeX", "\\textrm{\\html@mathml{" + ("L\\kern-.36em\\raisebox{" + latexRaiseA + "}{\\scriptstyle A}") + "\\kern-.15em\\TeX}{LaTeX}}"); // New KaTeX logo based on tweaking LaTeX logo + +defineMacro("\\KaTeX", "\\textrm{\\html@mathml{" + ("K\\kern-.17em\\raisebox{" + latexRaiseA + "}{\\scriptstyle A}") + "\\kern-.15em\\TeX}{KaTeX}}"); // \DeclareRobustCommand\hspace{\@ifstar\@hspacer\@hspace} +// \def\@hspace#1{\hskip #1\relax} +// \def\@hspacer#1{\vrule \@width\z@\nobreak +// \hskip #1\hskip \z@skip} + +defineMacro("\\hspace", "\\@ifstar\\@hspacer\\@hspace"); +defineMacro("\\@hspace", "\\hskip #1\\relax"); +defineMacro("\\@hspacer", "\\rule{0pt}{0pt}\\hskip #1\\relax"); ////////////////////////////////////////////////////////////////////// +// mathtools.sty +//\providecommand\ordinarycolon{:} + +defineMacro("\\ordinarycolon", ":"); //\def\vcentcolon{\mathrel{\mathop\ordinarycolon}} +//TODO(edemaine): Not yet centered. Fix via \raisebox or #726 + +defineMacro("\\vcentcolon", "\\mathrel{\\mathop\\ordinarycolon}"); // \providecommand*\dblcolon{\vcentcolon\mathrel{\mkern-.9mu}\vcentcolon} + +defineMacro("\\dblcolon", "\\html@mathml{" + "\\mathrel{\\vcentcolon\\mathrel{\\mkern-.9mu}\\vcentcolon}}" + "{\\mathop{\\char\"2237}}"); // \providecommand*\coloneqq{\vcentcolon\mathrel{\mkern-1.2mu}=} + +defineMacro("\\coloneqq", "\\html@mathml{" + "\\mathrel{\\vcentcolon\\mathrel{\\mkern-1.2mu}=}}" + "{\\mathop{\\char\"2254}}"); // ≔ +// \providecommand*\Coloneqq{\dblcolon\mathrel{\mkern-1.2mu}=} + +defineMacro("\\Coloneqq", "\\html@mathml{" + "\\mathrel{\\dblcolon\\mathrel{\\mkern-1.2mu}=}}" + "{\\mathop{\\char\"2237\\char\"3d}}"); // \providecommand*\coloneq{\vcentcolon\mathrel{\mkern-1.2mu}\mathrel{-}} + +defineMacro("\\coloneq", "\\html@mathml{" + "\\mathrel{\\vcentcolon\\mathrel{\\mkern-1.2mu}\\mathrel{-}}}" + "{\\mathop{\\char\"3a\\char\"2212}}"); // \providecommand*\Coloneq{\dblcolon\mathrel{\mkern-1.2mu}\mathrel{-}} + +defineMacro("\\Coloneq", "\\html@mathml{" + "\\mathrel{\\dblcolon\\mathrel{\\mkern-1.2mu}\\mathrel{-}}}" + "{\\mathop{\\char\"2237\\char\"2212}}"); // \providecommand*\eqqcolon{=\mathrel{\mkern-1.2mu}\vcentcolon} + +defineMacro("\\eqqcolon", "\\html@mathml{" + "\\mathrel{=\\mathrel{\\mkern-1.2mu}\\vcentcolon}}" + "{\\mathop{\\char\"2255}}"); // ≕ +// \providecommand*\Eqqcolon{=\mathrel{\mkern-1.2mu}\dblcolon} + +defineMacro("\\Eqqcolon", "\\html@mathml{" + "\\mathrel{=\\mathrel{\\mkern-1.2mu}\\dblcolon}}" + "{\\mathop{\\char\"3d\\char\"2237}}"); // \providecommand*\eqcolon{\mathrel{-}\mathrel{\mkern-1.2mu}\vcentcolon} + +defineMacro("\\eqcolon", "\\html@mathml{" + "\\mathrel{\\mathrel{-}\\mathrel{\\mkern-1.2mu}\\vcentcolon}}" + "{\\mathop{\\char\"2239}}"); // \providecommand*\Eqcolon{\mathrel{-}\mathrel{\mkern-1.2mu}\dblcolon} + +defineMacro("\\Eqcolon", "\\html@mathml{" + "\\mathrel{\\mathrel{-}\\mathrel{\\mkern-1.2mu}\\dblcolon}}" + "{\\mathop{\\char\"2212\\char\"2237}}"); // \providecommand*\colonapprox{\vcentcolon\mathrel{\mkern-1.2mu}\approx} + +defineMacro("\\colonapprox", "\\html@mathml{" + "\\mathrel{\\vcentcolon\\mathrel{\\mkern-1.2mu}\\approx}}" + "{\\mathop{\\char\"3a\\char\"2248}}"); // \providecommand*\Colonapprox{\dblcolon\mathrel{\mkern-1.2mu}\approx} + +defineMacro("\\Colonapprox", "\\html@mathml{" + "\\mathrel{\\dblcolon\\mathrel{\\mkern-1.2mu}\\approx}}" + "{\\mathop{\\char\"2237\\char\"2248}}"); // \providecommand*\colonsim{\vcentcolon\mathrel{\mkern-1.2mu}\sim} + +defineMacro("\\colonsim", "\\html@mathml{" + "\\mathrel{\\vcentcolon\\mathrel{\\mkern-1.2mu}\\sim}}" + "{\\mathop{\\char\"3a\\char\"223c}}"); // \providecommand*\Colonsim{\dblcolon\mathrel{\mkern-1.2mu}\sim} + +defineMacro("\\Colonsim", "\\html@mathml{" + "\\mathrel{\\dblcolon\\mathrel{\\mkern-1.2mu}\\sim}}" + "{\\mathop{\\char\"2237\\char\"223c}}"); // Some Unicode characters are implemented with macros to mathtools functions. + +defineMacro("\u2237", "\\dblcolon"); // :: + +defineMacro("\u2239", "\\eqcolon"); // -: + +defineMacro("\u2254", "\\coloneqq"); // := + +defineMacro("\u2255", "\\eqqcolon"); // =: + +defineMacro("\u2A74", "\\Coloneqq"); // ::= +////////////////////////////////////////////////////////////////////// +// colonequals.sty +// Alternate names for mathtools's macros: + +defineMacro("\\ratio", "\\vcentcolon"); +defineMacro("\\coloncolon", "\\dblcolon"); +defineMacro("\\colonequals", "\\coloneqq"); +defineMacro("\\coloncolonequals", "\\Coloneqq"); +defineMacro("\\equalscolon", "\\eqqcolon"); +defineMacro("\\equalscoloncolon", "\\Eqqcolon"); +defineMacro("\\colonminus", "\\coloneq"); +defineMacro("\\coloncolonminus", "\\Coloneq"); +defineMacro("\\minuscolon", "\\eqcolon"); +defineMacro("\\minuscoloncolon", "\\Eqcolon"); // \colonapprox name is same in mathtools and colonequals. + +defineMacro("\\coloncolonapprox", "\\Colonapprox"); // \colonsim name is same in mathtools and colonequals. + +defineMacro("\\coloncolonsim", "\\Colonsim"); // Additional macros, implemented by analogy with mathtools definitions: + +defineMacro("\\simcolon", "\\mathrel{\\sim\\mathrel{\\mkern-1.2mu}\\vcentcolon}"); +defineMacro("\\simcoloncolon", "\\mathrel{\\sim\\mathrel{\\mkern-1.2mu}\\dblcolon}"); +defineMacro("\\approxcolon", "\\mathrel{\\approx\\mathrel{\\mkern-1.2mu}\\vcentcolon}"); +defineMacro("\\approxcoloncolon", "\\mathrel{\\approx\\mathrel{\\mkern-1.2mu}\\dblcolon}"); // Present in newtxmath, pxfonts and txfonts + +defineMacro("\\notni", "\\html@mathml{\\not\\ni}{\\mathrel{\\char`\u220C}}"); +defineMacro("\\limsup", "\\DOTSB\\operatorname*{lim\\,sup}"); +defineMacro("\\liminf", "\\DOTSB\\operatorname*{lim\\,inf}"); ////////////////////////////////////////////////////////////////////// +// From amsopn.sty + +defineMacro("\\injlim", "\\DOTSB\\operatorname*{inj\\,lim}"); +defineMacro("\\projlim", "\\DOTSB\\operatorname*{proj\\,lim}"); +defineMacro("\\varlimsup", "\\DOTSB\\operatorname*{\\overline{lim}}"); +defineMacro("\\varliminf", "\\DOTSB\\operatorname*{\\underline{lim}}"); +defineMacro("\\varinjlim", "\\DOTSB\\operatorname*{\\underrightarrow{lim}}"); +defineMacro("\\varprojlim", "\\DOTSB\\operatorname*{\\underleftarrow{lim}}"); ////////////////////////////////////////////////////////////////////// +// MathML alternates for KaTeX glyphs in the Unicode private area + +defineMacro("\\gvertneqq", "\\html@mathml{\\@gvertneqq}{\u2269}"); +defineMacro("\\lvertneqq", "\\html@mathml{\\@lvertneqq}{\u2268}"); +defineMacro("\\ngeqq", "\\html@mathml{\\@ngeqq}{\u2271}"); +defineMacro("\\ngeqslant", "\\html@mathml{\\@ngeqslant}{\u2271}"); +defineMacro("\\nleqq", "\\html@mathml{\\@nleqq}{\u2270}"); +defineMacro("\\nleqslant", "\\html@mathml{\\@nleqslant}{\u2270}"); +defineMacro("\\nshortmid", "\\html@mathml{\\@nshortmid}{∤}"); +defineMacro("\\nshortparallel", "\\html@mathml{\\@nshortparallel}{∦}"); +defineMacro("\\nsubseteqq", "\\html@mathml{\\@nsubseteqq}{\u2288}"); +defineMacro("\\nsupseteqq", "\\html@mathml{\\@nsupseteqq}{\u2289}"); +defineMacro("\\varsubsetneq", "\\html@mathml{\\@varsubsetneq}{⊊}"); +defineMacro("\\varsubsetneqq", "\\html@mathml{\\@varsubsetneqq}{⫋}"); +defineMacro("\\varsupsetneq", "\\html@mathml{\\@varsupsetneq}{⊋}"); +defineMacro("\\varsupsetneqq", "\\html@mathml{\\@varsupsetneqq}{⫌}"); +defineMacro("\\imath", "\\html@mathml{\\@imath}{\u0131}"); +defineMacro("\\jmath", "\\html@mathml{\\@jmath}{\u0237}"); ////////////////////////////////////////////////////////////////////// +// stmaryrd and semantic +// The stmaryrd and semantic packages render the next four items by calling a +// glyph. Those glyphs do not exist in the KaTeX fonts. Hence the macros. + +defineMacro("\\llbracket", "\\html@mathml{" + "\\mathopen{[\\mkern-3.2mu[}}" + "{\\mathopen{\\char`\u27e6}}"); +defineMacro("\\rrbracket", "\\html@mathml{" + "\\mathclose{]\\mkern-3.2mu]}}" + "{\\mathclose{\\char`\u27e7}}"); +defineMacro("\u27e6", "\\llbracket"); // blackboard bold [ + +defineMacro("\u27e7", "\\rrbracket"); // blackboard bold ] + +defineMacro("\\lBrace", "\\html@mathml{" + "\\mathopen{\\{\\mkern-3.2mu[}}" + "{\\mathopen{\\char`\u2983}}"); +defineMacro("\\rBrace", "\\html@mathml{" + "\\mathclose{]\\mkern-3.2mu\\}}}" + "{\\mathclose{\\char`\u2984}}"); +defineMacro("\u2983", "\\lBrace"); // blackboard bold { + +defineMacro("\u2984", "\\rBrace"); // blackboard bold } +// TODO: Create variable sized versions of the last two items. I believe that +// will require new font glyphs. +// The stmaryrd function `\minuso` provides a "Plimsoll" symbol that +// superimposes the characters \circ and \mathminus. Used in chemistry. + +defineMacro("\\minuso", "\\mathbin{\\html@mathml{" + "{\\mathrlap{\\mathchoice{\\kern{0.145em}}{\\kern{0.145em}}" + "{\\kern{0.1015em}}{\\kern{0.0725em}}\\circ}{-}}}" + "{\\char`⦵}}"); +defineMacro("⦵", "\\minuso"); ////////////////////////////////////////////////////////////////////// +// texvc.sty +// The texvc package contains macros available in mediawiki pages. +// We omit the functions deprecated at +// https://en.wikipedia.org/wiki/Help:Displaying_a_formula#Deprecated_syntax +// We also omit texvc's \O, which conflicts with \text{\O} + +defineMacro("\\darr", "\\downarrow"); +defineMacro("\\dArr", "\\Downarrow"); +defineMacro("\\Darr", "\\Downarrow"); +defineMacro("\\lang", "\\langle"); +defineMacro("\\rang", "\\rangle"); +defineMacro("\\uarr", "\\uparrow"); +defineMacro("\\uArr", "\\Uparrow"); +defineMacro("\\Uarr", "\\Uparrow"); +defineMacro("\\N", "\\mathbb{N}"); +defineMacro("\\R", "\\mathbb{R}"); +defineMacro("\\Z", "\\mathbb{Z}"); +defineMacro("\\alef", "\\aleph"); +defineMacro("\\alefsym", "\\aleph"); +defineMacro("\\Alpha", "\\mathrm{A}"); +defineMacro("\\Beta", "\\mathrm{B}"); +defineMacro("\\bull", "\\bullet"); +defineMacro("\\Chi", "\\mathrm{X}"); +defineMacro("\\clubs", "\\clubsuit"); +defineMacro("\\cnums", "\\mathbb{C}"); +defineMacro("\\Complex", "\\mathbb{C}"); +defineMacro("\\Dagger", "\\ddagger"); +defineMacro("\\diamonds", "\\diamondsuit"); +defineMacro("\\empty", "\\emptyset"); +defineMacro("\\Epsilon", "\\mathrm{E}"); +defineMacro("\\Eta", "\\mathrm{H}"); +defineMacro("\\exist", "\\exists"); +defineMacro("\\harr", "\\leftrightarrow"); +defineMacro("\\hArr", "\\Leftrightarrow"); +defineMacro("\\Harr", "\\Leftrightarrow"); +defineMacro("\\hearts", "\\heartsuit"); +defineMacro("\\image", "\\Im"); +defineMacro("\\infin", "\\infty"); +defineMacro("\\Iota", "\\mathrm{I}"); +defineMacro("\\isin", "\\in"); +defineMacro("\\Kappa", "\\mathrm{K}"); +defineMacro("\\larr", "\\leftarrow"); +defineMacro("\\lArr", "\\Leftarrow"); +defineMacro("\\Larr", "\\Leftarrow"); +defineMacro("\\lrarr", "\\leftrightarrow"); +defineMacro("\\lrArr", "\\Leftrightarrow"); +defineMacro("\\Lrarr", "\\Leftrightarrow"); +defineMacro("\\Mu", "\\mathrm{M}"); +defineMacro("\\natnums", "\\mathbb{N}"); +defineMacro("\\Nu", "\\mathrm{N}"); +defineMacro("\\Omicron", "\\mathrm{O}"); +defineMacro("\\plusmn", "\\pm"); +defineMacro("\\rarr", "\\rightarrow"); +defineMacro("\\rArr", "\\Rightarrow"); +defineMacro("\\Rarr", "\\Rightarrow"); +defineMacro("\\real", "\\Re"); +defineMacro("\\reals", "\\mathbb{R}"); +defineMacro("\\Reals", "\\mathbb{R}"); +defineMacro("\\Rho", "\\mathrm{P}"); +defineMacro("\\sdot", "\\cdot"); +defineMacro("\\sect", "\\S"); +defineMacro("\\spades", "\\spadesuit"); +defineMacro("\\sub", "\\subset"); +defineMacro("\\sube", "\\subseteq"); +defineMacro("\\supe", "\\supseteq"); +defineMacro("\\Tau", "\\mathrm{T}"); +defineMacro("\\thetasym", "\\vartheta"); // TODO: defineMacro("\\varcoppa", "\\\mbox{\\coppa}"); + +defineMacro("\\weierp", "\\wp"); +defineMacro("\\Zeta", "\\mathrm{Z}"); ////////////////////////////////////////////////////////////////////// +// statmath.sty +// https://ctan.math.illinois.edu/macros/latex/contrib/statmath/statmath.pdf + +defineMacro("\\argmin", "\\DOTSB\\operatorname*{arg\\,min}"); +defineMacro("\\argmax", "\\DOTSB\\operatorname*{arg\\,max}"); +defineMacro("\\plim", "\\DOTSB\\mathop{\\operatorname{plim}}\\limits"); ////////////////////////////////////////////////////////////////////// +// braket.sty +// http://ctan.math.washington.edu/tex-archive/macros/latex/contrib/braket/braket.pdf + +defineMacro("\\bra", "\\mathinner{\\langle{#1}|}"); +defineMacro("\\ket", "\\mathinner{|{#1}\\rangle}"); +defineMacro("\\braket", "\\mathinner{\\langle{#1}\\rangle}"); +defineMacro("\\Bra", "\\left\\langle#1\\right|"); +defineMacro("\\Ket", "\\left|#1\\right\\rangle"); ////////////////////////////////////////////////////////////////////// +// actuarialangle.dtx + +defineMacro("\\angln", "{\\angl n}"); // Custom Khan Academy colors, should be moved to an optional package + +defineMacro("\\blue", "\\textcolor{##6495ed}{#1}"); +defineMacro("\\orange", "\\textcolor{##ffa500}{#1}"); +defineMacro("\\pink", "\\textcolor{##ff00af}{#1}"); +defineMacro("\\red", "\\textcolor{##df0030}{#1}"); +defineMacro("\\green", "\\textcolor{##28ae7b}{#1}"); +defineMacro("\\gray", "\\textcolor{gray}{#1}"); +defineMacro("\\purple", "\\textcolor{##9d38bd}{#1}"); +defineMacro("\\blueA", "\\textcolor{##ccfaff}{#1}"); +defineMacro("\\blueB", "\\textcolor{##80f6ff}{#1}"); +defineMacro("\\blueC", "\\textcolor{##63d9ea}{#1}"); +defineMacro("\\blueD", "\\textcolor{##11accd}{#1}"); +defineMacro("\\blueE", "\\textcolor{##0c7f99}{#1}"); +defineMacro("\\tealA", "\\textcolor{##94fff5}{#1}"); +defineMacro("\\tealB", "\\textcolor{##26edd5}{#1}"); +defineMacro("\\tealC", "\\textcolor{##01d1c1}{#1}"); +defineMacro("\\tealD", "\\textcolor{##01a995}{#1}"); +defineMacro("\\tealE", "\\textcolor{##208170}{#1}"); +defineMacro("\\greenA", "\\textcolor{##b6ffb0}{#1}"); +defineMacro("\\greenB", "\\textcolor{##8af281}{#1}"); +defineMacro("\\greenC", "\\textcolor{##74cf70}{#1}"); +defineMacro("\\greenD", "\\textcolor{##1fab54}{#1}"); +defineMacro("\\greenE", "\\textcolor{##0d923f}{#1}"); +defineMacro("\\goldA", "\\textcolor{##ffd0a9}{#1}"); +defineMacro("\\goldB", "\\textcolor{##ffbb71}{#1}"); +defineMacro("\\goldC", "\\textcolor{##ff9c39}{#1}"); +defineMacro("\\goldD", "\\textcolor{##e07d10}{#1}"); +defineMacro("\\goldE", "\\textcolor{##a75a05}{#1}"); +defineMacro("\\redA", "\\textcolor{##fca9a9}{#1}"); +defineMacro("\\redB", "\\textcolor{##ff8482}{#1}"); +defineMacro("\\redC", "\\textcolor{##f9685d}{#1}"); +defineMacro("\\redD", "\\textcolor{##e84d39}{#1}"); +defineMacro("\\redE", "\\textcolor{##bc2612}{#1}"); +defineMacro("\\maroonA", "\\textcolor{##ffbde0}{#1}"); +defineMacro("\\maroonB", "\\textcolor{##ff92c6}{#1}"); +defineMacro("\\maroonC", "\\textcolor{##ed5fa6}{#1}"); +defineMacro("\\maroonD", "\\textcolor{##ca337c}{#1}"); +defineMacro("\\maroonE", "\\textcolor{##9e034e}{#1}"); +defineMacro("\\purpleA", "\\textcolor{##ddd7ff}{#1}"); +defineMacro("\\purpleB", "\\textcolor{##c6b9fc}{#1}"); +defineMacro("\\purpleC", "\\textcolor{##aa87ff}{#1}"); +defineMacro("\\purpleD", "\\textcolor{##7854ab}{#1}"); +defineMacro("\\purpleE", "\\textcolor{##543b78}{#1}"); +defineMacro("\\mintA", "\\textcolor{##f5f9e8}{#1}"); +defineMacro("\\mintB", "\\textcolor{##edf2df}{#1}"); +defineMacro("\\mintC", "\\textcolor{##e0e5cc}{#1}"); +defineMacro("\\grayA", "\\textcolor{##f6f7f7}{#1}"); +defineMacro("\\grayB", "\\textcolor{##f0f1f2}{#1}"); +defineMacro("\\grayC", "\\textcolor{##e3e5e6}{#1}"); +defineMacro("\\grayD", "\\textcolor{##d6d8da}{#1}"); +defineMacro("\\grayE", "\\textcolor{##babec2}{#1}"); +defineMacro("\\grayF", "\\textcolor{##888d93}{#1}"); +defineMacro("\\grayG", "\\textcolor{##626569}{#1}"); +defineMacro("\\grayH", "\\textcolor{##3b3e40}{#1}"); +defineMacro("\\grayI", "\\textcolor{##21242c}{#1}"); +defineMacro("\\kaBlue", "\\textcolor{##314453}{#1}"); +defineMacro("\\kaGreen", "\\textcolor{##71B307}{#1}"); + +/** + * This file contains the “gullet” where macros are expanded + * until only non-macro tokens remain. + */ +// List of commands that act like macros but aren't defined as a macro, +// function, or symbol. Used in `isDefined`. +var implicitCommands = { + "\\relax": true, + // MacroExpander.js + "^": true, + // Parser.js + "_": true, + // Parser.js + "\\limits": true, + // Parser.js + "\\nolimits": true // Parser.js + +}; +class MacroExpander { + constructor(input, settings, mode) { + this.settings = void 0; + this.expansionCount = void 0; + this.lexer = void 0; + this.macros = void 0; + this.stack = void 0; + this.mode = void 0; + this.settings = settings; + this.expansionCount = 0; + this.feed(input); // Make new global namespace + + this.macros = new Namespace(macros, settings.macros); + this.mode = mode; + this.stack = []; // contains tokens in REVERSE order + } + /** + * Feed a new input string to the same MacroExpander + * (with existing macros etc.). + */ + + + feed(input) { + this.lexer = new Lexer(input, this.settings); + } + /** + * Switches between "text" and "math" modes. + */ + + + switchMode(newMode) { + this.mode = newMode; + } + /** + * Start a new group nesting within all namespaces. + */ + + + beginGroup() { + this.macros.beginGroup(); + } + /** + * End current group nesting within all namespaces. + */ + + + endGroup() { + this.macros.endGroup(); + } + /** + * Ends all currently nested groups (if any), restoring values before the + * groups began. Useful in case of an error in the middle of parsing. + */ + + + endGroups() { + this.macros.endGroups(); + } + /** + * Returns the topmost token on the stack, without expanding it. + * Similar in behavior to TeX's `\futurelet`. + */ + + + future() { + if (this.stack.length === 0) { + this.pushToken(this.lexer.lex()); + } + + return this.stack[this.stack.length - 1]; + } + /** + * Remove and return the next unexpanded token. + */ + + + popToken() { + this.future(); // ensure non-empty stack + + return this.stack.pop(); + } + /** + * Add a given token to the token stack. In particular, this get be used + * to put back a token returned from one of the other methods. + */ + + + pushToken(token) { + this.stack.push(token); + } + /** + * Append an array of tokens to the token stack. + */ + + + pushTokens(tokens) { + this.stack.push(...tokens); + } + /** + * Find an macro argument without expanding tokens and append the array of + * tokens to the token stack. Uses Token as a container for the result. + */ + + + scanArgument(isOptional) { + var start; + var end; + var tokens; + + if (isOptional) { + this.consumeSpaces(); // \@ifnextchar gobbles any space following it + + if (this.future().text !== "[") { + return null; + } + + start = this.popToken(); // don't include [ in tokens + + ({ + tokens, + end + } = this.consumeArg(["]"])); + } else { + ({ + tokens, + start, + end + } = this.consumeArg()); + } // indicate the end of an argument + + + this.pushToken(new Token("EOF", end.loc)); + this.pushTokens(tokens); + return start.range(end, ""); + } + /** + * Consume all following space tokens, without expansion. + */ + + + consumeSpaces() { + for (;;) { + var token = this.future(); + + if (token.text === " ") { + this.stack.pop(); + } else { + break; + } + } + } + /** + * Consume an argument from the token stream, and return the resulting array + * of tokens and start/end token. + */ + + + consumeArg(delims) { + // The argument for a delimited parameter is the shortest (possibly + // empty) sequence of tokens with properly nested {...} groups that is + // followed ... by this particular list of non-parameter tokens. + // The argument for an undelimited parameter is the next nonblank + // token, unless that token is ‘{’, when the argument will be the + // entire {...} group that follows. + var tokens = []; + var isDelimited = delims && delims.length > 0; + + if (!isDelimited) { + // Ignore spaces between arguments. As the TeXbook says: + // "After you have said ‘\def\row#1#2{...}’, you are allowed to + // put spaces between the arguments (e.g., ‘\row x n’), because + // TeX doesn’t use single spaces as undelimited arguments." + this.consumeSpaces(); + } + + var start = this.future(); + var tok; + var depth = 0; + var match = 0; + + do { + tok = this.popToken(); + tokens.push(tok); + + if (tok.text === "{") { + ++depth; + } else if (tok.text === "}") { + --depth; + + if (depth === -1) { + throw new ParseError("Extra }", tok); + } + } else if (tok.text === "EOF") { + throw new ParseError("Unexpected end of input in a macro argument" + ", expected '" + (delims && isDelimited ? delims[match] : "}") + "'", tok); + } + + if (delims && isDelimited) { + if ((depth === 0 || depth === 1 && delims[match] === "{") && tok.text === delims[match]) { + ++match; + + if (match === delims.length) { + // don't include delims in tokens + tokens.splice(-match, match); + break; + } + } else { + match = 0; + } + } + } while (depth !== 0 || isDelimited); // If the argument found ... has the form ‘{}’, + // ... the outermost braces enclosing the argument are removed + + + if (start.text === "{" && tokens[tokens.length - 1].text === "}") { + tokens.pop(); + tokens.shift(); + } + + tokens.reverse(); // to fit in with stack order + + return { + tokens, + start, + end: tok + }; + } + /** + * Consume the specified number of (delimited) arguments from the token + * stream and return the resulting array of arguments. + */ + + + consumeArgs(numArgs, delimiters) { + if (delimiters) { + if (delimiters.length !== numArgs + 1) { + throw new ParseError("The length of delimiters doesn't match the number of args!"); + } + + var delims = delimiters[0]; + + for (var i = 0; i < delims.length; i++) { + var tok = this.popToken(); + + if (delims[i] !== tok.text) { + throw new ParseError("Use of the macro doesn't match its definition", tok); + } + } + } + + var args = []; + + for (var _i = 0; _i < numArgs; _i++) { + args.push(this.consumeArg(delimiters && delimiters[_i + 1]).tokens); + } + + return args; + } + /** + * Expand the next token only once if possible. + * + * If the token is expanded, the resulting tokens will be pushed onto + * the stack in reverse order and will be returned as an array, + * also in reverse order. + * + * If not, the next token will be returned without removing it + * from the stack. This case can be detected by a `Token` return value + * instead of an `Array` return value. + * + * In either case, the next token will be on the top of the stack, + * or the stack will be empty. + * + * Used to implement `expandAfterFuture` and `expandNextToken`. + * + * If expandableOnly, only expandable tokens are expanded and + * an undefined control sequence results in an error. + */ + + + expandOnce(expandableOnly) { + var topToken = this.popToken(); + var name = topToken.text; + var expansion = !topToken.noexpand ? this._getExpansion(name) : null; + + if (expansion == null || expandableOnly && expansion.unexpandable) { + if (expandableOnly && expansion == null && name[0] === "\\" && !this.isDefined(name)) { + throw new ParseError("Undefined control sequence: " + name); + } + + this.pushToken(topToken); + return topToken; + } + + this.expansionCount++; + + if (this.expansionCount > this.settings.maxExpand) { + throw new ParseError("Too many expansions: infinite loop or " + "need to increase maxExpand setting"); + } + + var tokens = expansion.tokens; + var args = this.consumeArgs(expansion.numArgs, expansion.delimiters); + + if (expansion.numArgs) { + // paste arguments in place of the placeholders + tokens = tokens.slice(); // make a shallow copy + + for (var i = tokens.length - 1; i >= 0; --i) { + var tok = tokens[i]; + + if (tok.text === "#") { + if (i === 0) { + throw new ParseError("Incomplete placeholder at end of macro body", tok); + } + + tok = tokens[--i]; // next token on stack + + if (tok.text === "#") { + // ## → # + tokens.splice(i + 1, 1); // drop first # + } else if (/^[1-9]$/.test(tok.text)) { + // replace the placeholder with the indicated argument + tokens.splice(i, 2, ...args[+tok.text - 1]); + } else { + throw new ParseError("Not a valid argument number", tok); + } + } + } + } // Concatenate expansion onto top of stack. + + + this.pushTokens(tokens); + return tokens; + } + /** + * Expand the next token only once (if possible), and return the resulting + * top token on the stack (without removing anything from the stack). + * Similar in behavior to TeX's `\expandafter\futurelet`. + * Equivalent to expandOnce() followed by future(). + */ + + + expandAfterFuture() { + this.expandOnce(); + return this.future(); + } + /** + * Recursively expand first token, then return first non-expandable token. + */ + + + expandNextToken() { + for (;;) { + var expanded = this.expandOnce(); // expandOnce returns Token if and only if it's fully expanded. + + if (expanded instanceof Token) { + // \relax stops the expansion, but shouldn't get returned (a + // null return value couldn't get implemented as a function). + // the token after \noexpand is interpreted as if its meaning + // were ‘\relax’ + if (expanded.text === "\\relax" || expanded.treatAsRelax) { + this.stack.pop(); + } else { + return this.stack.pop(); // === expanded + } + } + } // Flow unable to figure out that this pathway is impossible. + // https://github.com/facebook/flow/issues/4808 + + + throw new Error(); // eslint-disable-line no-unreachable + } + /** + * Fully expand the given macro name and return the resulting list of + * tokens, or return `undefined` if no such macro is defined. + */ + + + expandMacro(name) { + return this.macros.has(name) ? this.expandTokens([new Token(name)]) : undefined; + } + /** + * Fully expand the given token stream and return the resulting list of tokens + */ + + + expandTokens(tokens) { + var output = []; + var oldStackLength = this.stack.length; + this.pushTokens(tokens); + + while (this.stack.length > oldStackLength) { + var expanded = this.expandOnce(true); // expand only expandable tokens + // expandOnce returns Token if and only if it's fully expanded. + + if (expanded instanceof Token) { + if (expanded.treatAsRelax) { + // the expansion of \noexpand is the token itself + expanded.noexpand = false; + expanded.treatAsRelax = false; + } + + output.push(this.stack.pop()); + } + } + + return output; + } + /** + * Fully expand the given macro name and return the result as a string, + * or return `undefined` if no such macro is defined. + */ + + + expandMacroAsText(name) { + var tokens = this.expandMacro(name); + + if (tokens) { + return tokens.map(token => token.text).join(""); + } else { + return tokens; + } + } + /** + * Returns the expanded macro as a reversed array of tokens and a macro + * argument count. Or returns `null` if no such macro. + */ + + + _getExpansion(name) { + var definition = this.macros.get(name); + + if (definition == null) { + // mainly checking for undefined here + return definition; + } // If a single character has an associated catcode other than 13 + // (active character), then don't expand it. + + + if (name.length === 1) { + var catcode = this.lexer.catcodes[name]; + + if (catcode != null && catcode !== 13) { + return; + } + } + + var expansion = typeof definition === "function" ? definition(this) : definition; + + if (typeof expansion === "string") { + var numArgs = 0; + + if (expansion.indexOf("#") !== -1) { + var stripped = expansion.replace(/##/g, ""); + + while (stripped.indexOf("#" + (numArgs + 1)) !== -1) { + ++numArgs; + } + } + + var bodyLexer = new Lexer(expansion, this.settings); + var tokens = []; + var tok = bodyLexer.lex(); + + while (tok.text !== "EOF") { + tokens.push(tok); + tok = bodyLexer.lex(); + } + + tokens.reverse(); // to fit in with stack using push and pop + + var expanded = { + tokens, + numArgs + }; + return expanded; + } + + return expansion; + } + /** + * Determine whether a command is currently "defined" (has some + * functionality), meaning that it's a macro (in the current group), + * a function, a symbol, or one of the special commands listed in + * `implicitCommands`. + */ + + + isDefined(name) { + return this.macros.has(name) || functions.hasOwnProperty(name) || symbols.math.hasOwnProperty(name) || symbols.text.hasOwnProperty(name) || implicitCommands.hasOwnProperty(name); + } + /** + * Determine whether a command is expandable. + */ + + + isExpandable(name) { + var macro = this.macros.get(name); + return macro != null ? typeof macro === "string" || typeof macro === "function" || !macro.unexpandable : functions.hasOwnProperty(name) && !functions[name].primitive; + } + +} + +/* eslint no-constant-condition:0 */ + +var unicodeAccents = { + "́": { + "text": "\\'", + "math": "\\acute" + }, + "̀": { + "text": "\\`", + "math": "\\grave" + }, + "̈": { + "text": "\\\"", + "math": "\\ddot" + }, + "̃": { + "text": "\\~", + "math": "\\tilde" + }, + "̄": { + "text": "\\=", + "math": "\\bar" + }, + "̆": { + "text": "\\u", + "math": "\\breve" + }, + "̌": { + "text": "\\v", + "math": "\\check" + }, + "̂": { + "text": "\\^", + "math": "\\hat" + }, + "̇": { + "text": "\\.", + "math": "\\dot" + }, + "̊": { + "text": "\\r", + "math": "\\mathring" + }, + "̋": { + "text": "\\H" + }, + "̧": { + "text": "\\c" + } +}; +var unicodeSymbols = { + "á": "á", + "à": "à", + "ä": "ä", + "ǟ": "ǟ", + "ã": "ã", + "ā": "ā", + "ă": "ă", + "ắ": "ắ", + "ằ": "ằ", + "ẵ": "ẵ", + "ǎ": "ǎ", + "â": "â", + "ấ": "ấ", + "ầ": "ầ", + "ẫ": "ẫ", + "ȧ": "ȧ", + "ǡ": "ǡ", + "å": "å", + "ǻ": "ǻ", + "ḃ": "ḃ", + "ć": "ć", + "ḉ": "ḉ", + "č": "č", + "ĉ": "ĉ", + "ċ": "ċ", + "ç": "ç", + "ď": "ď", + "ḋ": "ḋ", + "ḑ": "ḑ", + "é": "é", + "è": "è", + "ë": "ë", + "ẽ": "ẽ", + "ē": "ē", + "ḗ": "ḗ", + "ḕ": "ḕ", + "ĕ": "ĕ", + "ḝ": "ḝ", + "ě": "ě", + "ê": "ê", + "ế": "ế", + "ề": "ề", + "ễ": "ễ", + "ė": "ė", + "ȩ": "ȩ", + "ḟ": "ḟ", + "ǵ": "ǵ", + "ḡ": "ḡ", + "ğ": "ğ", + "ǧ": "ǧ", + "ĝ": "ĝ", + "ġ": "ġ", + "ģ": "ģ", + "ḧ": "ḧ", + "ȟ": "ȟ", + "ĥ": "ĥ", + "ḣ": "ḣ", + "ḩ": "ḩ", + "í": "í", + "ì": "ì", + "ï": "ï", + "ḯ": "ḯ", + "ĩ": "ĩ", + "ī": "ī", + "ĭ": "ĭ", + "ǐ": "ǐ", + "î": "î", + "ǰ": "ǰ", + "ĵ": "ĵ", + "ḱ": "ḱ", + "ǩ": "ǩ", + "ķ": "ķ", + "ĺ": "ĺ", + "ľ": "ľ", + "ļ": "ļ", + "ḿ": "ḿ", + "ṁ": "ṁ", + "ń": "ń", + "ǹ": "ǹ", + "ñ": "ñ", + "ň": "ň", + "ṅ": "ṅ", + "ņ": "ņ", + "ó": "ó", + "ò": "ò", + "ö": "ö", + "ȫ": "ȫ", + "õ": "õ", + "ṍ": "ṍ", + "ṏ": "ṏ", + "ȭ": "ȭ", + "ō": "ō", + "ṓ": "ṓ", + "ṑ": "ṑ", + "ŏ": "ŏ", + "ǒ": "ǒ", + "ô": "ô", + "ố": "ố", + "ồ": "ồ", + "ỗ": "ỗ", + "ȯ": "ȯ", + "ȱ": "ȱ", + "ő": "ő", + "ṕ": "ṕ", + "ṗ": "ṗ", + "ŕ": "ŕ", + "ř": "ř", + "ṙ": "ṙ", + "ŗ": "ŗ", + "ś": "ś", + "ṥ": "ṥ", + "š": "š", + "ṧ": "ṧ", + "ŝ": "ŝ", + "ṡ": "ṡ", + "ş": "ş", + "ẗ": "ẗ", + "ť": "ť", + "ṫ": "ṫ", + "ţ": "ţ", + "ú": "ú", + "ù": "ù", + "ü": "ü", + "ǘ": "ǘ", + "ǜ": "ǜ", + "ǖ": "ǖ", + "ǚ": "ǚ", + "ũ": "ũ", + "ṹ": "ṹ", + "ū": "ū", + "ṻ": "ṻ", + "ŭ": "ŭ", + "ǔ": "ǔ", + "û": "û", + "ů": "ů", + "ű": "ű", + "ṽ": "ṽ", + "ẃ": "ẃ", + "ẁ": "ẁ", + "ẅ": "ẅ", + "ŵ": "ŵ", + "ẇ": "ẇ", + "ẘ": "ẘ", + "ẍ": "ẍ", + "ẋ": "ẋ", + "ý": "ý", + "ỳ": "ỳ", + "ÿ": "ÿ", + "ỹ": "ỹ", + "ȳ": "ȳ", + "ŷ": "ŷ", + "ẏ": "ẏ", + "ẙ": "ẙ", + "ź": "ź", + "ž": "ž", + "ẑ": "ẑ", + "ż": "ż", + "Á": "Á", + "À": "À", + "Ä": "Ä", + "Ǟ": "Ǟ", + "Ã": "Ã", + "Ā": "Ā", + "Ă": "Ă", + "Ắ": "Ắ", + "Ằ": "Ằ", + "Ẵ": "Ẵ", + "Ǎ": "Ǎ", + "Â": "Â", + "Ấ": "Ấ", + "Ầ": "Ầ", + "Ẫ": "Ẫ", + "Ȧ": "Ȧ", + "Ǡ": "Ǡ", + "Å": "Å", + "Ǻ": "Ǻ", + "Ḃ": "Ḃ", + "Ć": "Ć", + "Ḉ": "Ḉ", + "Č": "Č", + "Ĉ": "Ĉ", + "Ċ": "Ċ", + "Ç": "Ç", + "Ď": "Ď", + "Ḋ": "Ḋ", + "Ḑ": "Ḑ", + "É": "É", + "È": "È", + "Ë": "Ë", + "Ẽ": "Ẽ", + "Ē": "Ē", + "Ḗ": "Ḗ", + "Ḕ": "Ḕ", + "Ĕ": "Ĕ", + "Ḝ": "Ḝ", + "Ě": "Ě", + "Ê": "Ê", + "Ế": "Ế", + "Ề": "Ề", + "Ễ": "Ễ", + "Ė": "Ė", + "Ȩ": "Ȩ", + "Ḟ": "Ḟ", + "Ǵ": "Ǵ", + "Ḡ": "Ḡ", + "Ğ": "Ğ", + "Ǧ": "Ǧ", + "Ĝ": "Ĝ", + "Ġ": "Ġ", + "Ģ": "Ģ", + "Ḧ": "Ḧ", + "Ȟ": "Ȟ", + "Ĥ": "Ĥ", + "Ḣ": "Ḣ", + "Ḩ": "Ḩ", + "Í": "Í", + "Ì": "Ì", + "Ï": "Ï", + "Ḯ": "Ḯ", + "Ĩ": "Ĩ", + "Ī": "Ī", + "Ĭ": "Ĭ", + "Ǐ": "Ǐ", + "Î": "Î", + "İ": "İ", + "Ĵ": "Ĵ", + "Ḱ": "Ḱ", + "Ǩ": "Ǩ", + "Ķ": "Ķ", + "Ĺ": "Ĺ", + "Ľ": "Ľ", + "Ļ": "Ļ", + "Ḿ": "Ḿ", + "Ṁ": "Ṁ", + "Ń": "Ń", + "Ǹ": "Ǹ", + "Ñ": "Ñ", + "Ň": "Ň", + "Ṅ": "Ṅ", + "Ņ": "Ņ", + "Ó": "Ó", + "Ò": "Ò", + "Ö": "Ö", + "Ȫ": "Ȫ", + "Õ": "Õ", + "Ṍ": "Ṍ", + "Ṏ": "Ṏ", + "Ȭ": "Ȭ", + "Ō": "Ō", + "Ṓ": "Ṓ", + "Ṑ": "Ṑ", + "Ŏ": "Ŏ", + "Ǒ": "Ǒ", + "Ô": "Ô", + "Ố": "Ố", + "Ồ": "Ồ", + "Ỗ": "Ỗ", + "Ȯ": "Ȯ", + "Ȱ": "Ȱ", + "Ő": "Ő", + "Ṕ": "Ṕ", + "Ṗ": "Ṗ", + "Ŕ": "Ŕ", + "Ř": "Ř", + "Ṙ": "Ṙ", + "Ŗ": "Ŗ", + "Ś": "Ś", + "Ṥ": "Ṥ", + "Š": "Š", + "Ṧ": "Ṧ", + "Ŝ": "Ŝ", + "Ṡ": "Ṡ", + "Ş": "Ş", + "Ť": "Ť", + "Ṫ": "Ṫ", + "Ţ": "Ţ", + "Ú": "Ú", + "Ù": "Ù", + "Ü": "Ü", + "Ǘ": "Ǘ", + "Ǜ": "Ǜ", + "Ǖ": "Ǖ", + "Ǚ": "Ǚ", + "Ũ": "Ũ", + "Ṹ": "Ṹ", + "Ū": "Ū", + "Ṻ": "Ṻ", + "Ŭ": "Ŭ", + "Ǔ": "Ǔ", + "Û": "Û", + "Ů": "Ů", + "Ű": "Ű", + "Ṽ": "Ṽ", + "Ẃ": "Ẃ", + "Ẁ": "Ẁ", + "Ẅ": "Ẅ", + "Ŵ": "Ŵ", + "Ẇ": "Ẇ", + "Ẍ": "Ẍ", + "Ẋ": "Ẋ", + "Ý": "Ý", + "Ỳ": "Ỳ", + "Ÿ": "Ÿ", + "Ỹ": "Ỹ", + "Ȳ": "Ȳ", + "Ŷ": "Ŷ", + "Ẏ": "Ẏ", + "Ź": "Ź", + "Ž": "Ž", + "Ẑ": "Ẑ", + "Ż": "Ż", + "ά": "ά", + "ὰ": "ὰ", + "ᾱ": "ᾱ", + "ᾰ": "ᾰ", + "έ": "έ", + "ὲ": "ὲ", + "ή": "ή", + "ὴ": "ὴ", + "ί": "ί", + "ὶ": "ὶ", + "ϊ": "ϊ", + "ΐ": "ΐ", + "ῒ": "ῒ", + "ῑ": "ῑ", + "ῐ": "ῐ", + "ό": "ό", + "ὸ": "ὸ", + "ύ": "ύ", + "ὺ": "ὺ", + "ϋ": "ϋ", + "ΰ": "ΰ", + "ῢ": "ῢ", + "ῡ": "ῡ", + "ῠ": "ῠ", + "ώ": "ώ", + "ὼ": "ὼ", + "Ύ": "Ύ", + "Ὺ": "Ὺ", + "Ϋ": "Ϋ", + "Ῡ": "Ῡ", + "Ῠ": "Ῠ", + "Ώ": "Ώ", + "Ὼ": "Ὼ" +}; + +/** + * This file contains the parser used to parse out a TeX expression from the + * input. Since TeX isn't context-free, standard parsers don't work particularly + * well. + * + * The strategy of this parser is as such: + * + * The main functions (the `.parse...` ones) take a position in the current + * parse string to parse tokens from. The lexer (found in Lexer.js, stored at + * this.gullet.lexer) also supports pulling out tokens at arbitrary places. When + * individual tokens are needed at a position, the lexer is called to pull out a + * token, which is then used. + * + * The parser has a property called "mode" indicating the mode that + * the parser is currently in. Currently it has to be one of "math" or + * "text", which denotes whether the current environment is a math-y + * one or a text-y one (e.g. inside \text). Currently, this serves to + * limit the functions which can be used in text mode. + * + * The main functions then return an object which contains the useful data that + * was parsed at its given point, and a new position at the end of the parsed + * data. The main functions can call each other and continue the parsing by + * using the returned position as a new starting point. + * + * There are also extra `.handle...` functions, which pull out some reused + * functionality into self-contained functions. + * + * The functions return ParseNodes. + */ +class Parser { + constructor(input, settings) { + this.mode = void 0; + this.gullet = void 0; + this.settings = void 0; + this.leftrightDepth = void 0; + this.nextToken = void 0; + // Start in math mode + this.mode = "math"; // Create a new macro expander (gullet) and (indirectly via that) also a + // new lexer (mouth) for this parser (stomach, in the language of TeX) + + this.gullet = new MacroExpander(input, settings, this.mode); // Store the settings for use in parsing + + this.settings = settings; // Count leftright depth (for \middle errors) + + this.leftrightDepth = 0; + } + /** + * Checks a result to make sure it has the right type, and throws an + * appropriate error otherwise. + */ + + + expect(text, consume) { + if (consume === void 0) { + consume = true; + } + + if (this.fetch().text !== text) { + throw new ParseError("Expected '" + text + "', got '" + this.fetch().text + "'", this.fetch()); + } + + if (consume) { + this.consume(); + } + } + /** + * Discards the current lookahead token, considering it consumed. + */ + + + consume() { + this.nextToken = null; + } + /** + * Return the current lookahead token, or if there isn't one (at the + * beginning, or if the previous lookahead token was consume()d), + * fetch the next token as the new lookahead token and return it. + */ + + + fetch() { + if (this.nextToken == null) { + this.nextToken = this.gullet.expandNextToken(); + } + + return this.nextToken; + } + /** + * Switches between "text" and "math" modes. + */ + + + switchMode(newMode) { + this.mode = newMode; + this.gullet.switchMode(newMode); + } + /** + * Main parsing function, which parses an entire input. + */ + + + parse() { + if (!this.settings.globalGroup) { + // Create a group namespace for the math expression. + // (LaTeX creates a new group for every $...$, $$...$$, \[...\].) + this.gullet.beginGroup(); + } // Use old \color behavior (same as LaTeX's \textcolor) if requested. + // We do this within the group for the math expression, so it doesn't + // pollute settings.macros. + + + if (this.settings.colorIsTextColor) { + this.gullet.macros.set("\\color", "\\textcolor"); + } + + try { + // Try to parse the input + var parse = this.parseExpression(false); // If we succeeded, make sure there's an EOF at the end + + this.expect("EOF"); // End the group namespace for the expression + + if (!this.settings.globalGroup) { + this.gullet.endGroup(); + } + + return parse; // Close any leftover groups in case of a parse error. + } finally { + this.gullet.endGroups(); + } + } + + /** + * Parses an "expression", which is a list of atoms. + * + * `breakOnInfix`: Should the parsing stop when we hit infix nodes? This + * happens when functions have higher precendence han infix + * nodes in implicit parses. + * + * `breakOnTokenText`: The text of the token that the expression should end + * with, or `null` if something else should end the + * expression. + */ + parseExpression(breakOnInfix, breakOnTokenText) { + var body = []; // Keep adding atoms to the body until we can't parse any more atoms (either + // we reached the end, a }, or a \right) + + while (true) { + // Ignore spaces in math mode + if (this.mode === "math") { + this.consumeSpaces(); + } + + var lex = this.fetch(); + + if (Parser.endOfExpression.indexOf(lex.text) !== -1) { + break; + } + + if (breakOnTokenText && lex.text === breakOnTokenText) { + break; + } + + if (breakOnInfix && functions[lex.text] && functions[lex.text].infix) { + break; + } + + var atom = this.parseAtom(breakOnTokenText); + + if (!atom) { + break; + } else if (atom.type === "internal") { + continue; + } + + body.push(atom); + } + + if (this.mode === "text") { + this.formLigatures(body); + } + + return this.handleInfixNodes(body); + } + /** + * Rewrites infix operators such as \over with corresponding commands such + * as \frac. + * + * There can only be one infix operator per group. If there's more than one + * then the expression is ambiguous. This can be resolved by adding {}. + */ + + + handleInfixNodes(body) { + var overIndex = -1; + var funcName; + + for (var i = 0; i < body.length; i++) { + if (body[i].type === "infix") { + if (overIndex !== -1) { + throw new ParseError("only one infix operator per group", body[i].token); + } + + overIndex = i; + funcName = body[i].replaceWith; + } + } + + if (overIndex !== -1 && funcName) { + var numerNode; + var denomNode; + var numerBody = body.slice(0, overIndex); + var denomBody = body.slice(overIndex + 1); + + if (numerBody.length === 1 && numerBody[0].type === "ordgroup") { + numerNode = numerBody[0]; + } else { + numerNode = { + type: "ordgroup", + mode: this.mode, + body: numerBody + }; + } + + if (denomBody.length === 1 && denomBody[0].type === "ordgroup") { + denomNode = denomBody[0]; + } else { + denomNode = { + type: "ordgroup", + mode: this.mode, + body: denomBody + }; + } + + var node; + + if (funcName === "\\\\abovefrac") { + node = this.callFunction(funcName, [numerNode, body[overIndex], denomNode], []); + } else { + node = this.callFunction(funcName, [numerNode, denomNode], []); + } + + return [node]; + } else { + return body; + } + } + /** + * Handle a subscript or superscript with nice errors. + */ + + + handleSupSubscript(name // For error reporting. + ) { + var symbolToken = this.fetch(); + var symbol = symbolToken.text; + this.consume(); + this.consumeSpaces(); // ignore spaces before sup/subscript argument + + var group = this.parseGroup(name); + + if (!group) { + throw new ParseError("Expected group after '" + symbol + "'", symbolToken); + } + + return group; + } + /** + * Converts the textual input of an unsupported command into a text node + * contained within a color node whose color is determined by errorColor + */ + + + formatUnsupportedCmd(text) { + var textordArray = []; + + for (var i = 0; i < text.length; i++) { + textordArray.push({ + type: "textord", + mode: "text", + text: text[i] + }); + } + + var textNode = { + type: "text", + mode: this.mode, + body: textordArray + }; + var colorNode = { + type: "color", + mode: this.mode, + color: this.settings.errorColor, + body: [textNode] + }; + return colorNode; + } + /** + * Parses a group with optional super/subscripts. + */ + + + parseAtom(breakOnTokenText) { + // The body of an atom is an implicit group, so that things like + // \left(x\right)^2 work correctly. + var base = this.parseGroup("atom", breakOnTokenText); // In text mode, we don't have superscripts or subscripts + + if (this.mode === "text") { + return base; + } // Note that base may be empty (i.e. null) at this point. + + + var superscript; + var subscript; + + while (true) { + // Guaranteed in math mode, so eat any spaces first. + this.consumeSpaces(); // Lex the first token + + var lex = this.fetch(); + + if (lex.text === "\\limits" || lex.text === "\\nolimits") { + // We got a limit control + if (base && base.type === "op") { + var limits = lex.text === "\\limits"; + base.limits = limits; + base.alwaysHandleSupSub = true; + } else if (base && base.type === "operatorname") { + if (base.alwaysHandleSupSub) { + base.limits = lex.text === "\\limits"; + } + } else { + throw new ParseError("Limit controls must follow a math operator", lex); + } + + this.consume(); + } else if (lex.text === "^") { + // We got a superscript start + if (superscript) { + throw new ParseError("Double superscript", lex); + } + + superscript = this.handleSupSubscript("superscript"); + } else if (lex.text === "_") { + // We got a subscript start + if (subscript) { + throw new ParseError("Double subscript", lex); + } + + subscript = this.handleSupSubscript("subscript"); + } else if (lex.text === "'") { + // We got a prime + if (superscript) { + throw new ParseError("Double superscript", lex); + } + + var prime = { + type: "textord", + mode: this.mode, + text: "\\prime" + }; // Many primes can be grouped together, so we handle this here + + var primes = [prime]; + this.consume(); // Keep lexing tokens until we get something that's not a prime + + while (this.fetch().text === "'") { + // For each one, add another prime to the list + primes.push(prime); + this.consume(); + } // If there's a superscript following the primes, combine that + // superscript in with the primes. + + + if (this.fetch().text === "^") { + primes.push(this.handleSupSubscript("superscript")); + } // Put everything into an ordgroup as the superscript + + + superscript = { + type: "ordgroup", + mode: this.mode, + body: primes + }; + } else { + // If it wasn't ^, _, or ', stop parsing super/subscripts + break; + } + } // Base must be set if superscript or subscript are set per logic above, + // but need to check here for type check to pass. + + + if (superscript || subscript) { + // If we got either a superscript or subscript, create a supsub + return { + type: "supsub", + mode: this.mode, + base: base, + sup: superscript, + sub: subscript + }; + } else { + // Otherwise return the original body + return base; + } + } + /** + * Parses an entire function, including its base and all of its arguments. + */ + + + parseFunction(breakOnTokenText, name // For determining its context + ) { + var token = this.fetch(); + var func = token.text; + var funcData = functions[func]; + + if (!funcData) { + return null; + } + + this.consume(); // consume command token + + if (name && name !== "atom" && !funcData.allowedInArgument) { + throw new ParseError("Got function '" + func + "' with no arguments" + (name ? " as " + name : ""), token); + } else if (this.mode === "text" && !funcData.allowedInText) { + throw new ParseError("Can't use function '" + func + "' in text mode", token); + } else if (this.mode === "math" && funcData.allowedInMath === false) { + throw new ParseError("Can't use function '" + func + "' in math mode", token); + } + + var { + args, + optArgs + } = this.parseArguments(func, funcData); + return this.callFunction(func, args, optArgs, token, breakOnTokenText); + } + /** + * Call a function handler with a suitable context and arguments. + */ + + + callFunction(name, args, optArgs, token, breakOnTokenText) { + var context = { + funcName: name, + parser: this, + token, + breakOnTokenText + }; + var func = functions[name]; + + if (func && func.handler) { + return func.handler(context, args, optArgs); + } else { + throw new ParseError("No function handler for " + name); + } + } + /** + * Parses the arguments of a function or environment + */ + + + parseArguments(func, // Should look like "\name" or "\begin{name}". + funcData) { + var totalArgs = funcData.numArgs + funcData.numOptionalArgs; + + if (totalArgs === 0) { + return { + args: [], + optArgs: [] + }; + } + + var args = []; + var optArgs = []; + + for (var i = 0; i < totalArgs; i++) { + var argType = funcData.argTypes && funcData.argTypes[i]; + var isOptional = i < funcData.numOptionalArgs; + + if (funcData.primitive && argType == null || // \sqrt expands into primitive if optional argument doesn't exist + funcData.type === "sqrt" && i === 1 && optArgs[0] == null) { + argType = "primitive"; + } + + var arg = this.parseGroupOfType("argument to '" + func + "'", argType, isOptional); + + if (isOptional) { + optArgs.push(arg); + } else if (arg != null) { + args.push(arg); + } else { + // should be unreachable + throw new ParseError("Null argument, please report this as a bug"); + } + } + + return { + args, + optArgs + }; + } + /** + * Parses a group when the mode is changing. + */ + + + parseGroupOfType(name, type, optional) { + switch (type) { + case "color": + return this.parseColorGroup(optional); + + case "size": + return this.parseSizeGroup(optional); + + case "url": + return this.parseUrlGroup(optional); + + case "math": + case "text": + return this.parseArgumentGroup(optional, type); + + case "hbox": + { + // hbox argument type wraps the argument in the equivalent of + // \hbox, which is like \text but switching to \textstyle size. + var group = this.parseArgumentGroup(optional, "text"); + return group != null ? { + type: "styling", + mode: group.mode, + body: [group], + style: "text" // simulate \textstyle + + } : null; + } + + case "raw": + { + var token = this.parseStringGroup("raw", optional); + return token != null ? { + type: "raw", + mode: "text", + string: token.text + } : null; + } + + case "primitive": + { + if (optional) { + throw new ParseError("A primitive argument cannot be optional"); + } + + var _group = this.parseGroup(name); + + if (_group == null) { + throw new ParseError("Expected group as " + name, this.fetch()); + } + + return _group; + } + + case "original": + case null: + case undefined: + return this.parseArgumentGroup(optional); + + default: + throw new ParseError("Unknown group type as " + name, this.fetch()); + } + } + /** + * Discard any space tokens, fetching the next non-space token. + */ + + + consumeSpaces() { + while (this.fetch().text === " ") { + this.consume(); + } + } + /** + * Parses a group, essentially returning the string formed by the + * brace-enclosed tokens plus some position information. + */ + + + parseStringGroup(modeName, // Used to describe the mode in error messages. + optional) { + var argToken = this.gullet.scanArgument(optional); + + if (argToken == null) { + return null; + } + + var str = ""; + var nextToken; + + while ((nextToken = this.fetch()).text !== "EOF") { + str += nextToken.text; + this.consume(); + } + + this.consume(); // consume the end of the argument + + argToken.text = str; + return argToken; + } + /** + * Parses a regex-delimited group: the largest sequence of tokens + * whose concatenated strings match `regex`. Returns the string + * formed by the tokens plus some position information. + */ + + + parseRegexGroup(regex, modeName // Used to describe the mode in error messages. + ) { + var firstToken = this.fetch(); + var lastToken = firstToken; + var str = ""; + var nextToken; + + while ((nextToken = this.fetch()).text !== "EOF" && regex.test(str + nextToken.text)) { + lastToken = nextToken; + str += lastToken.text; + this.consume(); + } + + if (str === "") { + throw new ParseError("Invalid " + modeName + ": '" + firstToken.text + "'", firstToken); + } + + return firstToken.range(lastToken, str); + } + /** + * Parses a color description. + */ + + + parseColorGroup(optional) { + var res = this.parseStringGroup("color", optional); + + if (res == null) { + return null; + } + + var match = /^(#[a-f0-9]{3}|#?[a-f0-9]{6}|[a-z]+)$/i.exec(res.text); + + if (!match) { + throw new ParseError("Invalid color: '" + res.text + "'", res); + } + + var color = match[0]; + + if (/^[0-9a-f]{6}$/i.test(color)) { + // We allow a 6-digit HTML color spec without a leading "#". + // This follows the xcolor package's HTML color model. + // Predefined color names are all missed by this RegEx pattern. + color = "#" + color; + } + + return { + type: "color-token", + mode: this.mode, + color + }; + } + /** + * Parses a size specification, consisting of magnitude and unit. + */ + + + parseSizeGroup(optional) { + var res; + var isBlank = false; // don't expand before parseStringGroup + + this.gullet.consumeSpaces(); + + if (!optional && this.gullet.future().text !== "{") { + res = this.parseRegexGroup(/^[-+]? *(?:$|\d+|\d+\.\d*|\.\d*) *[a-z]{0,2} *$/, "size"); + } else { + res = this.parseStringGroup("size", optional); + } + + if (!res) { + return null; + } + + if (!optional && res.text.length === 0) { + // Because we've tested for what is !optional, this block won't + // affect \kern, \hspace, etc. It will capture the mandatory arguments + // to \genfrac and \above. + res.text = "0pt"; // Enable \above{} + + isBlank = true; // This is here specifically for \genfrac + } + + var match = /([-+]?) *(\d+(?:\.\d*)?|\.\d+) *([a-z]{2})/.exec(res.text); + + if (!match) { + throw new ParseError("Invalid size: '" + res.text + "'", res); + } + + var data = { + number: +(match[1] + match[2]), + // sign + magnitude, cast to number + unit: match[3] + }; + + if (!validUnit(data)) { + throw new ParseError("Invalid unit: '" + data.unit + "'", res); + } + + return { + type: "size", + mode: this.mode, + value: data, + isBlank + }; + } + /** + * Parses an URL, checking escaped letters and allowed protocols, + * and setting the catcode of % as an active character (as in \hyperref). + */ + + + parseUrlGroup(optional) { + this.gullet.lexer.setCatcode("%", 13); // active character + + this.gullet.lexer.setCatcode("~", 12); // other character + + var res = this.parseStringGroup("url", optional); + this.gullet.lexer.setCatcode("%", 14); // comment character + + this.gullet.lexer.setCatcode("~", 13); // active character + + if (res == null) { + return null; + } // hyperref package allows backslashes alone in href, but doesn't + // generate valid links in such cases; we interpret this as + // "undefined" behaviour, and keep them as-is. Some browser will + // replace backslashes with forward slashes. + + + var url = res.text.replace(/\\([#$%&~_^{}])/g, '$1'); + return { + type: "url", + mode: this.mode, + url + }; + } + /** + * Parses an argument with the mode specified. + */ + + + parseArgumentGroup(optional, mode) { + var argToken = this.gullet.scanArgument(optional); + + if (argToken == null) { + return null; + } + + var outerMode = this.mode; + + if (mode) { + // Switch to specified mode + this.switchMode(mode); + } + + this.gullet.beginGroup(); + var expression = this.parseExpression(false, "EOF"); // TODO: find an alternative way to denote the end + + this.expect("EOF"); // expect the end of the argument + + this.gullet.endGroup(); + var result = { + type: "ordgroup", + mode: this.mode, + loc: argToken.loc, + body: expression + }; + + if (mode) { + // Switch mode back + this.switchMode(outerMode); + } + + return result; + } + /** + * Parses an ordinary group, which is either a single nucleus (like "x") + * or an expression in braces (like "{x+y}") or an implicit group, a group + * that starts at the current position, and ends right before a higher explicit + * group ends, or at EOF. + */ + + + parseGroup(name, // For error reporting. + breakOnTokenText) { + var firstToken = this.fetch(); + var text = firstToken.text; + var result; // Try to parse an open brace or \begingroup + + if (text === "{" || text === "\\begingroup") { + this.consume(); + var groupEnd = text === "{" ? "}" : "\\endgroup"; + this.gullet.beginGroup(); // If we get a brace, parse an expression + + var expression = this.parseExpression(false, groupEnd); + var lastToken = this.fetch(); + this.expect(groupEnd); // Check that we got a matching closing brace + + this.gullet.endGroup(); + result = { + type: "ordgroup", + mode: this.mode, + loc: SourceLocation.range(firstToken, lastToken), + body: expression, + // A group formed by \begingroup...\endgroup is a semi-simple group + // which doesn't affect spacing in math mode, i.e., is transparent. + // https://tex.stackexchange.com/questions/1930/when-should-one- + // use-begingroup-instead-of-bgroup + semisimple: text === "\\begingroup" || undefined + }; + } else { + // If there exists a function with this name, parse the function. + // Otherwise, just return a nucleus + result = this.parseFunction(breakOnTokenText, name) || this.parseSymbol(); + + if (result == null && text[0] === "\\" && !implicitCommands.hasOwnProperty(text)) { + if (this.settings.throwOnError) { + throw new ParseError("Undefined control sequence: " + text, firstToken); + } + + result = this.formatUnsupportedCmd(text); + this.consume(); + } + } + + return result; + } + /** + * Form ligature-like combinations of characters for text mode. + * This includes inputs like "--", "---", "``" and "''". + * The result will simply replace multiple textord nodes with a single + * character in each value by a single textord node having multiple + * characters in its value. The representation is still ASCII source. + * The group will be modified in place. + */ + + + formLigatures(group) { + var n = group.length - 1; + + for (var i = 0; i < n; ++i) { + var a = group[i]; // $FlowFixMe: Not every node type has a `text` property. + + var v = a.text; + + if (v === "-" && group[i + 1].text === "-") { + if (i + 1 < n && group[i + 2].text === "-") { + group.splice(i, 3, { + type: "textord", + mode: "text", + loc: SourceLocation.range(a, group[i + 2]), + text: "---" + }); + n -= 2; + } else { + group.splice(i, 2, { + type: "textord", + mode: "text", + loc: SourceLocation.range(a, group[i + 1]), + text: "--" + }); + n -= 1; + } + } + + if ((v === "'" || v === "`") && group[i + 1].text === v) { + group.splice(i, 2, { + type: "textord", + mode: "text", + loc: SourceLocation.range(a, group[i + 1]), + text: v + v + }); + n -= 1; + } + } + } + /** + * Parse a single symbol out of the string. Here, we handle single character + * symbols and special functions like \verb. + */ + + + parseSymbol() { + var nucleus = this.fetch(); + var text = nucleus.text; + + if (/^\\verb[^a-zA-Z]/.test(text)) { + this.consume(); + var arg = text.slice(5); + var star = arg.charAt(0) === "*"; + + if (star) { + arg = arg.slice(1); + } // Lexer's tokenRegex is constructed to always have matching + // first/last characters. + + + if (arg.length < 2 || arg.charAt(0) !== arg.slice(-1)) { + throw new ParseError("\\verb assertion failed --\n please report what input caused this bug"); + } + + arg = arg.slice(1, -1); // remove first and last char + + return { + type: "verb", + mode: "text", + body: arg, + star + }; + } // At this point, we should have a symbol, possibly with accents. + // First expand any accented base symbol according to unicodeSymbols. + + + if (unicodeSymbols.hasOwnProperty(text[0]) && !symbols[this.mode][text[0]]) { + // This behavior is not strict (XeTeX-compatible) in math mode. + if (this.settings.strict && this.mode === "math") { + this.settings.reportNonstrict("unicodeTextInMathMode", "Accented Unicode text character \"" + text[0] + "\" used in " + "math mode", nucleus); + } + + text = unicodeSymbols[text[0]] + text.substr(1); + } // Strip off any combining characters + + + var match = combiningDiacriticalMarksEndRegex.exec(text); + + if (match) { + text = text.substring(0, match.index); + + if (text === 'i') { + text = '\u0131'; // dotless i, in math and text mode + } else if (text === 'j') { + text = '\u0237'; // dotless j, in math and text mode + } + } // Recognize base symbol + + + var symbol; + + if (symbols[this.mode][text]) { + if (this.settings.strict && this.mode === 'math' && extraLatin.indexOf(text) >= 0) { + this.settings.reportNonstrict("unicodeTextInMathMode", "Latin-1/Unicode text character \"" + text[0] + "\" used in " + "math mode", nucleus); + } + + var group = symbols[this.mode][text].group; + var loc = SourceLocation.range(nucleus); + var s; + + if (ATOMS.hasOwnProperty(group)) { + // $FlowFixMe + var family = group; + s = { + type: "atom", + mode: this.mode, + family, + loc, + text + }; + } else { + // $FlowFixMe + s = { + type: group, + mode: this.mode, + loc, + text + }; + } // $FlowFixMe + + + symbol = s; + } else if (text.charCodeAt(0) >= 0x80) { + // no symbol for e.g. ^ + if (this.settings.strict) { + if (!supportedCodepoint(text.charCodeAt(0))) { + this.settings.reportNonstrict("unknownSymbol", "Unrecognized Unicode character \"" + text[0] + "\"" + (" (" + text.charCodeAt(0) + ")"), nucleus); + } else if (this.mode === "math") { + this.settings.reportNonstrict("unicodeTextInMathMode", "Unicode text character \"" + text[0] + "\" used in math mode", nucleus); + } + } // All nonmathematical Unicode characters are rendered as if they + // are in text mode (wrapped in \text) because that's what it + // takes to render them in LaTeX. Setting `mode: this.mode` is + // another natural choice (the user requested math mode), but + // this makes it more difficult for getCharacterMetrics() to + // distinguish Unicode characters without metrics and those for + // which we want to simulate the letter M. + + + symbol = { + type: "textord", + mode: "text", + loc: SourceLocation.range(nucleus), + text + }; + } else { + return null; // EOF, ^, _, {, }, etc. + } + + this.consume(); // Transform combining characters into accents + + if (match) { + for (var i = 0; i < match[0].length; i++) { + var accent = match[0][i]; + + if (!unicodeAccents[accent]) { + throw new ParseError("Unknown accent ' " + accent + "'", nucleus); + } + + var command = unicodeAccents[accent][this.mode] || unicodeAccents[accent].text; + + if (!command) { + throw new ParseError("Accent " + accent + " unsupported in " + this.mode + " mode", nucleus); + } + + symbol = { + type: "accent", + mode: this.mode, + loc: SourceLocation.range(nucleus), + label: command, + isStretchy: false, + isShifty: true, + // $FlowFixMe + base: symbol + }; + } + } // $FlowFixMe + + + return symbol; + } + +} +Parser.endOfExpression = ["}", "\\endgroup", "\\end", "\\right", "&"]; + +/** + * Provides a single function for parsing an expression using a Parser + * TODO(emily): Remove this + */ + +/** + * Parses an expression using a Parser, then returns the parsed result. + */ +var parseTree = function parseTree(toParse, settings) { + if (!(typeof toParse === 'string' || toParse instanceof String)) { + throw new TypeError('KaTeX can only parse string typed expression'); + } + + var parser = new Parser(toParse, settings); // Blank out any \df@tag to avoid spurious "Duplicate \tag" errors + + delete parser.gullet.macros.current["\\df@tag"]; + var tree = parser.parse(); // Prevent a color definition from persisting between calls to katex.render(). + + delete parser.gullet.macros.current["\\current@color"]; + delete parser.gullet.macros.current["\\color"]; // If the input used \tag, it will set the \df@tag macro to the tag. + // In this case, we separately parse the tag and wrap the tree. + + if (parser.gullet.macros.get("\\df@tag")) { + if (!settings.displayMode) { + throw new ParseError("\\tag works only in display equations"); + } + + parser.gullet.feed("\\df@tag"); + tree = [{ + type: "tag", + mode: "text", + body: tree, + tag: parser.parse() + }]; + } + + return tree; +}; + +/* eslint no-console:0 */ + +/** + * Parse and build an expression, and place that expression in the DOM node + * given. + */ +var render = function render(expression, baseNode, options) { + baseNode.textContent = ""; + var node = renderToDomTree(expression, options).toNode(); + baseNode.appendChild(node); +}; // KaTeX's styles don't work properly in quirks mode. Print out an error, and +// disable rendering. + + +if (typeof document !== "undefined") { + if (document.compatMode !== "CSS1Compat") { + typeof console !== "undefined" && console.warn("Warning: KaTeX doesn't work in quirks mode. Make sure your " + "website has a suitable doctype."); + + render = function render() { + throw new ParseError("KaTeX doesn't work in quirks mode."); + }; + } +} +/** + * Parse and build an expression, and return the markup for that. + */ + + +var renderToString = function renderToString(expression, options) { + var markup = renderToDomTree(expression, options).toMarkup(); + return markup; +}; +/** + * Parse an expression and return the parse tree. + */ + + +var generateParseTree = function generateParseTree(expression, options) { + var settings = new Settings(options); + return parseTree(expression, settings); +}; +/** + * If the given error is a KaTeX ParseError and options.throwOnError is false, + * renders the invalid LaTeX as a span with hover title giving the KaTeX + * error message. Otherwise, simply throws the error. + */ + + +var renderError = function renderError(error, expression, options) { + if (options.throwOnError || !(error instanceof ParseError)) { + throw error; + } + + var node = buildCommon.makeSpan(["katex-error"], [new SymbolNode(expression)]); + node.setAttribute("title", error.toString()); + node.setAttribute("style", "color:" + options.errorColor); + return node; +}; +/** + * Generates and returns the katex build tree. This is used for advanced + * use cases (like rendering to custom output). + */ + + +var renderToDomTree = function renderToDomTree(expression, options) { + var settings = new Settings(options); + + try { + var tree = parseTree(expression, settings); + return buildTree(tree, expression, settings); + } catch (error) { + return renderError(error, expression, settings); + } +}; +/** + * Generates and returns the katex build tree, with just HTML (no MathML). + * This is used for advanced use cases (like rendering to custom output). + */ + + +var renderToHTMLTree = function renderToHTMLTree(expression, options) { + var settings = new Settings(options); + + try { + var tree = parseTree(expression, settings); + return buildHTMLTree(tree, expression, settings); + } catch (error) { + return renderError(error, expression, settings); + } +}; + +var katex = { + /** + * Current KaTeX version + */ + version: "0.13.19", + + /** + * Renders the given LaTeX into an HTML+MathML combination, and adds + * it as a child to the specified DOM node. + */ + render, + + /** + * Renders the given LaTeX into an HTML+MathML combination string, + * for sending to the client. + */ + renderToString, + + /** + * KaTeX error, usually during parsing. + */ + ParseError, + + /** + * Parses the given LaTeX into KaTeX's internal parse tree structure, + * without rendering to HTML or MathML. + * + * NOTE: This method is not currently recommended for public use. + * The internal tree representation is unstable and is very likely + * to change. Use at your own risk. + */ + __parse: generateParseTree, + + /** + * Renders the given LaTeX into an HTML+MathML internal DOM tree + * representation, without flattening that representation to a string. + * + * NOTE: This method is not currently recommended for public use. + * The internal tree representation is unstable and is very likely + * to change. Use at your own risk. + */ + __renderToDomTree: renderToDomTree, + + /** + * Renders the given LaTeX into an HTML internal DOM tree representation, + * without MathML and without flattening that representation to a string. + * + * NOTE: This method is not currently recommended for public use. + * The internal tree representation is unstable and is very likely + * to change. Use at your own risk. + */ + __renderToHTMLTree: renderToHTMLTree, + + /** + * extends internal font metrics object with a new object + * each key in the new object represents a font name + */ + __setFontMetrics: setFontMetrics, + + /** + * adds a new symbol to builtin symbols table + */ + __defineSymbol: defineSymbol, + + /** + * adds a new macro to builtin macro list + */ + __defineMacro: defineMacro, + + /** + * Expose the dom tree node types, which can be useful for type checking nodes. + * + * NOTE: This method is not currently recommended for public use. + * The internal tree representation is unstable and is very likely + * to change. Use at your own risk. + */ + __domTree: { + Span, + Anchor, + SymbolNode, + SvgNode, + PathNode, + LineNode + } +}; + +export { katex as default }; diff --git a/core/bikeshed/pygments.css b/core/bikeshed/pygments.css new file mode 100644 index 00000000..691aeb82 --- /dev/null +++ b/core/bikeshed/pygments.css @@ -0,0 +1,74 @@ +pre { line-height: 125%; } +td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; } +span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; } +td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; } +span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; } +.highlight .hll { background-color: #ffffcc } +.highlight { background: #eeffcc; } +.highlight .c { color: #408090; font-style: italic } /* Comment */ +.highlight .err { border: 1px solid #FF0000 } /* Error */ +.highlight .k { color: #007020; font-weight: bold } /* Keyword */ +.highlight .o { color: #666666 } /* Operator */ +.highlight .ch { color: #408090; font-style: italic } /* Comment.Hashbang */ +.highlight .cm { color: #408090; font-style: italic } /* Comment.Multiline */ +.highlight .cp { color: #007020 } /* Comment.Preproc */ +.highlight .cpf { color: #408090; font-style: italic } /* Comment.PreprocFile */ +.highlight .c1 { color: #408090; font-style: italic } /* Comment.Single */ +.highlight .cs { color: #408090; background-color: #fff0f0 } /* Comment.Special */ +.highlight .gd { color: #A00000 } /* Generic.Deleted */ +.highlight .ge { font-style: italic } /* Generic.Emph */ +.highlight .gr { color: #FF0000 } /* Generic.Error */ +.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */ +.highlight .gi { color: #00A000 } /* Generic.Inserted */ +.highlight .go { color: #333333 } /* Generic.Output */ +.highlight .gp { color: #c65d09; font-weight: bold } /* Generic.Prompt */ +.highlight .gs { font-weight: bold } /* Generic.Strong */ +.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */ +.highlight .gt { color: #0044DD } /* Generic.Traceback */ +.highlight .kc { color: #007020; font-weight: bold } /* Keyword.Constant */ +.highlight .kd { color: #007020; font-weight: bold } /* Keyword.Declaration */ +.highlight .kn { color: #007020; font-weight: bold } /* Keyword.Namespace */ +.highlight .kp { color: #007020 } /* Keyword.Pseudo */ +.highlight .kr { color: #007020; font-weight: bold } /* Keyword.Reserved */ +.highlight .kt { color: #902000 } /* Keyword.Type */ +.highlight .m { color: #208050 } /* Literal.Number */ +.highlight .s { color: #4070a0 } /* Literal.String */ +.highlight .na { color: #4070a0 } /* Name.Attribute */ +.highlight .nb { color: #007020 } /* Name.Builtin */ +.highlight .nc { color: #0e84b5; font-weight: bold } /* Name.Class */ +.highlight .no { color: #60add5 } /* Name.Constant */ +.highlight .nd { color: #555555; font-weight: bold } /* Name.Decorator */ +.highlight .ni { color: #d55537; font-weight: bold } /* Name.Entity */ +.highlight .ne { color: #007020 } /* Name.Exception */ +.highlight .nf { color: #06287e } /* Name.Function */ +.highlight .nl { color: #002070; font-weight: bold } /* Name.Label */ +.highlight .nn { color: #0e84b5; font-weight: bold } /* Name.Namespace */ +.highlight .nt { color: #062873; font-weight: bold } /* Name.Tag */ +.highlight .nv { color: #bb60d5 } /* Name.Variable */ +.highlight .ow { color: #007020; font-weight: bold } /* Operator.Word */ +.highlight .w { color: #bbbbbb } /* Text.Whitespace */ +.highlight .mb { color: #208050 } /* Literal.Number.Bin */ +.highlight .mf { color: #208050 } /* Literal.Number.Float */ +.highlight .mh { color: #208050 } /* Literal.Number.Hex */ +.highlight .mi { color: #208050 } /* Literal.Number.Integer */ +.highlight .mo { color: #208050 } /* Literal.Number.Oct */ +.highlight .sa { color: #4070a0 } /* Literal.String.Affix */ +.highlight .sb { color: #4070a0 } /* Literal.String.Backtick */ +.highlight .sc { color: #4070a0 } /* Literal.String.Char */ +.highlight .dl { color: #4070a0 } /* Literal.String.Delimiter */ +.highlight .sd { color: #4070a0; font-style: italic } /* Literal.String.Doc */ +.highlight .s2 { color: #4070a0 } /* Literal.String.Double */ +.highlight .se { color: #4070a0; font-weight: bold } /* Literal.String.Escape */ +.highlight .sh { color: #4070a0 } /* Literal.String.Heredoc */ +.highlight .si { color: #70a0d0; font-style: italic } /* Literal.String.Interpol */ +.highlight .sx { color: #c65d09 } /* Literal.String.Other */ +.highlight .sr { color: #235388 } /* Literal.String.Regex */ +.highlight .s1 { color: #4070a0 } /* Literal.String.Single */ +.highlight .ss { color: #517918 } /* Literal.String.Symbol */ +.highlight .bp { color: #007020 } /* Name.Builtin.Pseudo */ +.highlight .fm { color: #06287e } /* Name.Function.Magic */ +.highlight .vc { color: #bb60d5 } /* Name.Variable.Class */ +.highlight .vg { color: #bb60d5 } /* Name.Variable.Global */ +.highlight .vi { color: #bb60d5 } /* Name.Variable.Instance */ +.highlight .vm { color: #bb60d5 } /* Name.Variable.Magic */ +.highlight .il { color: #208050 } /* Literal.Number.Integer.Long */ \ No newline at end of file diff --git a/core/binary/conventions.html b/core/binary/conventions.html new file mode 100644 index 00000000..079d7a59 --- /dev/null +++ b/core/binary/conventions.html @@ -0,0 +1,192 @@ + + + + + + + + + Conventions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Conventions

    +

    The binary format for WebAssembly modules is a dense linear encoding of their abstract syntax. +1

    +

    The format is defined by an attribute grammar whose only terminal symbols are bytes. +A byte sequence is a well-formed encoding of a module if and only if it is generated by the grammar.

    +

    Each production of this grammar has exactly one synthesized attribute: the abstract syntax that the respective byte sequence encodes. +Thus, the attribute grammar implicitly defines a decoding function +(i.e., a parsing function for the binary format).

    +

    Except for a few exceptions, the binary grammar closely mirrors the grammar of the abstract syntax.

    +
    +

    Note

    +

    Some phrases of abstract syntax have multiple possible encodings in the binary format. +For example, numbers may be encoded as if they had optional leading zeros. +Implementations of decoders must support all possible alternatives; +implementations of encoders can pick any allowed encoding.

    +
    +

    The recommended extension for files containing WebAssembly modules in binary format is “\(\mathtt{.wasm}\)” +and the recommended Media Type is “\(\mathtt{application/wasm}\)”.

    +
    +
    1
    +

    Additional encoding layers – for example, introducing compression – may be defined on top of the basic representation defined here. +However, such layers are outside the scope of the current specification.

    +
    +
    +
    +

    Grammar

    +

    The following conventions are adopted in defining grammar rules for the binary format. +They mirror the conventions used for abstract syntax. +In order to distinguish symbols of the binary syntax from symbols of the abstract syntax, \(\mathtt{typewriter}\) font is adopted for the former.

    +
      +

    • Terminal symbols are bytes expressed in hexadecimal notation: \(\def\mathdef1207#1{\mathtt{0x#1}}\mathdef1207{0F}\).

      • +

    • Nonterminal symbols are written in typewriter font: \(\mathtt{valtype}, \mathtt{instr}\).

      • +

    • \(B^n\) is a sequence of \(n\geq 0\) iterations of \(B\).

      • +

    • \(B^\ast\) is a possibly empty sequence of iterations of \(B\). +(This is a shorthand for \(B^n\) used where \(n\) is not relevant.)

      • +

    • \(B^?\) is an optional occurrence of \(B\). +(This is a shorthand for \(B^n\) where \(n \leq 1\).)

      • +

    • \(x{:}B\) denotes the same language as the nonterminal \(B\), but also binds the variable \(x\) to the attribute synthesized for \(B\).

      • +

    • Productions are written \(\mathtt{sym} ::= B_1 \Rightarrow A_1 ~|~ \dots ~|~ B_n \Rightarrow A_n\), where each \(A_i\) is the attribute that is synthesized for \(\mathtt{sym}\) in the given case, usually from attribute variables bound in \(B_i\).

      • +

    • Some productions are augmented by side conditions in parentheses, which restrict the applicability of the production. They provide a shorthand for a combinatorial expansion of the production into many separate cases.

      • +

    • If the same meta variable or non-terminal symbol appears multiple times in a production (in the syntax or in an attribute), then all those occurrences must have the same instantiation. +(This is a shorthand for a side condition requiring multiple different variables to be equal.)

      • +
    +
    +

    Note

    +

    For example, the binary grammar for number types is given as follows:

    +
    +\[\begin{split}\begin{array}{llcll@{\qquad\qquad}l} +\def\mathdef1168#1{{}}\mathdef1168{number types} & \href{../binary/types.html#binary-numtype}{\mathtt{numtype}} &::=& + \def\mathdef1208#1{\mathtt{0x#1}}\mathdef1208{7F} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}} \\ &&|& + \def\mathdef1209#1{\mathtt{0x#1}}\mathdef1209{7E} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}} \\ &&|& + \def\mathdef1210#1{\mathtt{0x#1}}\mathdef1210{7D} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}} \\ &&|& + \def\mathdef1211#1{\mathtt{0x#1}}\mathdef1211{7C} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}} \\ +\end{array}\end{split}\]
    +

    Consequently, the byte \(\def\mathdef1212#1{\mathtt{0x#1}}\mathdef1212{7F}\) encodes the type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\), +\(\def\mathdef1213#1{\mathtt{0x#1}}\mathdef1213{7E}\) encodes the type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}\), and so forth. +No other byte value is allowed as the encoding of a number type.

    +

    The binary grammar for limits is defined as follows:

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1168#1{{}}\mathdef1168{limits} & \href{../binary/types.html#binary-limits}{\mathtt{limits}} &::=& + \def\mathdef1214#1{\mathtt{0x#1}}\mathdef1214{00}~~n{:}\href{../binary/values.html#binary-int}{\def\mathdef1173#1{{\mathtt{u}#1}}\mathdef1173{\mathtt{32}}} &\Rightarrow& \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~\epsilon \} \\ &&|& + \def\mathdef1215#1{\mathtt{0x#1}}\mathdef1215{01}~~n{:}\href{../binary/values.html#binary-int}{\def\mathdef1173#1{{\mathtt{u}#1}}\mathdef1173{\mathtt{32}}}~~m{:}\href{../binary/values.html#binary-int}{\def\mathdef1173#1{{\mathtt{u}#1}}\mathdef1173{\mathtt{32}}} &\Rightarrow& \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m \} \\ +\end{array}\end{split}\]
    +

    That is, a limits pair is encoded as either the byte \(\def\mathdef1216#1{\mathtt{0x#1}}\mathdef1216{00}\) followed by the encoding of a \(\href{../syntax/values.html#syntax-int}{\mathit{u32}}\) value, +or the byte \(\def\mathdef1217#1{\mathtt{0x#1}}\mathdef1217{01}\) followed by two such encodings. +The variables \(n\) and \(m\) name the attributes of the respective \(\href{../binary/values.html#binary-int}{\def\mathdef1173#1{{\mathtt{u}#1}}\mathdef1173{\mathtt{32}}}\) nonterminals, which in this case are the actual unsigned integers those decode into. +The attribute of the complete production then is the abstract syntax for the limit, expressed in terms of the former values.

    +
    +
    +
    +

    Auxiliary Notation

    +

    When dealing with binary encodings the following notation is also used:

    +
      +

    • \(\epsilon\) denotes the empty byte sequence.

      • +

    • \(||B||\) is the length of the byte sequence generated from the production \(B\) in a derivation.

      • +
    +
    +
    +

    Vectors

    +

    Vectors are encoded with their \(\href{../binary/values.html#binary-int}{\def\mathdef1173#1{{\mathtt{u}#1}}\mathdef1173{\mathtt{32}}}\) length followed by the encoding of their element sequence.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef1168#1{{}}\mathdef1168{vector} & \href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\mathtt{B}) &::=& + n{:}\href{../binary/values.html#binary-int}{\def\mathdef1173#1{{\mathtt{u}#1}}\mathdef1173{\mathtt{32}}}~~(x{:}\mathtt{B})^n &\Rightarrow& x^n \\ +\end{array}\end{split}\]
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/binary/index.html b/core/binary/index.html new file mode 100644 index 00000000..3d8ffb86 --- /dev/null +++ b/core/binary/index.html @@ -0,0 +1,167 @@ + + + + + + + + + Binary Format — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Binary Format

    +
    + +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/binary/instructions.html b/core/binary/instructions.html new file mode 100644 index 00000000..66833c26 --- /dev/null +++ b/core/binary/instructions.html @@ -0,0 +1,775 @@ + + + + + + + + + Instructions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Instructions

    +

    Instructions are encoded by opcodes. +Each opcode is represented by a single byte, +and is followed by the instruction’s immediate arguments, where present. +The only exception are structured control instructions, which consist of several opcodes bracketing their nested instruction sequences.

    +
    +

    Note

    +

    Gaps in the byte code ranges for encoding instructions are reserved for future extensions.

    +
    +
    +

    Control Instructions

    +

    Control instructions have varying encodings. For structured instructions, the instruction sequences forming nested blocks are terminated with explicit opcodes for \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\) and \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}\).

    +

    Block types are encoded in special compressed form, by either the byte \(\def\mathdef1296#1{\mathtt{0x#1}}\mathdef1296{40}\) indicating the empty type, as a single value type, or as a type index encoded as a positive signed integer.

    +
    +\[\begin{split}\begin{array}{llcllll} +\def\mathdef1257#1{{}}\mathdef1257{block type} & \href{../binary/instructions.html#binary-blocktype}{\mathtt{blocktype}} &::=& + \def\mathdef1297#1{\mathtt{0x#1}}\mathdef1297{40} &\Rightarrow& \epsilon \\ &&|& + t{:}\href{../binary/types.html#binary-valtype}{\mathtt{valtype}} &\Rightarrow& t \\ &&|& + x{:}\href{../binary/values.html#binary-int}{\def\mathdef1267#1{{\mathtt{s}#1}}\mathdef1267{\mathtt{33}}} &\Rightarrow& x & (\mathrel{\mbox{if}} x \geq 0) \\ +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& + \def\mathdef1298#1{\mathtt{0x#1}}\mathdef1298{00} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}} \\ &&|& + \def\mathdef1299#1{\mathtt{0x#1}}\mathdef1299{01} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{nop}} \\ &&|& + \def\mathdef1300#1{\mathtt{0x#1}}\mathdef1300{02}~~\mathit{bt}{:}\href{../binary/instructions.html#binary-blocktype}{\mathtt{blocktype}}~~(\mathit{in}{:}\href{../binary/instructions.html#binary-instr}{\mathtt{instr}})^\ast~~\def\mathdef1301#1{\mathtt{0x#1}}\mathdef1301{0B} + &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~\mathit{bt}~\mathit{in}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\ &&|& + \def\mathdef1302#1{\mathtt{0x#1}}\mathdef1302{03}~~\mathit{bt}{:}\href{../binary/instructions.html#binary-blocktype}{\mathtt{blocktype}}~~(\mathit{in}{:}\href{../binary/instructions.html#binary-instr}{\mathtt{instr}})^\ast~~\def\mathdef1303#1{\mathtt{0x#1}}\mathdef1303{0B} + &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}~\mathit{bt}~\mathit{in}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\ &&|& + \def\mathdef1304#1{\mathtt{0x#1}}\mathdef1304{04}~~\mathit{bt}{:}\href{../binary/instructions.html#binary-blocktype}{\mathtt{blocktype}}~~(\mathit{in}{:}\href{../binary/instructions.html#binary-instr}{\mathtt{instr}})^\ast~~\def\mathdef1305#1{\mathtt{0x#1}}\mathdef1305{0B} + &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}~\mathit{bt}~\mathit{in}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}~\epsilon~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\ &&|& + \def\mathdef1306#1{\mathtt{0x#1}}\mathdef1306{04}~~\mathit{bt}{:}\href{../binary/instructions.html#binary-blocktype}{\mathtt{blocktype}}~~(\mathit{in}_1{:}\href{../binary/instructions.html#binary-instr}{\mathtt{instr}})^\ast~~ + \def\mathdef1307#1{\mathtt{0x#1}}\mathdef1307{05}~~(\mathit{in}_2{:}\href{../binary/instructions.html#binary-instr}{\mathtt{instr}})^\ast~~\def\mathdef1308#1{\mathtt{0x#1}}\mathdef1308{0B} + &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}~\mathit{bt}~\mathit{in}_1^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}~\mathit{in}_2^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\ &&|& + \def\mathdef1309#1{\mathtt{0x#1}}\mathdef1309{0C}~~l{:}\href{../binary/modules.html#binary-labelidx}{\mathtt{labelidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l \\ &&|& + \def\mathdef1310#1{\mathtt{0x#1}}\mathdef1310{0D}~~l{:}\href{../binary/modules.html#binary-labelidx}{\mathtt{labelidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_if}}~l \\ &&|& + \def\mathdef1311#1{\mathtt{0x#1}}\mathdef1311{0E}~~l^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-labelidx}{\mathtt{labelidx}})~~l_N{:}\href{../binary/modules.html#binary-labelidx}{\mathtt{labelidx}} + &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}~l^\ast~l_N \\ &&|& + \def\mathdef1312#1{\mathtt{0x#1}}\mathdef1312{0F} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}} \\ &&|& + \def\mathdef1313#1{\mathtt{0x#1}}\mathdef1313{10}~~x{:}\href{../binary/modules.html#binary-funcidx}{\mathtt{funcidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call}}~x \\ &&|& + \def\mathdef1314#1{\mathtt{0x#1}}\mathdef1314{11}~~y{:}\href{../binary/modules.html#binary-typeidx}{\mathtt{typeidx}}~~x{:}\href{../binary/modules.html#binary-tableidx}{\mathtt{tableidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}~x~y \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}\) opcode \(\def\mathdef1315#1{\mathtt{0x#1}}\mathdef1315{05}\) in the encoding of an \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}\) instruction can be omitted if the following instruction sequence is empty.

    +

    Unlike any other occurrence, the type index in a block type is encoded as a positive signed integer, so that its signed LEB128 bit pattern cannot collide with the encoding of value types or the special code \(\def\mathdef1316#1{\mathtt{0x#1}}\mathdef1316{40}\), which correspond to the LEB128 encoding of negative integers. +To avoid any loss in the range of allowed indices, it is treated as a 33 bit signed integer.

    +
    +
    +
    +

    Reference Instructions

    +

    Reference instructions are represented by single byte codes.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& \dots \\ &&|& + \def\mathdef1317#1{\mathtt{0x#1}}\mathdef1317{D0}~~t{:}\href{../binary/types.html#binary-reftype}{\mathtt{reftype}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t \\ &&|& + \def\mathdef1318#1{\mathtt{0x#1}}\mathdef1318{D1} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}is\_null}} \\ &&|& + \def\mathdef1319#1{\mathtt{0x#1}}\mathdef1319{D2}~~x{:}\href{../binary/modules.html#binary-funcidx}{\mathtt{funcidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~x \\ +\end{array}\end{split}\]
    +
    +
    +

    Parametric Instructions

    +

    Parametric instructions are represented by single byte codes, possibly followed by a type annotation.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& \dots \\ &&|& + \def\mathdef1320#1{\mathtt{0x#1}}\mathdef1320{1A} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{drop}} \\ &&|& + \def\mathdef1321#1{\mathtt{0x#1}}\mathdef1321{1B} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}} \\ &&|& + \def\mathdef1322#1{\mathtt{0x#1}}\mathdef1322{1C}~~t^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/types.html#binary-valtype}{\mathtt{valtype}}) &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}~t^\ast \\ +\end{array}\end{split}\]
    +
    +
    +

    Variable Instructions

    +

    Variable instructions are represented by byte codes followed by the encoding of the respective index.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& \dots \\ &&|& + \def\mathdef1323#1{\mathtt{0x#1}}\mathdef1323{20}~~x{:}\href{../binary/modules.html#binary-localidx}{\mathtt{localidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.get}}~x \\ &&|& + \def\mathdef1324#1{\mathtt{0x#1}}\mathdef1324{21}~~x{:}\href{../binary/modules.html#binary-localidx}{\mathtt{localidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.set}}~x \\ &&|& + \def\mathdef1325#1{\mathtt{0x#1}}\mathdef1325{22}~~x{:}\href{../binary/modules.html#binary-localidx}{\mathtt{localidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.tee}}~x \\ &&|& + \def\mathdef1326#1{\mathtt{0x#1}}\mathdef1326{23}~~x{:}\href{../binary/modules.html#binary-globalidx}{\mathtt{globalidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.get}}~x \\ &&|& + \def\mathdef1327#1{\mathtt{0x#1}}\mathdef1327{24}~~x{:}\href{../binary/modules.html#binary-globalidx}{\mathtt{globalidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.set}}~x \\ +\end{array}\end{split}\]
    +
    +
    +

    Table Instructions

    +

    Table instructions are represented either by a single byte or a one byte prefix followed by a variable-length unsigned integer.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& \dots \\ &&|& + \def\mathdef1328#1{\mathtt{0x#1}}\mathdef1328{25}~~x{:}\href{../binary/modules.html#binary-tableidx}{\mathtt{tableidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}~x \\ &&|& + \def\mathdef1329#1{\mathtt{0x#1}}\mathdef1329{26}~~x{:}\href{../binary/modules.html#binary-tableidx}{\mathtt{tableidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x \\ &&|& + \def\mathdef1330#1{\mathtt{0x#1}}\mathdef1330{FC}~~12{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~y{:}\href{../binary/modules.html#binary-elemidx}{\mathtt{elemidx}}~~x{:}\href{../binary/modules.html#binary-tableidx}{\mathtt{tableidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}~x~y \\ &&|& + \def\mathdef1331#1{\mathtt{0x#1}}\mathdef1331{FC}~~13{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~x{:}\href{../binary/modules.html#binary-elemidx}{\mathtt{elemidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem.drop}}~x \\ &&|& + \def\mathdef1332#1{\mathtt{0x#1}}\mathdef1332{FC}~~14{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~x{:}\href{../binary/modules.html#binary-tableidx}{\mathtt{tableidx}}~~y{:}\href{../binary/modules.html#binary-tableidx}{\mathtt{tableidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}~x~y \\ &&|& + \def\mathdef1333#1{\mathtt{0x#1}}\mathdef1333{FC}~~15{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~x{:}\href{../binary/modules.html#binary-tableidx}{\mathtt{tableidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.grow}}~x \\ &&|& + \def\mathdef1334#1{\mathtt{0x#1}}\mathdef1334{FC}~~16{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~x{:}\href{../binary/modules.html#binary-tableidx}{\mathtt{tableidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.size}}~x \\ &&|& + \def\mathdef1335#1{\mathtt{0x#1}}\mathdef1335{FC}~~17{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~x{:}\href{../binary/modules.html#binary-tableidx}{\mathtt{tableidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.fill}}~x \\ +\end{array}\end{split}\]
    +
    +
    +

    Memory Instructions

    +

    Each variant of memory instruction is encoded with a different byte code. Loads and stores are followed by the encoding of their \(\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\) immediate.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{memory argument} & \href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &::=& + a{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~o{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~a,~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~o \} \\ +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& \dots \\ &&|& + \def\mathdef1336#1{\mathtt{0x#1}}\mathdef1336{28}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~m \\ &&|& + \def\mathdef1337#1{\mathtt{0x#1}}\mathdef1337{29}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~m \\ &&|& + \def\mathdef1338#1{\mathtt{0x#1}}\mathdef1338{2A}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~m \\ &&|& + \def\mathdef1339#1{\mathtt{0x#1}}\mathdef1339{2B}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~m \\ &&|& + \def\mathdef1340#1{\mathtt{0x#1}}\mathdef1340{2C}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_s}~m \\ &&|& + \def\mathdef1341#1{\mathtt{0x#1}}\mathdef1341{2D}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_u}~m \\ &&|& + \def\mathdef1342#1{\mathtt{0x#1}}\mathdef1342{2E}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_s}~m \\ &&|& + \def\mathdef1343#1{\mathtt{0x#1}}\mathdef1343{2F}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_u}~m \\ &&|& + \def\mathdef1344#1{\mathtt{0x#1}}\mathdef1344{30}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_s}~m \\ &&|& + \def\mathdef1345#1{\mathtt{0x#1}}\mathdef1345{31}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_u}~m \\ &&|& + \def\mathdef1346#1{\mathtt{0x#1}}\mathdef1346{32}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_s}~m \\ &&|& + \def\mathdef1347#1{\mathtt{0x#1}}\mathdef1347{33}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_u}~m \\ &&|& + \def\mathdef1348#1{\mathtt{0x#1}}\mathdef1348{34}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_s}~m \\ &&|& + \def\mathdef1349#1{\mathtt{0x#1}}\mathdef1349{35}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_u}~m \\ &&|& + \def\mathdef1350#1{\mathtt{0x#1}}\mathdef1350{36}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~m \\ &&|& + \def\mathdef1351#1{\mathtt{0x#1}}\mathdef1351{37}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~m \\ &&|& + \def\mathdef1352#1{\mathtt{0x#1}}\mathdef1352{38}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~m \\ &&|& + \def\mathdef1353#1{\mathtt{0x#1}}\mathdef1353{39}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~m \\ &&|& + \def\mathdef1354#1{\mathtt{0x#1}}\mathdef1354{3A}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~m \\ &&|& + \def\mathdef1355#1{\mathtt{0x#1}}\mathdef1355{3B}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{16}~m \\ &&|& + \def\mathdef1356#1{\mathtt{0x#1}}\mathdef1356{3C}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~m \\ &&|& + \def\mathdef1357#1{\mathtt{0x#1}}\mathdef1357{3D}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{16}~m \\ &&|& + \def\mathdef1358#1{\mathtt{0x#1}}\mathdef1358{3E}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{32}~m \\ &&|& + \def\mathdef1359#1{\mathtt{0x#1}}\mathdef1359{3F}~~\def\mathdef1360#1{\mathtt{0x#1}}\mathdef1360{00} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.size}} \\ &&|& + \def\mathdef1361#1{\mathtt{0x#1}}\mathdef1361{40}~~\def\mathdef1362#1{\mathtt{0x#1}}\mathdef1362{00} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.grow}} \\ &&|& + \def\mathdef1363#1{\mathtt{0x#1}}\mathdef1363{FC}~~8{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~x{:}\href{../binary/modules.html#binary-dataidx}{\mathtt{dataidx}}~\def\mathdef1364#1{\mathtt{0x#1}}\mathdef1364{00} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~x \\ &&|& + \def\mathdef1365#1{\mathtt{0x#1}}\mathdef1365{FC}~~9{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~x{:}\href{../binary/modules.html#binary-dataidx}{\mathtt{dataidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data.drop}}~x \\ &&|& + \def\mathdef1366#1{\mathtt{0x#1}}\mathdef1366{FC}~~10{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~\def\mathdef1367#1{\mathtt{0x#1}}\mathdef1367{00}~~\def\mathdef1368#1{\mathtt{0x#1}}\mathdef1368{00} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}} \\ &&|& + \def\mathdef1369#1{\mathtt{0x#1}}\mathdef1369{FC}~~11{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~\def\mathdef1370#1{\mathtt{0x#1}}\mathdef1370{00} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}} \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    In future versions of WebAssembly, the additional zero bytes occurring in the encoding of the \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.size}}\), \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.grow}}\), \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}}\), and \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}}\) instructions may be used to index additional memories.

    +
    +
    +
    +

    Numeric Instructions

    +

    All variants of numeric instructions are represented by separate byte codes.

    +

    The \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}\) instructions are followed by the respective literal.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& \dots \\&&|& + \def\mathdef1371#1{\mathtt{0x#1}}\mathdef1371{41}~~n{:}\href{../binary/values.html#binary-int}{\def\mathdef1270#1{{\mathtt{i}#1}}\mathdef1270{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n \\ &&|& + \def\mathdef1372#1{\mathtt{0x#1}}\mathdef1372{42}~~n{:}\href{../binary/values.html#binary-int}{\def\mathdef1271#1{{\mathtt{i}#1}}\mathdef1271{\mathtt{64}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n \\ &&|& + \def\mathdef1373#1{\mathtt{0x#1}}\mathdef1373{43}~~z{:}\href{../binary/values.html#binary-float}{\def\mathdef1273#1{{\mathtt{f}#1}}\mathdef1273{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~z \\ &&|& + \def\mathdef1374#1{\mathtt{0x#1}}\mathdef1374{44}~~z{:}\href{../binary/values.html#binary-float}{\def\mathdef1274#1{{\mathtt{f}#1}}\mathdef1274{\mathtt{64}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~z \\ +\end{array}\end{split}\]
    +

    All other numeric instructions are plain opcodes without any immediates.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& \dots && \phantom{thisshouldbeenough} \\&&|& + \def\mathdef1375#1{\mathtt{0x#1}}\mathdef1375{45} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eqz}} \\ &&|& + \def\mathdef1376#1{\mathtt{0x#1}}\mathdef1376{46} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eq}} \\ &&|& + \def\mathdef1377#1{\mathtt{0x#1}}\mathdef1377{47} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ne}} \\ &&|& + \def\mathdef1378#1{\mathtt{0x#1}}\mathdef1378{48} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\mathsf{\_s} \\ &&|& + \def\mathdef1379#1{\mathtt{0x#1}}\mathdef1379{49} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\mathsf{\_u} \\ &&|& + \def\mathdef1380#1{\mathtt{0x#1}}\mathdef1380{4A} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\mathsf{\_s} \\ &&|& + \def\mathdef1381#1{\mathtt{0x#1}}\mathdef1381{4B} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\mathsf{\_u} \\ &&|& + \def\mathdef1382#1{\mathtt{0x#1}}\mathdef1382{4C} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\mathsf{\_s} \\ &&|& + \def\mathdef1383#1{\mathtt{0x#1}}\mathdef1383{4D} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\mathsf{\_u} \\ &&|& + \def\mathdef1384#1{\mathtt{0x#1}}\mathdef1384{4E} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\mathsf{\_s} \\ &&|& + \def\mathdef1385#1{\mathtt{0x#1}}\mathdef1385{4F} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\mathsf{\_u} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef1386#1{\mathtt{0x#1}}\mathdef1386{50} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eqz}} \\ &&|& + \def\mathdef1387#1{\mathtt{0x#1}}\mathdef1387{51} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eq}} \\ &&|& + \def\mathdef1388#1{\mathtt{0x#1}}\mathdef1388{52} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ne}} \\ &&|& + \def\mathdef1389#1{\mathtt{0x#1}}\mathdef1389{53} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\mathsf{\_s} \\ &&|& + \def\mathdef1390#1{\mathtt{0x#1}}\mathdef1390{54} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\mathsf{\_u} \\ &&|& + \def\mathdef1391#1{\mathtt{0x#1}}\mathdef1391{55} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\mathsf{\_s} \\ &&|& + \def\mathdef1392#1{\mathtt{0x#1}}\mathdef1392{56} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\mathsf{\_u} \\ &&|& + \def\mathdef1393#1{\mathtt{0x#1}}\mathdef1393{57} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\mathsf{\_s} \\ &&|& + \def\mathdef1394#1{\mathtt{0x#1}}\mathdef1394{58} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\mathsf{\_u} \\ &&|& + \def\mathdef1395#1{\mathtt{0x#1}}\mathdef1395{59} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\mathsf{\_s} \\ &&|& + \def\mathdef1396#1{\mathtt{0x#1}}\mathdef1396{5A} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\mathsf{\_u} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef1397#1{\mathtt{0x#1}}\mathdef1397{5B} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eq}} \\ &&|& + \def\mathdef1398#1{\mathtt{0x#1}}\mathdef1398{5C} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ne}} \\ &&|& + \def\mathdef1399#1{\mathtt{0x#1}}\mathdef1399{5D} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}} \\ &&|& + \def\mathdef1400#1{\mathtt{0x#1}}\mathdef1400{5E} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}} \\ &&|& + \def\mathdef1401#1{\mathtt{0x#1}}\mathdef1401{5F} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}} \\ &&|& + \def\mathdef1402#1{\mathtt{0x#1}}\mathdef1402{60} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef1403#1{\mathtt{0x#1}}\mathdef1403{61} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eq}} \\ &&|& + \def\mathdef1404#1{\mathtt{0x#1}}\mathdef1404{62} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ne}} \\ &&|& + \def\mathdef1405#1{\mathtt{0x#1}}\mathdef1405{63} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}} \\ &&|& + \def\mathdef1406#1{\mathtt{0x#1}}\mathdef1406{64} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}} \\ &&|& + \def\mathdef1407#1{\mathtt{0x#1}}\mathdef1407{65} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}} \\ &&|& + \def\mathdef1408#1{\mathtt{0x#1}}\mathdef1408{66} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef1409#1{\mathtt{0x#1}}\mathdef1409{67} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{clz}} \\ &&|& + \def\mathdef1410#1{\mathtt{0x#1}}\mathdef1410{68} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ctz}} \\ &&|& + \def\mathdef1411#1{\mathtt{0x#1}}\mathdef1411{69} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{popcnt}} \\ &&|& + \def\mathdef1412#1{\mathtt{0x#1}}\mathdef1412{6A} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}} \\ &&|& + \def\mathdef1413#1{\mathtt{0x#1}}\mathdef1413{6B} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sub}} \\ &&|& + \def\mathdef1414#1{\mathtt{0x#1}}\mathdef1414{6C} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}} \\ &&|& + \def\mathdef1415#1{\mathtt{0x#1}}\mathdef1415{6D} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\mathsf{\_s} \\ &&|& + \def\mathdef1416#1{\mathtt{0x#1}}\mathdef1416{6E} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\mathsf{\_u} \\ &&|& + \def\mathdef1417#1{\mathtt{0x#1}}\mathdef1417{6F} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rem}}\mathsf{\_s} \\ &&|& + \def\mathdef1418#1{\mathtt{0x#1}}\mathdef1418{70} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rem}}\mathsf{\_u} \\ &&|& + \def\mathdef1419#1{\mathtt{0x#1}}\mathdef1419{71} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{and}} \\ &&|& + \def\mathdef1420#1{\mathtt{0x#1}}\mathdef1420{72} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{or}} \\ &&|& + \def\mathdef1421#1{\mathtt{0x#1}}\mathdef1421{73} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{xor}} \\ &&|& + \def\mathdef1422#1{\mathtt{0x#1}}\mathdef1422{74} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shl}} \\ &&|& + \def\mathdef1423#1{\mathtt{0x#1}}\mathdef1423{75} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shr}}\mathsf{\_s} \\ &&|& + \def\mathdef1424#1{\mathtt{0x#1}}\mathdef1424{76} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shr}}\mathsf{\_u} \\ &&|& + \def\mathdef1425#1{\mathtt{0x#1}}\mathdef1425{77} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rotl}} \\ &&|& + \def\mathdef1426#1{\mathtt{0x#1}}\mathdef1426{78} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rotr}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef1427#1{\mathtt{0x#1}}\mathdef1427{79} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{clz}} \\ &&|& + \def\mathdef1428#1{\mathtt{0x#1}}\mathdef1428{7A} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ctz}} \\ &&|& + \def\mathdef1429#1{\mathtt{0x#1}}\mathdef1429{7B} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{popcnt}} \\ &&|& + \def\mathdef1430#1{\mathtt{0x#1}}\mathdef1430{7C} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}} \\ &&|& + \def\mathdef1431#1{\mathtt{0x#1}}\mathdef1431{7D} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sub}} \\ &&|& + \def\mathdef1432#1{\mathtt{0x#1}}\mathdef1432{7E} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}} \\ &&|& + \def\mathdef1433#1{\mathtt{0x#1}}\mathdef1433{7F} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\mathsf{\_s} \\ &&|& + \def\mathdef1434#1{\mathtt{0x#1}}\mathdef1434{80} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\mathsf{\_u} \\ &&|& + \def\mathdef1435#1{\mathtt{0x#1}}\mathdef1435{81} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rem}}\mathsf{\_s} \\ &&|& + \def\mathdef1436#1{\mathtt{0x#1}}\mathdef1436{82} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rem}}\mathsf{\_u} \\ &&|& + \def\mathdef1437#1{\mathtt{0x#1}}\mathdef1437{83} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{and}} \\ &&|& + \def\mathdef1438#1{\mathtt{0x#1}}\mathdef1438{84} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{or}} \\ &&|& + \def\mathdef1439#1{\mathtt{0x#1}}\mathdef1439{85} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{xor}} \\ &&|& + \def\mathdef1440#1{\mathtt{0x#1}}\mathdef1440{86} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shl}} \\ &&|& + \def\mathdef1441#1{\mathtt{0x#1}}\mathdef1441{87} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shr}}\mathsf{\_s} \\ &&|& + \def\mathdef1442#1{\mathtt{0x#1}}\mathdef1442{88} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shr}}\mathsf{\_u} \\ &&|& + \def\mathdef1443#1{\mathtt{0x#1}}\mathdef1443{89} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rotl}} \\ &&|& + \def\mathdef1444#1{\mathtt{0x#1}}\mathdef1444{8A} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rotr}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef1445#1{\mathtt{0x#1}}\mathdef1445{8B} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{abs}} \\ &&|& + \def\mathdef1446#1{\mathtt{0x#1}}\mathdef1446{8C} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{neg}} \\ &&|& + \def\mathdef1447#1{\mathtt{0x#1}}\mathdef1447{8D} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ceil}} \\ &&|& + \def\mathdef1448#1{\mathtt{0x#1}}\mathdef1448{8E} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{floor}} \\ &&|& + \def\mathdef1449#1{\mathtt{0x#1}}\mathdef1449{8F} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}} \\ &&|& + \def\mathdef1450#1{\mathtt{0x#1}}\mathdef1450{90} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{nearest}} \\ &&|& + \def\mathdef1451#1{\mathtt{0x#1}}\mathdef1451{91} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sqrt}} \\ &&|& + \def\mathdef1452#1{\mathtt{0x#1}}\mathdef1452{92} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}} \\ &&|& + \def\mathdef1453#1{\mathtt{0x#1}}\mathdef1453{93} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sub}} \\ &&|& + \def\mathdef1454#1{\mathtt{0x#1}}\mathdef1454{94} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}} \\ &&|& + \def\mathdef1455#1{\mathtt{0x#1}}\mathdef1455{95} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}} \\ &&|& + \def\mathdef1456#1{\mathtt{0x#1}}\mathdef1456{96} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{min}} \\ &&|& + \def\mathdef1457#1{\mathtt{0x#1}}\mathdef1457{97} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{max}} \\ &&|& + \def\mathdef1458#1{\mathtt{0x#1}}\mathdef1458{98} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{copysign}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef1459#1{\mathtt{0x#1}}\mathdef1459{99} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{abs}} \\ &&|& + \def\mathdef1460#1{\mathtt{0x#1}}\mathdef1460{9A} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{neg}} \\ &&|& + \def\mathdef1461#1{\mathtt{0x#1}}\mathdef1461{9B} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ceil}} \\ &&|& + \def\mathdef1462#1{\mathtt{0x#1}}\mathdef1462{9C} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{floor}} \\ &&|& + \def\mathdef1463#1{\mathtt{0x#1}}\mathdef1463{9D} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}} \\ &&|& + \def\mathdef1464#1{\mathtt{0x#1}}\mathdef1464{9E} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{nearest}} \\ &&|& + \def\mathdef1465#1{\mathtt{0x#1}}\mathdef1465{9F} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sqrt}} \\ &&|& + \def\mathdef1466#1{\mathtt{0x#1}}\mathdef1466{A0} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}} \\ &&|& + \def\mathdef1467#1{\mathtt{0x#1}}\mathdef1467{A1} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sub}} \\ &&|& + \def\mathdef1468#1{\mathtt{0x#1}}\mathdef1468{A2} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}} \\ &&|& + \def\mathdef1469#1{\mathtt{0x#1}}\mathdef1469{A3} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}} \\ &&|& + \def\mathdef1470#1{\mathtt{0x#1}}\mathdef1470{A4} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{min}} \\ &&|& + \def\mathdef1471#1{\mathtt{0x#1}}\mathdef1471{A5} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{max}} \\ &&|& + \def\mathdef1472#1{\mathtt{0x#1}}\mathdef1472{A6} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{copysign}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef1473#1{\mathtt{0x#1}}\mathdef1473{A7} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{wrap}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}} \\ &&|& + \def\mathdef1474#1{\mathtt{0x#1}}\mathdef1474{A8} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_s} \\ &&|& + \def\mathdef1475#1{\mathtt{0x#1}}\mathdef1475{A9} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_u} \\ &&|& + \def\mathdef1476#1{\mathtt{0x#1}}\mathdef1476{AA} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_s} \\ &&|& + \def\mathdef1477#1{\mathtt{0x#1}}\mathdef1477{AB} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_u} \\ &&|& + \def\mathdef1478#1{\mathtt{0x#1}}\mathdef1478{AC} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_s} \\ &&|& + \def\mathdef1479#1{\mathtt{0x#1}}\mathdef1479{AD} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_u} \\ &&|& + \def\mathdef1480#1{\mathtt{0x#1}}\mathdef1480{AE} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_s} \\ &&|& + \def\mathdef1481#1{\mathtt{0x#1}}\mathdef1481{AF} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_u} \\ &&|& + \def\mathdef1482#1{\mathtt{0x#1}}\mathdef1482{B0} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_s} \\ &&|& + \def\mathdef1483#1{\mathtt{0x#1}}\mathdef1483{B1} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_u} \\ &&|& + \def\mathdef1484#1{\mathtt{0x#1}}\mathdef1484{B2} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_s} \\ &&|& + \def\mathdef1485#1{\mathtt{0x#1}}\mathdef1485{B3} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_u} \\ &&|& + \def\mathdef1486#1{\mathtt{0x#1}}\mathdef1486{B4} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}\mathsf{\_s} \\ &&|& + \def\mathdef1487#1{\mathtt{0x#1}}\mathdef1487{B5} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}\mathsf{\_u} \\ &&|& + \def\mathdef1488#1{\mathtt{0x#1}}\mathdef1488{B6} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{demote}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}} \\ &&|& + \def\mathdef1489#1{\mathtt{0x#1}}\mathdef1489{B7} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_s} \\ &&|& + \def\mathdef1490#1{\mathtt{0x#1}}\mathdef1490{B8} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_u} \\ &&|& + \def\mathdef1491#1{\mathtt{0x#1}}\mathdef1491{B9} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}\mathsf{\_s} \\ &&|& + \def\mathdef1492#1{\mathtt{0x#1}}\mathdef1492{BA} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}\mathsf{\_u} \\ &&|& + \def\mathdef1493#1{\mathtt{0x#1}}\mathdef1493{BB} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{promote}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}} \\ &&|& + \def\mathdef1494#1{\mathtt{0x#1}}\mathdef1494{BC} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{reinterpret}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}} \\ &&|& + \def\mathdef1495#1{\mathtt{0x#1}}\mathdef1495{BD} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{reinterpret}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}} \\ &&|& + \def\mathdef1496#1{\mathtt{0x#1}}\mathdef1496{BE} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{reinterpret}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}} \\ &&|& + \def\mathdef1497#1{\mathtt{0x#1}}\mathdef1497{BF} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{reinterpret}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef1498#1{\mathtt{0x#1}}\mathdef1498{C0} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{8\_s} \\ &&|& + \def\mathdef1499#1{\mathtt{0x#1}}\mathdef1499{C1} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{16\_s} \\ &&|& + \def\mathdef1500#1{\mathtt{0x#1}}\mathdef1500{C2} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{8\_s} \\ &&|& + \def\mathdef1501#1{\mathtt{0x#1}}\mathdef1501{C3} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{16\_s} \\ &&|& + \def\mathdef1502#1{\mathtt{0x#1}}\mathdef1502{C4} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{32\_s} \\ +\end{array}\end{split}\]
    +

    The saturating truncation instructions all have a one byte prefix, +whereas the actual opcode is encoded by a variable-length unsigned integer.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& \dots && \phantom{thisshouldbeenough} \\&&|& + \def\mathdef1503#1{\mathtt{0x#1}}\mathdef1503{FC}~~0{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_s} \\ &&|& + \def\mathdef1504#1{\mathtt{0x#1}}\mathdef1504{FC}~~1{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_u} \\ &&|& + \def\mathdef1505#1{\mathtt{0x#1}}\mathdef1505{FC}~~2{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_s} \\ &&|& + \def\mathdef1506#1{\mathtt{0x#1}}\mathdef1506{FC}~~3{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_u} \\ &&|& + \def\mathdef1507#1{\mathtt{0x#1}}\mathdef1507{FC}~~4{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_s} \\ &&|& + \def\mathdef1508#1{\mathtt{0x#1}}\mathdef1508{FC}~~5{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_u} \\ &&|& + \def\mathdef1509#1{\mathtt{0x#1}}\mathdef1509{FC}~~6{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_s} \\ &&|& + \def\mathdef1510#1{\mathtt{0x#1}}\mathdef1510{FC}~~7{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_u} \\ +\end{array}\end{split}\]
    +
    +
    +

    Vector Instructions

    +

    All variants of vector instructions are represented by separate byte codes. +They all have a one byte prefix, whereas the actual opcode is encoded by a variable-length unsigned integer.

    +

    Vector loads and stores are followed by the encoding of their \(\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\) immediate.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{lane index} & \href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &::=& + l{:}\href{../binary/values.html#binary-byte}{\mathtt{byte}} &\Rightarrow& l \\ +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& \dots \\&&|& + \def\mathdef1511#1{\mathtt{0x#1}}\mathdef1511{FD}~~0{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~m \\ &&|& + \def\mathdef1512#1{\mathtt{0x#1}}\mathdef1512{FD}~~1{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8x8\_s}~m \\ &&|& + \def\mathdef1513#1{\mathtt{0x#1}}\mathdef1513{FD}~~2{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8x8\_u}~m \\ &&|& + \def\mathdef1514#1{\mathtt{0x#1}}\mathdef1514{FD}~~3{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16x4\_s}~m \\ &&|& + \def\mathdef1515#1{\mathtt{0x#1}}\mathdef1515{FD}~~4{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16x4\_u}~m \\ &&|& + \def\mathdef1516#1{\mathtt{0x#1}}\mathdef1516{FD}~~5{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32x2\_s}~m \\ &&|& + \def\mathdef1517#1{\mathtt{0x#1}}\mathdef1517{FD}~~6{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32x2\_u}~m \\ &&|& + \def\mathdef1518#1{\mathtt{0x#1}}\mathdef1518{FD}~~7{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_splat}~m \\ &&|& + \def\mathdef1519#1{\mathtt{0x#1}}\mathdef1519{FD}~~8{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_splat}~m \\ &&|& + \def\mathdef1520#1{\mathtt{0x#1}}\mathdef1520{FD}~~9{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_splat}~m \\ &&|& + \def\mathdef1521#1{\mathtt{0x#1}}\mathdef1521{FD}~~10{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{64\_splat}~m \\ &&|& + \def\mathdef1522#1{\mathtt{0x#1}}\mathdef1522{FD}~~92{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_zero}~m \\ &&|& + \def\mathdef1523#1{\mathtt{0x#1}}\mathdef1523{FD}~~93{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{64\_zero}~m \\ &&|& + \def\mathdef1524#1{\mathtt{0x#1}}\mathdef1524{FD}~~11{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~m \\ &&|& + \def\mathdef1525#1{\mathtt{0x#1}}\mathdef1525{FD}~~84{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}}~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_lane}~m~l \\ &&|& + \def\mathdef1526#1{\mathtt{0x#1}}\mathdef1526{FD}~~85{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}}~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_lane}~m~l \\ &&|& + \def\mathdef1527#1{\mathtt{0x#1}}\mathdef1527{FD}~~86{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}}~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_lane}~m~l \\ &&|& + \def\mathdef1528#1{\mathtt{0x#1}}\mathdef1528{FD}~~87{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}}~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{64\_lane}~m~l \\ &&|& + \def\mathdef1529#1{\mathtt{0x#1}}\mathdef1529{FD}~~88{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}}~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8\_lane}~m~l \\ &&|& + \def\mathdef1530#1{\mathtt{0x#1}}\mathdef1530{FD}~~89{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}}~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{16\_lane}~m~l \\ &&|& + \def\mathdef1531#1{\mathtt{0x#1}}\mathdef1531{FD}~~90{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}}~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{32\_lane}~m~l \\ &&|& + \def\mathdef1532#1{\mathtt{0x#1}}\mathdef1532{FD}~~91{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~m{:}\href{../binary/instructions.html#binary-memarg}{\mathtt{memarg}}~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{64\_lane}~m~l \\ +\end{array}\end{split}\]
    +

    The \(\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}\) instruction is followed by 16 immediate bytes, which are converted into a \(\href{../syntax/values.html#syntax-int}{\mathit{i128}}\) in \(\href{../exec/numerics.html#aux-littleendian}{\mathrm{littleendian}}\) byte order:

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& \dots \\&&|& + \def\mathdef1533#1{\mathtt{0x#1}}\mathdef1533{FD}~~12{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~(b{:}\href{../binary/values.html#binary-byte}{\mathtt{byte}})^{16} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~ + bytes_{\mathsf{i128}}^{-1}(b_{0}~\dots~b_{15}) \\ +\end{array}\end{split}\]
    +

    The \(\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}\) instruction is also followed by the encoding of 16 \(\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\) immediates.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& \dots \\&&|& + \def\mathdef1534#1{\mathtt{0x#1}}\mathdef1534{FD}~~13{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~(l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}})^{16} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}~l^{16} \\ +\end{array}\end{split}\]
    +

    \(\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\) and \(\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}\) instructions are followed by the encoding of a \(\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\) immediate.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& \dots \\&&|& + \def\mathdef1535#1{\mathtt{0x#1}}\mathdef1535{FD}~~21{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_s}~l \\ &&|& + \def\mathdef1536#1{\mathtt{0x#1}}\mathdef1536{FD}~~22{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_u}~l \\ &&|& + \def\mathdef1537#1{\mathtt{0x#1}}\mathdef1537{FD}~~23{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~l \\ &&|& + \def\mathdef1538#1{\mathtt{0x#1}}\mathdef1538{FD}~~24{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_s}~l \\ &&|& + \def\mathdef1539#1{\mathtt{0x#1}}\mathdef1539{FD}~~25{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_u}~l \\ &&|& + \def\mathdef1540#1{\mathtt{0x#1}}\mathdef1540{FD}~~26{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~l \\ &&|& + \def\mathdef1541#1{\mathtt{0x#1}}\mathdef1541{FD}~~27{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~l \\ &&|& + \def\mathdef1542#1{\mathtt{0x#1}}\mathdef1542{FD}~~28{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~l \\ &&|& + \def\mathdef1543#1{\mathtt{0x#1}}\mathdef1543{FD}~~29{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~l \\ &&|& + \def\mathdef1544#1{\mathtt{0x#1}}\mathdef1544{FD}~~30{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~l \\ &&|& + \def\mathdef1545#1{\mathtt{0x#1}}\mathdef1545{FD}~~31{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~l \\ &&|& + \def\mathdef1546#1{\mathtt{0x#1}}\mathdef1546{FD}~~32{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~l \\ &&|& + \def\mathdef1547#1{\mathtt{0x#1}}\mathdef1547{FD}~~33{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~l \\ &&|& + \def\mathdef1548#1{\mathtt{0x#1}}\mathdef1548{FD}~~34{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}}~~l{:}\href{../binary/instructions.html#binary-laneidx}{\mathtt{laneidx}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~l \\ +\end{array}\end{split}\]
    +

    All other vector instructions are plain opcodes without any immediates.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{instruction} & \href{../binary/instructions.html#binary-instr}{\mathtt{instr}} &::=& \dots && \phantom{vechaslongerinstructionnames} \\&&|& + \def\mathdef1549#1{\mathtt{0x#1}}\mathdef1549{FD}~~14{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{swizzle}} \\ &&|& + \def\mathdef1550#1{\mathtt{0x#1}}\mathdef1550{FD}~~15{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}} \\ &&|& + \def\mathdef1551#1{\mathtt{0x#1}}\mathdef1551{FD}~~16{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}} \\ &&|& + \def\mathdef1552#1{\mathtt{0x#1}}\mathdef1552{FD}~~17{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}} \\ &&|& + \def\mathdef1553#1{\mathtt{0x#1}}\mathdef1553{FD}~~18{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}} \\ &&|& + \def\mathdef1554#1{\mathtt{0x#1}}\mathdef1554{FD}~~19{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}} \\ &&|& + \def\mathdef1555#1{\mathtt{0x#1}}\mathdef1555{FD}~~20{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1556#1{\mathtt{0x#1}}\mathdef1556{FD}~~35{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}} \\ &&|& + \def\mathdef1557#1{\mathtt{0x#1}}\mathdef1557{FD}~~36{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}} \\ &&|& + \def\mathdef1558#1{\mathtt{0x#1}}\mathdef1558{FD}~~37{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_s} \\ &&|& + \def\mathdef1559#1{\mathtt{0x#1}}\mathdef1559{FD}~~38{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_u} \\ &&|& + \def\mathdef1560#1{\mathtt{0x#1}}\mathdef1560{FD}~~39{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_s} \\ &&|& + \def\mathdef1561#1{\mathtt{0x#1}}\mathdef1561{FD}~~40{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_u} \\ &&|& + \def\mathdef1562#1{\mathtt{0x#1}}\mathdef1562{FD}~~41{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_s} \\ &&|& + \def\mathdef1563#1{\mathtt{0x#1}}\mathdef1563{FD}~~42{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_u} \\ &&|& + \def\mathdef1564#1{\mathtt{0x#1}}\mathdef1564{FD}~~43{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_s} \\ &&|& + \def\mathdef1565#1{\mathtt{0x#1}}\mathdef1565{FD}~~44{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_u} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1566#1{\mathtt{0x#1}}\mathdef1566{FD}~~45{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}} \\ &&|& + \def\mathdef1567#1{\mathtt{0x#1}}\mathdef1567{FD}~~46{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}} \\ &&|& + \def\mathdef1568#1{\mathtt{0x#1}}\mathdef1568{FD}~~47{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_s} \\ &&|& + \def\mathdef1569#1{\mathtt{0x#1}}\mathdef1569{FD}~~48{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_u} \\ &&|& + \def\mathdef1570#1{\mathtt{0x#1}}\mathdef1570{FD}~~49{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_s} \\ &&|& + \def\mathdef1571#1{\mathtt{0x#1}}\mathdef1571{FD}~~50{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_u} \\ &&|& + \def\mathdef1572#1{\mathtt{0x#1}}\mathdef1572{FD}~~51{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_s} \\ &&|& + \def\mathdef1573#1{\mathtt{0x#1}}\mathdef1573{FD}~~52{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_u} \\ &&|& + \def\mathdef1574#1{\mathtt{0x#1}}\mathdef1574{FD}~~53{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_s} \\ &&|& + \def\mathdef1575#1{\mathtt{0x#1}}\mathdef1575{FD}~~54{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_u} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1576#1{\mathtt{0x#1}}\mathdef1576{FD}~~55{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}} \\ &&|& + \def\mathdef1577#1{\mathtt{0x#1}}\mathdef1577{FD}~~56{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}} \\ &&|& + \def\mathdef1578#1{\mathtt{0x#1}}\mathdef1578{FD}~~57{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_s} \\ &&|& + \def\mathdef1579#1{\mathtt{0x#1}}\mathdef1579{FD}~~58{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_u} \\ &&|& + \def\mathdef1580#1{\mathtt{0x#1}}\mathdef1580{FD}~~59{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_s} \\ &&|& + \def\mathdef1581#1{\mathtt{0x#1}}\mathdef1581{FD}~~60{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_u} \\ &&|& + \def\mathdef1582#1{\mathtt{0x#1}}\mathdef1582{FD}~~61{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_s} \\ &&|& + \def\mathdef1583#1{\mathtt{0x#1}}\mathdef1583{FD}~~62{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_u} \\ &&|& + \def\mathdef1584#1{\mathtt{0x#1}}\mathdef1584{FD}~~63{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_s} \\ &&|& + \def\mathdef1585#1{\mathtt{0x#1}}\mathdef1585{FD}~~64{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_u} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1586#1{\mathtt{0x#1}}\mathdef1586{FD}~~214{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}} \\ &&|& + \def\mathdef1587#1{\mathtt{0x#1}}\mathdef1587{FD}~~215{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}} \\ &&|& + \def\mathdef1588#1{\mathtt{0x#1}}\mathdef1588{FD}~~216{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_s} \\ &&|& + \def\mathdef1589#1{\mathtt{0x#1}}\mathdef1589{FD}~~217{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_s} \\ &&|& + \def\mathdef1590#1{\mathtt{0x#1}}\mathdef1590{FD}~~218{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_s} \\ &&|& + \def\mathdef1591#1{\mathtt{0x#1}}\mathdef1591{FD}~~219{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_s} \\ &&|& +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1592#1{\mathtt{0x#1}}\mathdef1592{FD}~~65{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}} \\ &&|& + \def\mathdef1593#1{\mathtt{0x#1}}\mathdef1593{FD}~~66{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}} \\ &&|& + \def\mathdef1594#1{\mathtt{0x#1}}\mathdef1594{FD}~~67{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}} \\ &&|& + \def\mathdef1595#1{\mathtt{0x#1}}\mathdef1595{FD}~~68{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}} \\ &&|& + \def\mathdef1596#1{\mathtt{0x#1}}\mathdef1596{FD}~~69{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}} \\ &&|& + \def\mathdef1597#1{\mathtt{0x#1}}\mathdef1597{FD}~~70{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1598#1{\mathtt{0x#1}}\mathdef1598{FD}~~71{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}} \\ &&|& + \def\mathdef1599#1{\mathtt{0x#1}}\mathdef1599{FD}~~72{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}} \\ &&|& + \def\mathdef1600#1{\mathtt{0x#1}}\mathdef1600{FD}~~73{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}} \\ &&|& + \def\mathdef1601#1{\mathtt{0x#1}}\mathdef1601{FD}~~74{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}} \\ &&|& + \def\mathdef1602#1{\mathtt{0x#1}}\mathdef1602{FD}~~75{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}} \\ &&|& + \def\mathdef1603#1{\mathtt{0x#1}}\mathdef1603{FD}~~76{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1604#1{\mathtt{0x#1}}\mathdef1604{FD}~~77{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{not}} \\ &&|& + \def\mathdef1605#1{\mathtt{0x#1}}\mathdef1605{FD}~~78{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{and}} \\ &&|& + \def\mathdef1606#1{\mathtt{0x#1}}\mathdef1606{FD}~~79{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{andnot}} \\ &&|& + \def\mathdef1607#1{\mathtt{0x#1}}\mathdef1607{FD}~~80{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{or}} \\ &&|& + \def\mathdef1608#1{\mathtt{0x#1}}\mathdef1608{FD}~~81{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{xor}} \\ &&|& + \def\mathdef1609#1{\mathtt{0x#1}}\mathdef1609{FD}~~82{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitselect}} \\ &&|& + \def\mathdef1610#1{\mathtt{0x#1}}\mathdef1610{FD}~~83{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{any\_true}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1611#1{\mathtt{0x#1}}\mathdef1611{FD}~~96{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}} \\ &&|& + \def\mathdef1612#1{\mathtt{0x#1}}\mathdef1612{FD}~~97{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}} \\ &&|& + \def\mathdef1613#1{\mathtt{0x#1}}\mathdef1613{FD}~~98{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{popcnt}} \\ &&|& + \def\mathdef1614#1{\mathtt{0x#1}}\mathdef1614{FD}~~99{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}} \\ &&|& + \def\mathdef1615#1{\mathtt{0x#1}}\mathdef1615{FD}~~100{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}} \\ &&|& + \def\mathdef1616#1{\mathtt{0x#1}}\mathdef1616{FD}~~101{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i16x8\_s} \\ &&|& + \def\mathdef1617#1{\mathtt{0x#1}}\mathdef1617{FD}~~102{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i16x8\_u} \\ &&|& + \def\mathdef1618#1{\mathtt{0x#1}}\mathdef1618{FD}~~107{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shl}} \\ &&|& + \def\mathdef1619#1{\mathtt{0x#1}}\mathdef1619{FD}~~108{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_s} \\ &&|& + \def\mathdef1620#1{\mathtt{0x#1}}\mathdef1620{FD}~~109{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_u} \\ &&|& + \def\mathdef1621#1{\mathtt{0x#1}}\mathdef1621{FD}~~110{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}} \\ &&|& + \def\mathdef1622#1{\mathtt{0x#1}}\mathdef1622{FD}~~111{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\mathsf{\_sat\_s} \\ &&|& + \def\mathdef1623#1{\mathtt{0x#1}}\mathdef1623{FD}~~112{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\mathsf{\_sat\_u} \\ &&|& + \def\mathdef1624#1{\mathtt{0x#1}}\mathdef1624{FD}~~113{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}} \\ &&|& + \def\mathdef1625#1{\mathtt{0x#1}}\mathdef1625{FD}~~114{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\mathsf{\_sat\_s} \\ &&|& + \def\mathdef1626#1{\mathtt{0x#1}}\mathdef1626{FD}~~115{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\mathsf{\_sat\_u} \\ &&|& + \def\mathdef1627#1{\mathtt{0x#1}}\mathdef1627{FD}~~118{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_s} \\ &&|& + \def\mathdef1628#1{\mathtt{0x#1}}\mathdef1628{FD}~~119{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_u} \\ &&|& + \def\mathdef1629#1{\mathtt{0x#1}}\mathdef1629{FD}~~120{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_s} \\ &&|& + \def\mathdef1630#1{\mathtt{0x#1}}\mathdef1630{FD}~~121{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_u} \\ &&|& + \def\mathdef1631#1{\mathtt{0x#1}}\mathdef1631{FD}~~123{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{avgr}}\mathsf{\_u} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1632#1{\mathtt{0x#1}}\mathdef1632{FD}~~124{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_i8x16\_s}\\ &&|& + \def\mathdef1633#1{\mathtt{0x#1}}\mathdef1633{FD}~~125{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_i8x16\_u}\\ &&|& + \def\mathdef1634#1{\mathtt{0x#1}}\mathdef1634{FD}~~128{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}} \\ &&|& + \def\mathdef1635#1{\mathtt{0x#1}}\mathdef1635{FD}~~129{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}} \\ &&|& + \def\mathdef1636#1{\mathtt{0x#1}}\mathdef1636{FD}~~130{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{q15mulr\_sat}}\mathsf{\_s} \\ &&|& + \def\mathdef1637#1{\mathtt{0x#1}}\mathdef1637{FD}~~131{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}} \\ &&|& + \def\mathdef1638#1{\mathtt{0x#1}}\mathdef1638{FD}~~132{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}} \\ &&|& + \def\mathdef1639#1{\mathtt{0x#1}}\mathdef1639{FD}~~133{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i32x4\_s} \\ &&|& + \def\mathdef1640#1{\mathtt{0x#1}}\mathdef1640{FD}~~134{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i32x4\_u} \\ &&|& + \def\mathdef1641#1{\mathtt{0x#1}}\mathdef1641{FD}~~135{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i8x16\_s} \\ &&|& + \def\mathdef1642#1{\mathtt{0x#1}}\mathdef1642{FD}~~136{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i8x16\_s} \\ &&|& + \def\mathdef1643#1{\mathtt{0x#1}}\mathdef1643{FD}~~137{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i8x16\_u} \\ &&|& + \def\mathdef1644#1{\mathtt{0x#1}}\mathdef1644{FD}~~138{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i8x16\_u} \\ &&|& + \def\mathdef1645#1{\mathtt{0x#1}}\mathdef1645{FD}~~139{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shl}} \\ &&|& + \def\mathdef1646#1{\mathtt{0x#1}}\mathdef1646{FD}~~140{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_s} \\ &&|& + \def\mathdef1647#1{\mathtt{0x#1}}\mathdef1647{FD}~~141{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_u} \\ &&|& + \def\mathdef1648#1{\mathtt{0x#1}}\mathdef1648{FD}~~142{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}} \\ &&|& + \def\mathdef1649#1{\mathtt{0x#1}}\mathdef1649{FD}~~143{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\mathsf{\_sat\_s} \\ &&|& + \def\mathdef1650#1{\mathtt{0x#1}}\mathdef1650{FD}~~144{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\mathsf{\_sat\_u} \\ &&|& + \def\mathdef1651#1{\mathtt{0x#1}}\mathdef1651{FD}~~145{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}} \\ &&|& + \def\mathdef1652#1{\mathtt{0x#1}}\mathdef1652{FD}~~146{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\mathsf{\_sat\_s} \\ &&|& + \def\mathdef1653#1{\mathtt{0x#1}}\mathdef1653{FD}~~147{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\mathsf{\_sat\_u} \\ &&|& + \def\mathdef1654#1{\mathtt{0x#1}}\mathdef1654{FD}~~149{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}} \\ &&|& + \def\mathdef1655#1{\mathtt{0x#1}}\mathdef1655{FD}~~150{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_s} \\ &&|& + \def\mathdef1656#1{\mathtt{0x#1}}\mathdef1656{FD}~~151{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_u} \\ &&|& + \def\mathdef1657#1{\mathtt{0x#1}}\mathdef1657{FD}~~152{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_s} \\ &&|& + \def\mathdef1658#1{\mathtt{0x#1}}\mathdef1658{FD}~~153{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_u} \\ &&|& + \def\mathdef1659#1{\mathtt{0x#1}}\mathdef1659{FD}~~155{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{avgr}}\mathsf{\_u} \\ &&|& + \def\mathdef1660#1{\mathtt{0x#1}}\mathdef1660{FD}~~156{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i8x16\_s}\\ &&|& + \def\mathdef1661#1{\mathtt{0x#1}}\mathdef1661{FD}~~157{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i8x16\_s}\\ &&|& + \def\mathdef1662#1{\mathtt{0x#1}}\mathdef1662{FD}~~158{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i8x16\_u}\\ &&|& + \def\mathdef1663#1{\mathtt{0x#1}}\mathdef1663{FD}~~159{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i8x16\_u}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} + \phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1664#1{\mathtt{0x#1}}\mathdef1664{FD}~~126{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_i16x8\_s}\\ &&|& + \def\mathdef1665#1{\mathtt{0x#1}}\mathdef1665{FD}~~127{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_i16x8\_u}\\ &&|& + \def\mathdef1666#1{\mathtt{0x#1}}\mathdef1666{FD}~~160{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}} \\ &&|& + \def\mathdef1667#1{\mathtt{0x#1}}\mathdef1667{FD}~~161{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}} \\ &&|& + \def\mathdef1668#1{\mathtt{0x#1}}\mathdef1668{FD}~~163{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}} \\ &&|& + \def\mathdef1669#1{\mathtt{0x#1}}\mathdef1669{FD}~~164{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}} \\ &&|& + \def\mathdef1670#1{\mathtt{0x#1}}\mathdef1670{FD}~~167{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i16x8\_s} \\ &&|& + \def\mathdef1671#1{\mathtt{0x#1}}\mathdef1671{FD}~~168{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i16x8\_s} \\ &&|& + \def\mathdef1672#1{\mathtt{0x#1}}\mathdef1672{FD}~~169{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i16x8\_u} \\ &&|& + \def\mathdef1673#1{\mathtt{0x#1}}\mathdef1673{FD}~~170{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i16x8\_u} \\ &&|& + \def\mathdef1674#1{\mathtt{0x#1}}\mathdef1674{FD}~~171{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shl}} \\ &&|& + \def\mathdef1675#1{\mathtt{0x#1}}\mathdef1675{FD}~~172{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_s} \\ &&|& + \def\mathdef1676#1{\mathtt{0x#1}}\mathdef1676{FD}~~173{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_u} \\ &&|& + \def\mathdef1677#1{\mathtt{0x#1}}\mathdef1677{FD}~~174{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}} \\ &&|& + \def\mathdef1678#1{\mathtt{0x#1}}\mathdef1678{FD}~~177{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}} \\ &&|& + \def\mathdef1679#1{\mathtt{0x#1}}\mathdef1679{FD}~~181{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}} \\ &&|& + \def\mathdef1680#1{\mathtt{0x#1}}\mathdef1680{FD}~~182{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_s} \\ &&|& + \def\mathdef1681#1{\mathtt{0x#1}}\mathdef1681{FD}~~183{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_u} \\ &&|& + \def\mathdef1682#1{\mathtt{0x#1}}\mathdef1682{FD}~~184{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_s} \\ &&|& + \def\mathdef1683#1{\mathtt{0x#1}}\mathdef1683{FD}~~185{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_u} \\ &&|& + \def\mathdef1684#1{\mathtt{0x#1}}\mathdef1684{FD}~~186{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{dot}}\mathsf{\_i16x8\_s}\\ &&|& + \def\mathdef1685#1{\mathtt{0x#1}}\mathdef1685{FD}~~188{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i16x8\_s}\\ &&|& + \def\mathdef1686#1{\mathtt{0x#1}}\mathdef1686{FD}~~189{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i16x8\_s}\\ &&|& + \def\mathdef1687#1{\mathtt{0x#1}}\mathdef1687{FD}~~190{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i16x8\_u}\\ &&|& + \def\mathdef1688#1{\mathtt{0x#1}}\mathdef1688{FD}~~191{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i16x8\_u}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} + \phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1689#1{\mathtt{0x#1}}\mathdef1689{FD}~~192{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}} \\ &&|& + \def\mathdef1690#1{\mathtt{0x#1}}\mathdef1690{FD}~~193{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}} \\ &&|& + \def\mathdef1691#1{\mathtt{0x#1}}\mathdef1691{FD}~~195{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}} \\ &&|& + \def\mathdef1692#1{\mathtt{0x#1}}\mathdef1692{FD}~~196{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}} \\ &&|& + \def\mathdef1693#1{\mathtt{0x#1}}\mathdef1693{FD}~~199{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i32x4\_s} \\ &&|& + \def\mathdef1694#1{\mathtt{0x#1}}\mathdef1694{FD}~~200{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i32x4\_s} \\ &&|& + \def\mathdef1695#1{\mathtt{0x#1}}\mathdef1695{FD}~~201{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i32x4\_u} \\ &&|& + \def\mathdef1696#1{\mathtt{0x#1}}\mathdef1696{FD}~~202{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i32x4\_u} \\ &&|& + \def\mathdef1697#1{\mathtt{0x#1}}\mathdef1697{FD}~~203{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shl}} \\ &&|& + \def\mathdef1698#1{\mathtt{0x#1}}\mathdef1698{FD}~~204{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_s} \\ &&|& + \def\mathdef1699#1{\mathtt{0x#1}}\mathdef1699{FD}~~205{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_u} \\ &&|& + \def\mathdef1700#1{\mathtt{0x#1}}\mathdef1700{FD}~~206{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}} \\ &&|& + \def\mathdef1701#1{\mathtt{0x#1}}\mathdef1701{FD}~~209{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}} \\ &&|& + \def\mathdef1702#1{\mathtt{0x#1}}\mathdef1702{FD}~~213{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}} \\ &&|& + \def\mathdef1703#1{\mathtt{0x#1}}\mathdef1703{FD}~~220{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i32x4\_s}\\ &&|& + \def\mathdef1704#1{\mathtt{0x#1}}\mathdef1704{FD}~~221{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i32x4\_s}\\ &&|& + \def\mathdef1705#1{\mathtt{0x#1}}\mathdef1705{FD}~~222{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i32x4\_u}\\ &&|& + \def\mathdef1706#1{\mathtt{0x#1}}\mathdef1706{FD}~~223{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i32x4\_u}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1707#1{\mathtt{0x#1}}\mathdef1707{FD}~~103{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ceil}} \\ &&|& + \def\mathdef1708#1{\mathtt{0x#1}}\mathdef1708{FD}~~104{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{floor}} \\ &&|& + \def\mathdef1709#1{\mathtt{0x#1}}\mathdef1709{FD}~~105{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}} \\ &&|& + \def\mathdef1710#1{\mathtt{0x#1}}\mathdef1710{FD}~~106{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{nearest}} \\ &&|& + \def\mathdef1711#1{\mathtt{0x#1}}\mathdef1711{FD}~~224{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}} \\ &&|& + \def\mathdef1712#1{\mathtt{0x#1}}\mathdef1712{FD}~~225{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}} \\ &&|& + \def\mathdef1713#1{\mathtt{0x#1}}\mathdef1713{FD}~~227{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sqrt}} \\ &&|& + \def\mathdef1714#1{\mathtt{0x#1}}\mathdef1714{FD}~~228{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}} \\ &&|& + \def\mathdef1715#1{\mathtt{0x#1}}\mathdef1715{FD}~~229{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}} \\ &&|& + \def\mathdef1716#1{\mathtt{0x#1}}\mathdef1716{FD}~~230{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}} \\ &&|& + \def\mathdef1717#1{\mathtt{0x#1}}\mathdef1717{FD}~~231{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{div}} \\ &&|& + \def\mathdef1718#1{\mathtt{0x#1}}\mathdef1718{FD}~~232{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}} \\ &&|& + \def\mathdef1719#1{\mathtt{0x#1}}\mathdef1719{FD}~~233{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}} \\ &&|& + \def\mathdef1720#1{\mathtt{0x#1}}\mathdef1720{FD}~~234{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{pmin}} \\ &&|& + \def\mathdef1721#1{\mathtt{0x#1}}\mathdef1721{FD}~~235{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{pmax}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1722#1{\mathtt{0x#1}}\mathdef1722{FD}~~116{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ceil}} \\ &&|& + \def\mathdef1723#1{\mathtt{0x#1}}\mathdef1723{FD}~~117{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{floor}} \\ &&|& + \def\mathdef1724#1{\mathtt{0x#1}}\mathdef1724{FD}~~122{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}} \\ &&|& + \def\mathdef1725#1{\mathtt{0x#1}}\mathdef1725{FD}~~148{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{nearest}} \\ &&|& + \def\mathdef1726#1{\mathtt{0x#1}}\mathdef1726{FD}~~236{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}} \\ &&|& + \def\mathdef1727#1{\mathtt{0x#1}}\mathdef1727{FD}~~237{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}} \\ &&|& + \def\mathdef1728#1{\mathtt{0x#1}}\mathdef1728{FD}~~239{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sqrt}} \\ &&|& + \def\mathdef1729#1{\mathtt{0x#1}}\mathdef1729{FD}~~240{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}} \\ &&|& + \def\mathdef1730#1{\mathtt{0x#1}}\mathdef1730{FD}~~241{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}} \\ &&|& + \def\mathdef1731#1{\mathtt{0x#1}}\mathdef1731{FD}~~242{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}} \\ &&|& + \def\mathdef1732#1{\mathtt{0x#1}}\mathdef1732{FD}~~243{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{div}} \\ &&|& + \def\mathdef1733#1{\mathtt{0x#1}}\mathdef1733{FD}~~244{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}} \\ &&|& + \def\mathdef1734#1{\mathtt{0x#1}}\mathdef1734{FD}~~245{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}} \\ &&|& + \def\mathdef1735#1{\mathtt{0x#1}}\mathdef1735{FD}~~246{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{pmin}} \\ &&|& + \def\mathdef1736#1{\mathtt{0x#1}}\mathdef1736{FD}~~247{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{pmax}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef1257#1{{}}\mathdef1257{instruction}} & \phantom{\href{../binary/instructions.html#binary-instr}{\mathtt{instr}}} &\phantom{::=}& \phantom{\dots} && \phantom{vechaslongerinstructionnames} \\[-2ex] &&|& + \def\mathdef1737#1{\mathtt{0x#1}}\mathdef1737{FD}~~248{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_f32x4\_s} \\ &&|& + \def\mathdef1738#1{\mathtt{0x#1}}\mathdef1738{FD}~~249{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_f32x4\_u} \\ &&|& + \def\mathdef1739#1{\mathtt{0x#1}}\mathdef1739{FD}~~250{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_i32x4\_s} \\ &&|& + \def\mathdef1740#1{\mathtt{0x#1}}\mathdef1740{FD}~~251{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_i32x4\_u} \\ &&|& + \def\mathdef1741#1{\mathtt{0x#1}}\mathdef1741{FD}~~252{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}}\mathsf{\_sat\_f64x2\_s\_zero}\\ &&|& + \def\mathdef1742#1{\mathtt{0x#1}}\mathdef1742{FD}~~253{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}}\mathsf{\_sat\_f64x2\_u\_zero}\\ &&|& + \def\mathdef1743#1{\mathtt{0x#1}}\mathdef1743{FD}~~254{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{convert}}\mathsf{\_low\_i32x4\_s}\\ &&|& + \def\mathdef1744#1{\mathtt{0x#1}}\mathdef1744{FD}~~255{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{convert}}\mathsf{\_low\_i32x4\_u}\\ &&|& + \def\mathdef1745#1{\mathtt{0x#1}}\mathdef1745{FD}~~94{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{demote}}\mathsf{\_f64x2\_zero}\\ &&|& + \def\mathdef1746#1{\mathtt{0x#1}}\mathdef1746{FD}~~95{:}\href{../binary/values.html#binary-int}{\def\mathdef1262#1{{\mathtt{u}#1}}\mathdef1262{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{promote}}\mathsf{\_low\_f32x4}\\ +\end{array}\end{split}\]
    +
    +
    +

    Expressions

    +

    Expressions are encoded by their instruction sequence terminated with an explicit \(\def\mathdef1747#1{\mathtt{0x#1}}\mathdef1747{0B}\) opcode for \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\).

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1257#1{{}}\mathdef1257{expression} & \href{../binary/instructions.html#binary-expr}{\mathtt{expr}} &::=& + (\mathit{in}{:}\href{../binary/instructions.html#binary-instr}{\mathtt{instr}})^\ast~~\def\mathdef1748#1{\mathtt{0x#1}}\mathdef1748{0B} &\Rightarrow& \mathit{in}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\ +\end{array}\end{split}\]
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/binary/modules.html b/core/binary/modules.html new file mode 100644 index 00000000..439735c5 --- /dev/null +++ b/core/binary/modules.html @@ -0,0 +1,539 @@ + + + + + + + + + Modules — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Modules

    +

    The binary encoding of modules is organized into sections. +Most sections correspond to one component of a module record, +except that function definitions are split into two sections, separating their type declarations in the function section from their bodies in the code section.

    +
    +

    Note

    +

    This separation enables parallel and streaming compilation of the functions in a module.

    +
    +
    +

    Indices

    +

    All indices are encoded with their respective value.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1749#1{{}}\mathdef1749{type index} & \href{../binary/modules.html#binary-typeidx}{\mathtt{typeidx}} &::=& x{:}\href{../binary/values.html#binary-int}{\def\mathdef1754#1{{\mathtt{u}#1}}\mathdef1754{\mathtt{32}}} &\Rightarrow& x \\ +\def\mathdef1749#1{{}}\mathdef1749{function index} & \href{../binary/modules.html#binary-funcidx}{\mathtt{funcidx}} &::=& x{:}\href{../binary/values.html#binary-int}{\def\mathdef1754#1{{\mathtt{u}#1}}\mathdef1754{\mathtt{32}}} &\Rightarrow& x \\ +\def\mathdef1749#1{{}}\mathdef1749{table index} & \href{../binary/modules.html#binary-tableidx}{\mathtt{tableidx}} &::=& x{:}\href{../binary/values.html#binary-int}{\def\mathdef1754#1{{\mathtt{u}#1}}\mathdef1754{\mathtt{32}}} &\Rightarrow& x \\ +\def\mathdef1749#1{{}}\mathdef1749{memory index} & \href{../binary/modules.html#binary-memidx}{\mathtt{memidx}} &::=& x{:}\href{../binary/values.html#binary-int}{\def\mathdef1754#1{{\mathtt{u}#1}}\mathdef1754{\mathtt{32}}} &\Rightarrow& x \\ +\def\mathdef1749#1{{}}\mathdef1749{global index} & \href{../binary/modules.html#binary-globalidx}{\mathtt{globalidx}} &::=& x{:}\href{../binary/values.html#binary-int}{\def\mathdef1754#1{{\mathtt{u}#1}}\mathdef1754{\mathtt{32}}} &\Rightarrow& x \\ +\def\mathdef1749#1{{}}\mathdef1749{element index} & \href{../binary/modules.html#binary-elemidx}{\mathtt{elemidx}} &::=& x{:}\href{../binary/values.html#binary-int}{\def\mathdef1754#1{{\mathtt{u}#1}}\mathdef1754{\mathtt{32}}} &\Rightarrow& x \\ +\def\mathdef1749#1{{}}\mathdef1749{data index} & \href{../binary/modules.html#binary-dataidx}{\mathtt{dataidx}} &::=& x{:}\href{../binary/values.html#binary-int}{\def\mathdef1754#1{{\mathtt{u}#1}}\mathdef1754{\mathtt{32}}} &\Rightarrow& x \\ +\def\mathdef1749#1{{}}\mathdef1749{local index} & \href{../binary/modules.html#binary-localidx}{\mathtt{localidx}} &::=& x{:}\href{../binary/values.html#binary-int}{\def\mathdef1754#1{{\mathtt{u}#1}}\mathdef1754{\mathtt{32}}} &\Rightarrow& x \\ +\def\mathdef1749#1{{}}\mathdef1749{label index} & \href{../binary/modules.html#binary-labelidx}{\mathtt{labelidx}} &::=& l{:}\href{../binary/values.html#binary-int}{\def\mathdef1754#1{{\mathtt{u}#1}}\mathdef1754{\mathtt{32}}} &\Rightarrow& l \\ +\end{array}\end{split}\]
    +
    +
    +

    Sections

    +

    Each section consists of

    +
      +

    • a one-byte section id,

      • +

    • the \(\href{../syntax/values.html#syntax-int}{\mathit{u32}}\) size of the contents, in bytes,

      • +

    • the actual contents, whose structure is depended on the section id.

      • +
    +

    Every section is optional; an omitted section is equivalent to the section being present with empty contents.

    +

    The following parameterized grammar rule defines the generic structure of a section with id \(N\) and contents described by the grammar \(\mathtt{B}\).

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad}l} +\def\mathdef1749#1{{}}\mathdef1749{section} & \href{../binary/modules.html#binary-section}{\mathtt{section}}_N(\mathtt{B}) &::=& + N{:}\href{../binary/values.html#binary-byte}{\mathtt{byte}}~~\mathit{size}{:}\href{../binary/values.html#binary-int}{\def\mathdef1754#1{{\mathtt{u}#1}}\mathdef1754{\mathtt{32}}}~~\mathit{cont}{:}\mathtt{B} + &\Rightarrow& \mathit{cont} & (\mathrel{\mbox{if}} \mathit{size} = ||\mathtt{B}||) \\ &&|& + \epsilon &\Rightarrow& \epsilon +\end{array}\end{split}\]
    +

    For most sections, the contents \(\mathtt{B}\) encodes a vector. +In these cases, the empty result \(\epsilon\) is interpreted as the empty vector.

    +
    +

    Note

    +

    Other than for unknown custom sections, +the \(\mathit{size}\) is not required for decoding, but can be used to skip sections when navigating through a binary. +The module is malformed if the size does not match the length of the binary contents \(\mathtt{B}\).

    +
    +

    The following section ids are used:

    + ++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Id

    Section

    0

    custom section

    1

    type section

    2

    import section

    3

    function section

    4

    table section

    5

    memory section

    6

    global section

    7

    export section

    8

    start section

    9

    element section

    10

    code section

    11

    data section

    12

    data count section

    +
    +
    +

    Custom Section

    +

    Custom sections have the id 0. +They are intended to be used for debugging information or third-party extensions, and are ignored by the WebAssembly semantics. +Their contents consist of a name further identifying the custom section, followed by an uninterpreted sequence of bytes for custom use.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1749#1{{}}\mathdef1749{custom section} & \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}} &::=& + \href{../binary/modules.html#binary-section}{\mathtt{section}}_0(\href{../binary/modules.html#binary-customsec}{\mathtt{custom}}) \\ +\def\mathdef1749#1{{}}\mathdef1749{custom data} & \href{../binary/modules.html#binary-customsec}{\mathtt{custom}} &::=& + \href{../binary/values.html#binary-name}{\mathtt{name}}~~\href{../binary/values.html#binary-byte}{\mathtt{byte}}^\ast \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    If an implementation interprets the data of a custom section, then errors in that data, or the placement of the section, must not invalidate the module.

    +
    +
    +
    +

    Type Section

    +

    The type section has the id 1. +It decodes into a vector of function types that represent the \(\href{../syntax/modules.html#syntax-module}{\mathsf{types}}\) component of a module.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1749#1{{}}\mathdef1749{type section} & \href{../binary/modules.html#binary-typesec}{\mathtt{typesec}} &::=& + \mathit{ft}^\ast{:\,}\href{../binary/modules.html#binary-section}{\mathtt{section}}_1(\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/types.html#binary-functype}{\mathtt{functype}})) &\Rightarrow& \mathit{ft}^\ast \\ +\end{array}\end{split}\]
    +
    +
    +

    Import Section

    +

    The import section has the id 2. +It decodes into a vector of imports that represent the \(\href{../syntax/modules.html#syntax-module}{\mathsf{imports}}\) component of a module.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1749#1{{}}\mathdef1749{import section} & \href{../binary/modules.html#binary-importsec}{\mathtt{importsec}} &::=& + \mathit{im}^\ast{:}\href{../binary/modules.html#binary-section}{\mathtt{section}}_2(\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-import}{\mathtt{import}})) &\Rightarrow& \mathit{im}^\ast \\ +\def\mathdef1749#1{{}}\mathdef1749{import} & \href{../binary/modules.html#binary-import}{\mathtt{import}} &::=& + \mathit{mod}{:}\href{../binary/values.html#binary-name}{\mathtt{name}}~~\mathit{nm}{:}\href{../binary/values.html#binary-name}{\mathtt{name}}~~d{:}\href{../binary/modules.html#binary-importdesc}{\mathtt{importdesc}} + &\Rightarrow& \{ \href{../syntax/modules.html#syntax-import}{\mathsf{module}}~\mathit{mod}, \href{../syntax/modules.html#syntax-import}{\mathsf{name}}~\mathit{nm}, \href{../syntax/modules.html#syntax-import}{\mathsf{desc}}~d \} \\ +\def\mathdef1749#1{{}}\mathdef1749{import description} & \href{../binary/modules.html#binary-importdesc}{\mathtt{importdesc}} &::=& + \def\mathdef1788#1{\mathtt{0x#1}}\mathdef1788{00}~~x{:}\href{../binary/modules.html#binary-typeidx}{\mathtt{typeidx}} &\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{func}}~x \\ &&|& + \def\mathdef1789#1{\mathtt{0x#1}}\mathdef1789{01}~~\mathit{tt}{:}\href{../binary/types.html#binary-tabletype}{\mathtt{tabletype}} &\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{table}}~\mathit{tt} \\ &&|& + \def\mathdef1790#1{\mathtt{0x#1}}\mathdef1790{02}~~\mathit{mt}{:}\href{../binary/types.html#binary-memtype}{\mathtt{memtype}} &\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{mem}}~\mathit{mt} \\ &&|& + \def\mathdef1791#1{\mathtt{0x#1}}\mathdef1791{03}~~\mathit{gt}{:}\href{../binary/types.html#binary-globaltype}{\mathtt{globaltype}} &\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{global}}~\mathit{gt} \\ +\end{array}\end{split}\]
    +
    +
    +

    Function Section

    +

    The function section has the id 3. +It decodes into a vector of type indices that represent the \(\href{../syntax/modules.html#syntax-func}{\mathsf{type}}\) fields of the functions in the \(\href{../syntax/modules.html#syntax-module}{\mathsf{funcs}}\) component of a module. +The \(\href{../syntax/modules.html#syntax-func}{\mathsf{locals}}\) and \(\href{../syntax/modules.html#syntax-func}{\mathsf{body}}\) fields of the respective functions are encoded separately in the code section.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1749#1{{}}\mathdef1749{function section} & \href{../binary/modules.html#binary-funcsec}{\mathtt{funcsec}} &::=& + x^\ast{:}\href{../binary/modules.html#binary-section}{\mathtt{section}}_3(\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-typeidx}{\mathtt{typeidx}})) &\Rightarrow& x^\ast \\ +\end{array}\end{split}\]
    +
    +
    +

    Table Section

    +

    The table section has the id 4. +It decodes into a vector of tables that represent the \(\href{../syntax/modules.html#syntax-module}{\mathsf{tables}}\) component of a module.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1749#1{{}}\mathdef1749{table section} & \href{../binary/modules.html#binary-tablesec}{\mathtt{tablesec}} &::=& + \mathit{tab}^\ast{:}\href{../binary/modules.html#binary-section}{\mathtt{section}}_4(\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-table}{\mathtt{table}})) &\Rightarrow& \mathit{tab}^\ast \\ +\def\mathdef1749#1{{}}\mathdef1749{table} & \href{../binary/modules.html#binary-table}{\mathtt{table}} &::=& + \mathit{tt}{:}\href{../binary/types.html#binary-tabletype}{\mathtt{tabletype}} &\Rightarrow& \{ \href{../syntax/modules.html#syntax-table}{\mathsf{type}}~\mathit{tt} \} \\ +\end{array}\end{split}\]
    +
    +
    +

    Memory Section

    +

    The memory section has the id 5. +It decodes into a vector of memories that represent the \(\href{../syntax/modules.html#syntax-module}{\mathsf{mems}}\) component of a module.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1749#1{{}}\mathdef1749{memory section} & \href{../binary/modules.html#binary-memsec}{\mathtt{memsec}} &::=& + \mathit{mem}^\ast{:}\href{../binary/modules.html#binary-section}{\mathtt{section}}_5(\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-mem}{\mathtt{mem}})) &\Rightarrow& \mathit{mem}^\ast \\ +\def\mathdef1749#1{{}}\mathdef1749{memory} & \href{../binary/modules.html#binary-mem}{\mathtt{mem}} &::=& + \mathit{mt}{:}\href{../binary/types.html#binary-memtype}{\mathtt{memtype}} &\Rightarrow& \{ \href{../syntax/modules.html#syntax-mem}{\mathsf{type}}~\mathit{mt} \} \\ +\end{array}\end{split}\]
    +
    +
    +

    Global Section

    +

    The global section has the id 6. +It decodes into a vector of globals that represent the \(\href{../syntax/modules.html#syntax-module}{\mathsf{globals}}\) component of a module.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1749#1{{}}\mathdef1749{global section} & \href{../binary/modules.html#binary-globalsec}{\mathtt{globalsec}} &::=& + \mathit{glob}^\ast{:}\href{../binary/modules.html#binary-section}{\mathtt{section}}_6(\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-global}{\mathtt{global}})) &\Rightarrow& \mathit{glob}^\ast \\ +\def\mathdef1749#1{{}}\mathdef1749{global} & \href{../binary/modules.html#binary-global}{\mathtt{global}} &::=& + \mathit{gt}{:}\href{../binary/types.html#binary-globaltype}{\mathtt{globaltype}}~~e{:}\href{../binary/instructions.html#binary-expr}{\mathtt{expr}} + &\Rightarrow& \{ \href{../syntax/modules.html#syntax-global}{\mathsf{type}}~\mathit{gt}, \href{../syntax/modules.html#syntax-global}{\mathsf{init}}~e \} \\ +\end{array}\end{split}\]
    +
    +
    +

    Export Section

    +

    The export section has the id 7. +It decodes into a vector of exports that represent the \(\href{../syntax/modules.html#syntax-module}{\mathsf{exports}}\) component of a module.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1749#1{{}}\mathdef1749{export section} & \href{../binary/modules.html#binary-exportsec}{\mathtt{exportsec}} &::=& + \mathit{ex}^\ast{:}\href{../binary/modules.html#binary-section}{\mathtt{section}}_7(\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-export}{\mathtt{export}})) &\Rightarrow& \mathit{ex}^\ast \\ +\def\mathdef1749#1{{}}\mathdef1749{export} & \href{../binary/modules.html#binary-export}{\mathtt{export}} &::=& + \mathit{nm}{:}\href{../binary/values.html#binary-name}{\mathtt{name}}~~d{:}\href{../binary/modules.html#binary-exportdesc}{\mathtt{exportdesc}} + &\Rightarrow& \{ \href{../syntax/modules.html#syntax-export}{\mathsf{name}}~\mathit{nm}, \href{../syntax/modules.html#syntax-export}{\mathsf{desc}}~d \} \\ +\def\mathdef1749#1{{}}\mathdef1749{export description} & \href{../binary/modules.html#binary-exportdesc}{\mathtt{exportdesc}} &::=& + \def\mathdef1792#1{\mathtt{0x#1}}\mathdef1792{00}~~x{:}\href{../binary/modules.html#binary-funcidx}{\mathtt{funcidx}} &\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{func}}~x \\ &&|& + \def\mathdef1793#1{\mathtt{0x#1}}\mathdef1793{01}~~x{:}\href{../binary/modules.html#binary-tableidx}{\mathtt{tableidx}} &\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{table}}~x \\ &&|& + \def\mathdef1794#1{\mathtt{0x#1}}\mathdef1794{02}~~x{:}\href{../binary/modules.html#binary-memidx}{\mathtt{memidx}} &\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{mem}}~x \\ &&|& + \def\mathdef1795#1{\mathtt{0x#1}}\mathdef1795{03}~~x{:}\href{../binary/modules.html#binary-globalidx}{\mathtt{globalidx}} &\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{global}}~x \\ +\end{array}\end{split}\]
    +
    +
    +

    Start Section

    +

    The start section has the id 8. +It decodes into an optional start function that represents the \(\href{../syntax/modules.html#syntax-module}{\mathsf{start}}\) component of a module.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1749#1{{}}\mathdef1749{start section} & \href{../binary/modules.html#binary-startsec}{\mathtt{startsec}} &::=& + \mathit{st}^?{:}\href{../binary/modules.html#binary-section}{\mathtt{section}}_8(\href{../binary/modules.html#binary-start}{\mathtt{start}}) &\Rightarrow& \mathit{st}^? \\ +\def\mathdef1749#1{{}}\mathdef1749{start function} & \href{../binary/modules.html#binary-start}{\mathtt{start}} &::=& + x{:}\href{../binary/modules.html#binary-funcidx}{\mathtt{funcidx}} &\Rightarrow& \{ \href{../syntax/modules.html#syntax-start}{\mathsf{func}}~x \} \\ +\end{array}\end{split}\]
    +
    +
    +

    Element Section

    +

    The element section has the id 9. +It decodes into a vector of element segments that represent the \(\href{../syntax/modules.html#syntax-module}{\mathsf{elems}}\) component of a module.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1749#1{{}}\mathdef1749{element section} & \href{../binary/modules.html#binary-elemsec}{\mathtt{elemsec}} &::=& + \mathit{seg}^\ast{:}\href{../binary/modules.html#binary-section}{\mathtt{section}}_9(\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-elem}{\mathtt{elem}})) &\Rightarrow& \mathit{seg} \\ +\def\mathdef1749#1{{}}\mathdef1749{element segment} & \href{../binary/modules.html#binary-elem}{\mathtt{elem}} &::=& + \def\mathdef1796#1{\mathtt{0x#1}}\mathdef1796{00}~~e{:}\href{../binary/instructions.html#binary-expr}{\mathtt{expr}}~~y^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-funcidx}{\mathtt{funcidx}}) + &\Rightarrow& \\&&&\quad + \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~((\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~y)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}})^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-elem}{\mathsf{table}}~0, \href{../syntax/modules.html#syntax-elem}{\mathsf{offset}}~e \} \} \\ &&|& + \def\mathdef1797#1{\mathtt{0x#1}}\mathdef1797{01}~~\mathit{et}:\href{../binary/modules.html#binary-elemkind}{\mathtt{elemkind}}~~y^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-funcidx}{\mathtt{funcidx}}) + &\Rightarrow& \\&&&\quad + \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~\mathit{et}, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~((\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~y)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}})^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{passive}} \} \\ &&|& + \def\mathdef1798#1{\mathtt{0x#1}}\mathdef1798{02}~~x{:}\href{../binary/modules.html#binary-tableidx}{\mathtt{tableidx}}~~e{:}\href{../binary/instructions.html#binary-expr}{\mathtt{expr}}~~\mathit{et}:\href{../binary/modules.html#binary-elemkind}{\mathtt{elemkind}}~~y^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-funcidx}{\mathtt{funcidx}}) + &\Rightarrow& \\&&&\quad + \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~\mathit{et}, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~((\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~y)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}})^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-elem}{\mathsf{table}}~x, \href{../syntax/modules.html#syntax-elem}{\mathsf{offset}}~e \} \} \\ &&|& + \def\mathdef1799#1{\mathtt{0x#1}}\mathdef1799{03}~~\mathit{et}:\href{../binary/modules.html#binary-elemkind}{\mathtt{elemkind}}~~y^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-funcidx}{\mathtt{funcidx}}) + &\Rightarrow& \\&&&\quad + \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~\mathit{et}, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~((\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~y)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}})^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{declarative}} \} \\ &&|& + \def\mathdef1800#1{\mathtt{0x#1}}\mathdef1800{04}~~e{:}\href{../binary/instructions.html#binary-expr}{\mathtt{expr}}~~\mathit{el}^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/instructions.html#binary-expr}{\mathtt{expr}}) + &\Rightarrow& \\&&&\quad + \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~\mathit{el}^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-elem}{\mathsf{table}}~0, \href{../syntax/modules.html#syntax-elem}{\mathsf{offset}}~e \} \} \\ &&|& + \def\mathdef1801#1{\mathtt{0x#1}}\mathdef1801{05}~~\mathit{et}:\href{../binary/types.html#binary-reftype}{\mathtt{reftype}}~~\mathit{el}^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/instructions.html#binary-expr}{\mathtt{expr}}) + &\Rightarrow& \\&&&\quad + \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~et, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~\mathit{el}^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{passive}} \} \\ &&|& + \def\mathdef1802#1{\mathtt{0x#1}}\mathdef1802{06}~~x{:}\href{../binary/modules.html#binary-tableidx}{\mathtt{tableidx}}~~e{:}\href{../binary/instructions.html#binary-expr}{\mathtt{expr}}~~\mathit{et}:\href{../binary/types.html#binary-reftype}{\mathtt{reftype}}~~\mathit{el}^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/instructions.html#binary-expr}{\mathtt{expr}}) + &\Rightarrow& \\&&&\quad + \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~et, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~\mathit{el}^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-elem}{\mathsf{table}}~x, \href{../syntax/modules.html#syntax-elem}{\mathsf{offset}}~e \} \} \\ &&|& + \def\mathdef1803#1{\mathtt{0x#1}}\mathdef1803{07}~~\mathit{et}:\href{../binary/types.html#binary-reftype}{\mathtt{reftype}}~~\mathit{el}^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/instructions.html#binary-expr}{\mathtt{expr}}) + &\Rightarrow& \\&&&\quad + \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~et, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~\mathit{el}^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{declarative}} \} \\ +\def\mathdef1749#1{{}}\mathdef1749{element kind} & \href{../binary/modules.html#binary-elemkind}{\mathtt{elemkind}} &::=& + \def\mathdef1804#1{\mathtt{0x#1}}\mathdef1804{00} &\Rightarrow& \href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}} \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The initial byte can be interpreted as a bitfield. +Bit 0 indicates a passive or declarative segment, +bit 1 indicates the presence of an explicit table index for an active segment and otherwise distinguishes passive from declarative segments, +bit 2 indicates the use of element type and element expressions instead of element kind and element indices.

    +

    Additional element kinds may be added in future versions of WebAssembly.

    +
    +
    +
    +

    Code Section

    +

    The code section has the id 10. +It decodes into a vector of code entries that are pairs of value type vectors and expressions. +They represent the \(\href{../syntax/modules.html#syntax-func}{\mathsf{locals}}\) and \(\href{../syntax/modules.html#syntax-func}{\mathsf{body}}\) field of the functions in the \(\href{../syntax/modules.html#syntax-module}{\mathsf{funcs}}\) component of a module. +The \(\href{../syntax/modules.html#syntax-func}{\mathsf{type}}\) fields of the respective functions are encoded separately in the function section.

    +

    The encoding of each code entry consists of

    +
      +

    • the \(\href{../syntax/values.html#syntax-int}{\mathit{u32}}\) size of the function code in bytes,

      • +

    • the actual function code, which in turn consists of

      +
        +

      • the declaration of locals,

        • +

      • the function body as an expression.

        • +
      +
      • +
    +

    Local declarations are compressed into a vector whose entries consist of

    +
      +

    • a \(\href{../syntax/values.html#syntax-int}{\mathit{u32}}\) count,

      • +

    • a value type,

      • +
    +

    denoting count locals of the same value type.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad}l} +\def\mathdef1749#1{{}}\mathdef1749{code section} & \href{../binary/modules.html#binary-codesec}{\mathtt{codesec}} &::=& + \mathit{code}^\ast{:}\href{../binary/modules.html#binary-section}{\mathtt{section}}_{10}(\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-code}{\mathtt{code}})) + &\Rightarrow& \mathit{code}^\ast \\ +\def\mathdef1749#1{{}}\mathdef1749{code} & \href{../binary/modules.html#binary-code}{\mathtt{code}} &::=& + \mathit{size}{:}\href{../binary/values.html#binary-int}{\def\mathdef1754#1{{\mathtt{u}#1}}\mathdef1754{\mathtt{32}}}~~\mathit{code}{:}\href{../binary/modules.html#binary-func}{\mathtt{func}} + &\Rightarrow& \mathit{code} & (\mathrel{\mbox{if}} \mathit{size} = ||\href{../binary/modules.html#binary-func}{\mathtt{func}}||) \\ +\def\mathdef1749#1{{}}\mathdef1749{function} & \href{../binary/modules.html#binary-func}{\mathtt{func}} &::=& + (t^\ast)^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-local}{\mathtt{locals}})~~e{:}\href{../binary/instructions.html#binary-expr}{\mathtt{expr}} + &\Rightarrow& \href{../syntax/conventions.html#notation-concat}{\mathrm{concat}}((t^\ast)^\ast), e^\ast + & (\mathrel{\mbox{if}} |\href{../syntax/conventions.html#notation-concat}{\mathrm{concat}}((t^\ast)^\ast)| < 2^{32}) \\ +\def\mathdef1749#1{{}}\mathdef1749{locals} & \href{../binary/modules.html#binary-local}{\mathtt{locals}} &::=& + n{:}\href{../binary/values.html#binary-int}{\def\mathdef1754#1{{\mathtt{u}#1}}\mathdef1754{\mathtt{32}}}~~t{:}\href{../binary/types.html#binary-valtype}{\mathtt{valtype}} &\Rightarrow& t^n \\ +\end{array}\end{split}\]
    +

    Here, \(\mathit{code}\) ranges over pairs \((\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}^\ast, \href{../syntax/instructions.html#syntax-expr}{\mathit{expr}})\). +The meta function \(\href{../syntax/conventions.html#notation-concat}{\mathrm{concat}}((t^\ast)^\ast)\) concatenates all sequences \(t_i^\ast\) in \((t^\ast)^\ast\). +Any code for which the length of the resulting sequence is out of bounds of the maximum size of a vector is malformed.

    +
    +

    Note

    +

    Like with sections, the code \(\mathit{size}\) is not needed for decoding, but can be used to skip functions when navigating through a binary. +The module is malformed if a size does not match the length of the respective function code.

    +
    +
    +
    +

    Data Section

    +

    The data section has the id 11. +It decodes into a vector of data segments that represent the \(\href{../syntax/modules.html#syntax-module}{\mathsf{datas}}\) component of a module.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1749#1{{}}\mathdef1749{data section} & \href{../binary/modules.html#binary-datasec}{\mathtt{datasec}} &::=& + \mathit{seg}^\ast{:}\href{../binary/modules.html#binary-section}{\mathtt{section}}_{11}(\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/modules.html#binary-data}{\mathtt{data}})) &\Rightarrow& \mathit{seg} \\ +\def\mathdef1749#1{{}}\mathdef1749{data segment} & \href{../binary/modules.html#binary-data}{\mathtt{data}} &::=& + \def\mathdef1805#1{\mathtt{0x#1}}\mathdef1805{00}~~e{:}\href{../binary/instructions.html#binary-expr}{\mathtt{expr}}~~b^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/values.html#binary-byte}{\mathtt{byte}}) + &\Rightarrow& \{ \href{../syntax/modules.html#syntax-data}{\mathsf{init}}~b^\ast, \href{../syntax/modules.html#syntax-data}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-datamode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-data}{\mathsf{memory}}~0, \href{../syntax/modules.html#syntax-data}{\mathsf{offset}}~e \} \} \\ &&|& + \def\mathdef1806#1{\mathtt{0x#1}}\mathdef1806{01}~~b^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/values.html#binary-byte}{\mathtt{byte}}) + &\Rightarrow& \{ \href{../syntax/modules.html#syntax-data}{\mathsf{init}}~b^\ast, \href{../syntax/modules.html#syntax-data}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-datamode}{\mathsf{passive}} \} \\ &&|& + \def\mathdef1807#1{\mathtt{0x#1}}\mathdef1807{02}~~x{:}\href{../binary/modules.html#binary-memidx}{\mathtt{memidx}}~~e{:}\href{../binary/instructions.html#binary-expr}{\mathtt{expr}}~~b^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/values.html#binary-byte}{\mathtt{byte}}) + &\Rightarrow& \{ \href{../syntax/modules.html#syntax-data}{\mathsf{init}}~b^\ast, \href{../syntax/modules.html#syntax-data}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-datamode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-data}{\mathsf{memory}}~x, \href{../syntax/modules.html#syntax-data}{\mathsf{offset}}~e \} \} \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The initial byte can be interpreted as a bitfield. +Bit 0 indicates a passive segment, +bit 1 indicates the presence of an explicit memory index for an active segment.

    +

    In the current version of WebAssembly, at most one memory may be defined or +imported in a single module, so all valid active data +segments have a \(\href{../syntax/modules.html#syntax-data}{\mathsf{memory}}\) value of \(0\).

    +
    +
    +
    +

    Data Count Section

    +

    The data count section has the id 12. +It decodes into an optional u32 that represents the number of data segments in the data section. If this count does not match the length of the data segment vector, the module is malformed.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1749#1{{}}\mathdef1749{data count section} & \href{../binary/modules.html#binary-datacountsec}{\mathtt{datacountsec}} &::=& + \mathit{n}^?{:}\href{../binary/modules.html#binary-section}{\mathtt{section}}_{12}(\href{../binary/values.html#binary-int}{\def\mathdef1754#1{{\mathtt{u}#1}}\mathdef1754{\mathtt{32}}}) &\Rightarrow& \mathit{n}^? \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The data count section is used to simplify single-pass validation. Since the +data section occurs after the code section, the \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}\) and +\(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data.drop}}\) instructions would not be able to check whether the data +segment index is valid until the data section is read. The data count section +occurs before the code section, so a single-pass validator can use this count +instead of deferring validation.

    +
    +
    +
    +

    Modules

    +

    The encoding of a module starts with a preamble containing a 4-byte magic number (the string \(\def\mathdef1808#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef1808{\backslash0asm}\)) and a version field. +The current version of the WebAssembly binary format is 1.

    +

    The preamble is followed by a sequence of sections. +Custom sections may be inserted at any place in this sequence, +while other sections must occur at most once and in the prescribed order. +All sections can be empty.

    +

    The lengths of vectors produced by the (possibly empty) function and code section must match up.

    +

    Similarly, the optional data count must match the length of the data segment vector. +Furthermore, it must be present if any \(data index <syntax-dataidx>\) occurs in the code section.

    +
    +\[\begin{split}\begin{array}{llcllll} +\def\mathdef1749#1{{}}\mathdef1749{magic} & \href{../binary/modules.html#binary-magic}{\mathtt{magic}} &::=& + \def\mathdef1809#1{\mathtt{0x#1}}\mathdef1809{00}~\def\mathdef1810#1{\mathtt{0x#1}}\mathdef1810{61}~\def\mathdef1811#1{\mathtt{0x#1}}\mathdef1811{73}~\def\mathdef1812#1{\mathtt{0x#1}}\mathdef1812{6D} \\ +\def\mathdef1749#1{{}}\mathdef1749{version} & \href{../binary/modules.html#binary-version}{\mathtt{version}} &::=& + \def\mathdef1813#1{\mathtt{0x#1}}\mathdef1813{01}~\def\mathdef1814#1{\mathtt{0x#1}}\mathdef1814{00}~\def\mathdef1815#1{\mathtt{0x#1}}\mathdef1815{00}~\def\mathdef1816#1{\mathtt{0x#1}}\mathdef1816{00} \\ +\def\mathdef1749#1{{}}\mathdef1749{module} & \href{../binary/modules.html#binary-module}{\mathtt{module}} &::=& + \href{../binary/modules.html#binary-magic}{\mathtt{magic}} \\ &&& + \href{../binary/modules.html#binary-version}{\mathtt{version}} \\ &&& + \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}}^\ast \\ &&& + \href{../syntax/types.html#syntax-functype}{\mathit{functype}}^\ast{:\,}\href{../binary/modules.html#binary-typesec}{\mathtt{typesec}} \\ &&& + \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}}^\ast \\ &&& + \href{../syntax/modules.html#syntax-import}{\mathit{import}}^\ast{:\,}\href{../binary/modules.html#binary-importsec}{\mathtt{importsec}} \\ &&& + \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}}^\ast \\ &&& + \href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}}^n{:\,}\href{../binary/modules.html#binary-funcsec}{\mathtt{funcsec}} \\ &&& + \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}}^\ast \\ &&& + \href{../syntax/modules.html#syntax-table}{\mathit{table}}^\ast{:\,}\href{../binary/modules.html#binary-tablesec}{\mathtt{tablesec}} \\ &&& + \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}}^\ast \\ &&& + \href{../syntax/modules.html#syntax-mem}{\mathit{mem}}^\ast{:\,}\href{../binary/modules.html#binary-memsec}{\mathtt{memsec}} \\ &&& + \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}}^\ast \\ &&& + \href{../syntax/modules.html#syntax-global}{\mathit{global}}^\ast{:\,}\href{../binary/modules.html#binary-globalsec}{\mathtt{globalsec}} \\ &&& + \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}}^\ast \\ &&& + \href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast{:\,}\href{../binary/modules.html#binary-exportsec}{\mathtt{exportsec}} \\ &&& + \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}}^\ast \\ &&& + \href{../syntax/modules.html#syntax-start}{\mathit{start}}^?{:\,}\href{../binary/modules.html#binary-startsec}{\mathtt{startsec}} \\ &&& + \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}}^\ast \\ &&& + \href{../syntax/modules.html#syntax-elem}{\mathit{elem}}^\ast{:\,}\href{../binary/modules.html#binary-elemsec}{\mathtt{elemsec}} \\ &&& + \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}}^\ast \\ &&& + m^?{:\,}\href{../binary/modules.html#binary-datacountsec}{\mathtt{datacountsec}} \\ &&& + \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}}^\ast \\ &&& + \mathit{code}^n{:\,}\href{../binary/modules.html#binary-codesec}{\mathtt{codesec}} \\ &&& + \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}}^\ast \\ &&& + \href{../syntax/modules.html#syntax-data}{\mathit{data}}^m{:\,}\href{../binary/modules.html#binary-datasec}{\mathtt{datasec}} \\ &&& + \href{../binary/modules.html#binary-customsec}{\mathtt{customsec}}^\ast + \quad\Rightarrow\quad \{~ + \begin{array}[t]{@{}l@{}} + \href{../syntax/modules.html#syntax-module}{\mathsf{types}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}^\ast, \\ + \href{../syntax/modules.html#syntax-module}{\mathsf{funcs}}~\href{../syntax/modules.html#syntax-func}{\mathit{func}}^n, \\ + \href{../syntax/modules.html#syntax-module}{\mathsf{tables}}~\href{../syntax/modules.html#syntax-table}{\mathit{table}}^\ast, \\ + \href{../syntax/modules.html#syntax-module}{\mathsf{mems}}~\href{../syntax/modules.html#syntax-mem}{\mathit{mem}}^\ast, \\ + \href{../syntax/modules.html#syntax-module}{\mathsf{globals}}~\href{../syntax/modules.html#syntax-global}{\mathit{global}}^\ast, \\ + \href{../syntax/modules.html#syntax-module}{\mathsf{elems}}~\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}^\ast, \\ + \href{../syntax/modules.html#syntax-module}{\mathsf{datas}}~\href{../syntax/modules.html#syntax-data}{\mathit{data}}^m, \\ + \href{../syntax/modules.html#syntax-module}{\mathsf{start}}~\href{../syntax/modules.html#syntax-start}{\mathit{start}}^?, \\ + \href{../syntax/modules.html#syntax-module}{\mathsf{imports}}~\href{../syntax/modules.html#syntax-import}{\mathit{import}}^\ast, \\ + \href{../syntax/modules.html#syntax-module}{\mathsf{exports}}~\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast ~\} \\ + \end{array} \\ &&& + (\mathrel{\mbox{if}} m^? \neq \epsilon \vee \href{../syntax/modules.html#syntax-dataidx}{\mathrm{dataidx}}(\mathit{code}^n) = \emptyset) \\ +\end{array}\end{split}\]
    +

    where for each \(t_i^\ast, e_i\) in \(\mathit{code}^n\),

    +
    +\[\begin{split}\href{../syntax/modules.html#syntax-func}{\mathit{func}}^n[i] = \{ \href{../syntax/modules.html#syntax-func}{\mathsf{type}}~\href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}}^n[i], \href{../syntax/modules.html#syntax-func}{\mathsf{locals}}~t_i^\ast, \href{../syntax/modules.html#syntax-func}{\mathsf{body}}~e_i \} ) \\\end{split}\]
    +
    +

    Note

    +

    The version of the WebAssembly binary format may increase in the future +if backward-incompatible changes have to be made to the format. +However, such changes are expected to occur very infrequently, if ever. +The binary format is intended to be forward-compatible, +such that future extensions can be made without incrementing its version.

    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/binary/types.html b/core/binary/types.html new file mode 100644 index 00000000..31573886 --- /dev/null +++ b/core/binary/types.html @@ -0,0 +1,217 @@ + + + + + + + + + Types — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Types

    +
    +

    Note

    +

    In some places, possible types include both type constructors or types denoted by type indices. +Thus, the binary format for type constructors corresponds to the encodings of small negative \(\href{../binary/values.html#binary-sint}{\href{../syntax/values.html#syntax-int}{\mathit{s}N}}\) values, such that they can unambiguously occur in the same place as (positive) type indices.

    +
    +
    +

    Number Types

    +

    Number types are encoded by a single byte.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef1817#1{{}}\mathdef1817{number type} & \href{../binary/types.html#binary-numtype}{\mathtt{numtype}} &::=& + \def\mathdef1856#1{\mathtt{0x#1}}\mathdef1856{7F} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}} \\ &&|& + \def\mathdef1857#1{\mathtt{0x#1}}\mathdef1857{7E} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}} \\ &&|& + \def\mathdef1858#1{\mathtt{0x#1}}\mathdef1858{7D} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}} \\ &&|& + \def\mathdef1859#1{\mathtt{0x#1}}\mathdef1859{7C} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}} \\ +\end{array}\end{split}\]
    +
    +
    +

    Vector Types

    +

    Vector types are also encoded by a single byte.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef1817#1{{}}\mathdef1817{vector type} & \href{../binary/types.html#binary-vectype}{\mathtt{vectype}} &::=& + \def\mathdef1860#1{\mathtt{0x#1}}\mathdef1860{7B} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}} \\ +\end{array}\end{split}\]
    +
    +
    +

    Reference Types

    +

    Reference types are also encoded by a single byte.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef1817#1{{}}\mathdef1817{reference type} & \href{../binary/types.html#binary-reftype}{\mathtt{reftype}} &::=& + \def\mathdef1861#1{\mathtt{0x#1}}\mathdef1861{70} &\Rightarrow& \href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}} \\ &&|& + \def\mathdef1862#1{\mathtt{0x#1}}\mathdef1862{6F} &\Rightarrow& \href{../syntax/types.html#syntax-reftype}{\mathsf{externref}} \\ +\end{array}\end{split}\]
    +
    +
    +

    Value Types

    +

    Value types are encoded with their respective encoding as a number type, vector type, or reference type.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef1817#1{{}}\mathdef1817{value type} & \href{../binary/types.html#binary-valtype}{\mathtt{valtype}} &::=& + t{:}\href{../binary/types.html#binary-numtype}{\mathtt{numtype}} &\Rightarrow& t \\ &&|& + t{:}\href{../binary/types.html#binary-vectype}{\mathtt{vectype}} &\Rightarrow& t \\ &&|& + t{:}\href{../binary/types.html#binary-reftype}{\mathtt{reftype}} &\Rightarrow& t \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    Value types can occur in contexts where type indices are also allowed, such as in the case of block types. +Thus, the binary format for types corresponds to the signed LEB128 encoding of small negative \(\href{../syntax/values.html#syntax-int}{\mathit{s}N}\) values, so that they can coexist with (positive) type indices in the future.

    +
    +
    +
    +

    Result Types

    +

    Result types are encoded by the respective vectors of value types `.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef1817#1{{}}\mathdef1817{result type} & \href{../binary/types.html#binary-resulttype}{\mathtt{resulttype}} &::=& + t^\ast{:\,}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/types.html#binary-valtype}{\mathtt{valtype}}) &\Rightarrow& [t^\ast] \\ +\end{array}\end{split}\]
    +
    +
    +

    Function Types

    +

    Function types are encoded by the byte \(\def\mathdef1863#1{\mathtt{0x#1}}\mathdef1863{60}\) followed by the respective vectors of parameter and result types.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef1817#1{{}}\mathdef1817{function type} & \href{../binary/types.html#binary-functype}{\mathtt{functype}} &::=& + \def\mathdef1864#1{\mathtt{0x#1}}\mathdef1864{60}~~\mathit{rt}_1{:\,}\href{../binary/types.html#binary-resulttype}{\mathtt{resulttype}}~~\mathit{rt}_2{:\,}\href{../binary/types.html#binary-resulttype}{\mathtt{resulttype}} + &\Rightarrow& \mathit{rt}_1 \href{../syntax/types.html#syntax-functype}{\rightarrow} \mathit{rt}_2 \\ +\end{array}\end{split}\]
    +
    +
    +

    Limits

    +

    Limits are encoded with a preceding flag indicating whether a maximum is present.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1817#1{{}}\mathdef1817{limits} & \href{../binary/types.html#binary-limits}{\mathtt{limits}} &::=& + \def\mathdef1865#1{\mathtt{0x#1}}\mathdef1865{00}~~n{:}\href{../binary/values.html#binary-int}{\def\mathdef1822#1{{\mathtt{u}#1}}\mathdef1822{\mathtt{32}}} &\Rightarrow& \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~\epsilon \} \\ &&|& + \def\mathdef1866#1{\mathtt{0x#1}}\mathdef1866{01}~~n{:}\href{../binary/values.html#binary-int}{\def\mathdef1822#1{{\mathtt{u}#1}}\mathdef1822{\mathtt{32}}}~~m{:}\href{../binary/values.html#binary-int}{\def\mathdef1822#1{{\mathtt{u}#1}}\mathdef1822{\mathtt{32}}} &\Rightarrow& \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m \} \\ +\end{array}\end{split}\]
    +
    +
    +

    Memory Types

    +

    Memory types are encoded with their limits.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef1817#1{{}}\mathdef1817{memory type} & \href{../binary/types.html#binary-memtype}{\mathtt{memtype}} &::=& + \mathit{lim}{:}\href{../binary/types.html#binary-limits}{\mathtt{limits}} &\Rightarrow& \mathit{lim} \\ +\end{array}\end{split}\]
    +
    +
    +

    Table Types

    +

    Table types are encoded with their limits and the encoding of their element reference type.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1817#1{{}}\mathdef1817{table type} & \href{../binary/types.html#binary-tabletype}{\mathtt{tabletype}} &::=& + \mathit{et}{:}\href{../binary/types.html#binary-reftype}{\mathtt{reftype}}~~\mathit{lim}{:}\href{../binary/types.html#binary-limits}{\mathtt{limits}} &\Rightarrow& \mathit{lim}~\mathit{et} \\ +\end{array}\end{split}\]
    +
    +
    +

    Global Types

    +

    Global types are encoded by their value type and a flag for their mutability.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef1817#1{{}}\mathdef1817{global type} & \href{../binary/types.html#binary-globaltype}{\mathtt{globaltype}} &::=& + t{:}\href{../binary/types.html#binary-valtype}{\mathtt{valtype}}~~m{:}\href{../binary/types.html#binary-mut}{\mathtt{mut}} &\Rightarrow& m~t \\ +\def\mathdef1817#1{{}}\mathdef1817{mutability} & \href{../binary/types.html#binary-mut}{\mathtt{mut}} &::=& + \def\mathdef1867#1{\mathtt{0x#1}}\mathdef1867{00} &\Rightarrow& \href{../syntax/types.html#syntax-mut}{\mathsf{const}} \\ &&|& + \def\mathdef1868#1{\mathtt{0x#1}}\mathdef1868{01} &\Rightarrow& \href{../syntax/types.html#syntax-mut}{\mathsf{var}} \\ +\end{array}\end{split}\]
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/binary/values.html b/core/binary/values.html new file mode 100644 index 00000000..7efd7ff7 --- /dev/null +++ b/core/binary/values.html @@ -0,0 +1,208 @@ + + + + + + + + + Values — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Values

    +
    +

    Bytes

    +

    Bytes encode themselves.

    +
    +\[\begin{split}\begin{array}{llcll@{\qquad}l} +\def\mathdef1869#1{{}}\mathdef1869{byte} & \href{../binary/values.html#binary-byte}{\mathtt{byte}} &::=& + \def\mathdef1908#1{\mathtt{0x#1}}\mathdef1908{00} &\Rightarrow& \def\mathdef1909#1{\mathtt{0x#1}}\mathdef1909{00} \\ &&|&& + \dots \\ &&|& + \def\mathdef1910#1{\mathtt{0x#1}}\mathdef1910{FF} &\Rightarrow& \def\mathdef1911#1{\mathtt{0x#1}}\mathdef1911{FF} \\ +\end{array}\end{split}\]
    +
    +
    +

    Integers

    +

    All integers are encoded using the LEB128 variable-length integer encoding, in either unsigned or signed variant.

    +

    Unsigned integers are encoded in unsigned LEB128 format. +As an additional constraint, the total number of bytes encoding a value of type \(\href{../syntax/values.html#syntax-int}{\mathit{u}N}\) must not exceed \(\mathrm{ceil}(N/7)\) bytes.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad}l} +\def\mathdef1869#1{{}}\mathdef1869{unsigned integer} & \href{../binary/values.html#binary-int}{\def\mathdef1870#1{{\mathtt{u}#1}}\mathdef1870{N}} &::=& + n{:}\href{../binary/values.html#binary-byte}{\mathtt{byte}} &\Rightarrow& n & (\mathrel{\mbox{if}} n < 2^7 \wedge n < 2^N) \\ &&|& + n{:}\href{../binary/values.html#binary-byte}{\mathtt{byte}}~~m{:}\def\mathdef1912#1{{\mathtt{u}#1}}\mathdef1912{(N\mathtt{-7})} &\Rightarrow& + 2^7\cdot m + (n-2^7) & (\mathrel{\mbox{if}} n \geq 2^7 \wedge N > 7) \\ +\end{array}\end{split}\]
    +

    Signed integers are encoded in signed LEB128 format, which uses a two’s complement representation. +As an additional constraint, the total number of bytes encoding a value of type \(\href{../syntax/values.html#syntax-int}{\mathit{s}N}\) must not exceed \(\mathrm{ceil}(N/7)\) bytes.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad}l} +\def\mathdef1869#1{{}}\mathdef1869{signed integer} & \href{../binary/values.html#binary-int}{\def\mathdef1876#1{{\mathtt{s}#1}}\mathdef1876{N}} &::=& + n{:}\href{../binary/values.html#binary-byte}{\mathtt{byte}} &\Rightarrow& n & (\mathrel{\mbox{if}} n < 2^6 \wedge n < 2^{N-1}) \\ &&|& + n{:}\href{../binary/values.html#binary-byte}{\mathtt{byte}} &\Rightarrow& n-2^7 & (\mathrel{\mbox{if}} 2^6 \leq n < 2^7 \wedge n \geq 2^7-2^{N-1}) \\ &&|& + n{:}\href{../binary/values.html#binary-byte}{\mathtt{byte}}~~m{:}\def\mathdef1913#1{{\mathtt{s}#1}}\mathdef1913{(N\mathtt{-7})} &\Rightarrow& + 2^7\cdot m + (n-2^7) & (\mathrel{\mbox{if}} n \geq 2^7 \wedge N > 7) \\ +\end{array}\end{split}\]
    +

    Uninterpreted integers are encoded as signed integers.

    +
    +\[\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef1869#1{{}}\mathdef1869{uninterpreted integer} & \href{../binary/values.html#binary-int}{\def\mathdef1881#1{{\mathtt{i}#1}}\mathdef1881{N}} &::=& + n{:}\href{../binary/values.html#binary-int}{\def\mathdef1876#1{{\mathtt{s}#1}}\mathdef1876{N}} &\Rightarrow& i & (\mathrel{\mbox{if}} n = \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}}(i)) +\end{array}\]
    +
    +

    Note

    +

    The side conditions \(N > 7\) in the productions for non-terminal bytes of the \(\def\mathdef1914#1{{\mathit{u#1}}}\mathdef1914{}\) and \(\def\mathdef1915#1{{\mathit{s#1}}}\mathdef1915{}\) encodings restrict the encoding’s length. +However, “trailing zeros” are still allowed within these bounds. +For example, \(\def\mathdef1916#1{\mathtt{0x#1}}\mathdef1916{03}\) and \(\def\mathdef1917#1{\mathtt{0x#1}}\mathdef1917{83}~\def\mathdef1918#1{\mathtt{0x#1}}\mathdef1918{00}\) are both well-formed encodings for the value \(3\) as a \(\href{../syntax/values.html#syntax-int}{\mathit{u8}}\). +Similarly, either of \(\def\mathdef1919#1{\mathtt{0x#1}}\mathdef1919{7e}\) and \(\def\mathdef1920#1{\mathtt{0x#1}}\mathdef1920{FE}~\def\mathdef1921#1{\mathtt{0x#1}}\mathdef1921{7F}\) and \(\def\mathdef1922#1{\mathtt{0x#1}}\mathdef1922{FE}~\def\mathdef1923#1{\mathtt{0x#1}}\mathdef1923{FF}~\def\mathdef1924#1{\mathtt{0x#1}}\mathdef1924{7F}\) are well-formed encodings of the value \(-2\) as a \(\href{../syntax/values.html#syntax-int}{\mathit{s16}}\).

    +

    The side conditions on the value \(n\) of terminal bytes further enforce that +any unused bits in these bytes must be \(0\) for positive values and \(1\) for negative ones. +For example, \(\def\mathdef1925#1{\mathtt{0x#1}}\mathdef1925{83}~\def\mathdef1926#1{\mathtt{0x#1}}\mathdef1926{10}\) is malformed as a \(\href{../syntax/values.html#syntax-int}{\mathit{u8}}\) encoding. +Similarly, both \(\def\mathdef1927#1{\mathtt{0x#1}}\mathdef1927{83}~\def\mathdef1928#1{\mathtt{0x#1}}\mathdef1928{3E}\) and \(\def\mathdef1929#1{\mathtt{0x#1}}\mathdef1929{FF}~\def\mathdef1930#1{\mathtt{0x#1}}\mathdef1930{7B}\) are malformed as \(\href{../syntax/values.html#syntax-int}{\mathit{s8}}\) encodings.

    +
    +
    +
    +

    Floating-Point

    +

    Floating-point values are encoded directly by their IEEE 754-2019 (Section 3.4) bit pattern in little endian byte order:

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef1869#1{{}}\mathdef1869{floating-point value} & \href{../binary/values.html#binary-float}{\def\mathdef1884#1{{\mathtt{f}#1}}\mathdef1884{N}} &::=& + b^\ast{:\,}\href{../binary/values.html#binary-byte}{\mathtt{byte}}^{N/8} &\Rightarrow& \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-float}{\mathit{f}N}}^{-1}(b^\ast) \\ +\end{array}\end{split}\]
    +
    +
    +

    Names

    +

    Names are encoded as a vector of bytes containing the Unicode (Section 3.9) UTF-8 encoding of the name’s character sequence.

    +
    +\[\begin{split}\begin{array}{llclllll} +\def\mathdef1869#1{{}}\mathdef1869{name} & \href{../binary/values.html#binary-name}{\mathtt{name}} &::=& + b^\ast{:}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/values.html#binary-byte}{\mathtt{byte}}) &\Rightarrow& \href{../syntax/values.html#syntax-name}{\mathit{name}} + && (\mathrel{\mbox{if}} \href{../binary/values.html#binary-utf8}{\mathrm{utf8}}(\href{../syntax/values.html#syntax-name}{\mathit{name}}) = b^\ast) \\ +\end{array}\end{split}\]
    +

    The auxiliary \(\href{../binary/values.html#binary-utf8}{\mathrm{utf8}}\) function expressing this encoding is defined as follows:

    +
    +\[\begin{split}\begin{array}{@{}l@{}} +\begin{array}{@{}lcl@{\qquad}l@{}} +\href{../binary/values.html#binary-utf8}{\mathrm{utf8}}(c^\ast) &=& (\href{../binary/values.html#binary-utf8}{\mathrm{utf8}}(c))^\ast \\[1ex] +\href{../binary/values.html#binary-utf8}{\mathrm{utf8}}(c) &=& b & + (\begin{array}[t]{@{}c@{~}l@{}} + \mathrel{\mbox{if}} & c < \def\mathdef1931#1{\mathrm{U{+}#1}}\mathdef1931{80} \\ + \wedge & c = b) \\ + \end{array} \\ +\href{../binary/values.html#binary-utf8}{\mathrm{utf8}}(c) &=& b_1~b_2 & + (\begin{array}[t]{@{}c@{~}l@{}} + \mathrel{\mbox{if}} & \def\mathdef1932#1{\mathrm{U{+}#1}}\mathdef1932{80} \leq c < \def\mathdef1933#1{\mathrm{U{+}#1}}\mathdef1933{800} \\ + \wedge & c = 2^6(b_1-\def\mathdef1934#1{\mathtt{0x#1}}\mathdef1934{C0})+(b_2-\def\mathdef1935#1{\mathtt{0x#1}}\mathdef1935{80})) \\ + \end{array} \\ +\href{../binary/values.html#binary-utf8}{\mathrm{utf8}}(c) &=& b_1~b_2~b_3 & + (\begin{array}[t]{@{}c@{~}l@{}} + \mathrel{\mbox{if}} & \def\mathdef1936#1{\mathrm{U{+}#1}}\mathdef1936{800} \leq c < \def\mathdef1937#1{\mathrm{U{+}#1}}\mathdef1937{D800} \vee \def\mathdef1938#1{\mathrm{U{+}#1}}\mathdef1938{E000} \leq c < \def\mathdef1939#1{\mathrm{U{+}#1}}\mathdef1939{10000} \\ + \wedge & c = 2^{12}(b_1-\def\mathdef1940#1{\mathtt{0x#1}}\mathdef1940{E0})+2^6(b_2-\def\mathdef1941#1{\mathtt{0x#1}}\mathdef1941{80})+(b_3-\def\mathdef1942#1{\mathtt{0x#1}}\mathdef1942{80})) \\ + \end{array} \\ +\href{../binary/values.html#binary-utf8}{\mathrm{utf8}}(c) &=& b_1~b_2~b_3~b_4 & + (\begin{array}[t]{@{}c@{~}l@{}} + \mathrel{\mbox{if}} & \def\mathdef1943#1{\mathrm{U{+}#1}}\mathdef1943{10000} \leq c < \def\mathdef1944#1{\mathrm{U{+}#1}}\mathdef1944{110000} \\ + \wedge & c = 2^{18}(b_1-\def\mathdef1945#1{\mathtt{0x#1}}\mathdef1945{F0})+2^{12}(b_2-\def\mathdef1946#1{\mathtt{0x#1}}\mathdef1946{80})+2^6(b_3-\def\mathdef1947#1{\mathtt{0x#1}}\mathdef1947{80})+(b_4-\def\mathdef1948#1{\mathtt{0x#1}}\mathdef1948{80})) \\ + \end{array} \\ +\end{array} \\ +\mathrel{\mbox{where}} b_2, b_3, b_4 < \def\mathdef1949#1{\mathtt{0x#1}}\mathdef1949{C0} \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    Unlike in some other formats, name strings are not 0-terminated.

    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/exec/conventions.html b/core/exec/conventions.html new file mode 100644 index 00000000..2004b56b --- /dev/null +++ b/core/exec/conventions.html @@ -0,0 +1,207 @@ + + + + + + + + + Conventions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Conventions

    +

    WebAssembly code is executed when instantiating a module or invoking an exported function on the resulting module instance.

    +

    Execution behavior is defined in terms of an abstract machine that models the program state. +It includes a stack, which records operand values and control constructs, and an abstract store containing global state.

    +

    For each instruction, there is a rule that specifies the effect of its execution on the program state. +Furthermore, there are rules describing the instantiation of a module. +As with validation, all rules are given in two equivalent forms:

    +
      +

    1. In prose, describing the execution in intuitive form.

      2. +

    2. In formal notation, describing the rule in mathematical form. 1

      3. +
    +
    +

    Note

    +

    As with validation, the prose and formal rules are equivalent, +so that understanding of the formal notation is not required to read this specification. +The formalism offers a more concise description in notation that is used widely in programming languages semantics and is readily amenable to mathematical proof.

    +
    +
    +

    Prose Notation

    +

    Execution is specified by stylised, step-wise rules for each instruction of the abstract syntax. +The following conventions are adopted in stating these rules.

    +
      +

    • The execution rules implicitly assume a given store \(S\).

      • +

    • The execution rules also assume the presence of an implicit stack +that is modified by pushing or popping +values, labels, and frames.

      • +

    • Certain rules require the stack to contain at least one frame. +The most recent frame is referred to as the current frame.

      • +

    • Both the store and the current frame are mutated by replacing some of their components. +Such replacement is assumed to apply globally.

      • +

    • The execution of an instruction may trap, +in which case the entire computation is aborted and no further modifications to the store are performed by it. (Other computations can still be initiated afterwards.)

      • +

    • The execution of an instruction may also end in a jump to a designated target, +which defines the next instruction to execute.

      • +

    • Execution can enter and exit instruction sequences that form blocks.

      • +

    • Instruction sequences are implicitly executed in order, unless a trap or jump occurs.

      • +

    • In various places the rules contain assertions expressing crucial invariants about the program state.

      • +
    +
    +
    +

    Formal Notation

    +
    +

    Note

    +

    This section gives a brief explanation of the notation for specifying execution formally. +For the interested reader, a more thorough introduction can be found in respective text books. 2

    +
    +

    The formal execution rules use a standard approach for specifying operational semantics, rendering them into reduction rules. +Every rule has the following general form:

    +
    +\[\mathit{configuration} \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad \mathit{configuration}\]
    +

    A configuration is a syntactic description of a program state. +Each rule specifies one step of execution. +As long as there is at most one reduction rule applicable to a given configuration, reduction – and thereby execution – is deterministic. +WebAssembly has only very few exceptions to this, which are noted explicitly in this specification.

    +

    For WebAssembly, a configuration typically is a tuple \((S; F; \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast)\) consisting of the current store \(S\), the call frame \(F\) of the current function, and the sequence of instructions that is to be executed. +(A more precise definition is given later.)

    +

    To avoid unnecessary clutter, the store \(S\) and the frame \(F\) are omitted from reduction rules that do not touch them.

    +

    There is no separate representation of the stack. +Instead, it is conveniently represented as part of the configuration’s instruction sequence. +In particular, values are defined to coincide with \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}\) instructions, +and a sequence of \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}\) instructions can be interpreted as an operand “stack” that grows to the right.

    +
    +

    Note

    +

    For example, the reduction rule for the \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}\) instruction can be given as follows:

    +
    +\[(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n_2)~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}} \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(n_1 + n_2) \mathbin{\mathrm{mod}} 2^{32})\]
    +

    Per this rule, two \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}\) instructions and the \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}\) instruction itself are removed from the instruction stream and replaced with one new \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}\) instruction. +This can be interpreted as popping two value off the stack and pushing the result.

    +

    When no result is produced, an instruction reduces to the empty sequence:

    +
    +\[\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{nop}} \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad \epsilon\]
    +
    +

    Labels and frames are similarly defined to be part of an instruction sequence.

    +

    The order of reduction is determined by the definition of an appropriate evaluation context.

    +

    Reduction terminates when no more reduction rules are applicable. +Soundness of the WebAssembly type system guarantees that this is only the case when the original instruction sequence has either been reduced to a sequence of \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}\) instructions, which can be interpreted as the values of the resulting operand stack, +or if a trap occurred.

    +
    +

    Note

    +

    For example, the following instruction sequence,

    +
    +\[(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_2)~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{neg}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_3)~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}}\]
    +

    terminates after three steps:

    +
    +\[\begin{split}\begin{array}{ll} +& (\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_2)~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{neg}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_3)~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}} \\ +\href{../exec/conventions.html#formal-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_4)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_3)~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}} \\ +\href{../exec/conventions.html#formal-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_5)~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}} \\ +\href{../exec/conventions.html#formal-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_6) \\ +\end{array}\end{split}\]
    +

    where \(x_4 = -x_2\) and \(x_5 = -x_2 + x_3\) and \(x_6 = x_1 \cdot (-x_2 + x_3)\).

    +
    +
    +
    1
    +

    The semantics is derived from the following article: +Andreas Haas, Andreas Rossberg, Derek Schuff, Ben Titzer, Dan Gohman, Luke Wagner, Alon Zakai, JF Bastien, Michael Holman. Bringing the Web up to Speed with WebAssembly. Proceedings of the 38th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2017). ACM 2017.

    +
    +
    2
    +

    For example: Benjamin Pierce. Types and Programming Languages. The MIT Press 2002

    +
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/exec/index.html b/core/exec/index.html new file mode 100644 index 00000000..14a4537b --- /dev/null +++ b/core/exec/index.html @@ -0,0 +1,162 @@ + + + + + + + + + Execution — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Execution

    +
    + +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/exec/instructions.html b/core/exec/instructions.html new file mode 100644 index 00000000..add88423 --- /dev/null +++ b/core/exec/instructions.html @@ -0,0 +1,2443 @@ + + + + + + + + + Instructions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Instructions

    +

    WebAssembly computation is performed by executing individual instructions.

    +
    +

    Numeric Instructions

    +

    Numeric instructions are defined in terms of the generic numeric operators. +The mapping of numeric instructions to their underlying operators is expressed by the following definition:

    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\mathit{op}_{\mathsf{i}N}(n_1,\dots,n_k) &=& \mathrm{i}\mathit{op}_N(n_1,\dots,n_k) \\ +\mathit{op}_{\mathsf{f}N}(z_1,\dots,z_k) &=& \mathrm{f}\mathit{op}_N(z_1,\dots,z_k) \\ +\end{array}\end{split}\]
    +

    And for conversion operators:

    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\mathit{cvtop}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?}_{t_1,t_2}(c) &=& \mathit{cvtop}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?}_{|t_1|,|t_2|}(c) \\ +\end{array}\end{split}\]
    +

    Where the underlying operators are partial, the corresponding instruction will trap when the result is not defined. +Where the underlying operators are non-deterministic, because they may return one of multiple possible NaN values, so are the corresponding instructions.

    +
    +

    Note

    +

    For example, the result of instruction \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}\) applied to operands \(i_1, i_2\) +invokes \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}_{\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}}(i_1, i_2)\), +which maps to the generic \(\href{../exec/numerics.html#op-iadd}{\mathrm{iadd}}_{32}(i_1, i_2)\) via the above definition. +Similarly, \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_s}\) applied to \(z\) +invokes \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}^{\mathsf{s}}_{\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}},\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}}(z)\), +which maps to the generic \(\href{../exec/numerics.html#op-trunc-s}{\mathrm{trunc}^{\mathsf{s}}}_{32,64}(z)\).

    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\)

    +
      +

    1. Push the value \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) to the stack.

      2. +
    +
    +

    Note

    +

    No formal reduction rule is required for this instruction, since \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}\) instructions already are values.

    +
    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}\)

    +
      +

    1. Assert: due to validation, a value of value type \(t\) is on the top of the stack.

      2. +

    2. Pop the value \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1\) from the stack.

      3. +

    3. If \(\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}_t(c_1)\) is defined, then:

      +
        +

      1. Let \(c\) be a possible result of computing \(\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}_t(c_1)\).

        2. +

      2. Push the value \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) to the stack.

        3. +
      +
      4. +

    4. Else:

      +
        +

      1. Trap.

        2. +
      +
      5. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~t\mathsf{.}\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) + & (\mathrel{\mbox{if}} c \in \href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}_t(c_1)) \\ +(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~t\mathsf{.}\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} + & (\mathrel{\mbox{if}} \href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}_{t}(c_1) = \{\}) +\end{array}\end{split}\]
    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}\)

    +
      +

    1. Assert: due to validation, two values of value type \(t\) are on the top of the stack.

      2. +

    2. Pop the value \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2\) from the stack.

      3. +

    3. Pop the value \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1\) from the stack.

      4. +

    4. If \(\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}_t(c_1, c_2)\) is defined, then:

      +
        +

      1. Let \(c\) be a possible result of computing \(\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}_t(c_1, c_2)\).

        2. +

      2. Push the value \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) to the stack.

        3. +
      +
      5. +

    5. Else:

      +
        +

      1. Trap.

        2. +
      +
      6. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~t\mathsf{.}\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) + & (\mathrel{\mbox{if}} c \in \href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}_t(c_1,c_2)) \\ +(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~t\mathsf{.}\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} + & (\mathrel{\mbox{if}} \href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}_{t}(c_1,c2) = \{\}) +\end{array}\end{split}\]
    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-testop}{\mathit{testop}}\)

    +
      +

    1. Assert: due to validation, a value of value type \(t\) is on the top of the stack.

      2. +

    2. Pop the value \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1\) from the stack.

      3. +

    3. Let \(c\) be the result of computing \(\href{../syntax/instructions.html#syntax-testop}{\mathit{testop}}_t(c_1)\).

      4. +

    4. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) to the stack.

      5. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~t\mathsf{.}\href{../syntax/instructions.html#syntax-testop}{\mathit{testop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) + & (\mathrel{\mbox{if}} c = \href{../syntax/instructions.html#syntax-testop}{\mathit{testop}}_t(c_1)) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-relop}{\mathit{relop}}\)

    +
      +

    1. Assert: due to validation, two values of value type \(t\) are on the top of the stack.

      2. +

    2. Pop the value \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2\) from the stack.

      3. +

    3. Pop the value \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1\) from the stack.

      4. +

    4. Let \(c\) be the result of computing \(\href{../syntax/instructions.html#syntax-relop}{\mathit{relop}}_t(c_1, c_2)\).

      5. +

    5. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) to the stack.

      6. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~t\mathsf{.}\href{../syntax/instructions.html#syntax-relop}{\mathit{relop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) + & (\mathrel{\mbox{if}} c = \href{../syntax/instructions.html#syntax-relop}{\mathit{relop}}_t(c_1,c_2)) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(t_2\mathsf{.}\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}\mathsf{\_}t_1\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?\)

    +
      +

    1. Assert: due to validation, a value of value type \(t_1\) is on the top of the stack.

      2. +

    2. Pop the value \(t_1.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1\) from the stack.

      3. +

    3. If \(\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?}_{t_1,t_2}(c_1)\) is defined:

      +
        +

      1. Let \(c_2\) be a possible result of computing \(\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?}_{t_1,t_2}(c_1)\).

        2. +

      2. Push the value \(t_2.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2\) to the stack.

        3. +
      +
      4. +

    4. Else:

      +
        +

      1. Trap.

        2. +
      +
      5. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +(t_1\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~t_2\mathsf{.}\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}\mathsf{\_}t_1\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^? &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (t_2\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2) + & (\mathrel{\mbox{if}} c_2 \in \href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?}_{t_1,t_2}(c_1)) \\ +(t_1\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~t_2\mathsf{.}\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}\mathsf{\_}t_1\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^? &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} + & (\mathrel{\mbox{if}} \href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?}_{t_1,t_2}(c_1) = \{\}) +\end{array}\end{split}\]
    +
    +
    +
    +

    Reference Instructions

    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t\)

    +
      +

    1. Push the value \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t\) to the stack.

      2. +
    +
    +

    Note

    +

    No formal reduction rule is required for this instruction, since the \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}\) instruction is already a value.

    +
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}is\_null}}\)

    +
      +

    1. Assert: due to validation, a reference value is on the top of the stack.

      2. +

    2. Pop the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) from the stack.

      3. +

    3. If \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) is \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t\), then:

      +
        +

      1. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1\) to the stack.

        2. +
      +
      4. +

    4. Else:

      +
        +

      1. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0\) to the stack.

        2. +
      +
      5. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +\href{../exec/runtime.html#syntax-val}{\mathit{val}}~\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}is\_null}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1 + & (\mathrel{\mbox{if}} \href{../exec/runtime.html#syntax-val}{\mathit{val}} = \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t) \\ +\href{../exec/runtime.html#syntax-val}{\mathit{val}}~\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}is\_null}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0 + & (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}}[x]\) exists.

      3. +

    3. Let \(a\) be the function address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}}[x]\).

      4. +

    4. Push the value \(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref}}~a\) to the stack.

      5. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +F; \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~x &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& F; \href{../exec/runtime.html#syntax-ref}{\mathsf{ref}}~a + & (\mathrel{\mbox{if}} a = F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}}[x]) \\ +\end{array}\end{split}\]
    +
    +
    +
    +

    Vector Instructions

    +

    Most vector instructions are defined in terms of generic numeric operators applied lane-wise based on the shape.

    +
    +\[\begin{array}{lll@{\qquad}l} +\mathit{op}_{t\mathsf{x}N}(n_1,\dots,n_k) &=& + \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t\mathsf{x}N}(op_t(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(n_1) ~\dots~ \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(n_k)) +\end{array}\]
    +
    +

    Note

    +

    For example, the result of instruction \(\mathsf{i32x4}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}\) applied to operands \(i_1, i_2\) +invokes \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}_{\mathsf{i32x4}}(i_1, i_2)\), which maps to +\(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\mathsf{i32x4}}(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}_{\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}}(i_1^+, i_2^+))\), +where \(i_1^+\) and \(i_2^+\) are sequences resulting from invoking +\(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\mathsf{i32x4}}(i_1)\) and \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\mathsf{i32x4}}(i_2)\) +respectively.

    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\)

    +
      +

    1. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) to the stack.

      2. +
    +
    +

    Note

    +

    No formal reduction rule is required for this instruction, since \(\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}\) instructions coincide with values.

    +
    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}}\)

    +
      +

    1. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      3. +

    3. Let \(c\) be the result of computing \(\href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}}_{\mathsf{i128}}(c_1)\).

      4. +

    4. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) to the stack.

      5. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) + & (\mathrel{\mbox{if}} c = \href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}}_{\mathsf{i128}}(c_1)) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}}\)

    +
      +

    1. Assert: due to validation, two values of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) are on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2\) from the stack.

      3. +

    3. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      4. +

    4. Let \(c\) be the result of computing \(\href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}}_{\mathsf{i128}}(c_1, c_2)\).

      5. +

    5. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) to the stack.

      6. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2)~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) + & (\mathrel{\mbox{if}} c = \href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}}_{\mathsf{i128}}(c_1, c_2)) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}}\)

    +
      +

    1. Assert: due to validation, three values of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) are on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_3\) from the stack.

      3. +

    3. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2\) from the stack.

      4. +

    4. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      5. +

    5. Let \(c\) be the result of computing \(\href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}}_{\mathsf{i128}}(c_1, c_2, c_3)\).

      6. +

    6. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) to the stack.

      7. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_3)~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) + & (\mathrel{\mbox{if}} c = \href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}}_{\mathsf{i128}}(c_1, c_2, c_3)) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{any\_true}}\)

    +
      +

    1. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      3. +

    3. Let \(i\) be the result of computing \(\href{../exec/numerics.html#op-ine}{\mathrm{ine}}_{128}(c_1, 0)\).

      4. +

    4. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) onto the stack.

      5. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{any\_true}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i) + & (\mathrel{\mbox{if}} i = \href{../exec/numerics.html#op-ine}{\mathrm{ine}}_{128}(c_1, 0)) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\mathsf{i8x16.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{swizzle}}\)

    +
      +

    1. Assert: due to validation, two values of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) are on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2\) from the stack.

      3. +

    3. Let \(i^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{i8x16}(c_2)\).

      4. +

    4. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      5. +

    5. Let \(j^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{i8x16}(c_1)\).

      6. +

    6. Let \(c^\ast\) be the concatenation of the two sequences \(j^\ast~0^{240}\)

      7. +

    7. Let \(c'\) be the result of \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{i8x16}(c^\ast[ i^\ast[0] ] \dots c^\ast[ i^\ast[15] ])\).

      8. +

    8. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c'\) onto the stack.

      9. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2)~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{swizzle}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c') +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & i^\ast = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{i8x16}(c_2) \\ + \wedge & c^\ast = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{i8x16}(c_1)~0^{240} \\ + \wedge & c' = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{i8x16}(c^\ast[ i^\ast[0] ] \dots c^\ast[ i^\ast[15] ]) + \end{array} +\end{array}\end{split}\]
    +
    +
    +

    \(\mathsf{i8x16.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}~x^\ast\)

    +
      +

    1. Assert: due to validation, two values of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) are on the top of the stack.

      2. +

    2. Assert: due to validation, for all \(x_i\) in \(x^\ast\) it holds that \(x_i < 32\).

      3. +

    3. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2\) from the stack.

      4. +

    4. Let \(i_2^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{i8x16}(c_2)\).

      5. +

    5. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      6. +

    6. Let \(i_1^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{i8x16}(c_1)\).

      7. +

    7. Let \(i^\ast\) be the concatenation of the two sequences \(i_1^\ast~i_2^\ast\).

      8. +

    8. Let \(c\) be the result of \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{i8x16}(i^\ast[x^\ast[0]] \dots i^\ast[x^\ast[15]])\).

      9. +

    9. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) onto the stack.

      10. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2)~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}~x^\ast &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & i^\ast = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{i8x16}(c_1)~\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{i8x16}(c_2) \\ + \wedge & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{i8x16}(i^\ast[x^\ast[0]] \dots i^\ast[x^\ast[15]]) + \end{array} +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}\)

    +
      +

    1. Let \(t\) be the type \(\href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}})\).

      2. +

    2. Assert: due to validation, a value of value type \(t\) is on the top of the stack.

      3. +

    3. Pop the value \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1\) from the stack.

      4. +

    4. Let \(N\) be the integer \(\href{../valid/instructions.html#aux-dim}{\mathrm{dim}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}})\).

      5. +

    5. Let \(c\) be the result of \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(c_1^N)\).

      6. +

    6. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) to the stack.

      7. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) + & (\mathrel{\mbox{if}} t = \href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}) + \wedge c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(c_1^{\href{../valid/instructions.html#aux-dim}{\mathrm{dim}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}})})) + \\ +\end{array}\end{split}\]
    +
    +
    +

    \(t_1\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?~x\)

    +
      +

    1. Assert: due to validation, \(x < N\).

      2. +

    2. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      3. +

    3. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      4. +

    4. Let \(i^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}N}(c_1)\).

      5. +

    5. Let \(t_2\) be the type \(\href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(t_1\mathsf{x}N)\).

      6. +

    6. Let \(c_2\) be the result of computing \(\href{../exec/numerics.html#op-extend-u}{\mathrm{extend}}^{sx^?}_{t_1,t_2}(i^\ast[x])\).

      7. +

    7. Push the value \(t_2.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2\) to the stack.

      8. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~t_1\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~x &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (t_2\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & t_2 = \href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(t_1\mathsf{x}N) \\ + \wedge & c_2 = \href{../exec/numerics.html#op-extend-u}{\mathrm{extend}}^{sx^?}_{t_1,t_2}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}N}(c_1)[x]) + \end{array} +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~x\)

    +
      +

    1. Assert: due to validation, \(x < \href{../valid/instructions.html#aux-dim}{\mathrm{dim}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}})\).

      2. +

    2. Let \(t_1\) be the type \(\href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}})\).

      3. +

    3. Assert: due to validation, a value of value type \(t_1\) is on the top of the stack.

      4. +

    4. Pop the value \(t_1.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1\) from the stack.

      5. +

    5. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      6. +

    6. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2\) from the stack.

      7. +

    7. Let \(i^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(c_2)\).

      8. +

    8. Let \(c\) be the result of computing \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(i^\ast \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} [x] = c_1)\)

      9. +

    9. Push \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) on the stack.

      10. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +(t_1\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2)~\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~x &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & i^\ast = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(c_2)) \\ + \wedge & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(i^\ast \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} [x] = c_1) + \end{array} +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}}\)

    +
      +

    1. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      3. +

    3. Let \(c\) be the result of computing \(\href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(c_1)\).

      4. +

    4. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) to the stack.

      5. +
    +
    +\[\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) + & (\mathrel{\mbox{if}} c = \href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(c_1)) +\end{array}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}\)

    +
      +

    1. Assert: due to validation, two values of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) are on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2\) from the stack.

      3. +

    3. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      4. +

    4. If \(\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(c_1, c_2)\) is defined:

      +
        +

      1. Let \(c\) be a possible result of computing \(\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(c_1, c_2)\).

        2. +

      2. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) to the stack.

        3. +
      +
      5. +

    5. Else:

      +
        +

      1. Trap.

        2. +
      +
      6. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2)~\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) + & (\mathrel{\mbox{if}} c \in \href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(c_1, c_2)) \\ +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2)~\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} + & (\mathrel{\mbox{if}} \href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(c_1, c_2) = \{\}) +\end{array}\end{split}\]
    +
    +
    +

    \(t\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vrelop}}\)

    +
      +

    1. Assert: due to validation, two values of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) are on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2\) from the stack.

      3. +

    3. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      4. +

    4. Let \(i^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(c_1)\).

      5. +

    5. Let \(j^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(c_2)\).

      6. +

    6. Let \(c\) be the result of computing \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t\mathsf{x}N}(\href{../exec/numerics.html#op-extend-s}{\mathrm{extend}^{\mathsf{s}}}_{1,|t|}(\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vrelop}}_t(i^\ast, j^\ast)))\).

      7. +

    7. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) to the stack.

      8. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2)~t\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vrelop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t\mathsf{x}N}(\href{../exec/numerics.html#op-extend-s}{\mathrm{extend}^{\mathsf{s}}}_{1,|t|}(\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vrelop}}_t(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(c_1), \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(c_2))))) + \end{array} +\end{array}\end{split}\]
    +
    +
    +

    \(t\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-vishiftop}{\mathit{vishiftop}}\)

    +
      +

    1. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s\) from the stack.

      3. +

    3. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      4. +

    4. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      5. +

    5. Let \(i^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(c_1)\).

      6. +

    6. Let \(c\) be \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t\mathsf{x}N}(\href{../syntax/instructions.html#syntax-vishiftop}{\mathit{vishiftop}}_{t}(i^\ast, s^N))\).

      7. +

    7. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) to the stack.

      8. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~t\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-vishiftop}{\mathit{vishiftop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & i^\ast = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(c_1) \\ + \wedge & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t\mathsf{x}N}(\href{../syntax/instructions.html#syntax-vishiftop}{\mathit{vishiftop}}_{t}(i^\ast, s^N))) + \end{array} +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}}\)

    +
      +

    1. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      3. +

    3. Let \(i_1^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(c_1)\)

      4. +

    4. Let \(i\) be the result of computing \(\href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(\bigwedge(i_1 \neq 0)^\ast)\).

      5. +

    5. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) onto the stack.

      6. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & i_1^\ast = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}}(c) \\ + \wedge & i = \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(\bigwedge(i_1 \neq 0)^\ast) + \end{array} +\end{array}\end{split}\]
    +
    +
    +

    \(t\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}\)

    +
      +

    1. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      3. +

    3. Let \(i_1^N\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(c)\).

      4. +

    4. Let \(B\) be the bit width \(|t|\) of value type \(t\).

      5. +

    5. Let \(i_2^N\) be the sequence as a result of computing \(\href{../exec/numerics.html#op-ilt-s}{\mathrm{ilt\_s}}_{B}(i_1^N, 0^N)\).

      6. +

    6. Let \(c\) be the integer \(\href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_{32}^{-1}(i_2^N~0^{32-N})\).

      7. +

    7. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) onto the stack.

      8. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~t\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) + & (\mathrel{\mbox{if}} c = \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_{32}^{-1}(\href{../exec/numerics.html#op-ilt-s}{\mathrm{ilt\_s}}_{|t|}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(c), 0^N))) + \\ +\end{array}\end{split}\]
    +
    +
    +

    \(t_2\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_}t_1\mathsf{x}M\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\)

    +
      +

    1. Assert: due to syntax, \(N = 2\cdot M\).

      2. +

    2. Assert: due to validation, two values of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) are on the top of the stack.

      3. +

    3. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2\) from the stack.

      4. +

    4. Let \(d_2^M\) be the result of computing \(\href{../exec/numerics.html#op-narrow-u}{\mathrm{narrow}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_2))\).

      5. +

    5. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      6. +

    6. Let \(d_1^M\) be the result of computing \(\href{../exec/numerics.html#op-narrow-u}{\mathrm{narrow}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1))\).

      7. +

    7. Let \(c\) be the result of \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t_2\mathsf{x}N}(d_1^M~d_2^M)\).

      8. +

    8. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) onto the stack.

      9. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2)~t_2\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\_t_1\mathsf{x}M\_\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & d_1^M = \href{../exec/numerics.html#op-narrow-u}{\mathrm{narrow}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}( \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1)) \\ + \wedge & d_2^M = \href{../exec/numerics.html#op-narrow-u}{\mathrm{narrow}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}( \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_2)) \\ + \wedge & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t_2\mathsf{x}N}(d_1^M~d_2^M) + \end{array} +\end{array}\end{split}\]
    +
    +
    +

    \(t_2\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}\mathsf{\_}t_1\mathsf{x}M\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\)

    +
      +

    1. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      3. +

    3. Let \(i^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1)\).

      4. +

    4. Let \(c\) be the result of computing \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t_2\mathsf{x}N}(\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}(i^\ast))\)

      5. +

    5. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) onto the stack.

      6. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~t_2\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}\mathsf{\_}t_1\mathsf{x}M\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) \\ +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t_2\mathsf{x}N}(\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1))) + \end{array} +\end{array}\end{split}\]
    +
    +
    +

    \(t_2\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_}t_1\mathsf{x}M\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?\)

    +
      +

    1. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      3. +

    3. If \(\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\) is \(\mathsf{low}\), then:

      +
        +

      1. Let \(i^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1)[0 \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N]\).

        2. +
      +
      4. +

    4. Else:

      +
        +

      1. Let \(i^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1)[N \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N]\).

        2. +
      +
      5. +

    5. Let \(j^\ast\) be the result of computing \(\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?}_{|t_1|,|t_2|}(i^\ast)\).

      6. +

    6. Let \(c\) be the result of computing \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t_2\mathsf{x}N}(j^\ast)\).

      7. +

    7. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) onto the stack.

      8. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~t_2\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_}t_1\mathsf{x}M\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^? &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) \\ +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t_2\mathsf{x}N}(\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?}_{|t_1|,|t_2|}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1)[\href{../syntax/instructions.html#syntax-half}{\mathit{half}}(0, N) \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N])) + \end{array} +\end{array}\end{split}\]
    +

    where:

    +
    +\[\begin{split}\begin{array}{lcl} +\mathsf{low}(x, y) &=& x \\ +\mathsf{high}(x, y) &=& y \\ +\end{array}\end{split}\]
    +
    +
    +

    \(t_2\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}\mathsf{\_}t_1\mathsf{x}M\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\mathsf{\_zero}\)

    +
      +

    1. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      3. +

    3. Let \(i^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1)\).

      4. +

    4. Let \(j^\ast\) be the result of computing \(\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}(i^\ast)\) concatenated with the vector \(0^M\).

      5. +

    5. Let \(c\) be the result of computing \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t_2\mathsf{x}N}(j^\ast)\).

      6. +

    6. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) onto the stack.

      7. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~t_2\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}\mathsf{\_}t_1\mathsf{x}M\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\mathsf{\_zero} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) \\ +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t_2\mathsf{x}N}(\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1))~0^M) + \end{array} +\end{array}\end{split}\]
    +
    +
    +

    \(\mathsf{i32x4.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{dot}}\mathsf{\_i16x8\_s}\)

    +
      +

    1. Assert: due to validation, two values of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2\) from the stack.

      3. +

    3. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      4. +

    4. Let \((i_1~i_2)^\ast\) be the result of computing \(\href{../exec/numerics.html#op-imul}{\mathrm{imul}}_{32}(\href{../exec/numerics.html#op-extend-s}{\mathrm{extend}^{\mathsf{s}}}_{16,32}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}}(c_1)), \href{../exec/numerics.html#op-extend-s}{\mathrm{extend}^{\mathsf{s}}}_{16,32}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}}(c_2)))\)

      5. +

    5. Let \(j^\ast\) be the result of computing \(\href{../exec/numerics.html#op-iadd}{\mathrm{iadd}}_{32}(i_1, i_2)^\ast\).

      6. +

    6. Let \(c\) be the result of computing \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}}(j^\ast)\).

      7. +

    7. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) onto the stack.

      8. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2)~\mathsf{i32x4.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{dot}}\mathsf{\_i16x8\_s} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) \\ +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & (i_1~i_2)^\ast = \href{../exec/numerics.html#op-imul}{\mathrm{imul}}_{32}(\href{../exec/numerics.html#op-extend-s}{\mathrm{extend}^{\mathsf{s}}}_{16,32}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}}(c_1)), \href{../exec/numerics.html#op-extend-s}{\mathrm{extend}^{\mathsf{s}}}_{16,32}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}}(c_2))) \\ + \wedge & j^\ast = \href{../exec/numerics.html#op-iadd}{\mathrm{iadd}}_{32}(i_1, i_2)^\ast \\ + \wedge & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}}(j^\ast) + \end{array} +\end{array}\end{split}\]
    +
    +
    +

    \(t_2\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_}t_1\mathsf{x}M\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\)

    +
      +

    1. Assert: due to validation, two values of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2\) from the stack.

      3. +

    3. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      4. +

    4. If \(\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\) is \(\mathsf{low}\), then:

      +
        +

      1. Let \(i^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1)[0 \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N]\).

        2. +

      2. Let \(j^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_2)[0 \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N]\).

        3. +
      +
      5. +

    5. Else:

      +
        +

      1. Let \(i^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1)[N \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N]\).

        2. +

      2. Let \(j^\ast\) be the sequence \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_2)[N \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N]\).

        3. +
      +
      6. +

    6. Let \(c\) be the result of computing \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t_2\mathsf{x}N}(\href{../exec/numerics.html#op-imul}{\mathrm{imul}}_{t_2\mathsf{x}N}(\href{../exec/numerics.html#op-extend-u}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}(i^\ast), \href{../exec/numerics.html#op-extend-u}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}(j^\ast)))\)

      7. +

    7. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) onto the stack.

      8. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_2)~t_2\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_}t_1\mathsf{x}M\_\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) \\ +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & i^\ast = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1)[\href{../syntax/instructions.html#syntax-half}{\mathit{half}}(0, N) \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N] \\ + \wedge & j^\ast = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_2)[\href{../syntax/instructions.html#syntax-half}{\mathit{half}}(0, N) \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N] \\ + \wedge & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t_2\mathsf{x}N}(\href{../exec/numerics.html#op-imul}{\mathrm{imul}}_{t_2\mathsf{x}N}(\href{../exec/numerics.html#op-extend-u}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}(i^\ast), \href{../exec/numerics.html#op-extend-u}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}(j^\ast))) + \end{array}\end{split}\]
    +

    where:

    +
    +\[\begin{split}\begin{array}{lcl} +\mathsf{low}(x, y) &=& x \\ +\mathsf{high}(x, y) &=& y \\ +\end{array}\end{split}\]
    +
    +
    +

    \(t_2\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\_t_1\mathsf{x}M\_\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\)

    +
      +

    1. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1\) from the stack.

      3. +

    3. Let \((i_1~i_2)^\ast\) be the sequence \(\href{../exec/numerics.html#op-extend-u}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1))\).

      4. +

    4. Let \(j^\ast\) be the result of computing \(\href{../exec/numerics.html#op-iadd}{\mathrm{iadd}}_{N}(i_1, i_2)^\ast\).

      5. +

    5. Let c be the result of computing \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t_2\mathsf{x}N}(j^\ast)\).

      6. +

    6. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\) to the stack.

      7. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c_1)~t_2\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\_t_1\mathsf{x}M\_\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c) \\ +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & (i_1~i_2)^\ast = \href{../exec/numerics.html#op-extend-u}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{|t_1|,|t_2|}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t_1\mathsf{x}M}(c_1)) \\ + \wedge & j^\ast = \href{../exec/numerics.html#op-iadd}{\mathrm{iadd}}_{N}(i_1, i_2)^\ast \\ + \wedge & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t_2\mathsf{x}N}(j^\ast) + \end{array} +\end{array}\end{split}\]
    +
    +
    +
    +

    Parametric Instructions

    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{drop}}\)

    +
      +

    1. Assert: due to validation, a value is on the top of the stack.

      2. +

    2. Pop the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) from the stack.

      3. +
    +
    +\[\begin{array}{lcl@{\qquad}l} +\href{../exec/runtime.html#syntax-val}{\mathit{val}}~~\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{drop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \epsilon +\end{array}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}~(t^\ast)^?\)

    +
      +

    1. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) from the stack.

      3. +

    3. Assert: due to validation, two more values (of the same value type) are on the top of the stack.

      4. +

    4. Pop the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}_2\) from the stack.

      5. +

    5. Pop the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}_1\) from the stack.

      6. +

    6. If \(c\) is not \(0\), then:

      +
        +

      1. Push the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}_1\) back to the stack.

        2. +
      +
      7. +

    7. Else:

      +
        +

      1. Push the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}_2\) back to the stack.

        2. +
      +
      8. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +\href{../exec/runtime.html#syntax-val}{\mathit{val}}_1~\href{../exec/runtime.html#syntax-val}{\mathit{val}}_2~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}~t^? &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../exec/runtime.html#syntax-val}{\mathit{val}}_1 + & (\mathrel{\mbox{if}} c \neq 0) \\ +\href{../exec/runtime.html#syntax-val}{\mathit{val}}_1~\href{../exec/runtime.html#syntax-val}{\mathit{val}}_2~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}~t^? &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../exec/runtime.html#syntax-val}{\mathit{val}}_2 + & (\mathrel{\mbox{if}} c = 0) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    In future versions of WebAssembly, \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}\) may allow more than one value per choice.

    +
    +
    +
    +
    +

    Variable Instructions

    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.get}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}[x]\) exists.

      3. +

    3. Let \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) be the value \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}[x]\).

      4. +

    4. Push the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) to the stack.

      5. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +F; (\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.get}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& F; \href{../exec/runtime.html#syntax-val}{\mathit{val}} + & (\mathrel{\mbox{if}} F.\href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}[x] = \href{../exec/runtime.html#syntax-val}{\mathit{val}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.set}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}[x]\) exists.

      3. +

    3. Assert: due to validation, a value is on the top of the stack.

      4. +

    4. Pop the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) from the stack.

      5. +

    5. Replace \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}[x]\) with the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\).

      6. +
    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +F; \href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.set}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& F'; \epsilon + & (\mathrel{\mbox{if}} F' = F \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}[x] = \href{../exec/runtime.html#syntax-val}{\mathit{val}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.tee}}~x\)

    +
      +

    1. Assert: due to validation, a value is on the top of the stack.

      2. +

    2. Pop the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) from the stack.

      3. +

    3. Push the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) to the stack.

      4. +

    4. Push the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) to the stack.

      5. +

    5. Execute the instruction \((\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.set}}~x)\).

      6. +
    +
    +\[\begin{array}{lcl@{\qquad}l} +\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.tee}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../exec/runtime.html#syntax-val}{\mathit{val}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.set}}~x) +\end{array}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.get}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{globaladdrs}}[x]\) exists.

      3. +

    3. Let \(a\) be the global address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{globaladdrs}}[x]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[a]\) exists.

      5. +

    5. Let \(\mathit{glob}\) be the global instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[a]\).

      6. +

    6. Let \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) be the value \(\mathit{glob}.\href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}}\).

      7. +

    7. Push the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) to the stack.

      8. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.get}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-val}{\mathit{val}} +\end{array} +\\ \qquad + (\mathrel{\mbox{if}} S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{globaladdrs}}[x]].\href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}} = \href{../exec/runtime.html#syntax-val}{\mathit{val}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.set}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{globaladdrs}}[x]\) exists.

      3. +

    3. Let \(a\) be the global address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{globaladdrs}}[x]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[a]\) exists.

      5. +

    5. Let \(\mathit{glob}\) be the global instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[a]\).

      6. +

    6. Assert: due to validation, a value is on the top of the stack.

      7. +

    7. Pop the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) from the stack.

      8. +

    8. Replace \(\mathit{glob}.\href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}}\) with the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\).

      9. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; \href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.set}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S'; F; \epsilon +\end{array} +\\ \qquad +(\mathrel{\mbox{if}} S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{globaladdrs}}[x]].\href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}} = \href{../exec/runtime.html#syntax-val}{\mathit{val}}) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    Validation ensures that the global is, in fact, marked as mutable.

    +
    +
    +
    +
    +

    Table Instructions

    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\) exists.

      3. +

    3. Let \(a\) be the table address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a]\) exists.

      5. +

    5. Let \(\mathit{tab}\) be the table instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a]\).

      6. +

    6. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      7. +

    7. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) from the stack.

      8. +

    8. If \(i\) is not smaller than the length of \(\mathit{tab}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\), then:

      +
        +

      1. Trap.

        2. +
      +
      9. +

    9. Let \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) be the value \(\mathit{tab}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}[i]\).

      10. +

    10. Push the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) to the stack.

      11. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-val}{\mathit{val}} +\end{array} +\\ \qquad + (\mathrel{\mbox{if}} S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}[i] = \href{../exec/runtime.html#syntax-val}{\mathit{val}}) \\ +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} +\end{array} +\\ \qquad + (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\) exists.

      3. +

    3. Let \(a\) be the table address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a]\) exists.

      5. +

    5. Let \(\mathit{tab}\) be the table instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a]\).

      6. +

    6. Assert: due to validation, a reference value is on the top of the stack.

      7. +

    7. Pop the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) from the stack.

      8. +

    8. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      9. +

    9. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) from the stack.

      10. +

    10. If \(i\) is not smaller than the length of \(\mathit{tab}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\), then:

      +
        +

      1. Trap.

        2. +
      +
      11. +

    11. Replace the element \(\mathit{tab}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}[i]\) with \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\).

      12. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S'; F; \epsilon +\end{array} +\\ \qquad + (\mathrel{\mbox{if}} S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}[i] = \href{../exec/runtime.html#syntax-val}{\mathit{val}}) \\ +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} +\end{array} +\\ \qquad + (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.size}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\) exists.

      3. +

    3. Let \(a\) be the table address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a]\) exists.

      5. +

    5. Let \(\mathit{tab}\) be the table instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a]\).

      6. +

    6. Let \(\mathit{sz}\) be the length of \(\mathit{tab}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\).

      7. +

    7. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\mathit{sz}\) to the stack.

      8. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.size}}~x &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\mathit{sz}) +\end{array} +\\ \qquad + (\mathrel{\mbox{if}} |S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}| = \mathit{sz}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.grow}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\) exists.

      3. +

    3. Let \(a\) be the table address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a]\) exists.

      5. +

    5. Let \(\mathit{tab}\) be the table instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a]\).

      6. +

    6. Let \(\mathit{sz}\) be the length of \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a]\).

      7. +

    7. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      8. +

    8. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n\) from the stack.

      9. +

    9. Assert: due to validation, a reference value is on the top of the stack.

      10. +

    10. Pop the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) from the stack.

      11. +

    11. Either, try growing \(\mathit{table}\) by \(n\) entries with initialization value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\):

      12. +
    +
    +
      +

    1. If it succeeds, push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\mathit{sz}\) to the stack.

      2. +

    2. Else, push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(-1)\) to the stack.

      3. +
    +
    +
      +

    1. Or, push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(-1)\) to the stack.

      2. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; \href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.grow}}~x &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S'; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\mathit{sz}) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x] = a \\ + \wedge & \mathit{sz} = |S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}| \\ + \wedge & S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a] = \href{../exec/modules.html#grow-table}{\mathrm{growtable}}(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a], n, \href{../exec/runtime.html#syntax-val}{\mathit{val}})) \\[1ex] + \end{array} +\\[1ex] +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.grow}}~x &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{-1}) +\end{array} +\end{array}\end{split}\]
    +
    +

    Note

    +

    The \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.grow}}\) instruction is non-deterministic. +It may either succeed, returning the old table size \(\mathit{sz}\), +or fail, returning \({-1}\). +Failure must occur if the referenced table instance has a maximum size defined that would be exceeded. +However, failure can occur in other cases as well. +In practice, the choice depends on the resources available to the embedder.

    +
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.fill}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\) exists.

      3. +

    3. Let \(\mathit{ta}\) be the table address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\mathit{ta}]\) exists.

      5. +

    5. Let \(\mathit{tab}\) be the table instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\mathit{ta}]\).

      6. +

    6. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      7. +

    7. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n\) from the stack.

      8. +

    8. Assert: due to validation, a reference value is on the top of the stack.

      9. +

    9. Pop the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) from the stack.

      10. +

    10. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      11. +

    11. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) from the stack.

      12. +

    12. If \(i + n\) is larger than the length of \(\mathit{tab}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\), then:

      +
        +

      1. Trap.

        2. +
      +
      13. +
    +
      +

    1. If \(n\) is \(0\), then:

      +
        +

      1. Return.

        2. +
      +
      2. +

    2. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) to the stack.

      3. +

    3. Push the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) to the stack.

      4. +

    4. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x\).

      5. +

    5. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(i+1)\) to the stack.

      6. +

    6. Push the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) to the stack.

      7. +

    7. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(n-1)\) to the stack.

      8. +

    8. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.fill}}~x\).

      9. +
    +
    +\[\begin{split}\begin{array}{l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.fill}}~x) + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} + \\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & i + n > |S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|) \\[1ex] + \end{array} +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.fill}}~x) + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad S; F; \epsilon + \\ \qquad + (\mathrel{\mbox{otherwise}}) +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n+1)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.fill}}~x) + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow} + \\ \qquad S; F; + \begin{array}[t]{@{}l@{}} + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x) \\ + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i+1)~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.fill}}~x) \\ + \end{array} + \\ \qquad + (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}~x~y\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\) exists.

      3. +

    3. Let \(\mathit{ta}_x\) be the table address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\mathit{ta}_x]\) exists.

      5. +

    5. Let \(\mathit{tab}_x\) be the table instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\mathit{ta}_x]\).

      6. +

    6. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[y]\) exists.

      7. +

    7. Let \(\mathit{ta}_y\) be the table address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[y]\).

      8. +

    8. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\mathit{ta}_y]\) exists.

      9. +

    9. Let \(\mathit{tab}_y\) be the table instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\mathit{ta}_y]\).

      10. +

    10. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      11. +

    11. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n\) from the stack.

      12. +

    12. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      13. +

    13. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s\) from the stack.

      14. +

    14. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      15. +

    15. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d\) from the stack.

      16. +

    16. If \(s + n\) is larger than the length of \(\mathit{tab}_y.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\) or \(d + n\) is larger than the length of \(\mathit{tab}_x.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\), then:

      +
        +

      1. Trap.

        2. +
      +
      17. +

    17. If \(n = 0\), then:

      18. +
    +
    +
      +

    1. Return.

      2. +
    +
    +
      +

    1. If \(d \leq s\), then:

      2. +
    +
    +
      +

    1. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d\) to the stack.

      2. +

    2. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s\) to the stack.

      3. +

    3. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}~y\).

      4. +

    4. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x\).

      5. +

    5. Assert: due to the earlier check against the table size, \(d+1 < 2^{32}\).

      6. +

    6. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(d+1)\) to the stack.

      7. +

    7. Assert: due to the earlier check against the table size, \(s+1 < 2^{32}\).

      8. +

    8. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(s+1)\) to the stack.

      9. +
    +
    +
      +

    1. Else:

      2. +
    +
    +
      +

    1. Assert: due to the earlier check against the table size, \(d+n-1 < 2^{32}\).

      2. +

    2. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(d+n-1)\) to the stack.

      3. +

    3. Assert: due to the earlier check against the table size, \(s+n-1 < 2^{32}\).

      4. +

    4. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(s+n-1)\) to the stack.

      5. +
    +
      +

    1. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}~y\).

      2. +
    +
      +

    1. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x\).

      2. +

    2. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d\) to the stack.

      3. +

    3. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s\) to the stack.

      4. +
    +
    +
      +

    1. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(n-1)\) to the stack.

      2. +

    2. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}~x~y\).

      3. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}~x~y) + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} + \\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & s + n > |S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[y]].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}| \\ + \vee & d + n > |S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|) \\[1ex] + \end{array} +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}~x~y) + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad S; F; \epsilon + \\ \qquad + (\mathrel{\mbox{otherwise}}) +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n+1)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}~x~y) + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow} + \\ \qquad S; F; + \begin{array}[t]{@{}l@{}} + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}~y)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x) \\ + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d+1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s+1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}~x~y) \\ + \end{array} + \\ \qquad + (\mathrel{\mbox{otherwise}}, \mathrel{\mbox{if}} d \leq s) +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n+1)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}~x~y) + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow} + \\ \qquad S; F; + \begin{array}[t]{@{}l@{}} + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d+n-1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s+n-1)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}~y)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x) \\ + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}~x~y) \\ + \end{array} + \\ \qquad + (\mathrel{\mbox{otherwise}}, \mathrel{\mbox{if}} d > s) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}~x~y\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\) exists.

      3. +

    3. Let \(\mathit{ta}\) be the table address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\mathit{ta}]\) exists.

      5. +

    5. Let \(\mathit{tab}\) be the table instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\mathit{ta}]\).

      6. +

    6. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{elemaddrs}}[y]\) exists.

      7. +

    7. Let \(\mathit{ea}\) be the element address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{elemaddrs}}[y]\).

      8. +

    8. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}[\mathit{ea}]\) exists.

      9. +

    9. Let \(\mathit{elem}\) be the element instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}[\mathit{ea}]\).

      10. +

    10. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      11. +

    11. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n\) from the stack.

      12. +

    12. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      13. +

    13. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s\) from the stack.

      14. +

    14. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      15. +

    15. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d\) from the stack.

      16. +

    16. If \(s + n\) is larger than the length of \(\mathit{elem}.\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}\) or \(d + n\) is larger than the length of \(\mathit{tab}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\), then:

      +
        +

      1. Trap.

        2. +
      +
      17. +

    17. If \(n = 0\), then:

      +
        +

      1. Return.

        2. +
      +
      18. +

    18. Let \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) be the reference value \(\mathit{elem}.\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}[s]\).

      19. +

    19. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d\) to the stack.

      20. +

    20. Push the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) to the stack.

      21. +

    21. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x\).

      22. +

    22. Assert: due to the earlier check against the table size, \(d+1 < 2^{32}\).

      23. +

    23. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(d+1)\) to the stack.

      24. +

    24. Assert: due to the earlier check against the segment size, \(s+1 < 2^{32}\).

      25. +

    25. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(s+1)\) to the stack.

      26. +

    26. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(n-1)\) to the stack.

      27. +

    27. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}~x~y\).

      28. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}~x~y) + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} + \\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & s + n > |S.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{elemaddrs}}[y]].\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}| \\ + \vee & d + n > |S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|) \\[1ex] + \end{array} +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}~x~y) + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad S; F; \epsilon + \\ \qquad + (\mathrel{\mbox{otherwise}}) +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n+1)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}~x~y) + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow} + \\ \qquad S; F; + \begin{array}[t]{@{}l@{}} + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x) \\ + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d+1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s+1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}~x~y) \\ + \end{array} + \\ \qquad + (\mathrel{\mbox{otherwise}}, \mathrel{\mbox{if}} \href{../exec/runtime.html#syntax-val}{\mathit{val}} = S.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{elemaddrs}}[y]].\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}[s]) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem.drop}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{elemaddrs}}[x]\) exists.

      3. +

    3. Let \(a\) be the element address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{elemaddrs}}[x]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}[a]\) exists.

      5. +

    5. Replace \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}[a]\) with the element instance \(\{\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}~\epsilon\}\).

      6. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem.drop}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S'; F; \epsilon +\end{array} +\\ \qquad + (\mathrel{\mbox{if}} S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{elems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{elemaddrs}}[x]] = \{ \href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}~\epsilon \}) \\ +\end{array}\end{split}\]
    +
    +
    +
    +

    Memory Instructions

    +
    +

    Note

    +

    The alignment \(\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}\) in load and store instructions does not affect the semantics. +It is an indication that the offset \(\mathit{ea}\) at which the memory is accessed is intended to satisfy the property \(\mathit{ea} \mathbin{\mathrm{mod}} 2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}} = 0\). +A WebAssembly implementation can use this hint to optimize for the intended use. +Unaligned access violating that property is still allowed and must succeed regardless of the annotation. +However, it may be substantially slower on some hardware.

    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\) and \(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\) exists.

      3. +

    3. Let \(a\) be the memory address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\) exists.

      5. +

    5. Let \(\mathit{mem}\) be the memory instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\).

      6. +

    6. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      7. +

    7. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) from the stack.

      8. +

    8. Let \(\mathit{ea}\) be the integer \(i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}\).

      9. +

    9. If \(N\) is not part of the instruction, then:

      +
        +

      1. Let \(N\) be the bit width \(|t|\) of number type \(t\).

        2. +
      +
      10. +

    10. If \(\mathit{ea} + N/8\) is larger than the length of \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\), then:

      +
        +

      1. Trap.

        2. +
      +
      11. +

    11. Let \(b^\ast\) be the byte sequence \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]\).

      12. +

    12. If \(N\) and \(\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\) are part of the instruction, then:

      +
        +

      1. Let \(n\) be the integer for which \(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}}(n) = b^\ast\).

        2. +

      2. Let \(c\) be the result of computing \(\href{../exec/numerics.html#op-extend-u}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{N,|t|}(n)\).

        3. +
      +
      13. +

    13. Else:

      +
        +

      1. Let \(c\) be the constant for which \(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_t(c) = b^\ast\).

        2. +
      +
      14. +

    14. Push the value \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) to the stack.

      15. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(t.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; (t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ + \wedge & \mathit{ea} + |t|/8 \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}| \\ + \wedge & \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_t(c) = S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} |t|/8]) \\[1ex] + \end{array} +\\[1ex] +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(t.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& + S; F; (t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\href{../exec/numerics.html#op-extend-u}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{N,|t|}(n)) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ + \wedge & \mathit{ea} + N/8 \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}| \\ + \wedge & \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}}(n) = S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]) \\[1ex] + \end{array} +\\[1ex] +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~k)~(t.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}({N}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}})^?~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} +\end{array} +\\ \qquad + (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{M}\mathsf{x}N\_\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\) exists.

      3. +

    3. Let \(a\) be the memory address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\) exists.

      5. +

    5. Let \(\mathit{mem}\) be the memory instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\).

      6. +

    6. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      7. +

    7. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) from the stack.

      8. +

    8. Let \(\mathit{ea}\) be the integer \(i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}\).

      9. +

    9. If \(\mathit{ea} + M \cdot N /8\) is larger than the length of \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\), then:

      +
      +
        +

      1. Trap.

        2. +
      +
      +
      10. +

    10. Let \(b^\ast\) be the byte sequence \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} M \cdot N /8]\).

      11. +

    11. Let \(m_k\) be the integer for which \(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}M}}(m_k) = b^\ast[k \cdot M/8 \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} M/8]\).

      12. +

    12. Let \(W\) be the integer \(M \cdot 2\).

      13. +

    13. Let \(n_k\) be the result of \(\href{../exec/numerics.html#op-extend-u}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{M,W}(m_k)\).

      14. +

    14. Let \(c\) be the result of computing \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\mathit{i}W\mathsf{x}N}(n_0 \dots n_{N-1})\).

      15. +

    15. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) to the stack.

      16. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{M}\mathsf{x}N\_\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& + S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ + \wedge & \mathit{ea} + M \cdot N / 8 \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}| \\ + \wedge & \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}M}}(m_k) = S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} + k \cdot M/8 \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} M/8]) \\ + \wedge & W = M \cdot 2 \\ + \wedge & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\mathit{i}W\mathsf{x}N}(\href{../exec/numerics.html#op-extend-u}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{M,W}(m_0) \dots \href{../exec/numerics.html#op-extend-u}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{M,W}(m_{N-1})) + \end{array} +\\[1ex] +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~k)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{M}\mathsf{x}N\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} +\end{array} +\\ \qquad + (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_splat}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\) exists.

      3. +

    3. Let \(a\) be the memory address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\) exists.

      5. +

    5. Let \(\mathit{mem}\) be the memory instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\).

      6. +

    6. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      7. +

    7. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) from the stack.

      8. +

    8. Let \(\mathit{ea}\) be the integer \(i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}\).

      9. +

    9. If \(\mathit{ea} + N/8\) is larger than the length of \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\), then:

      +
      +
        +

      1. Trap.

        2. +
      +
      +
      10. +

    10. Let \(b^\ast\) be the byte sequence \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]\).

      11. +

    11. Let \(n\) be the integer for which \(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}}(n) = b^\ast\).

      12. +

    12. Let \(L\) be the integer \(128 / N\).

      13. +

    13. Let \(c\) be the result of computing \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}\mathsf{x}L}(n^L)\).

      14. +

    14. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) to the stack.

      15. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_splat}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ + \wedge & \mathit{ea} + N/8 \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}| \\ + \wedge & \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}}(n) = S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]) \\ + \wedge & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}\mathsf{x}L}(n^L) + \end{array} +\\[1ex] +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~k)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_splat}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} +\end{array} +\\ \qquad + (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_zero}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\) exists.

      3. +

    3. Let \(a\) be the memory address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\) exists.

      5. +

    5. Let \(\mathit{mem}\) be the memory instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\).

      6. +

    6. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      7. +

    7. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) from the stack.

      8. +

    8. Let \(\mathit{ea}\) be the integer \(i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}\).

      9. +

    9. If \(\mathit{ea} + N/8\) is larger than the length of \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\), then:

      +
      +
        +

      1. Trap.

        2. +
      +
      +
      10. +

    10. Let \(b^\ast\) be the byte sequence \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]\).

      11. +

    11. Let \(n\) be the integer for which \(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}}(n) = b^\ast\).

      12. +

    12. Let \(c\) be the result of \(\href{../exec/numerics.html#op-extend-u}{\mathrm{extend}^{\mathsf{u}}}_{N,128}(n)\).

      13. +

    13. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) to the stack.

      14. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_zero}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ + \wedge & \mathit{ea} + N/8 \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}| \\ + \wedge & \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}}(n) = S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]) \\ + \wedge & c = \href{../exec/numerics.html#op-extend-u}{\mathrm{extend}^{\mathsf{u}}}_{N,128}(n) + \end{array} +\\[1ex] +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~k)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_zero}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} +\end{array} +\\ \qquad + (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\) exists.

      3. +

    3. Let \(a\) be the memory address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\) exists.

      5. +

    5. Let \(\mathit{mem}\) be the memory instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\).

      6. +

    6. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      7. +

    7. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~v\) from the stack.

      8. +

    8. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      9. +

    9. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) from the stack.

      10. +

    10. Let \(\mathit{ea}\) be the integer \(i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}\).

      11. +

    11. If \(\mathit{ea} + N/8\) is larger than the length of \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\), then:

      +
        +

      1. Trap.

        2. +
      +
      12. +

    12. Let \(b^\ast\) be the byte sequence \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]\).

      13. +

    13. Let \(r\) be the constant for which \(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}}(r) = b^\ast\).

      14. +

    14. Let \(L\) be \(128 / N\).

      15. +

    15. Let \(c\) be the result of computing \(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\mathsf{i}N\mathsf{x}L}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\mathsf{i}N\mathsf{x}L}(v) \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} [x] = r)\).

      16. +

    16. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) to the stack.

      17. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~v)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ + \wedge & \mathit{ea} + N/8 \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}| \\ + \wedge & \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}}(r) = S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]) \\ + \wedge & L = 128/N \\ + \wedge & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\mathsf{i}N\mathsf{x}L}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\mathsf{i}N\mathsf{x}L}(v) \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} [x] = r) + \end{array} +\\[1ex] +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~k)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~v)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} +\end{array} +\\ \qquad + (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\) and \(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}{N}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\) exists.

      3. +

    3. Let \(a\) be the memory address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\) exists.

      5. +

    5. Let \(\mathit{mem}\) be the memory instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\).

      6. +

    6. Assert: due to validation, a value of value type \(t\) is on the top of the stack.

      7. +

    7. Pop the value \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) from the stack.

      8. +

    8. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      9. +

    9. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) from the stack.

      10. +

    10. Let \(\mathit{ea}\) be the integer \(i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}\).

      11. +

    11. If \(N\) is not part of the instruction, then:

      +
        +

      1. Let \(N\) be the bit width \(|t|\) of number type \(t\).

        2. +
      +
      12. +

    12. If \(\mathit{ea} + N/8\) is larger than the length of \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\), then:

      +
        +

      1. Trap.

        2. +
      +
      13. +

    13. If \(N\) is part of the instruction, then:

      +
        +

      1. Let \(n\) be the result of computing \(\href{../exec/numerics.html#op-wrap}{\mathrm{wrap}}_{|t|,N}(c)\).

        2. +

      2. Let \(b^\ast\) be the byte sequence \(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}}(n)\).

        3. +
      +
      14. +

    14. Else:

      +
        +

      1. Let \(b^\ast\) be the byte sequence \(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_t(c)\).

        2. +
      +
      15. +

    15. Replace the bytes \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]\) with \(b^\ast\).

      16. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(t.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S'; F; \epsilon +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ + \wedge & \mathit{ea} + |t|/8 \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}| \\ + \wedge & S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} |t|/8] = \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_t(c)) \\[1ex] + \end{array} +\\[1ex] +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(t.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}{N}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S'; F; \epsilon +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ + \wedge & \mathit{ea} + N/8 \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}| \\ + \wedge & S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8] = \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}}(\href{../exec/numerics.html#op-wrap}{\mathrm{wrap}}_{|t|,N}(c)) \\[1ex] + \end{array} +\\[1ex] +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~k)~(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(t.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}{N}^?~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} +\end{array} +\\ \qquad + (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}{N}\mathsf{\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\) exists.

      3. +

    3. Let \(a\) be the memory address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\) exists.

      5. +

    5. Let \(\mathit{mem}\) be the memory instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\).

      6. +

    6. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) is on the top of the stack.

      7. +

    7. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) from the stack.

      8. +

    8. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      9. +

    9. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) from the stack.

      10. +

    10. Let \(\mathit{ea}\) be the integer \(i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}\).

      11. +

    11. If \(\mathit{ea} + N/8\) is larger than the length of \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\), then:

      +
        +

      1. Trap.

        2. +
      +
      12. +

    12. Let \(L\) be \(128/N\).

      13. +

    13. Let \(b^\ast\) be the byte sequence \(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\mathsf{i}N\mathsf{x}L}(c)[x])\).

      14. +

    14. Replace the bytes \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]\) with \(b^\ast\).

      15. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}{N}\mathsf{\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S'; F; \epsilon +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ + \wedge & \mathit{ea} + N \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}| \\ + \wedge & L = 128/N \\ + \wedge & S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8] = \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}N}}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\mathsf{i}N\mathsf{x}L}(c)[x]) + \end{array} +\\[1ex] +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~k)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}{N}\mathsf{\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} +\end{array} +\\ \qquad + (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.size}}\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\) exists.

      3. +

    3. Let \(a\) be the memory address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\) exists.

      5. +

    5. Let \(\mathit{mem}\) be the memory instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\).

      6. +

    6. Let \(\mathit{sz}\) be the length of \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\) divided by the page size.

      7. +

    7. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\mathit{sz}\) to the stack.

      8. +
    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.size}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\mathit{sz}) +\end{array} +\\ \qquad + (\mathrel{\mbox{if}} |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}| = \mathit{sz}\cdot64\,\mathrm{Ki}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.grow}}\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\) exists.

      3. +

    3. Let \(a\) be the memory address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\) exists.

      5. +

    5. Let \(\mathit{mem}\) be the memory instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\).

      6. +

    6. Let \(\mathit{sz}\) be the length of \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\) divided by the page size.

      7. +

    7. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      8. +

    8. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n\) from the stack.

      9. +

    9. Let \(\mathit{err}\) be the \(\href{../syntax/values.html#syntax-int}{\mathit{i32}}\) value \(2^{32}-1\), for which \(\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_{32}(\mathit{err})\) is \(-1\).

      10. +

    10. Either, try growing \(\mathit{mem}\) by \(n\) pages:

      11. +
    +
    +
      +

    1. If it succeeds, push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\mathit{sz}\) to the stack.

      2. +

    2. Else, push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\mathit{err}\) to the stack.

      3. +
    +
    +
      +

    1. Or, push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\mathit{err}\) to the stack.

      2. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.grow}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S'; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\mathit{sz}) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0] = a \\ + \wedge & \mathit{sz} = |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}|/64\,\mathrm{Ki} \\ + \wedge & S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a] = \href{../exec/modules.html#grow-mem}{\mathrm{growmem}}(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a], n)) \\[1ex] + \end{array} +\\[1ex] +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.grow}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_{32}^{-1}(-1)) +\end{array} +\end{array}\end{split}\]
    +
    +

    Note

    +

    The \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.grow}}\) instruction is non-deterministic. +It may either succeed, returning the old memory size \(\mathit{sz}\), +or fail, returning \({-1}\). +Failure must occur if the referenced memory instance has a maximum size defined that would be exceeded. +However, failure can occur in other cases as well. +In practice, the choice depends on the resources available to the embedder.

    +
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}}\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\) exists.

      3. +

    3. Let \(\mathit{ma}\) be the memory address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[\mathit{ma}]\) exists.

      5. +

    5. Let \(\mathit{mem}\) be the memory instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[\mathit{ma}]\).

      6. +

    6. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      7. +

    7. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n\) from the stack.

      8. +

    8. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      9. +

    9. Pop the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) from the stack.

      10. +

    10. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      11. +

    11. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d\) from the stack.

      12. +

    12. If \(d + n\) is larger than the length of \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\), then:

      +
        +

      1. Trap.

        2. +
      +
      13. +

    13. If \(n = 0\), then:

      +
        +

      1. Return.

        2. +
      +
      14. +

    14. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d\) to the stack.

      15. +

    15. Push the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) to the stack.

      16. +

    16. Execute the instruction \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~\{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~0, \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~0 \}\).

      17. +

    17. Assert: due to the earlier check against the memory size, \(d+1 < 2^{32}\).

      18. +

    18. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(d+1)\) to the stack.

      19. +

    19. Push the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) to the stack.

      20. +

    20. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(n-1)\) to the stack.

      21. +

    21. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}}\).

      22. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}} + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} + \\ \qquad + (\mathrel{\mbox{if}} d + n > |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[x]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}|) +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0)~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}} + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad S; F; \epsilon + \\ \qquad + (\mathrel{\mbox{otherwise}}) +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n+1)~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}} + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow} + \\ \qquad S; F; + \begin{array}[t]{@{}l@{}} + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~\{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~0, \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~0 \}) \\ + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d+1)~\href{../exec/runtime.html#syntax-val}{\mathit{val}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}} \\ + \end{array} + \\ \qquad + (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}}\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\) exists.

      3. +

    3. Let \(\mathit{ma}\) be the memory address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[\mathit{ma}]\) exists.

      5. +

    5. Let \(\mathit{mem}\) be the memory instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[\mathit{ma}]\).

      6. +

    6. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      7. +

    7. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n\) from the stack.

      8. +

    8. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      9. +

    9. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s\) from the stack.

      10. +

    10. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      11. +

    11. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d\) from the stack.

      12. +

    12. If \(s + n\) is larger than the length of \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\) or \(d + n\) is larger than the length of \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\), then:

      +
        +

      1. Trap.

        2. +
      +
      13. +

    13. If \(n = 0\), then:

      14. +
    +
    +
      +

    1. Return.

      2. +
    +
    +
      +

    1. If \(d \leq s\), then:

      2. +
    +
    +
      +

    1. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d\) to the stack.

      2. +

    2. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s\) to the stack.

      3. +

    3. Execute the instruction \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_u}~\{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~0, \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~0 \}\).

      4. +

    4. Execute the instruction \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~\{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~0, \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~0 \}\).

      5. +

    5. Assert: due to the earlier check against the memory size, \(d+1 < 2^{32}\).

      6. +

    6. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(d+1)\) to the stack.

      7. +

    7. Assert: due to the earlier check against the memory size, \(s+1 < 2^{32}\).

      8. +

    8. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(s+1)\) to the stack.

      9. +
    +
    +
      +

    1. Else:

      2. +
    +
    +
      +

    1. Assert: due to the earlier check against the memory size, \(d+n-1 < 2^{32}\).

      2. +

    2. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(d+n-1)\) to the stack.

      3. +

    3. Assert: due to the earlier check against the memory size, \(s+n-1 < 2^{32}\).

      4. +

    4. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(s+n-1)\) to the stack.

      5. +

    5. Execute the instruction \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_u}~\{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~0, \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~0 \}\).

      6. +

    6. Execute the instruction \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~\{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~0, \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~0 \}\).

      7. +

    7. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d\) to the stack.

      8. +

    8. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s\) to the stack.

      9. +
    +
    +
      +

    1. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(n-1)\) to the stack.

      2. +

    2. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}}\).

      3. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}} + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} + \\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & s + n > |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}| \\ + \vee & d + n > |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}|) \\[1ex] + \end{array} +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0)~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}} + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad S; F; \epsilon + \\ \qquad + (\mathrel{\mbox{otherwise}}) +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n+1)~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}} + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow} + \\ \qquad S; F; + \begin{array}[t]{@{}l@{}} + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d) \\ + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_u}~\{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~0, \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~0 \}) \\ + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~\{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~0, \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~0 \}) \\ + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d+1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s+1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}} \\ + \end{array} + \\ \qquad + (\mathrel{\mbox{otherwise}}, \mathrel{\mbox{if}} d \leq s) +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n+1)~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}} + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow} + \\ \qquad S; F; + \begin{array}[t]{@{}l@{}} + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d+n-1) \\ + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s+n-1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_u}~\{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~0, \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~0 \}) \\ + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~\{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~0, \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~0 \}) \\ + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}} \\ + \end{array} + \\ \qquad + (\mathrel{\mbox{otherwise}}, \mathrel{\mbox{if}} d > s) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\) exists.

      3. +

    3. Let \(\mathit{ma}\) be the memory address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[0]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[\mathit{ma}]\) exists.

      5. +

    5. Let \(\mathit{mem}\) be the memory instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[\mathit{ma}]\).

      6. +

    6. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{dataaddrs}}[x]\) exists.

      7. +

    7. Let \(\mathit{da}\) be the data address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{dataaddrs}}[x]\).

      8. +

    8. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}[\mathit{da}]\) exists.

      9. +

    9. Let \(\mathit{data}\) be the data instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}[\mathit{da}]\).

      10. +

    10. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      11. +

    11. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n\) from the stack.

      12. +

    12. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      13. +

    13. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s\) from the stack.

      14. +

    14. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      15. +

    15. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d\) from the stack.

      16. +

    16. If \(s + n\) is larger than the length of \(\mathit{data}.\href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}\) or \(d + n\) is larger than the length of \(\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\), then:

      +
        +

      1. Trap.

        2. +
      +
      17. +

    17. If \(n = 0\), then:

      +
        +

      1. Return.

        2. +
      +
      18. +

    18. Let \(b\) be the byte \(\mathit{data}.\href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}[s]\).

      19. +

    19. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d\) to the stack.

      20. +

    20. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~b\) to the stack.

      21. +

    21. Execute the instruction \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~\{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~0, \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~0 \}\).

      22. +

    22. Assert: due to the earlier check against the memory size, \(d+1 < 2^{32}\).

      23. +

    23. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(d+1)\) to the stack.

      24. +

    24. Assert: due to the earlier check against the memory size, \(s+1 < 2^{32}\).

      25. +

    25. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(s+1)\) to the stack.

      26. +

    26. Push the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~(n-1)\) to the stack.

      27. +

    27. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~x\).

      28. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~x) + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} + \\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & s + n > |S.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{dataaddrs}}[x]].\href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}| \\ + \vee & d + n > |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[x]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}|) \\[1ex] + \end{array} +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~x) + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad S; F; \epsilon + \\ \qquad + (\mathrel{\mbox{otherwise}}) +\\[1ex] +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n+1)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~x) + \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow} + \\ \qquad S; F; + \begin{array}[t]{@{}l@{}} + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~b)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~\{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~0, \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~0 \}) \\ + (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~d+1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~s+1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~x) \\ + \end{array} + \\ \qquad + (\mathrel{\mbox{otherwise}}, \mathrel{\mbox{if}} b = S.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{dataaddrs}}[x]].\href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}[s]) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data.drop}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{dataaddrs}}[x]\) exists.

      3. +

    3. Let \(a\) be the data address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{dataaddrs}}[x]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}[a]\) exists.

      5. +

    5. Replace \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}[a]\) with the data instance \(\{\href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}~\epsilon\}\).

      6. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data.drop}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S'; F; \epsilon +\end{array} +\\ \qquad + (\mathrel{\mbox{if}} S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{datas}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{dataaddrs}}[x]] = \{ \href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}~\epsilon \}) \\ +\end{array}\end{split}\]
    +
    +
    +
    +

    Control Instructions

    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{nop}}\)

    +
      +

    1. Do nothing.

      2. +
    +
    +\[\begin{array}{lcl@{\qquad}l} +\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{nop}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \epsilon +\end{array}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}\)

    +
      +

    1. Trap.

      2. +
    +
    +\[\begin{array}{lcl@{\qquad}l} +\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} +\end{array}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\)

    +
      +

    1. Assert: due to validation, \(\href{../exec/runtime.html#exec-expand}{\mathrm{expand}}_F(\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}})\) is defined.

      2. +

    2. Let \([t_1^m] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^n]\) be the function type \(\href{../exec/runtime.html#exec-expand}{\mathrm{expand}}_F(\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}})\).

      3. +

    3. Let \(L\) be the label whose arity is \(n\) and whose continuation is the end of the block.

      4. +

    4. Assert: due to validation, there are at least \(m\) values on the top of the stack.

      5. +

    5. Pop the values \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m\) from the stack.

      6. +

    6. Enter the block \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) with label \(L\).

      7. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{lcl} +F; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^m~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~\mathit{bt}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& + F; \href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\epsilon\}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} + \\&&\quad (\mathrel{\mbox{if}} \href{../exec/runtime.html#exec-expand}{\mathrm{expand}}_F(\mathit{bt}) = [t_1^m] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^n]) +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}~\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\)

    +
      +

    1. Assert: due to validation, \(\href{../exec/runtime.html#exec-expand}{\mathrm{expand}}_F(\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}})\) is defined.

      2. +

    2. Let \([t_1^m] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^n]\) be the function type \(\href{../exec/runtime.html#exec-expand}{\mathrm{expand}}_F(\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}})\).

      3. +

    3. Let \(L\) be the label whose arity is \(m\) and whose continuation is the start of the loop.

      4. +

    4. Assert: due to validation, there are at least \(m\) values on the top of the stack.

      5. +

    5. Pop the values \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m\) from the stack.

      6. +

    6. Enter the block \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) with label \(L\).

      7. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{lcl} +F; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^m~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}~\mathit{bt}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& + F; \href{../exec/runtime.html#syntax-label}{\mathsf{label}}_m\{\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}~\mathit{bt}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} + \\&&\quad (\mathrel{\mbox{if}} \href{../exec/runtime.html#exec-expand}{\mathrm{expand}}_F(\mathit{bt}) = [t_1^m] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^n]) +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}~\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_1^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_2^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\)

    +
      +

    1. Assert: due to validation, \(\href{../exec/runtime.html#exec-expand}{\mathrm{expand}}_F(\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}})\) is defined.

      2. +

    2. Let \([t_1^m] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^n]\) be the function type \(\href{../exec/runtime.html#exec-expand}{\mathrm{expand}}_F(\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}})\).

      3. +

    3. Let \(L\) be the label whose arity is \(n\) and whose continuation is the end of the \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}\) instruction.

      4. +

    4. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      5. +

    5. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) from the stack.

      6. +

    6. Assert: due to validation, there are at least \(m\) values on the top of the stack.

      7. +

    7. Pop the values \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m\) from the stack.

      8. +

    8. If \(c\) is non-zero, then:

      +
        +

      1. Enter the block \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_1^\ast\) with label \(L\).

        2. +
      +
      9. +

    9. Else:

      +
        +

      1. Enter the block \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_2^\ast\) with label \(L\).

        2. +
      +
      10. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{lcl} +F; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^m~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}~\mathit{bt}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_1^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_2^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& + F; \href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\epsilon\}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_1^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} + \\&&\quad (\mathrel{\mbox{if}} c \neq 0 \wedge \href{../exec/runtime.html#exec-expand}{\mathrm{expand}}_F(\mathit{bt}) = [t_1^m] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^n]) \\ +F; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^m~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}~\mathit{bt}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_1^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_2^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& + F; \href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\epsilon\}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_2^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} + \\&&\quad (\mathrel{\mbox{if}} c = 0 \wedge \href{../exec/runtime.html#exec-expand}{\mathrm{expand}}_F(\mathit{bt}) = [t_1^m] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^n]) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l\)

    +
      +

    1. Assert: due to validation, the stack contains at least \(l+1\) labels.

      2. +

    2. Let \(L\) be the \(l\)-th label appearing on the stack, starting from the top and counting from zero.

      3. +

    3. Let \(n\) be the arity of \(L\).

      4. +

    4. Assert: due to validation, there are at least \(n\) values on the top of the stack.

      5. +

    5. Pop the values \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n\) from the stack.

      6. +

    6. Repeat \(l+1\) times:

      +
        +

      1. While the top of the stack is a value, do:

        +
          +

        1. Pop the value from the stack.

          2. +
        +
        2. +

      2. Assert: due to validation, the top of the stack now is a label.

        3. +

      3. Pop the label from the stack.

        4. +
      +
      7. +

    7. Push the values \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n\) to the stack.

      8. +

    8. Jump to the continuation of \(L\).

      9. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{lcl@{\qquad}l} +\href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\}~\href{../exec/runtime.html#syntax-ctxt-block}{B}^l[\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)]~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_if}}~l\)

    +
      +

    1. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\) from the stack.

      3. +

    3. If \(c\) is non-zero, then:

      +
        +

      1. Execute the instruction \((\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)\).

        2. +
      +
      4. +

    4. Else:

      +
        +

      1. Do nothing.

        2. +
      +
      5. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_if}}~l) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l) + & (\mathrel{\mbox{if}} c \neq 0) \\ +(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_if}}~l) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \epsilon + & (\mathrel{\mbox{if}} c = 0) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}~l^\ast~l_N\)

    +
      +

    1. Assert: due to validation, a value of value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      2. +

    2. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) from the stack.

      3. +

    3. If \(i\) is smaller than the length of \(l^\ast\), then:

      +
        +

      1. Let \(l_i\) be the label \(l^\ast[i]\).

        2. +

      2. Execute the instruction \((\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l_i)\).

        3. +
      +
      4. +

    4. Else:

      +
        +

      1. Execute the instruction \((\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l_N)\).

        2. +
      +
      5. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{lcl@{\qquad}l} +(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}~l^\ast~l_N) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l_i) + & (\mathrel{\mbox{if}} l^\ast[i] = l_i) \\ +(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}~l^\ast~l_N) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l_N) + & (\mathrel{\mbox{if}} |l^\ast| \leq i) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Let \(n\) be the arity of \(F\).

      3. +

    3. Assert: due to validation, there are at least \(n\) values on the top of the stack.

      4. +

    4. Pop the results \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n\) from the stack.

      5. +

    5. Assert: due to validation, the stack contains at least one frame.

      6. +

    6. While the top of the stack is not a frame, do:

      +
        +

      1. Pop the top element from the stack.

        2. +
      +
      7. +

    7. Assert: the top of the stack is the frame \(F\).

      8. +

    8. Pop the frame from the stack.

      9. +

    9. Push \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n\) to the stack.

      10. +

    10. Jump to the instruction after the original call that pushed the frame.

      11. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{lcl@{\qquad}l} +\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}_n\{F\}~\href{../exec/runtime.html#syntax-ctxt-block}{B}^k[\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}]~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call}}~x\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}}[x]\) exists.

      3. +

    3. Let \(a\) be the function address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}}[x]\).

      4. +

    4. Invoke the function instance at address \(a\).

      5. +
    +
    +\[\begin{array}{lcl@{\qquad}l} +F; (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call}}~x) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& F; (\href{../exec/runtime.html#syntax-invoke}{\mathsf{invoke}}~a) + & (\mathrel{\mbox{if}} F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}}[x] = a) +\end{array}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}~x~y\)

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\) exists.

      3. +

    3. Let \(\mathit{ta}\) be the table address \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]\).

      4. +

    4. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\mathit{ta}]\) exists.

      5. +

    5. Let \(\mathit{tab}\) be the table instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[\mathit{ta}]\).

      6. +

    6. Assert: due to validation, \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{types}}[y]\) exists.

      7. +

    7. Let \(\mathit{ft}_{\mathrm{expect}}\) be the function type \(F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{types}}[y]\).

      8. +

    8. Assert: due to validation, a value with value type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) is on the top of the stack.

      9. +

    9. Pop the value \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i\) from the stack.

      10. +

    10. If \(i\) is not smaller than the length of \(\mathit{tab}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\), then:

      +
        +

      1. Trap.

        2. +
      +
      11. +

    11. Let \(r\) be the reference \(\mathit{tab}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}[i]\).

      12. +

    12. If \(r\) is \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t\), then:

      +
        +

      1. Trap.

        2. +
      +
      13. +

    13. Assert: due to validation of table mutation, \(r\) is a function reference.

      14. +

    14. Let \(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref}}~a\) be the function reference \(r\).

      15. +

    15. Assert: due to validation of table mutation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a]\) exists.

      16. +

    16. Let \(\mathit{f}\) be the function instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a]\).

      17. +

    17. Let \(\mathit{ft}_{\mathrm{actual}}\) be the function type \(\mathit{f}.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}\).

      18. +

    18. If \(\mathit{ft}_{\mathrm{actual}}\) and \(\mathit{ft}_{\mathrm{expect}}\) differ, then:

      +
        +

      1. Trap.

        2. +
      +
      19. +

    19. Invoke the function instance at address \(a\).

      20. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}~x~y) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; (\href{../exec/runtime.html#syntax-invoke}{\mathsf{invoke}}~a) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x]].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}[i] = \href{../exec/runtime.html#syntax-ref}{\mathsf{ref}}~a \\ + \wedge & S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a] = f \\ + \wedge & F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{types}}[y] = f.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}) + \end{array} +\\[1ex] +\begin{array}{lcl@{\qquad}l} +S; F; (\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}~x~y) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} +\end{array} +\\ \qquad + (\mathrel{\mbox{otherwise}}) +\end{array}\end{split}\]
    +
    +
    +
    +

    Blocks

    +

    The following auxiliary rules define the semantics of executing an instruction sequence +that forms a block.

    +
    +

    Entering \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) with label \(L\)

    +
      +

    1. Push \(L\) to the stack.

      2. +

    2. Jump to the start of the instruction sequence \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\).

      3. +
    +
    +

    Note

    +

    No formal reduction rule is needed for entering an instruction sequence, +because the label \(L\) is embedded in the administrative instruction that structured control instructions reduce to directly.

    +
    +
    +
    +

    Exiting \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) with label \(L\)

    +

    When the end of a block is reached without a jump or trap aborting it, then the following steps are performed.

    +
      +

    1. Let \(m\) be the number of values on the top of the stack.

      2. +

    2. Pop the values \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m\) from the stack.

      3. +

    3. Assert: due to validation, the label \(L\) is now on the top of the stack.

      4. +

    4. Pop the label from the stack.

      5. +

    5. Push \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m\) back to the stack.

      6. +

    6. Jump to the position after the \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\) of the structured control instruction associated with the label \(L\).

      7. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{lcl@{\qquad}l} +\href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../exec/runtime.html#syntax-val}{\mathit{val}}^m +\end{array}\end{split}\]
    +
    +

    Note

    +

    This semantics also applies to the instruction sequence contained in a \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}\) instruction. +Therefore, execution of a loop falls off the end, unless a backwards branch is performed explicitly.

    +
    +
    +
    +
    +

    Function Calls

    +

    The following auxiliary rules define the semantics of invoking a function instance +through one of the call instructions +and returning from it.

    +
    +

    Invocation of function address \(a\)

    +
      +

    1. Assert: due to validation, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a]\) exists.

      2. +

    2. Let \(f\) be the function instance, \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a]\).

      3. +

    3. Let \([t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^m]\) be the function type \(f.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}\).

      4. +

    4. Let \(t^\ast\) be the list of value types \(f.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{code}}.\href{../syntax/modules.html#syntax-func}{\mathsf{locals}}\).

      5. +

    5. Let \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\) be the expression \(f.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{code}}.\href{../syntax/modules.html#syntax-func}{\mathsf{body}}\).

      6. +

    6. Assert: due to validation, \(n\) values are on the top of the stack.

      7. +

    7. Pop the values \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n\) from the stack.

      8. +

    8. Let \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}_0^\ast\) be the list of zero values of types \(t^\ast\).

      9. +

    9. Let \(F\) be the frame \(\{ \href{../exec/runtime.html#syntax-frame}{\mathsf{module}}~f.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{module}}, \href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~(\href{../exec/runtime.html#default-val}{\mathrm{default}}_t)^\ast \}\).

      10. +

    10. Push the activation of \(F\) with arity \(m\) to the stack.

      11. +

    11. Let \(L\) be the label whose arity is \(m\) and whose continuation is the end of the function.

      12. +

    12. Enter the instruction sequence \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) with label \(L\).

      13. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~(\href{../exec/runtime.html#syntax-invoke}{\mathsf{invoke}}~a) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; \href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}_m\{F\}~\href{../exec/runtime.html#syntax-label}{\mathsf{label}}_m\{\}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a] = f \\ + \wedge & f.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}} = [t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^m] \\ + \wedge & f.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{code}} = \{ \href{../syntax/modules.html#syntax-func}{\mathsf{type}}~x, \href{../syntax/modules.html#syntax-func}{\mathsf{locals}}~t^k, \href{../syntax/modules.html#syntax-func}{\mathsf{body}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \} \\ + \wedge & F = \{ \href{../exec/runtime.html#syntax-frame}{\mathsf{module}}~f.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{module}}, ~\href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~(\href{../exec/runtime.html#default-val}{\mathrm{default}}_t)^k \}) + \end{array} \\ +\end{array}\end{split}\]
    +
    +
    +

    Returning from a function

    +

    When the end of a function is reached without a jump (i.e., \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}\)) or trap aborting it, then the following steps are performed.

    +
      +

    1. Let \(F\) be the current frame.

      2. +

    2. Let \(n\) be the arity of the activation of \(F\).

      3. +

    3. Assert: due to validation, there are \(n\) values on the top of the stack.

      4. +

    4. Pop the results \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n\) from the stack.

      5. +

    5. Assert: due to validation, the frame \(F\) is now on the top of the stack.

      6. +

    6. Pop the frame from the stack.

      7. +

    7. Push \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n\) back to the stack.

      8. +

    8. Jump to the instruction after the original call.

      9. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{lcl@{\qquad}l} +\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}_n\{F\}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n +\end{array}\end{split}\]
    +
    +
    +

    Host Functions

    +

    Invoking a host function has non-deterministic behavior. +It may either terminate with a trap or return regularly. +However, in the latter case, it must consume and produce the right number and types of WebAssembly values on the stack, +according to its function type.

    +

    A host function may also modify the store. +However, all store modifications must result in an extension of the original store, i.e., they must only modify mutable contents and must not have instances removed. +Furthermore, the resulting store must be valid, i.e., all data and code in it is well-typed.

    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{l} +\begin{array}{lcl@{\qquad}l} +S; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~(\href{../exec/runtime.html#syntax-invoke}{\mathsf{invoke}}~a) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S'; \href{../exec/runtime.html#syntax-result}{\mathit{result}} +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a] = \{ \href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~[t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^m], \href{../exec/runtime.html#syntax-funcinst}{\mathsf{hostcode}}~\mathit{hf} \} \\ + \wedge & (S'; \href{../exec/runtime.html#syntax-result}{\mathit{result}}) \in \mathit{hf}(S; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n)) \\ + \end{array} \\ +\begin{array}{lcl@{\qquad}l} +S; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~(\href{../exec/runtime.html#syntax-invoke}{\mathsf{invoke}}~a) &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~(\href{../exec/runtime.html#syntax-invoke}{\mathsf{invoke}}~a) +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{if}} & S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a] = \{ \href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~[t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^m], \href{../exec/runtime.html#syntax-funcinst}{\mathsf{hostcode}}~\mathit{hf} \} \\ + \wedge & \bot \in \mathit{hf}(S; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n)) \\ + \end{array} \\ +\end{array}\end{split}\]
    +

    Here, \(\mathit{hf}(S; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n)\) denotes the implementation-defined execution of host function \(\mathit{hf}\) in current store \(S\) with arguments \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n\). +It yields a set of possible outcomes, where each element is either a pair of a modified store \(S'\) and a result +or the special value \(\bot\) indicating divergence. +A host function is non-deterministic if there is at least one argument for which the set of outcomes is not singular.

    +

    For a WebAssembly implementation to be sound in the presence of host functions, +every host function instance must be valid, +which means that it adheres to suitable pre- and post-conditions: +under a valid store \(S\), and given arguments \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n\) matching the ascribed parameter types \(t_1^n\), +executing the host function must yield a non-empty set of possible outcomes each of which is either divergence or consists of a valid store \(S'\) that is an extension of \(S\) and a result matching the ascribed return types \(t_2^m\). +All these notions are made precise in the Appendix.

    +
    +

    Note

    +

    A host function can call back into WebAssembly by invoking a function exported from a module. +However, the effects of any such call are subsumed by the non-deterministic behavior allowed for the host function.

    +
    +
    +
    +
    +

    Expressions

    +

    An expression is evaluated relative to a current frame pointing to its containing module instance.

    +
      +

    1. Jump to the start of the instruction sequence \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) of the expression.

      2. +

    2. Execute the instruction sequence.

      3. +

    3. Assert: due to validation, the top of the stack contains a value.

      4. +

    4. Pop the value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) from the stack.

      5. +
    +

    The value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) is the result of the evaluation.

    +
    +\[S; F; \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast \href{../exec/conventions.html#formal-notation}{\hookrightarrow} S'; F'; \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}'^\ast +\qquad (\mathrel{\mbox{if}} S; F; \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \href{../exec/conventions.html#formal-notation}{\hookrightarrow} S'; F'; \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}'^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}})\]
    +
    +

    Note

    +

    Evaluation iterates this reduction rule until reaching a value. +Expressions constituting function bodies are executed during function invocation.

    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/exec/modules.html b/core/exec/modules.html new file mode 100644 index 00000000..103c3cfb --- /dev/null +++ b/core/exec/modules.html @@ -0,0 +1,729 @@ + + + + + + + + + Modules — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Modules

    +

    For modules, the execution semantics primarily defines instantiation, which allocates instances for a module and its contained definitions, initializes tables and memories from contained element and data segments, and invokes the start function if present. It also includes invocation of exported functions.

    +

    Instantiation depends on a number of auxiliary notions for type-checking imports and allocating instances.

    +
    +

    External Typing

    +

    For the purpose of checking external values against imports, +such values are classified by external types. +The following auxiliary typing rules specify this typing relation relative to a store \(S\) in which the referenced instances live.

    +
    +

    \(\href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~a\)

    +
      +

    • The store entry \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a]\) must exist.

      • +

    • Then \(\href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~a\) is valid with external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a].\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}\).

      • +
    +
    +\[\frac{ +}{ + S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~a : \href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a].\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}} +}\]
    +
    +
    +

    \(\href{../exec/runtime.html#syntax-externval}{\mathsf{table}}~a\)

    +
      +

    • The store entry \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a]\) must exist.

      • +

    • Then \(\href{../exec/runtime.html#syntax-externval}{\mathsf{table}}~a\) is valid with external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}}\).

      • +
    +
    +\[\frac{ +}{ + S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathsf{table}}~a : \href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}[a].\href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}} +}\]
    +
    +
    +

    \(\href{../exec/runtime.html#syntax-externval}{\mathsf{mem}}~a\)

    +
      +

    • The store entry \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]\) must exist.

      • +

    • Then \(\href{../exec/runtime.html#syntax-externval}{\mathsf{mem}}~a\) is valid with external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a].\href{../exec/runtime.html#syntax-meminst}{\mathsf{type}}\).

      • +
    +
    +\[\frac{ +}{ + S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathsf{mem}}~a : \href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a].\href{../exec/runtime.html#syntax-meminst}{\mathsf{type}} +}\]
    +
    +
    +

    \(\href{../exec/runtime.html#syntax-externval}{\mathsf{global}}~a\)

    +
      +

    • The store entry \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[a]\) must exist.

      • +

    • Then \(\href{../exec/runtime.html#syntax-externval}{\mathsf{global}}~a\) is valid with external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[a].\href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}}\).

      • +
    +
    +\[\frac{ +}{ + S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathsf{global}}~a : \href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}[a].\href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}} +}\]
    +
    +
    +
    +

    Value Typing

    +

    For the purpose of checking argument values against the parameter types of exported functions, +values are classified by value types. +The following auxiliary typing rules specify this typing relation relative to a store \(S\) in which possibly referenced addresses live.

    +
    +

    Numeric Values \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\)

    + +
    +\[\frac{ +}{ + S \href{../appendix/properties.html#valid-val}{\vdash} t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c : t +}\]
    +
    +
    +

    Null References \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t\)

    + +
    +\[\frac{ +}{ + S \href{../appendix/properties.html#valid-val}{\vdash} \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t : t +}\]
    +
    +
    +

    Function References \(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref}}~a\)

    +
      +

    • The external value \(\href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~a\) must be valid.

      • +

    • Then the value is valid with reference type \(\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}\).

      • +
    +
    +\[\frac{ + S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~a : \href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}} +}{ + S \href{../appendix/properties.html#valid-val}{\vdash} \href{../exec/runtime.html#syntax-ref}{\mathsf{ref}}~a : \href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}} +}\]
    +
    +
    +

    External References \(\href{../exec/runtime.html#syntax-ref.extern}{\mathsf{ref{.}extern}}~a\)

    +
      +

    • The value is valid with reference type \(\href{../syntax/types.html#syntax-reftype}{\mathsf{externref}}\).

      • +
    +
    +\[\frac{ +}{ + S \href{../appendix/properties.html#valid-val}{\vdash} \href{../exec/runtime.html#syntax-ref.extern}{\mathsf{ref{.}extern}}~a : \href{../syntax/types.html#syntax-reftype}{\mathsf{externref}} +}\]
    +
    +
    +
    +

    Allocation

    +

    New instances of functions, tables, memories, and globals are allocated in a store \(S\), as defined by the following auxiliary functions.

    +
    +

    Functions

    +
      +

    1. Let \(\href{../syntax/modules.html#syntax-func}{\mathit{func}}\) be the function to allocate and \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\) its module instance.

      2. +

    2. Let \(a\) be the first free function address in \(S\).

      3. +

    3. Let \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\) be the function type \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{types}}[\href{../syntax/modules.html#syntax-func}{\mathit{func}}.\href{../syntax/modules.html#syntax-func}{\mathsf{type}}]\).

      4. +

    4. Let \(\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}\) be the function instance \(\{ \href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{module}}~\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{code}}~\href{../syntax/modules.html#syntax-func}{\mathit{func}} \}\).

      5. +

    5. Append \(\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}\) to the \(\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}\) of \(S\).

      6. +

    6. Return \(a\).

      7. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{rlll} +\href{../exec/modules.html#alloc-func}{\mathrm{allocfunc}}(S, \href{../syntax/modules.html#syntax-func}{\mathit{func}}, \href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}) &=& S', \href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} \\[1ex] +\mbox{where:} \hfill \\ +\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} &=& |S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}| \\ +\href{../syntax/types.html#syntax-functype}{\mathit{functype}} &=& \href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{types}}[\href{../syntax/modules.html#syntax-func}{\mathit{func}}.\href{../syntax/modules.html#syntax-func}{\mathsf{type}}] \\ +\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}} &=& \{ \href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{module}}~\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{code}}~\href{../syntax/modules.html#syntax-func}{\mathit{func}} \} \\ +S' &=& S \href{../syntax/conventions.html#notation-compose}{\oplus} \{\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}~\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}\} \\ +\end{array}\end{split}\]
    +
    +
    +

    Host Functions

    +
      +

    1. Let \(\href{../exec/runtime.html#syntax-hostfunc}{\mathit{hostfunc}}\) be the host function to allocate and \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\) its function type.

      2. +

    2. Let \(a\) be the first free function address in \(S\).

      3. +

    3. Let \(\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}\) be the function instance \(\{ \href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{hostcode}}~\href{../exec/runtime.html#syntax-hostfunc}{\mathit{hostfunc}} \}\).

      4. +

    4. Append \(\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}\) to the \(\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}\) of \(S\).

      5. +

    5. Return \(a\).

      6. +
    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{rlll} +\href{../exec/modules.html#alloc-hostfunc}{\mathrm{allochostfunc}}(S, \href{../syntax/types.html#syntax-functype}{\mathit{functype}}, \href{../exec/runtime.html#syntax-hostfunc}{\mathit{hostfunc}}) &=& S', \href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} \\[1ex] +\mbox{where:} \hfill \\ +\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} &=& |S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}| \\ +\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}} &=& \{ \href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{hostcode}}~\href{../exec/runtime.html#syntax-hostfunc}{\mathit{hostfunc}} \} \\ +S' &=& S \href{../syntax/conventions.html#notation-compose}{\oplus} \{\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}~\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}\} \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    Host functions are never allocated by the WebAssembly semantics itself, +but may be allocated by the embedder.

    +
    +
    +
    +

    Tables

    +
      +

    1. Let \(\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\) be the table type to allocate and \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}\) the initialization value.

      2. +

    2. Let \((\{\href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m^?\}~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}})\) be the structure of table type \(\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\).

      3. +

    3. Let \(a\) be the first free table address in \(S\).

      4. +

    4. Let \(\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}\) be the table instance \(\{ \href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}, \href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}~\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^n \}\) with \(n\) elements set to \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}\).

      5. +

    5. Append \(\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}\) to the \(\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}\) of \(S\).

      6. +

    6. Return \(a\).

      7. +
    +
    +\[\begin{split}\begin{array}{rlll} +\href{../exec/modules.html#alloc-table}{\mathrm{alloctable}}(S, \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}, \href{../exec/runtime.html#syntax-ref}{\mathit{ref}}) &=& S', \href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}} \\[1ex] +\mbox{where:} \hfill \\ +\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} &=& \{\href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m^?\}~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}} \\ +\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}} &=& |S.\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}| \\ +\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}} &=& \{ \href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}, \href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}~\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^n \} \\ +S' &=& S \href{../syntax/conventions.html#notation-compose}{\oplus} \{\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}~\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}\} \\ +\end{array}\end{split}\]
    +
    +
    +

    Memories

    +
      +

    1. Let \(\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\) be the memory type to allocate.

      2. +

    2. Let \(\{\href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m^?\}\) be the structure of memory type \(\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\).

      3. +

    3. Let \(a\) be the first free memory address in \(S\).

      4. +

    4. Let \(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}\) be the memory instance \(\{ \href{../exec/runtime.html#syntax-meminst}{\mathsf{type}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}, \href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}~(\def\mathdef2106#1{\mathtt{0x#1}}\mathdef2106{00})^{n \cdot 64\,\mathrm{Ki}} \}\) that contains \(n\) pages of zeroed bytes.

      5. +

    5. Append \(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}\) to the \(\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}\) of \(S\).

      6. +

    6. Return \(a\).

      7. +
    +
    +\[\begin{split}\begin{array}{rlll} +\href{../exec/modules.html#alloc-mem}{\mathrm{allocmem}}(S, \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}) &=& S', \href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}} \\[1ex] +\mbox{where:} \hfill \\ +\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} &=& \{\href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m^?\} \\ +\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}} &=& |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}| \\ +\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}} &=& \{ \href{../exec/runtime.html#syntax-meminst}{\mathsf{type}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}, \href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}~(\def\mathdef2107#1{\mathtt{0x#1}}\mathdef2107{00})^{n \cdot 64\,\mathrm{Ki}} \} \\ +S' &=& S \href{../syntax/conventions.html#notation-compose}{\oplus} \{\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}~\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}\} \\ +\end{array}\end{split}\]
    +
    +
    +

    Globals

    +
      +

    1. Let \(\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}\) be the global type to allocate and \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}\) the value to initialize the global with.

      2. +

    2. Let \(a\) be the first free global address in \(S\).

      3. +

    3. Let \(\href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}\) be the global instance \(\{ \href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}, \href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}} \}\).

      4. +

    4. Append \(\href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}\) to the \(\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}\) of \(S\).

      5. +

    5. Return \(a\).

      6. +
    +
    +\[\begin{split}\begin{array}{rlll} +\href{../exec/modules.html#alloc-global}{\mathrm{allocglobal}}(S, \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}, \href{../exec/runtime.html#syntax-val}{\mathit{val}}) &=& S', \href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}} \\[1ex] +\mbox{where:} \hfill \\ +\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}} &=& |S.\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}| \\ +\href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}} &=& \{ \href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}, \href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}} \} \\ +S' &=& S \href{../syntax/conventions.html#notation-compose}{\oplus} \{\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}~\href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}\} \\ +\end{array}\end{split}\]
    +
    +
    +

    Element segments

    +
      +

    1. Let \(\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}\) be the elements’ type and \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast\) the vector of references to allocate.

      2. +

    2. Let \(a\) be the first free element address in \(S\).

      3. +

    3. Let \(\href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}\) be the element instance \(\{ \href{../exec/runtime.html#syntax-eleminst}{\mathsf{type}}~t, \href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}~\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast \}\).

      4. +

    4. Append \(\href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}\) to the \(\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}\) of \(S\).

      5. +

    5. Return \(a\).

      6. +
    +
    +\[\begin{split}\begin{array}{rlll} +\href{../exec/modules.html#alloc-elem}{\mathrm{allocelem}}(S, \href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}, \href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast) &=& S', \href{../exec/runtime.html#syntax-elemaddr}{\mathit{elemaddr}} \\[1ex] +\mbox{where:} \hfill \\ +\href{../exec/runtime.html#syntax-elemaddr}{\mathit{elemaddr}} &=& |S.\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}| \\ +\href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}} &=& \{ \href{../exec/runtime.html#syntax-eleminst}{\mathsf{type}}~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}, \href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}~\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast \} \\ +S' &=& S \href{../syntax/conventions.html#notation-compose}{\oplus} \{\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}~\href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}\} \\ +\end{array}\end{split}\]
    +
    +
    +

    Data segments

    +
      +

    1. Let \(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}\) be the vector of bytes to allocate.

      2. +

    2. Let \(a\) be the first free data address in \(S\).

      3. +

    3. Let \(\href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}\) be the data instance \(\{ \href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}~\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}} \}\).

      4. +

    4. Append \(\href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}\) to the \(\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}\) of \(S\).

      5. +

    5. Return \(a\).

      6. +
    +
    +\[\begin{split}\begin{array}{rlll} +\href{../exec/modules.html#alloc-data}{\mathrm{allocdata}}(S, \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}) &=& S', \href{../exec/runtime.html#syntax-dataaddr}{\mathit{dataaddr}} \\[1ex] +\mbox{where:} \hfill \\ +\href{../exec/runtime.html#syntax-dataaddr}{\mathit{dataaddr}} &=& |S.\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}| \\ +\href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}} &=& \{ \href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}~\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}} \} \\ +S' &=& S \href{../syntax/conventions.html#notation-compose}{\oplus} \{\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}~\href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}\} \\ +\end{array}\end{split}\]
    +
    +
    +

    Growing tables

    +
      +

    1. Let \(\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}\) be the table instance to grow, \(n\) the number of elements by which to grow it, and \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}\) the initialization value.

      2. +

    2. Let \(\mathit{len}\) be \(n\) added to the length of \(\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\).

      3. +

    3. If \(\mathit{len}\) is larger than or equal to \(2^{32}\), then fail.

      4. +

    4. Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t\) be the structure of table type \(\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}}\).

      5. +

    5. Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}'\) be \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}\) with \(\href{../syntax/types.html#syntax-limits}{\mathsf{min}}\) updated to \(\mathit{len}\).

      6. +

    6. If \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}'\) is not valid, then fail.

      7. +

    7. Append \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^n\) to \(\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}\).

      8. +

    8. Set \(\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}}\) to the table type \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}'~t\).

      9. +
    +
    +\[\begin{split}\begin{array}{rllll} +\href{../exec/modules.html#grow-table}{\mathrm{growtable}}(\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}, n, \href{../exec/runtime.html#syntax-ref}{\mathit{ref}}) &=& \href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}} \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}} = \href{../syntax/types.html#syntax-limits}{\mathit{limits}}'~t \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}} = \href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}~\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^n \\ + && ( + \begin{array}[t]{@{}r@{~}l@{}} + \mathrel{\mbox{if}} & \mathit{len} = n + |\href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}| \\ + \wedge & \mathit{len} < 2^{32} \\ + \wedge & \href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t = \href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}.\href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}} \\ + \wedge & \href{../syntax/types.html#syntax-limits}{\mathit{limits}}' = \href{../syntax/types.html#syntax-limits}{\mathit{limits}} \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../syntax/types.html#syntax-limits}{\mathsf{min}} = \mathit{len} \\ + \wedge & \href{../valid/types.html#valid-limits}{\vdash} \href{../syntax/types.html#syntax-limits}{\mathit{limits}}' \mathrel{\mbox{ok}} \\ + \end{array} \\ +\end{array}\end{split}\]
    +
    +
    +

    Growing memories

    +
      +

    1. Let \(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}\) be the memory instance to grow and \(n\) the number of pages by which to grow it.

      2. +

    2. Assert: The length of \(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\) is divisible by the page size \(64\,\mathrm{Ki}\).

      3. +

    3. Let \(\mathit{len}\) be \(n\) added to the length of \(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\) divided by the page size \(64\,\mathrm{Ki}\).

      4. +

    4. If \(\mathit{len}\) is larger than \(2^{16}\), then fail.

      5. +

    5. Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}\) be the structure of memory type \(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{type}}\).

      6. +

    6. Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}'\) be \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}\) with \(\href{../syntax/types.html#syntax-limits}{\mathsf{min}}\) updated to \(\mathit{len}\).

      7. +

    7. If \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}'\) is not valid, then fail.

      8. +

    8. Append \(n\) times \(64\,\mathrm{Ki}\) bytes with value \(\def\mathdef2108#1{\mathtt{0x#1}}\mathdef2108{00}\) to \(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}\).

      9. +

    9. Set \(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{type}}\) to the memory type \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}'\).

      10. +
    +
    +\[\begin{split}\begin{array}{rllll} +\href{../exec/modules.html#grow-mem}{\mathrm{growmem}}(\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}, n) &=& \href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}} \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-meminst}{\mathsf{type}} = \href{../syntax/types.html#syntax-limits}{\mathit{limits}}' \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-meminst}{\mathsf{data}} = \href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}~(\def\mathdef2109#1{\mathtt{0x#1}}\mathdef2109{00})^{n \cdot 64\,\mathrm{Ki}} \\ + && ( + \begin{array}[t]{@{}r@{~}l@{}} + \mathrel{\mbox{if}} & \mathit{len} = n + |\href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}| / 64\,\mathrm{Ki} \\ + \wedge & \mathit{len} \leq 2^{16} \\ + \wedge & \href{../syntax/types.html#syntax-limits}{\mathit{limits}} = \href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{type}} \\ + \wedge & \href{../syntax/types.html#syntax-limits}{\mathit{limits}}' = \href{../syntax/types.html#syntax-limits}{\mathit{limits}} \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../syntax/types.html#syntax-limits}{\mathsf{min}} = \mathit{len} \\ + \wedge & \href{../valid/types.html#valid-limits}{\vdash} \href{../syntax/types.html#syntax-limits}{\mathit{limits}}' \mathrel{\mbox{ok}} \\ + \end{array} \\ +\end{array}\end{split}\]
    +
    +
    +

    Modules

    +

    The allocation function for modules requires a suitable list of external values that are assumed to match the import vector of the module, +a list of initialization values for the module’s globals, +and list of reference vectors for the module’s element segments.

    +
      +

    1. Let \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}\) be the module to allocate and \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{im}}^\ast\) the vector of external values providing the module’s imports, \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\) the initialization values of the module’s globals, and \((\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast)^\ast\) the reference vectors of the module’s element segments.

      2. +

    2. For each function \(\href{../syntax/modules.html#syntax-func}{\mathit{func}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{funcs}}\), do:

      +
        +

      1. Let \(\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}_i\) be the function address resulting from allocating \(\href{../syntax/modules.html#syntax-func}{\mathit{func}}_i\) for the module instance \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\) defined below.

        2. +
      +
      3. +

    3. For each table \(\href{../syntax/modules.html#syntax-table}{\mathit{table}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{tables}}\), do:

      +
        +

      1. Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_i~t_i\) be the table type \(\href{../syntax/modules.html#syntax-table}{\mathit{table}}_i.\href{../syntax/modules.html#syntax-table}{\mathsf{type}}\).

        2. +
      +

      b. Let \(\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}_i\) be the table address resulting from allocating \(\href{../syntax/modules.html#syntax-table}{\mathit{table}}_i.\href{../syntax/modules.html#syntax-table}{\mathsf{type}}\) +with initialization value \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t_i\).

      +
      4. +

    4. For each memory \(\href{../syntax/modules.html#syntax-mem}{\mathit{mem}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{mems}}\), do:

      +
        +

      1. Let \(\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}_i\) be the memory address resulting from allocating \(\href{../syntax/modules.html#syntax-mem}{\mathit{mem}}_i.\href{../syntax/modules.html#syntax-mem}{\mathsf{type}}\).

        2. +
      +
      5. +

    5. For each global \(\href{../syntax/modules.html#syntax-global}{\mathit{global}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{globals}}\), do:

      +
        +

      1. Let \(\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}_i\) be the global address resulting from allocating \(\href{../syntax/modules.html#syntax-global}{\mathit{global}}_i.\href{../syntax/modules.html#syntax-global}{\mathsf{type}}\) with initializer value \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast[i]\).

        2. +
      +
      6. +

    6. For each element segment \(\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{elems}}\), do:

      +
        +

      1. Let \(\href{../exec/runtime.html#syntax-elemaddr}{\mathit{elemaddr}}_i\) be the element address resulting from allocating a element instance of reference type \(\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}_i.\href{../syntax/modules.html#syntax-elem}{\mathsf{type}}\) with contents \((\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast)^\ast[i]\).

        2. +
      +
      7. +

    7. For each data segment \(\href{../syntax/modules.html#syntax-data}{\mathit{data}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{datas}}\), do:

      +
        +

      1. Let \(\href{../exec/runtime.html#syntax-dataaddr}{\mathit{dataaddr}}_i\) be the data address resulting from allocating a data instance with contents \(\href{../syntax/modules.html#syntax-data}{\mathit{data}}_i.\href{../syntax/modules.html#syntax-data}{\mathsf{init}}\).

        2. +
      +
      8. +

    8. Let \(\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}^\ast\) be the concatenation of the function addresses \(\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}_i\) in index order.

      9. +

    9. Let \(\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}^\ast\) be the concatenation of the table addresses \(\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}_i\) in index order.

      10. +

    10. Let \(\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}^\ast\) be the concatenation of the memory addresses \(\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}_i\) in index order.

      11. +

    11. Let \(\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}^\ast\) be the concatenation of the global addresses \(\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}_i\) in index order.

      12. +

    12. Let \(\href{../exec/runtime.html#syntax-elemaddr}{\mathit{elemaddr}}^\ast\) be the concatenation of the element addresses \(\href{../exec/runtime.html#syntax-elemaddr}{\mathit{elemaddr}}_i\) in index order.

      13. +

    13. Let \(\href{../exec/runtime.html#syntax-dataaddr}{\mathit{dataaddr}}^\ast\) be the concatenation of the data addresses \(\href{../exec/runtime.html#syntax-dataaddr}{\mathit{dataaddr}}_i\) in index order.

      14. +

    14. Let \(\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}_{\mathrm{mod}}^\ast\) be the list of function addresses extracted from \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{im}}^\ast\), concatenated with \(\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}^\ast\).

      15. +

    15. Let \(\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}_{\mathrm{mod}}^\ast\) be the list of table addresses extracted from \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{im}}^\ast\), concatenated with \(\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}^\ast\).

      16. +

    16. Let \(\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}_{\mathrm{mod}}^\ast\) be the list of memory addresses extracted from \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{im}}^\ast\), concatenated with \(\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}^\ast\).

      17. +

    17. Let \(\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}_{\mathrm{mod}}^\ast\) be the list of global addresses extracted from \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{im}}^\ast\), concatenated with \(\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}^\ast\).

      18. +

    18. For each export \(\href{../syntax/modules.html#syntax-export}{\mathit{export}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{exports}}\), do:

      +
        +

      1. If \(\href{../syntax/modules.html#syntax-export}{\mathit{export}}_i\) is a function export for function index \(x\), then let \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_i\) be the external value \(\href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~(\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}_{\mathrm{mod}}^\ast[x])\).

        2. +

      2. Else, if \(\href{../syntax/modules.html#syntax-export}{\mathit{export}}_i\) is a table export for table index \(x\), then let \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_i\) be the external value \(\href{../exec/runtime.html#syntax-externval}{\mathsf{table}}~(\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}_{\mathrm{mod}}^\ast[x])\).

        3. +

      3. Else, if \(\href{../syntax/modules.html#syntax-export}{\mathit{export}}_i\) is a memory export for memory index \(x\), then let \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_i\) be the external value \(\href{../exec/runtime.html#syntax-externval}{\mathsf{mem}}~(\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}_{\mathrm{mod}}^\ast[x])\).

        4. +

      4. Else, if \(\href{../syntax/modules.html#syntax-export}{\mathit{export}}_i\) is a global export for global index \(x\), then let \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_i\) be the external value \(\href{../exec/runtime.html#syntax-externval}{\mathsf{global}}~(\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}_{\mathrm{mod}}^\ast[x])\).

        5. +

      5. Let \(\href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}_i\) be the export instance \(\{\href{../exec/runtime.html#syntax-exportinst}{\mathsf{name}}~(\href{../syntax/modules.html#syntax-export}{\mathit{export}}_i.\href{../syntax/modules.html#syntax-export}{\mathsf{name}}), \href{../exec/runtime.html#syntax-exportinst}{\mathsf{value}}~\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_i\}\).

        6. +
      +
      19. +

    19. Let \(\href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}^\ast\) be the concatenation of the export instances \(\href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}_i\) in index order.

      20. +

    20. Let \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\) be the module instance \(\{\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{types}}~(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{types}}),\) \(\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}_{\mathrm{mod}}^\ast,\) \(\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}~\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}_{\mathrm{mod}}^\ast,\) \(\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}~\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}_{\mathrm{mod}}^\ast,\) \(\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{globaladdrs}}~\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}_{\mathrm{mod}}^\ast,\) \(\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{exports}}~\href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}^\ast\}\).

      21. +

    21. Return \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\).

      22. +
    +
    +\[\begin{split}~\\ +\begin{array}{rlll} +\href{../exec/modules.html#alloc-module}{\mathrm{allocmodule}}(S, \href{../syntax/modules.html#syntax-module}{\mathit{module}}, \href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{im}}^\ast, \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast, (\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast)^\ast) &=& S', \href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}} +\end{array}\end{split}\]
    +

    where:

    +
    +\[\begin{split}\begin{array}{@{}rlll@{}} +\href{../syntax/modules.html#syntax-table}{\mathit{table}}^\ast &=& \href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{tables}} \\ +\href{../syntax/modules.html#syntax-mem}{\mathit{mem}}^\ast &=& \href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{mems}} \\ +\href{../syntax/modules.html#syntax-global}{\mathit{global}}^\ast &=& \href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{globals}} \\ +\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}^\ast &=& \href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{elems}} \\ +\href{../syntax/modules.html#syntax-data}{\mathit{data}}^\ast &=& \href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{datas}} \\ +\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast &=& \href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{exports}} \\[1ex] +\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}} &=& \{~ + \begin{array}[t]{@{}l@{}} + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{types}}~\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{types}}, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}}~\href{../exec/runtime.html#syntax-externval}{\mathrm{funcs}}(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{im}}^\ast)~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}~\href{../exec/runtime.html#syntax-externval}{\mathrm{tables}}(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{im}}^\ast)~\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}~\href{../exec/runtime.html#syntax-externval}{\mathrm{mems}}(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{im}}^\ast)~\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{globaladdrs}}~\href{../exec/runtime.html#syntax-externval}{\mathrm{globals}}(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{im}}^\ast)~\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{elemaddrs}}~\href{../exec/runtime.html#syntax-elemaddr}{\mathit{elemaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{dataaddrs}}~\href{../exec/runtime.html#syntax-dataaddr}{\mathit{dataaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{exports}}~\href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}^\ast ~\} + \end{array} \\[1ex] +S_1, \href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}^\ast &=& + \href{../exec/modules.html#alloc-func}{\mathrm{allocfunc}}^\ast(S, \href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{funcs}}, \href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}) \\ +S_2, \href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}^\ast &=& + \href{../exec/modules.html#alloc-table}{\mathrm{alloctable}}^\ast(S_1, (\href{../syntax/modules.html#syntax-table}{\mathit{table}}.\href{../syntax/modules.html#syntax-table}{\mathsf{type}})^\ast, (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t)^\ast) + \quad (\mathrel{\mbox{where}} (\href{../syntax/modules.html#syntax-table}{\mathit{table}}.\href{../syntax/modules.html#syntax-table}{\mathsf{type}})^\ast = (\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t)^\ast) \\ +S_3, \href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}^\ast &=& + \href{../exec/modules.html#alloc-mem}{\mathrm{allocmem}}^\ast(S_2, (\href{../syntax/modules.html#syntax-mem}{\mathit{mem}}.\href{../syntax/modules.html#syntax-mem}{\mathsf{type}})^\ast) \\ +S_4, \href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}^\ast &=& + \href{../exec/modules.html#alloc-global}{\mathrm{allocglobal}}^\ast(S_3, (\href{../syntax/modules.html#syntax-global}{\mathit{global}}.\href{../syntax/modules.html#syntax-global}{\mathsf{type}})^\ast, \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast) \\ +S_5, \href{../exec/runtime.html#syntax-elemaddr}{\mathit{elemaddr}}^\ast &=& + \href{../exec/modules.html#alloc-elem}{\mathrm{allocelem}}^\ast(S_4, (\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}.\href{../syntax/modules.html#syntax-elem}{\mathsf{type}})^\ast, (\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast)^\ast) \\ +S', \href{../exec/runtime.html#syntax-dataaddr}{\mathit{dataaddr}}^\ast &=& + \href{../exec/modules.html#alloc-data}{\mathrm{allocdata}}^\ast(S_5, (\href{../syntax/modules.html#syntax-data}{\mathit{data}}.\href{../syntax/modules.html#syntax-data}{\mathsf{init}})^\ast) \\ +\href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}^\ast &=& + \{ \href{../exec/runtime.html#syntax-exportinst}{\mathsf{name}}~(\href{../syntax/modules.html#syntax-export}{\mathit{export}}.\href{../syntax/modules.html#syntax-export}{\mathsf{name}}), \href{../exec/runtime.html#syntax-exportinst}{\mathsf{value}}~\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{ex}} \}^\ast \\[1ex] +\href{../exec/runtime.html#syntax-externval}{\mathrm{funcs}}(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{ex}}^\ast) &=& (\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}}[x])^\ast + \qquad~ (\mathrel{\mbox{where}} x^\ast = \href{../syntax/modules.html#syntax-exportdesc}{\mathrm{funcs}}(\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast)) \\ +\href{../exec/runtime.html#syntax-externval}{\mathrm{tables}}(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{ex}}^\ast) &=& (\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[x])^\ast + \qquad (\mathrel{\mbox{where}} x^\ast = \href{../syntax/modules.html#syntax-exportdesc}{\mathrm{tables}}(\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast)) \\ +\href{../exec/runtime.html#syntax-externval}{\mathrm{mems}}(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{ex}}^\ast) &=& (\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[x])^\ast + \qquad (\mathrel{\mbox{where}} x^\ast = \href{../syntax/modules.html#syntax-exportdesc}{\mathrm{mems}}(\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast)) \\ +\href{../exec/runtime.html#syntax-externval}{\mathrm{globals}}(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_{\mathrm{ex}}^\ast) &=& (\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{globaladdrs}}[x])^\ast + \qquad\!\!\! (\mathrel{\mbox{where}} x^\ast = \href{../syntax/modules.html#syntax-exportdesc}{\mathrm{globals}}(\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast)) \\ +\end{array}\end{split}\]
    +

    Here, the notation \(\mathrm{allocx}^\ast\) is shorthand for multiple allocations of object kind \(X\), defined as follows:

    +
    +\[\begin{split}\begin{array}{rlll} +\mathrm{allocx}^\ast(S_0, X^n, \dots) &=& S_n, a^n \\[1ex] +\mbox{where for all $i < n$:} \hfill \\ +S_{i+1}, a^n[i] &=& \mathrm{allocx}(S_i, X^n[i], \dots) +\end{array}\end{split}\]
    +

    Moreover, if the dots \(\dots\) are a sequence \(A^n\) (as for globals or tables), then the elements of this sequence are passed to the allocation function pointwise.

    +
    +

    Note

    +

    The definition of module allocation is mutually recursive with the allocation of its associated functions, because the resulting module instance \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\) is passed to the function allocator as an argument, in order to form the necessary closures. +In an implementation, this recursion is easily unraveled by mutating one or the other in a secondary step.

    +
    +
    +
    +
    +

    Instantiation

    +

    Given a store \(S\), a module \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}\) is instantiated with a list of external values \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^n\) supplying the required imports as follows.

    +

    Instantiation checks that the module is valid and the provided imports match the declared types, +and may fail with an error otherwise. +Instantiation can also result in a trap from executing the start function. +It is up to the embedder to define how such conditions are reported.

    +
      +

    1. If \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}\) is not valid, then:

      +
        +

      1. Fail.

        2. +
      +
      2. +

    2. Assert: \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}\) is valid with external types \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}_{\mathrm{im}}^m\) classifying its imports.

      3. +

    3. If the number \(m\) of imports is not equal to the number \(n\) of provided external values, then:

      +
        +

      1. Fail.

        2. +
      +
      4. +

    4. For each external value \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_i\) in \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^n\) and external type \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}'_i\) in \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}_{\mathrm{im}}^n\), do:

      +
        +

      1. If \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}_i\) is not valid with an external type \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}_i\) in store \(S\), then:

        +
          +

        1. Fail.

          2. +
        +
        2. +

      2. If \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}_i\) does not match \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}'_i\), then:

        +
          +

        1. Fail.

          2. +
        +
        3. +
      +
      5. +
    +
      +

    1. Let \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}_{\mathrm{init}}\) be the auxiliary module instance \(\{\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{globaladdrs}}~\href{../exec/runtime.html#syntax-externval}{\mathrm{globals}}(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^n), \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}}~\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}}\}\) that only consists of the imported globals and the imported and allocated functions from the final module instance \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\), defined below.

      2. +

    2. Let \(F_{\mathrm{init}}\) be the auxiliary frame \(\{ \href{../exec/runtime.html#syntax-frame}{\mathsf{module}}~\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}_{\mathrm{init}}, \href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}~\epsilon \}\).

      3. +

    3. Push the frame \(F_{\mathrm{init}}\) to the stack.

      4. +

    4. Let \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\) be the vector of global initialization values determined by \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}\) and \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^n\). These may be calculated as follows.

      +
        +

      1. For each global \(\href{../syntax/modules.html#syntax-global}{\mathit{global}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{globals}}\), do:

        +
          +

        1. Let \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}_i\) be the result of evaluating the initializer expression \(\href{../syntax/modules.html#syntax-global}{\mathit{global}}_i.\href{../syntax/modules.html#syntax-global}{\mathsf{init}}\).

          2. +
        +
        2. +

      2. Assert: due to validation, the frame \(F_{\mathrm{init}}\) is now on the top of the stack.

        3. +

      3. Let \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\) be the concatenation of \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}_i\) in index order.

        4. +
      +
      5. +

    5. Let \((\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast)^\ast\) be the list of reference vectors determined by the element segments in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}\). These may be calculated as follows.

      +
      +
        +

      1. For each element segment \(\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{elems}}\), and for each element expression \(\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}_{ij}\) in \(\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}_i.\href{../syntax/modules.html#syntax-elem}{\mathsf{init}}\), do:

        +
          +

        1. Let \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}_{ij}\) be the result of evaluating the initializer expression \(\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}_{ij}\).

          2. +
        +
        2. +

      2. Let \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast_i\) be the concatenation of function elements \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}_{ij}\) in order of index \(j\).

        3. +

      3. Let \((\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast)^\ast\) be the concatenation of function element vectors \(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast_i\) in order of index \(i\).

        4. +
      +
      +
      6. +

    6. Pop the frame \(F_{\mathrm{init}}\) from the stack.

      7. +

    7. Let \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\) be a new module instance allocated from \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}\) in store \(S\) with imports \(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^n\), global initializer values \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\), and element segment contents \((\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast)^\ast\), and let \(S'\) be the extended store produced by module allocation.

      8. +

    8. Let \(F\) be the auxiliary frame \(\{ \href{../exec/runtime.html#syntax-frame}{\mathsf{module}}~\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}, \href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}~\epsilon \}\).

      9. +

    9. Push the frame \(F\) to the stack.

      10. +

    10. For each element segment \(\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{elems}}\) whose mode is of the form \(\href{../syntax/modules.html#syntax-elemmode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-elem}{\mathsf{table}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}}_i, \href{../syntax/modules.html#syntax-elem}{\mathsf{offset}}~\mathit{einstr}^\ast_i~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \}\), do:

      +
        +

      1. Let \(n\) be the length of the vector \(\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}_i.\href{../syntax/modules.html#syntax-elem}{\mathsf{init}}\).

        2. +

      2. Execute the instruction sequence \(\mathit{einstr}^\ast_i\).

        3. +

      3. Execute the instruction \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0\).

        4. +

      4. Execute the instruction \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n\).

        5. +

      5. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}}_i~i\).

        6. +

      6. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem.drop}}~i\).

        7. +
      +
      11. +

    11. For each data segment \(\href{../syntax/modules.html#syntax-data}{\mathit{data}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{datas}}\) whose mode is of the form \(\href{../syntax/modules.html#syntax-datamode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-data}{\mathsf{memory}}~\href{../syntax/modules.html#syntax-memidx}{\mathit{memidx}}_i, \href{../syntax/modules.html#syntax-data}{\mathsf{offset}}~\mathit{dinstr}^\ast_i~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \}\), do:

      +
        +

      1. Assert: \(\href{../syntax/modules.html#syntax-memidx}{\mathit{memidx}}_i\) is \(0\).

        2. +

      2. Let \(n\) be the length of the vector \(\href{../syntax/modules.html#syntax-data}{\mathit{data}}_i.\href{../syntax/modules.html#syntax-data}{\mathsf{init}}\).

        3. +

      3. Execute the instruction sequence \(\mathit{dinstr}^\ast_i\).

        4. +

      4. Execute the instruction \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0\).

        5. +

      5. Execute the instruction \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n\).

        6. +

      6. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~i\).

        7. +

      7. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data.drop}}~i\).

        8. +
      +
      12. +

    12. If the start function \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{start}}\) is not empty, then:

      +
        +

      1. Let \(\href{../syntax/modules.html#syntax-start}{\mathit{start}}\) be the start function \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{start}}\).

        2. +

      2. Execute the instruction \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call}}~\href{../syntax/modules.html#syntax-start}{\mathit{start}}.\href{../syntax/modules.html#syntax-start}{\mathsf{func}}\).

        3. +
      +
      13. +

    13. Assert: due to validation, the frame \(F\) is now on the top of the stack.

      14. +

    14. Pop the frame \(F\) from the stack.

      15. +
    +
    +\[\begin{split}~\\ +\begin{array}{@{}rcll} +\href{../exec/modules.html#exec-instantiation}{\mathrm{instantiate}}(S, \href{../syntax/modules.html#syntax-module}{\mathit{module}}, \href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^k) &=& S'; F; + \begin{array}[t]{@{}l@{}} + \mathrm{runelem}_0(\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}^n[0])~\dots~\mathrm{runelem}_{n-1}(\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}^n[n-1]) \\ + \mathrm{rundata}_0(\href{../syntax/modules.html#syntax-data}{\mathit{data}}^m[0])~\dots~\mathrm{rundata}_{m-1}(\href{../syntax/modules.html#syntax-data}{\mathit{data}}^m[m-1]) \\ + (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call}}~\href{../syntax/modules.html#syntax-start}{\mathit{start}}.\href{../syntax/modules.html#syntax-start}{\mathsf{func}})^? \\ + \end{array} \\ +&(\mathrel{\mbox{if}} + & \href{../valid/modules.html#valid-module}{\vdash} \href{../syntax/modules.html#syntax-module}{\mathit{module}} : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}_{\mathrm{im}}^k \href{../syntax/types.html#syntax-functype}{\rightarrow} \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}_{\mathrm{ex}}^\ast \\ + &\wedge& (S \href{../exec/modules.html#valid-externval}{\vdash} \href{../exec/runtime.html#syntax-externval}{\mathit{externval}} : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}})^k \\ + &\wedge& (\href{../exec/modules.html#match-externtype}{\vdash} \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}} \href{../exec/modules.html#match-externtype}{\leq} \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}_{\mathrm{im}})^k \\[1ex] + &\wedge& \href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{globals}} = \href{../syntax/modules.html#syntax-global}{\mathit{global}}^\ast \\ + &\wedge& \href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{elems}} = \href{../syntax/modules.html#syntax-elem}{\mathit{elem}}^n \\ + &\wedge& \href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{datas}} = \href{../syntax/modules.html#syntax-data}{\mathit{data}}^m \\ + &\wedge& \href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{start}} = \href{../syntax/modules.html#syntax-start}{\mathit{start}}^? \\ + &\wedge& (\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}_{\mathrm{g}} = \href{../syntax/modules.html#syntax-global}{\mathit{global}}.GINIT)^\ast \\ + &\wedge& (\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}_{\mathrm{e}}^\ast = \href{../syntax/modules.html#syntax-elem}{\mathit{elem}}.EINIT)^n \\[1ex] + &\wedge& S', \href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}} = \href{../exec/modules.html#alloc-module}{\mathrm{allocmodule}}(S, \href{../syntax/modules.html#syntax-module}{\mathit{module}}, \href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^k, \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast, (\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast)^n) \\ + &\wedge& F = \{ \href{../exec/runtime.html#syntax-frame}{\mathsf{module}}~\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}, \href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}~\epsilon \} \\[1ex] + &\wedge& (S'; F; \href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}_{\mathrm{g}} \href{../exec/conventions.html#formal-notation}{\hookrightarrow}^\ast S'; F; \href{../exec/runtime.html#syntax-val}{\mathit{val}}~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}})^\ast \\ + &\wedge& ((S'; F; \href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}_{\mathrm{e}} \href{../exec/conventions.html#formal-notation}{\hookrightarrow}^\ast S'; F; \href{../exec/runtime.html#syntax-ref}{\mathit{ref}}~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}})^\ast)^n \\ + &\wedge& (\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}} = \href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}}[\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}.\href{../syntax/modules.html#syntax-elem}{\mathsf{table}}])^\ast \\ + &\wedge& (\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}} = \href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}}[\href{../syntax/modules.html#syntax-data}{\mathit{data}}.\href{../syntax/modules.html#syntax-data}{\mathsf{memory}}])^\ast \\ + &\wedge& (\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} = \href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}}[\href{../syntax/modules.html#syntax-start}{\mathit{start}}.\href{../syntax/modules.html#syntax-start}{\mathsf{func}}])^?) +\end{array}\end{split}\]
    +

    where:

    +
    +\[\begin{split}\begin{array}{@{}l} +\mathrm{runelem}_i(\{\href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~\mathit{et}, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^n, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{passive}}\}) \quad=\quad \epsilon \\ +\mathrm{runelem}_i(\{\href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~\mathit{et}, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^n, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{active}} \{\href{../syntax/modules.html#syntax-elem}{\mathsf{table}}~0, \href{../syntax/modules.html#syntax-elem}{\mathsf{offset}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\}\}) \quad=\\ \qquad + \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}~i)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem.drop}}~i) \\ +\mathrm{runelem}_i(\{\href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~\mathit{et}, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^n, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{declarative}}\}) \quad=\\ \qquad + (\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem.drop}}~i) \\[1ex] +\mathrm{rundata}_i(\{\href{../syntax/modules.html#syntax-data}{\mathsf{init}}~b^n, DMODE~\href{../syntax/modules.html#syntax-datamode}{\mathsf{passive}}\}) \quad=\quad \epsilon \\ +\mathrm{rundata}_i(\{\href{../syntax/modules.html#syntax-data}{\mathsf{init}}~b^n, DMODE~\href{../syntax/modules.html#syntax-datamode}{\mathsf{active}} \{\href{../syntax/modules.html#syntax-data}{\mathsf{memory}}~0, \href{../syntax/modules.html#syntax-data}{\mathsf{offset}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\}\}) \quad=\\ \qquad + \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~i)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data.drop}}~i) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    Module allocation and the evaluation of global initializers and element segments are mutually recursive because the global initialization values \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\) and element segment contents \((\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}^\ast)^\ast\) are passed to the module allocator while depending on the module instance \(\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}\) and store \(S'\) returned by allocation. +However, this recursion is just a specification device. +In practice, the initialization values can be determined beforehand by staging module allocation such that first, the module’s own \(function instances <syntax-funcinst>\) are pre-allocated in the store, then the initializer expressions are evaluated, then the rest of the module instance is allocated, and finally the new function instances’ \(\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}\) fields are set to that module instance. +This is possible because validation ensures that initialization expressions cannot actually call a function, only take their reference.

    +

    All failure conditions are checked before any observable mutation of the store takes place. +Store mutation is not atomic; +it happens in individual steps that may be interleaved with other threads.

    +

    Evaluation of constant expressions does not affect the store.

    +
    +
    +
    +

    Invocation

    +

    Once a module has been instantiated, any exported function can be invoked externally via its function address \(\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}\) in the store \(S\) and an appropriate list \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\) of argument values.

    +

    Invocation may fail with an error if the arguments do not fit the function type. +Invocation can also result in a trap. +It is up to the embedder to define how such conditions are reported.

    +
    +

    Note

    +

    If the embedder API performs type checks itself, either statically or dynamically, before performing an invocation, then no failure other than traps can occur.

    +
    +

    The following steps are performed:

    +
      +

    1. Assert: \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}]\) exists.

      2. +

    2. Let \(\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}\) be the function instance \(S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}]\).

      3. +

    3. Let \([t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^m]\) be the function type \(\href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}\).

      4. +

    4. If the length \(|\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast|\) of the provided argument values is different from the number \(n\) of expected arguments, then:

      +
        +

      1. Fail.

        2. +
      +
      5. +

    5. For each value type \(t_i\) in \(t_1^n\) and corresponding value \(val_i\) in \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\), do:

      +
        +

      1. If \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}_i\) is not valid with value type \(t_i\), then:

        +
          +

        1. Fail.

          2. +
        +
        2. +
      +
      6. +

    6. Let \(F\) be the dummy frame \(\{ \href{../exec/runtime.html#syntax-frame}{\mathsf{module}}~\{\}, \href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}~\epsilon \}\).

      7. +

    7. Push the frame \(F\) to the stack.

      8. +

    8. Push the values \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast\) to the stack.

      9. +

    9. Invoke the function instance at address \(\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}\).

      10. +
    +

    Once the function has returned, the following steps are executed:

    +
      +

    1. Assert: due to validation, \(m\) values are on the top of the stack.

      2. +

    2. Pop \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}_{\mathrm{res}}^m\) from the stack.

      3. +
    +

    The values \(\href{../exec/runtime.html#syntax-val}{\mathit{val}}_{\mathrm{res}}^m\) are returned as the results of the invocation.

    +
    +\[\begin{split}~\\[-1ex] +\begin{array}{@{}lcl} +\href{../exec/modules.html#exec-invocation}{\mathrm{invoke}}(S, \href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}, \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n) &=& S; F; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~(\href{../exec/runtime.html#syntax-invoke}{\mathsf{invoke}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}) \\ + &(\mathrel{\mbox{if}} & S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}].\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}} = [t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^m] \\ + &\wedge& (S \href{../appendix/properties.html#valid-val}{\vdash} \href{../exec/runtime.html#syntax-val}{\mathit{val}} : t_1)^n \\ + &\wedge& F = \{ \href{../exec/runtime.html#syntax-frame}{\mathsf{module}}~\{\}, \href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}~\epsilon \}) \\ +\end{array}\end{split}\]
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/exec/numerics.html b/core/exec/numerics.html new file mode 100644 index 00000000..b1f6963e --- /dev/null +++ b/core/exec/numerics.html @@ -0,0 +1,1565 @@ + + + + + + + + + Numerics — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Numerics

    +

    Numeric primitives are defined in a generic manner, by operators indexed over a bit width \(N\).

    +

    Some operators are non-deterministic, because they can return one of several possible results (such as different NaN values). +Technically, each operator thus returns a set of allowed values. +For convenience, deterministic results are expressed as plain values, which are assumed to be identified with a respective singleton set.

    +

    Some operators are partial, because they are not defined on certain inputs. +Technically, an empty set of results is returned for these inputs.

    +

    In formal notation, each operator is defined by equational clauses that apply in decreasing order of precedence. +That is, the first clause that is applicable to the given arguments defines the result. +In some cases, similar clauses are combined into one by using the notation \(\pm\) or \(\mp\). +When several of these placeholders occur in a single clause, then they must be resolved consistently: either the upper sign is chosen for all of them or the lower sign.

    +
    +

    Note

    +

    For example, the \(\href{../exec/numerics.html#op-fcopysign}{\mathrm{fcopysign}}\) operator is defined as follows:

    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fcopysign}{\mathrm{fcopysign}}_N(\pm p_1, \pm p_2) &=& \pm p_1 \\ +\href{../exec/numerics.html#op-fcopysign}{\mathrm{fcopysign}}_N(\pm p_1, \mp p_2) &=& \mp p_1 \\ +\end{array}\end{split}\]
    +

    This definition is to be read as a shorthand for the following expansion of each clause into two separate ones:

    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fcopysign}{\mathrm{fcopysign}}_N(+ p_1, + p_2) &=& + p_1 \\ +\href{../exec/numerics.html#op-fcopysign}{\mathrm{fcopysign}}_N(- p_1, - p_2) &=& - p_1 \\ +\href{../exec/numerics.html#op-fcopysign}{\mathrm{fcopysign}}_N(+ p_1, - p_2) &=& - p_1 \\ +\href{../exec/numerics.html#op-fcopysign}{\mathrm{fcopysign}}_N(- p_1, + p_2) &=& + p_1 \\ +\end{array}\end{split}\]
    +
    +

    Numeric operators are lifted to input sequences by applying the operator element-wise, returning a sequence of results. When there are multiple inputs, they must be of equal length.

    +
    +\[\begin{array}{lll@{\qquad}l} +op(c_1^n, \dots, c_k^n) &=& op(c_1^n[0], \dots, c_k^n[0])~\dots~op(c_1^n[n-1], \dots, c_k^n[n-1]) +\end{array}\]
    +
    +

    Note

    +

    For example, the unary operator \(\href{../exec/numerics.html#op-fabs}{\mathrm{fabs}}\), when given a sequence of floating-point values, return a sequence of floating-point results:

    +
    +\[\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-fabs}{\mathrm{fabs}}_N(z^n) &=& \href{../exec/numerics.html#op-fabs}{\mathrm{fabs}}_N(z[0])~\dots~\href{../exec/numerics.html#op-fabs}{\mathrm{fabs}}_N(z[n]) +\end{array}\]
    +

    The binary operator \(\href{../exec/numerics.html#op-iadd}{\mathrm{iadd}}\), when given two sequences of integers of the same length, \(n\), return a sequence of integer results:

    +
    +\[\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-iadd}{\mathrm{iadd}}_N(i_1^n, i_2^n) &=& \href{../exec/numerics.html#op-iadd}{\mathrm{iadd}}_N(i_1[0], i_2[0])~\dots~\href{../exec/numerics.html#op-iadd}{\mathrm{iadd}}_N(i_1[n], i_2[n]) +\end{array}\]
    +
    +

    Conventions:

    +
      +

    • The meta variable \(d\) is used to range over single bits.

      • +

    • The meta variable \(p\) is used to range over (signless) magnitudes of floating-point values, including \(\href{../syntax/values.html#syntax-float}{\mathsf{nan}}\) and \(\infty\).

      • +

    • The meta variable \(q\) is used to range over (signless) rational magnitudes, excluding \(\href{../syntax/values.html#syntax-float}{\mathsf{nan}}\) or \(\infty\).

      • +

    • The notation \(f^{-1}\) denotes the inverse of a bijective function \(f\).

      • +

    • Truncation of rational values is written \(\href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(\pm q)\), with the usual mathematical definition:

      +
      +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(\pm q) &=& \pm i & (\mathrel{\mbox{if}} i \in \mathbb{N} \wedge +q - 1 < i \leq +q) \\ +\end{array}\end{split}\]
      +
      • +
    +
      +

    • Saturation of integers is written \(\href{../exec/numerics.html#aux-sat-u}{\mathrm{sat}^{\mathsf{u}}}_N(i)\) and \(\href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(i)\). The arguments to these two functions range over arbitrary signed integers.

      +
        +

      • Unsigned saturation, \(\href{../exec/numerics.html#aux-sat-u}{\mathrm{sat}^{\mathsf{u}}}_N(i)\) clamps \(i\) to between \(0\) and \(2^N-1\):

        +
        +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#aux-sat-u}{\mathrm{sat}^{\mathsf{u}}}_N(i) &=& 2^N-1 & (\mathrel{\mbox{if}} i > 2^N-1)\\ +\href{../exec/numerics.html#aux-sat-u}{\mathrm{sat}^{\mathsf{u}}}_N(i) &=& 0 & (\mathrel{\mbox{if}} i < 0) \\ +\href{../exec/numerics.html#aux-sat-u}{\mathrm{sat}^{\mathsf{u}}}_N(i) &=& i & (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
        +
        • +

      • Signed saturation, \(\href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(i)\) clamps \(i\) to between \(-2^{N-1}\) and \(2^{N-1}-1\):

        • +
      +
      +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(i) &=& \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N^{-1}(-2^{N-1}) & (\mathrel{\mbox{if}} i < -2^{N-1})\\ +\href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(i) &=& \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N^{-1}(2^{N-1}-1) & (\mathrel{\mbox{if}} i > 2^{N-1}-1)\\ +\href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(i) &=& i & (\mathrel{\mbox{otherwise}}) +\end{array}\end{split}\]
      +
      • +
    +
    +

    Representations

    +

    Numbers have an underlying binary representation as a sequence of bits:

    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#aux-bits}{\mathrm{bits}}_{\mathsf{i}N}(i) &=& \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i) \\ +\href{../exec/numerics.html#aux-bits}{\mathrm{bits}}_{\mathsf{f}N}(z) &=& \href{../exec/numerics.html#aux-fbits}{\mathrm{fbits}}_N(z) \\ +\end{array}\end{split}\]
    +

    Each of these functions is a bijection, hence they are invertible.

    +
    +

    Integers

    +

    Integers are represented as base two unsigned numbers:

    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i) &=& d_{N-1}~\dots~d_0 & (i = 2^{N-1}\cdot d_{N-1} + \dots + 2^0\cdot d_0) \\ +\end{array}\end{split}\]
    +

    Boolean operators like \(\wedge\), \(\vee\), or \(\veebar\) are lifted to bit sequences of equal length by applying them pointwise.

    +
    +
    +

    Floating-Point

    +

    Floating-point values are represented in the respective binary format defined by IEEE 754-2019 (Section 3.4):

    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#aux-fbits}{\mathrm{fbits}}_N(\pm (1+m\cdot 2^{-M})\cdot 2^e) &=& \href{../exec/numerics.html#aux-fsign}{\mathrm{fsign}}({\pm})~\href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_E(e+\href{../exec/numerics.html#aux-fbias}{\mathrm{fbias}}_N)~\href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_M(m) \\ +\href{../exec/numerics.html#aux-fbits}{\mathrm{fbits}}_N(\pm (0+m\cdot 2^{-M})\cdot 2^e) &=& \href{../exec/numerics.html#aux-fsign}{\mathrm{fsign}}({\pm})~(0)^E~\href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_M(m) \\ +\href{../exec/numerics.html#aux-fbits}{\mathrm{fbits}}_N(\pm \infty) &=& \href{../exec/numerics.html#aux-fsign}{\mathrm{fsign}}({\pm})~(1)^E~(0)^M \\ +\href{../exec/numerics.html#aux-fbits}{\mathrm{fbits}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-fsign}{\mathrm{fsign}}({\pm})~(1)^E~\href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_M(n) \\[1ex] +\href{../exec/numerics.html#aux-fbias}{\mathrm{fbias}}_N &=& 2^{E-1}-1 \\ +\href{../exec/numerics.html#aux-fsign}{\mathrm{fsign}}({+}) &=& 0 \\ +\href{../exec/numerics.html#aux-fsign}{\mathrm{fsign}}({-}) &=& 1 \\ +\end{array}\end{split}\]
    +

    where \(M = \href{../syntax/values.html#aux-significand}{\mathrm{signif}}(N)\) and \(E = \href{../syntax/values.html#aux-exponent}{\mathrm{expon}}(N)\).

    +
    +
    +

    Storage

    +

    When a number is stored into memory, it is converted into a sequence of bytes in little endian byte order:

    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_t(i) &=& \href{../exec/numerics.html#aux-littleendian}{\mathrm{littleendian}}(\href{../exec/numerics.html#aux-bits}{\mathrm{bits}}_t(i)) \\[1ex] +\href{../exec/numerics.html#aux-littleendian}{\mathrm{littleendian}}(\epsilon) &=& \epsilon \\ +\href{../exec/numerics.html#aux-littleendian}{\mathrm{littleendian}}(d^8~{d'}^\ast~) &=& \href{../exec/numerics.html#aux-littleendian}{\mathrm{littleendian}}({d'}^\ast)~\href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_8^{-1}(d^8) \\ +\end{array}\end{split}\]
    +

    Again these functions are invertable bijections.

    +
    +
    +

    Vectors

    +

    Numeric vectors have the same underlying representation as an \(\href{../syntax/values.html#syntax-int}{\mathit{i128}}\). They can also be interpreted as a sequence of numeric values packed into a \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) with a particular \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\).

    +
    +\[\begin{split}\begin{array}{l} +\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(c) &=& + c_0~\dots~c_{N-1} \\ +\end{array} +\\ \qquad + \begin{array}[t]{@{}r@{~}l@{}} + (\mathrel{\mbox{where}} & B = |t| / 8 \\ + \wedge & b^{16} = bytes_{\href{../syntax/values.html#syntax-int}{\mathit{i128}}}(c) \\ + \wedge & c_i = \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{t}^{-1}(b^{16}[i \cdot B \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} B])) + \end{array} +\end{array}\end{split}\]
    +

    These functions are bijections, so they are invertible.

    +
    +
    +
    +

    Integer Operations

    +
    +

    Sign Interpretation

    +

    Integer operators are defined on \(\href{../syntax/values.html#syntax-int}{\mathit{i}N}\) values. +Operators that use a signed interpretation convert the value using the following definition, which takes the two’s complement when the value lies in the upper half of the value range (i.e., its most significant bit is \(1\)):

    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i) &=& i & (0 \leq i < 2^{N-1}) \\ +\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i) &=& i - 2^N & (2^{N-1} \leq i < 2^N) \\ +\end{array}\end{split}\]
    +

    This function is bijective, and hence invertible.

    +
    +
    +

    Boolean Interpretation

    +

    The integer result of predicates – i.e., tests and relational operators – is defined with the help of the following auxiliary function producing the value \(1\) or \(0\) depending on a condition.

    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(C) &=& 1 & (\mathrel{\mbox{if}} C) \\ +\href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(C) &=& 0 & (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-iadd}{\mathrm{iadd}}_N(i_1, i_2)\)

    +
      +

    • Return the result of adding \(i_1\) and \(i_2\) modulo \(2^N\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-iadd}{\mathrm{iadd}}_N(i_1, i_2) &=& (i_1 + i_2) \mathbin{\mathrm{mod}} 2^N +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-isub}{\mathrm{isub}}_N(i_1, i_2)\)

    +
      +

    • Return the result of subtracting \(i_2\) from \(i_1\) modulo \(2^N\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-isub}{\mathrm{isub}}_N(i_1, i_2) &=& (i_1 - i_2 + 2^N) \mathbin{\mathrm{mod}} 2^N +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-imul}{\mathrm{imul}}_N(i_1, i_2)\)

    +
      +

    • Return the result of multiplying \(i_1\) and \(i_2\) modulo \(2^N\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-imul}{\mathrm{imul}}_N(i_1, i_2) &=& (i_1 \cdot i_2) \mathbin{\mathrm{mod}} 2^N +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-idiv-u}{\mathrm{idiv\_u}}_N(i_1, i_2)\)

    +
      +

    • If \(i_2\) is \(0\), then the result is undefined.

      • +

    • Else, return the result of dividing \(i_1\) by \(i_2\), truncated toward zero.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-idiv-u}{\mathrm{idiv\_u}}_N(i_1, 0) &=& \{\} \\ +\href{../exec/numerics.html#op-idiv-u}{\mathrm{idiv\_u}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(i_1 / i_2) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    This operator is partial.

    +
    +
    +
    +

    \(\href{../exec/numerics.html#op-idiv-s}{\mathrm{idiv\_s}}_N(i_1, i_2)\)

    +
      +

    • Let \(j_1\) be the signed interpretation of \(i_1\).

      • +

    • Let \(j_2\) be the signed interpretation of \(i_2\).

      • +

    • If \(j_2\) is \(0\), then the result is undefined.

      • +

    • Else if \(j_1\) divided by \(j_2\) is \(2^{N-1}\), then the result is undefined.

      • +

    • Else, return the result of dividing \(j_1\) by \(j_2\), truncated toward zero.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-idiv-s}{\mathrm{idiv\_s}}_N(i_1, 0) &=& \{\} \\ +\href{../exec/numerics.html#op-idiv-s}{\mathrm{idiv\_s}}_N(i_1, i_2) &=& \{\} \qquad\qquad (\mathrel{\mbox{if}} \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_1) / \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_2) = 2^{N-1}) \\ +\href{../exec/numerics.html#op-idiv-s}{\mathrm{idiv\_s}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N^{-1}(\href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_1) / \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_2))) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    This operator is partial. +Besides division by \(0\), the result of \((-2^{N-1})/(-1) = +2^{N-1}\) is not representable as an \(N\)-bit signed integer.

    +
    +
    +
    +

    \(\href{../exec/numerics.html#op-irem-u}{\mathrm{irem\_u}}_N(i_1, i_2)\)

    +
      +

    • If \(i_2\) is \(0\), then the result is undefined.

      • +

    • Else, return the remainder of dividing \(i_1\) by \(i_2\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-irem-u}{\mathrm{irem\_u}}_N(i_1, 0) &=& \{\} \\ +\href{../exec/numerics.html#op-irem-u}{\mathrm{irem\_u}}_N(i_1, i_2) &=& i_1 - i_2 \cdot \href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(i_1 / i_2) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    This operator is partial.

    +

    As long as both operators are defined, +it holds that \(i_1 = i_2\cdot\href{../exec/numerics.html#op-idiv-u}{\mathrm{idiv\_u}}(i_1, i_2) + \href{../exec/numerics.html#op-irem-u}{\mathrm{irem\_u}}(i_1, i_2)\).

    +
    +
    +
    +

    \(\href{../exec/numerics.html#op-irem-s}{\mathrm{irem\_s}}_N(i_1, i_2)\)

    +
      +

    • Let \(j_1\) be the signed interpretation of \(i_1\).

      • +

    • Let \(j_2\) be the signed interpretation of \(i_2\).

      • +

    • If \(i_2\) is \(0\), then the result is undefined.

      • +

    • Else, return the remainder of dividing \(j_1\) by \(j_2\), with the sign of the dividend \(j_1\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-irem-s}{\mathrm{irem\_s}}_N(i_1, 0) &=& \{\} \\ +\href{../exec/numerics.html#op-irem-s}{\mathrm{irem\_s}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N^{-1}(j_1 - j_2 \cdot \href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(j_1 / j_2)) \\ + && (\mathrel{\mbox{where}} j_1 = \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_1) \wedge j_2 = \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_2)) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    This operator is partial.

    +

    As long as both operators are defined, +it holds that \(i_1 = i_2\cdot\href{../exec/numerics.html#op-idiv-s}{\mathrm{idiv\_s}}(i_1, i_2) + \href{../exec/numerics.html#op-irem-s}{\mathrm{irem\_s}}(i_1, i_2)\).

    +
    +
    +
    +

    \(\href{../exec/numerics.html#op-inot}{\mathrm{inot}}_N(i)\)

    +
      +

    • Return the bitwise negation of \(i\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-inot}{\mathrm{inot}}_N(i) &=& \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N^{-1}(\href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i) \veebar \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(2^N-1)) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-iand}{\mathrm{iand}}_N(i_1, i_2)\)

    +
      +

    • Return the bitwise conjunction of \(i_1\) and \(i_2\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-iand}{\mathrm{iand}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N^{-1}(\href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i_1) \wedge \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i_2)) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-iandnot}{\mathrm{iandnot}}_N(i_1, i_2)\)

    +
      +

    • Return the bitwise conjunction of \(i_1\) and the bitwise negation of \(i_2\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-iandnot}{\mathrm{iandnot}}_N(i_1, i_2) &=& \href{../exec/numerics.html#op-iand}{\mathrm{iand}}_N(i_1, \href{../exec/numerics.html#op-inot}{\mathrm{inot}}_N(i2)) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ior}{\mathrm{ior}}_N(i_1, i_2)\)

    +
      +

    • Return the bitwise disjunction of \(i_1\) and \(i_2\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ior}{\mathrm{ior}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N^{-1}(\href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i_1) \vee \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i_2)) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ixor}{\mathrm{ixor}}_N(i_1, i_2)\)

    +
      +

    • Return the bitwise exclusive disjunction of \(i_1\) and \(i_2\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ixor}{\mathrm{ixor}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N^{-1}(\href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i_1) \veebar \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i_2)) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ishl}{\mathrm{ishl}}_N(i_1, i_2)\)

    +
      +

    • Let \(k\) be \(i_2\) modulo \(N\).

      • +

    • Return the result of shifting \(i_1\) left by \(k\) bits, modulo \(2^N\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ishl}{\mathrm{ishl}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N^{-1}(d_2^{N-k}~0^k) + & (\mathrel{\mbox{if}} \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i_1) = d_1^k~d_2^{N-k} \wedge k = i_2 \mathbin{\mathrm{mod}} N) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ishr-u}{\mathrm{ishr\_u}}_N(i_1, i_2)\)

    +
      +

    • Let \(k\) be \(i_2\) modulo \(N\).

      • +

    • Return the result of shifting \(i_1\) right by \(k\) bits, extended with \(0\) bits.

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ishr-u}{\mathrm{ishr\_u}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N^{-1}(0^k~d_1^{N-k}) + & (\mathrel{\mbox{if}} \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i_1) = d_1^{N-k}~d_2^k \wedge k = i_2 \mathbin{\mathrm{mod}} N) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ishr-s}{\mathrm{ishr\_s}}_N(i_1, i_2)\)

    +
      +

    • Let \(k\) be \(i_2\) modulo \(N\).

      • +

    • Return the result of shifting \(i_1\) right by \(k\) bits, extended with the most significant bit of the original value.

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ishr-s}{\mathrm{ishr\_s}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N^{-1}(d_0^{k+1}~d_1^{N-k-1}) + & (\mathrel{\mbox{if}} \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i_1) = d_0~d_1^{N-k-1}~d_2^k \wedge k = i_2 \mathbin{\mathrm{mod}} N) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-irotl}{\mathrm{irotl}}_N(i_1, i_2)\)

    +
      +

    • Let \(k\) be \(i_2\) modulo \(N\).

      • +

    • Return the result of rotating \(i_1\) left by \(k\) bits.

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-irotl}{\mathrm{irotl}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N^{-1}(d_2^{N-k}~d_1^k) + & (\mathrel{\mbox{if}} \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i_1) = d_1^k~d_2^{N-k} \wedge k = i_2 \mathbin{\mathrm{mod}} N) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-irotr}{\mathrm{irotr}}_N(i_1, i_2)\)

    +
      +

    • Let \(k\) be \(i_2\) modulo \(N\).

      • +

    • Return the result of rotating \(i_1\) right by \(k\) bits.

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-irotr}{\mathrm{irotr}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N^{-1}(d_2^k~d_1^{N-k}) + & (\mathrel{\mbox{if}} \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i_1) = d_1^{N-k}~d_2^k \wedge k = i_2 \mathbin{\mathrm{mod}} N) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-iclz}{\mathrm{iclz}}_N(i)\)

    +
      +

    • Return the count of leading zero bits in \(i\); all bits are considered leading zeros if \(i\) is \(0\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-iclz}{\mathrm{iclz}}_N(i) &=& k & (\mathrel{\mbox{if}} \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i) = 0^k~(1~d^\ast)^?) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ictz}{\mathrm{ictz}}_N(i)\)

    +
      +

    • Return the count of trailing zero bits in \(i\); all bits are considered trailing zeros if \(i\) is \(0\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ictz}{\mathrm{ictz}}_N(i) &=& k & (\mathrel{\mbox{if}} \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i) = (d^\ast~1)^?~0^k) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ipopcnt}{\mathrm{ipopcnt}}_N(i)\)

    +
      +

    • Return the count of non-zero bits in \(i\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ipopcnt}{\mathrm{ipopcnt}}_N(i) &=& k & (\mathrel{\mbox{if}} \href{../exec/numerics.html#aux-ibits}{\mathrm{ibits}}_N(i) = (0^\ast~1)^k~0^\ast) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ieqz}{\mathrm{ieqz}}_N(i)\)

    +
      +

    • Return \(1\) if \(i\) is zero, \(0\) otherwise.

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ieqz}{\mathrm{ieqz}}_N(i) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(i = 0) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ieq}{\mathrm{ieq}}_N(i_1, i_2)\)

    +
      +

    • Return \(1\) if \(i_1\) equals \(i_2\), \(0\) otherwise.

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ieq}{\mathrm{ieq}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(i_1 = i_2) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ine}{\mathrm{ine}}_N(i_1, i_2)\)

    +
      +

    • Return \(1\) if \(i_1\) does not equal \(i_2\), \(0\) otherwise.

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ine}{\mathrm{ine}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(i_1 \neq i_2) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ilt-u}{\mathrm{ilt\_u}}_N(i_1, i_2)\)

    +
      +

    • Return \(1\) if \(i_1\) is less than \(i_2\), \(0\) otherwise.

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ilt-u}{\mathrm{ilt\_u}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(i_1 < i_2) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ilt-s}{\mathrm{ilt\_s}}_N(i_1, i_2)\)

    + +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ilt-s}{\mathrm{ilt\_s}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_1) < \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_2)) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-igt-u}{\mathrm{igt\_u}}_N(i_1, i_2)\)

    +
      +

    • Return \(1\) if \(i_1\) is greater than \(i_2\), \(0\) otherwise.

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-igt-u}{\mathrm{igt\_u}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(i_1 > i_2) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-igt-s}{\mathrm{igt\_s}}_N(i_1, i_2)\)

    + +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-igt-s}{\mathrm{igt\_s}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_1) > \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_2)) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ile-u}{\mathrm{ile\_u}}_N(i_1, i_2)\)

    +
      +

    • Return \(1\) if \(i_1\) is less than or equal to \(i_2\), \(0\) otherwise.

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ile-u}{\mathrm{ile\_u}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(i_1 \leq i_2) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ile-s}{\mathrm{ile\_s}}_N(i_1, i_2)\)

    + +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ile-s}{\mathrm{ile\_s}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_1) \leq \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_2)) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ige-u}{\mathrm{ige\_u}}_N(i_1, i_2)\)

    +
      +

    • Return \(1\) if \(i_1\) is greater than or equal to \(i_2\), \(0\) otherwise.

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ige-u}{\mathrm{ige\_u}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(i_1 \geq i_2) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ige-s}{\mathrm{ige\_s}}_N(i_1, i_2)\)

    + +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ige-s}{\mathrm{ige\_s}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_1) \geq \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_2)) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-iextendn-s}{\mathrm{iextend}M\mathrm{\_s}}_N(i)\)

    +
      +

    • Return \(\href{../exec/numerics.html#op-extend-s}{\mathrm{extend}^{\mathsf{s}}}_{M,N}(i)\).

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-iextendn-s}{\mathrm{iextend}M\mathrm{\_s}}_{N}(i) &=& \href{../exec/numerics.html#op-extend-s}{\mathrm{extend}^{\mathsf{s}}}_{M,N}(i) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ibitselect}{\mathrm{ibitselect}}_N(i_1, i_2, i_3)\)

    +
      +

    • Let \(j_1\) be the bitwise conjunction of \(i_1\) and \(i_3\).

      • +

    • Let \(j_3'\) be the bitwise negation of \(i_3\).

      • +

    • Let \(j_2\) be the bitwise conjunction of \(i_2\) and \(j_3'\).

      • +

    • Return the bitwise disjunction of \(j_1\) and \(j_2\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ibitselect}{\mathrm{ibitselect}}_N(i_1, i_2, i_3) &=& \href{../exec/numerics.html#op-ior}{\mathrm{ior}}_N(\href{../exec/numerics.html#op-iand}{\mathrm{iand}}_N(i_1, i_3), \href{../exec/numerics.html#op-iand}{\mathrm{iand}}_N(i_2, \href{../exec/numerics.html#op-inot}{\mathrm{inot}}_N(i_3))) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-iabs}{\mathrm{iabs}}_N(i)\)

    +
      +

    • Let \(j\) be the signed interpretation of \(i\).

      • +

    • If \(j\) greater than or equal to \(0\), then return \(i\).

      • +

    • Else return the negation of j, modulo \(2^N\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-iabs}{\mathrm{iabs}}_N(i) &=& i & (\mathrel{\mbox{if}} \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i) \ge 0) \\ +\href{../exec/numerics.html#op-iabs}{\mathrm{iabs}}_N(i) &=& -\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i) \mathbin{\mathrm{mod}} 2^N & (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ineg}{\mathrm{ineg}}_N(i)\)

    +
      +

    • Return the result of negating \(i\), modulo \(2^N\).

      • +
    +
    +\[\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ineg}{\mathrm{ineg}}_N(i) &=& (2^N - i) \mathbin{\mathrm{mod}} 2^N +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-imin-u}{\mathrm{imin\_u}}_N(i_1, i_2)\)

    +
      +

    • Return \(i_1\) if \(\href{../exec/numerics.html#op-ilt-u}{\mathrm{ilt\_u}}_N(i_1, i_2)\) is \(1\), return \(i_2\) otherwise.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-imin-u}{\mathrm{imin\_u}}_N(i_1, i_2) &=& i_1 & (\mathrel{\mbox{if}} \href{../exec/numerics.html#op-ilt-u}{\mathrm{ilt\_u}}_N(i_1, i_2) = 1)\\ +\href{../exec/numerics.html#op-imin-u}{\mathrm{imin\_u}}_N(i_1, i_2) &=& i_2 & (\mathrel{\mbox{otherwise}}) +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-imin-s}{\mathrm{imin\_s}}_N(i_1, i_2)\)

    +
      +

    • Return \(i_1\) if \(\href{../exec/numerics.html#op-ilt-s}{\mathrm{ilt\_s}}_N(i_1, i_2)\) is \(1\), return \(i_2\) otherwise.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-imin-u}{\mathrm{imin\_u}}_N(i_1, i_2) &=& i_1 & (\mathrel{\mbox{if}} \href{../exec/numerics.html#op-ilt-s}{\mathrm{ilt\_s}}_N(i_1, i_2) = 1)\\ +\href{../exec/numerics.html#op-imin-u}{\mathrm{imin\_u}}_N(i_1, i_2) &=& i_2 & (\mathrel{\mbox{otherwise}}) +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-imax-u}{\mathrm{imax\_u}}_N(i_1, i_2)\)

    +
      +

    • Return \(i_1\) if \(\href{../exec/numerics.html#op-igt-u}{\mathrm{igt\_u}}_N(i_1, i_2)\) is \(1\), return \(i_2\) otherwise.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-imin-u}{\mathrm{imin\_u}}_N(i_1, i_2) &=& i_1 & (\mathrel{\mbox{if}} \href{../exec/numerics.html#op-igt-u}{\mathrm{igt\_u}}_N(i_1, i_2) = 1)\\ +\href{../exec/numerics.html#op-imin-u}{\mathrm{imin\_u}}_N(i_1, i_2) &=& i_2 & (\mathrel{\mbox{otherwise}}) +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-imax-s}{\mathrm{imax\_s}}_N(i_1, i_2)\)

    +
      +

    • Return \(i_1\) if \(\href{../exec/numerics.html#op-igt-s}{\mathrm{igt\_s}}_N(i_1, i_2)\) is \(1\), return \(i_2\) otherwise.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-imin-u}{\mathrm{imin\_u}}_N(i_1, i_2) &=& i_1 & (\mathrel{\mbox{if}} \href{../exec/numerics.html#op-igt-s}{\mathrm{igt\_s}}_N(i_1, i_2) = 1)\\ +\href{../exec/numerics.html#op-imin-u}{\mathrm{imin\_u}}_N(i_1, i_2) &=& i_2 & (\mathrel{\mbox{otherwise}}) +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-iaddsat-u}{\mathrm{iaddsat\_u}}_N(i_1, i_2)\)

    +
      +

    • Let \(i\) be the result of adding \(i_1\) and \(i_2\).

      • +

    • Return \(\href{../exec/numerics.html#aux-sat-u}{\mathrm{sat}^{\mathsf{u}}}_N(i)\).

      • +
    +
    +\[\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-iaddsat-u}{\mathrm{iaddsat\_u}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-sat-u}{\mathrm{sat}^{\mathsf{u}}}_N(i_1 + i_2) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-iaddsat-s}{\mathrm{iaddsat\_s}}_N(i_1, i_2)\)

    +
      +

    • Let \(j_1\) be the signed interpretation of \(i_1\)

      • +

    • Let \(j_2\) be the signed interpretation of \(i_2\)

      • +

    • Let \(j\) be the result of adding \(j_1\) and \(j_2\).

      • +

    • Return \(\href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(j)\).

      • +
    +
    +\[\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-iaddsat-s}{\mathrm{iaddsat\_s}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_1) + \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_2)) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-isubsat-u}{\mathrm{isubsat\_u}}_N(i_1, i_2)\)

    +
      +

    • Let \(i\) be the result of subtracting \(i_2\) from \(i_1\).

      • +

    • Return \(\href{../exec/numerics.html#aux-sat-u}{\mathrm{sat}^{\mathsf{u}}}_N(i)\).

      • +
    +
    +\[\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-isubsat-u}{\mathrm{isubsat\_u}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-sat-u}{\mathrm{sat}^{\mathsf{u}}}_N(i_1 - i_2) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-isubsat-s}{\mathrm{isubsat\_s}}_N(i_1, i_2)\)

    +
      +

    • Let \(j_1\) be the signed interpretation of \(i_1\)

      • +

    • Let \(j_2\) be the signed interpretation of \(i_2\)

      • +

    • Let \(j\) be the result of subtracting \(j_2\) from \(j_1\).

      • +

    • Return \(\href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(j)\).

      • +
    +
    +\[\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-isubsat-s}{\mathrm{isubsat\_s}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_1) - \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N(i_2)) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-iavgr-u}{\mathrm{iavgr\_u}}_N(i_1, i_2)\)

    +
      +

    • Let \(j\) be the result of adding \(i_1\), \(i_2\), and \(1\).

      • +

    • Return the result of dividing \(j\) by \(2\), truncated toward zero.

      • +
    +
    +\[\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-iavgr-u}{\mathrm{iavgr\_u}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}((i_1 + i_2 + 1) / 2) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-iq15mulrsat-s}{\mathrm{iq15mulrsat\_s}}_N(i_1, i_2)\)

    +
      +

    • Return the result of \(\href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(\href{../exec/numerics.html#op-ishr-s}{\mathrm{ishr\_s}}_N(i_1 \cdot i_2 + 2^{14}, 15))\).

      • +
    +
    +\[\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-iq15mulrsat-s}{\mathrm{iq15mulrsat\_s}}_N(i_1, i_2) &=& \href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(\href{../exec/numerics.html#op-ishr-s}{\mathrm{ishr\_s}}_N(i_1 \cdot i_2 + 2^{14}, 15)) +\end{array}\]
    +
    +
    +
    +

    Floating-Point Operations

    +

    Floating-point arithmetic follows the IEEE 754-2019 standard, +with the following qualifications:

    +
      +

    • All operators use round-to-nearest ties-to-even, except where otherwise specified. +Non-default directed rounding attributes are not supported.

      • +

    • Following the recommendation that operators propagate NaN payloads from their operands is permitted but not required.

      • +

    • All operators use “non-stop” mode, and floating-point exceptions are not otherwise observable. +In particular, neither alternate floating-point exception handling attributes nor operators on status flags are supported. +There is no observable difference between quiet and signalling NaNs.

      • +
    +
    +

    Note

    +

    Some of these limitations may be lifted in future versions of WebAssembly.

    +
    +
    +

    Rounding

    +

    Rounding always is round-to-nearest ties-to-even, in correspondence with IEEE 754-2019 (Section 4.3.1).

    +

    An exact floating-point number is a rational number that is exactly representable as a floating-point number of given bit width \(N\).

    +

    A limit number for a given floating-point bit width \(N\) is a positive or negative number whose magnitude is the smallest power of \(2\) that is not exactly representable as a floating-point number of width \(N\) (that magnitude is \(2^{128}\) for \(N = 32\) and \(2^{1024}\) for \(N = 64\)).

    +

    A candidate number is either an exact floating-point number or a positive or negative limit number for the given bit width \(N\).

    +

    A candidate pair is a pair \(z_1,z_2\) of candidate numbers, such that no candidate number exists that lies between the two.

    +

    A real number \(r\) is converted to a floating-point value of bit width \(N\) as follows:

    +
      +

    • If \(r\) is \(0\), then return \(+0\).

      • +

    • Else if \(r\) is an exact floating-point number, then return \(r\).

      • +

    • Else if \(r\) greater than or equal to the positive limit, then return \(+\infty\).

      • +

    • Else if \(r\) is less than or equal to the negative limit, then return \(-\infty\).

      • +

    • Else if \(z_1\) and \(z_2\) are a candidate pair such that \(z_1 < r < z_2\), then:

      +
        +

      • If \(|r - z_1| < |r - z_2|\), then let \(z\) be \(z_1\).

        • +

      • Else if \(|r - z_1| > |r - z_2|\), then let \(z\) be \(z_2\).

        • +

      • Else if \(|r - z_1| = |r - z_2|\) and the significand of \(z_1\) is even, then let \(z\) be \(z_1\).

        • +

      • Else, let \(z\) be \(z_2\).

        • +
      +
      • +

    • If \(z\) is \(0\), then:

      +
        +

      • If \(r < 0\), then return \(-0\).

        • +

      • Else, return \(+0\).

        • +
      +
      • +

    • Else if \(z\) is a limit number, then:

      +
        +

      • If \(r < 0\), then return \(-\infty\).

        • +

      • Else, return \(+\infty\).

        • +
      +
      • +

    • Else, return \(z\).

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(0) &=& +0 \\ +\href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(r) &=& r & (\mathrel{\mbox{if}} r \in \mathrm{exact}_N) \\ +\href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(r) &=& +\infty & (\mathrel{\mbox{if}} r \geq +\mathrm{limit}_N) \\ +\href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(r) &=& -\infty & (\mathrel{\mbox{if}} r \leq -\mathrm{limit}_N) \\ +\href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(r) &=& \mathrm{closest}_N(r, z_1, z_2) & (\mathrel{\mbox{if}} z_1 < r < z_2 \wedge (z_1,z_2) \in \mathrm{candidatepair}_N) \\[1ex] +\mathrm{closest}_N(r, z_1, z_2) &=& \mathrm{rectify}_N(r, z_1) & (\mathrel{\mbox{if}} |r-z_1|<|r-z_2|) \\ +\mathrm{closest}_N(r, z_1, z_2) &=& \mathrm{rectify}_N(r, z_2) & (\mathrel{\mbox{if}} |r-z_1|>|r-z_2|) \\ +\mathrm{closest}_N(r, z_1, z_2) &=& \mathrm{rectify}_N(r, z_1) & (\mathrel{\mbox{if}} |r-z_1|=|r-z_2| \wedge \mathrm{even}_N(z_1)) \\ +\mathrm{closest}_N(r, z_1, z_2) &=& \mathrm{rectify}_N(r, z_2) & (\mathrel{\mbox{if}} |r-z_1|=|r-z_2| \wedge \mathrm{even}_N(z_2)) \\[1ex] +\mathrm{rectify}_N(r, \pm \mathrm{limit}_N) &=& \pm \infty \\ +\mathrm{rectify}_N(r, 0) &=& +0 \qquad (r \geq 0) \\ +\mathrm{rectify}_N(r, 0) &=& -0 \qquad (r < 0) \\ +\mathrm{rectify}_N(r, z) &=& z \\ +\end{array}\end{split}\]
    +

    where:

    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\mathrm{exact}_N &=& \href{../syntax/values.html#syntax-float}{\mathit{f}N} \cap \mathbb{Q} \\ +\mathrm{limit}_N &=& 2^{2^{\href{../syntax/values.html#aux-exponent}{\mathrm{expon}}(N)-1}} \\ +\mathrm{candidate}_N &=& \mathrm{exact}_N \cup \{+\mathrm{limit}_N, -\mathrm{limit}_N\} \\ +\mathrm{candidatepair}_N &=& \{ (z_1, z_2) \in \mathrm{candidate}_N^2 ~|~ z_1 < z_2 \wedge \forall z \in \mathrm{candidate}_N, z \leq z_1 \vee z \geq z_2\} \\[1ex] +\mathrm{even}_N((d + m\cdot 2^{-M}) \cdot 2^e) &\Leftrightarrow& m \mathbin{\mathrm{mod}} 2 = 0 \\ +\mathrm{even}_N(\pm \mathrm{limit}_N) &\Leftrightarrow& \mathrm{true} \\ +\end{array}\end{split}\]
    +
    +
    +

    NaN Propagation

    +

    When the result of a floating-point operator other than \(\href{../exec/numerics.html#op-fneg}{\mathrm{fneg}}\), \(\href{../exec/numerics.html#op-fabs}{\mathrm{fabs}}\), or \(\href{../exec/numerics.html#op-fcopysign}{\mathrm{fcopysign}}\) is a NaN, +then its sign is non-deterministic and the payload is computed as follows:

    +
      +

    • If the payload of all NaN inputs to the operator is canonical (including the case that there are no NaN inputs), then the payload of the output is canonical as well.

      • +

    • Otherwise the payload is picked non-deterministically among all arithmetic NaNs; that is, its most significant bit is \(1\) and all others are unspecified.

      • +
    +

    This non-deterministic result is expressed by the following auxiliary function producing a set of allowed outputs from a set of inputs:

    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z^\ast\} &=& \{ + \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), - \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n) ~|~ n = \href{../syntax/values.html#aux-canon}{\mathrm{canon}}_N \} + & (\mathrel{\mbox{if}} \forall \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n) \in z^\ast,~ n = \href{../syntax/values.html#aux-canon}{\mathrm{canon}}_N) \\ +\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z^\ast\} &=& \{ + \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), - \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n) ~|~ n \geq \href{../syntax/values.html#aux-canon}{\mathrm{canon}}_N \} + & (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(z_1, z_2)\)

    +
      +

    • If either \(z_1\) or \(z_2\) is a NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z_1, z_2\}\).

      • +

    • Else if both \(z_1\) and \(z_2\) are infinities of opposite signs, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\}\).

      • +

    • Else if both \(z_1\) and \(z_2\) are infinities of equal sign, then return that infinity.

      • +

    • Else if one of \(z_1\) or \(z_2\) is an infinity, then return that infinity.

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes of opposite sign, then return positive zero.

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes of equal sign, then return that zero.

      • +

    • Else if one of \(z_1\) or \(z_2\) is a zero, then return the other operand.

      • +

    • Else if both \(z_1\) and \(z_2\) are values with the same magnitude but opposite signs, then return positive zero.

      • +

    • Else return the result of adding \(z_1\) and \(z_2\), rounded to the nearest representable value.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2\} \\ +\href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(z_1, \pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_1\} \\ +\href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(\pm \infty, \mp \infty) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} \\ +\href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(\pm \infty, \pm \infty) &=& \pm \infty \\ +\href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(z_1, \pm \infty) &=& \pm \infty \\ +\href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(\pm \infty, z_2) &=& \pm \infty \\ +\href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(\pm 0, \mp 0) &=& +0 \\ +\href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(\pm 0, \pm 0) &=& \pm 0 \\ +\href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(z_1, \pm 0) &=& z_1 \\ +\href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(\pm 0, z_2) &=& z_2 \\ +\href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(\pm q, \mp q) &=& +0 \\ +\href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(z_1, z_2) &=& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(z_1 + z_2) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(z_1, z_2)\)

    +
      +

    • If either \(z_1\) or \(z_2\) is a NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z_1, z_2\}\).

      • +

    • Else if both \(z_1\) and \(z_2\) are infinities of equal signs, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\}\).

      • +

    • Else if both \(z_1\) and \(z_2\) are infinities of opposite sign, then return \(z_1\).

      • +

    • Else if \(z_1\) is an infinity, then return that infinity.

      • +

    • Else if \(z_2\) is an infinity, then return that infinity negated.

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes of equal sign, then return positive zero.

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes of opposite sign, then return \(z_1\).

      • +

    • Else if \(z_2\) is a zero, then return \(z_1\).

      • +

    • Else if \(z_1\) is a zero, then return \(z_2\) negated.

      • +

    • Else if both \(z_1\) and \(z_2\) are the same value, then return positive zero.

      • +

    • Else return the result of subtracting \(z_2\) from \(z_1\), rounded to the nearest representable value.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2\} \\ +\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(z_1, \pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_1\} \\ +\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(\pm \infty, \pm \infty) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} \\ +\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(\pm \infty, \mp \infty) &=& \pm \infty \\ +\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(z_1, \pm \infty) &=& \mp \infty \\ +\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(\pm \infty, z_2) &=& \pm \infty \\ +\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(\pm 0, \pm 0) &=& +0 \\ +\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(\pm 0, \mp 0) &=& \pm 0 \\ +\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(z_1, \pm 0) &=& z_1 \\ +\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(\pm 0, \pm q_2) &=& \mp q_2 \\ +\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(\pm q, \pm q) &=& +0 \\ +\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(z_1, z_2) &=& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(z_1 - z_2) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    Up to the non-determinism regarding NaNs, it always holds that \(\href{../exec/numerics.html#op-fsub}{\mathrm{fsub}}_N(z_1, z_2) = \href{../exec/numerics.html#op-fadd}{\mathrm{fadd}}_N(z_1, \href{../exec/numerics.html#op-fneg}{\mathrm{fneg}}_N(z_2))\).

    +
    +
    +
    +

    \(\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(z_1, z_2)\)

    +
      +

    • If either \(z_1\) or \(z_2\) is a NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z_1, z_2\}\).

      • +

    • Else if one of \(z_1\) and \(z_2\) is a zero and the other an infinity, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\}\).

      • +

    • Else if both \(z_1\) and \(z_2\) are infinities of equal sign, then return positive infinity.

      • +

    • Else if both \(z_1\) and \(z_2\) are infinities of opposite sign, then return negative infinity.

      • +

    • Else if one of \(z_1\) or \(z_2\) is an infinity and the other a value with equal sign, then return positive infinity.

      • +

    • Else if one of \(z_1\) or \(z_2\) is an infinity and the other a value with opposite sign, then return negative infinity.

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes of equal sign, then return positive zero.

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes of opposite sign, then return negative zero.

      • +

    • Else return the result of multiplying \(z_1\) and \(z_2\), rounded to the nearest representable value.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2\} \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(z_1, \pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_1\} \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(\pm \infty, \pm 0) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(\pm \infty, \mp 0) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(\pm 0, \pm \infty) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(\pm 0, \mp \infty) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(\pm \infty, \pm \infty) &=& +\infty \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(\pm \infty, \mp \infty) &=& -\infty \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(\pm q_1, \pm \infty) &=& +\infty \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(\pm q_1, \mp \infty) &=& -\infty \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(\pm \infty, \pm q_2) &=& +\infty \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(\pm \infty, \mp q_2) &=& -\infty \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(\pm 0, \pm 0) &=& + 0 \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(\pm 0, \mp 0) &=& - 0 \\ +\href{../exec/numerics.html#op-fmul}{\mathrm{fmul}}_N(z_1, z_2) &=& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(z_1 \cdot z_2) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(z_1, z_2)\)

    +
      +

    • If either \(z_1\) or \(z_2\) is a NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z_1, z_2\}\).

      • +

    • Else if both \(z_1\) and \(z_2\) are infinities, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\}\).

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z_1, z_2\}\).

      • +

    • Else if \(z_1\) is an infinity and \(z_2\) a value with equal sign, then return positive infinity.

      • +

    • Else if \(z_1\) is an infinity and \(z_2\) a value with opposite sign, then return negative infinity.

      • +

    • Else if \(z_2\) is an infinity and \(z_1\) a value with equal sign, then return positive zero.

      • +

    • Else if \(z_2\) is an infinity and \(z_1\) a value with opposite sign, then return negative zero.

      • +

    • Else if \(z_1\) is a zero and \(z_2\) a value with equal sign, then return positive zero.

      • +

    • Else if \(z_1\) is a zero and \(z_2\) a value with opposite sign, then return negative zero.

      • +

    • Else if \(z_2\) is a zero and \(z_1\) a value with equal sign, then return positive infinity.

      • +

    • Else if \(z_2\) is a zero and \(z_1\) a value with opposite sign, then return negative infinity.

      • +

    • Else return the result of dividing \(z_1\) by \(z_2\), rounded to the nearest representable value.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2\} \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(z_1, \pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_1\} \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(\pm \infty, \pm \infty) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(\pm \infty, \mp \infty) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(\pm 0, \pm 0) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(\pm 0, \mp 0) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(\pm \infty, \pm q_2) &=& +\infty \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(\pm \infty, \mp q_2) &=& -\infty \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(\pm q_1, \pm \infty) &=& +0 \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(\pm q_1, \mp \infty) &=& -0 \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(\pm 0, \pm q_2) &=& +0 \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(\pm 0, \mp q_2) &=& -0 \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(\pm q_1, \pm 0) &=& +\infty \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(\pm q_1, \mp 0) &=& -\infty \\ +\href{../exec/numerics.html#op-fdiv}{\mathrm{fdiv}}_N(z_1, z_2) &=& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(z_1 / z_2) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fmin}{\mathrm{fmin}}_N(z_1, z_2)\)

    +
      +

    • If either \(z_1\) or \(z_2\) is a NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z_1, z_2\}\).

      • +

    • Else if one of \(z_1\) or \(z_2\) is a negative infinity, then return negative infinity.

      • +

    • Else if one of \(z_1\) or \(z_2\) is a positive infinity, then return the other value.

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes of opposite signs, then return negative zero.

      • +

    • Else return the smaller value of \(z_1\) and \(z_2\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fmin}{\mathrm{fmin}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2\} \\ +\href{../exec/numerics.html#op-fmin}{\mathrm{fmin}}_N(z_1, \pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_1\} \\ +\href{../exec/numerics.html#op-fmin}{\mathrm{fmin}}_N(+ \infty, z_2) &=& z_2 \\ +\href{../exec/numerics.html#op-fmin}{\mathrm{fmin}}_N(- \infty, z_2) &=& - \infty \\ +\href{../exec/numerics.html#op-fmin}{\mathrm{fmin}}_N(z_1, + \infty) &=& z_1 \\ +\href{../exec/numerics.html#op-fmin}{\mathrm{fmin}}_N(z_1, - \infty) &=& - \infty \\ +\href{../exec/numerics.html#op-fmin}{\mathrm{fmin}}_N(\pm 0, \mp 0) &=& -0 \\ +\href{../exec/numerics.html#op-fmin}{\mathrm{fmin}}_N(z_1, z_2) &=& z_1 & (\mathrel{\mbox{if}} z_1 \leq z_2) \\ +\href{../exec/numerics.html#op-fmin}{\mathrm{fmin}}_N(z_1, z_2) &=& z_2 & (\mathrel{\mbox{if}} z_2 \leq z_1) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fmax}{\mathrm{fmax}}_N(z_1, z_2)\)

    +
      +

    • If either \(z_1\) or \(z_2\) is a NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z_1, z_2\}\).

      • +

    • Else if one of \(z_1\) or \(z_2\) is a positive infinity, then return positive infinity.

      • +

    • Else if one of \(z_1\) or \(z_2\) is a negative infinity, then return the other value.

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes of opposite signs, then return positive zero.

      • +

    • Else return the larger value of \(z_1\) and \(z_2\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fmax}{\mathrm{fmax}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2\} \\ +\href{../exec/numerics.html#op-fmax}{\mathrm{fmax}}_N(z_1, \pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_1\} \\ +\href{../exec/numerics.html#op-fmax}{\mathrm{fmax}}_N(+ \infty, z_2) &=& + \infty \\ +\href{../exec/numerics.html#op-fmax}{\mathrm{fmax}}_N(- \infty, z_2) &=& z_2 \\ +\href{../exec/numerics.html#op-fmax}{\mathrm{fmax}}_N(z_1, + \infty) &=& + \infty \\ +\href{../exec/numerics.html#op-fmax}{\mathrm{fmax}}_N(z_1, - \infty) &=& z_1 \\ +\href{../exec/numerics.html#op-fmax}{\mathrm{fmax}}_N(\pm 0, \mp 0) &=& +0 \\ +\href{../exec/numerics.html#op-fmax}{\mathrm{fmax}}_N(z_1, z_2) &=& z_1 & (\mathrel{\mbox{if}} z_1 \geq z_2) \\ +\href{../exec/numerics.html#op-fmax}{\mathrm{fmax}}_N(z_1, z_2) &=& z_2 & (\mathrel{\mbox{if}} z_2 \geq z_1) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fcopysign}{\mathrm{fcopysign}}_N(z_1, z_2)\)

    +
      +

    • If \(z_1\) and \(z_2\) have the same sign, then return \(z_1\).

      • +

    • Else return \(z_1\) with negated sign.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fcopysign}{\mathrm{fcopysign}}_N(\pm p_1, \pm p_2) &=& \pm p_1 \\ +\href{../exec/numerics.html#op-fcopysign}{\mathrm{fcopysign}}_N(\pm p_1, \mp p_2) &=& \mp p_1 \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fabs}{\mathrm{fabs}}_N(z)\)

    +
      +

    • If \(z\) is a NaN, then return \(z\) with positive sign.

      • +

    • Else if \(z\) is an infinity, then return positive infinity.

      • +

    • Else if \(z\) is a zero, then return positive zero.

      • +

    • Else if \(z\) is a positive value, then \(z\).

      • +

    • Else return \(z\) negated.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fabs}{\mathrm{fabs}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& +\href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n) \\ +\href{../exec/numerics.html#op-fabs}{\mathrm{fabs}}_N(\pm \infty) &=& +\infty \\ +\href{../exec/numerics.html#op-fabs}{\mathrm{fabs}}_N(\pm 0) &=& +0 \\ +\href{../exec/numerics.html#op-fabs}{\mathrm{fabs}}_N(\pm q) &=& +q \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fneg}{\mathrm{fneg}}_N(z)\)

    +
      +

    • If \(z\) is a NaN, then return \(z\) with negated sign.

      • +

    • Else if \(z\) is an infinity, then return that infinity negated.

      • +

    • Else if \(z\) is a zero, then return that zero negated.

      • +

    • Else return \(z\) negated.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fneg}{\mathrm{fneg}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \mp \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n) \\ +\href{../exec/numerics.html#op-fneg}{\mathrm{fneg}}_N(\pm \infty) &=& \mp \infty \\ +\href{../exec/numerics.html#op-fneg}{\mathrm{fneg}}_N(\pm 0) &=& \mp 0 \\ +\href{../exec/numerics.html#op-fneg}{\mathrm{fneg}}_N(\pm q) &=& \mp q \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fsqrt}{\mathrm{fsqrt}}_N(z)\)

    +
      +

    • If \(z\) is a NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z\}\).

      • +

    • Else if \(z\) is negative infinity, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\}\).

      • +

    • Else if \(z\) is positive infinity, then return positive infinity.

      • +

    • Else if \(z\) is a zero, then return that zero.

      • +

    • Else if \(z\) has a negative sign, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\}\).

      • +

    • Else return the square root of \(z\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fsqrt}{\mathrm{fsqrt}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)\} \\ +\href{../exec/numerics.html#op-fsqrt}{\mathrm{fsqrt}}_N(- \infty) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} \\ +\href{../exec/numerics.html#op-fsqrt}{\mathrm{fsqrt}}_N(+ \infty) &=& + \infty \\ +\href{../exec/numerics.html#op-fsqrt}{\mathrm{fsqrt}}_N(\pm 0) &=& \pm 0 \\ +\href{../exec/numerics.html#op-fsqrt}{\mathrm{fsqrt}}_N(- q) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} \\ +\href{../exec/numerics.html#op-fsqrt}{\mathrm{fsqrt}}_N(+ q) &=& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N\left(\sqrt{q}\right) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fceil}{\mathrm{fceil}}_N(z)\)

    +
      +

    • If \(z\) is a NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z\}\).

      • +

    • Else if \(z\) is an infinity, then return \(z\).

      • +

    • Else if \(z\) is a zero, then return \(z\).

      • +

    • Else if \(z\) is smaller than \(0\) but greater than \(-1\), then return negative zero.

      • +

    • Else return the smallest integral value that is not smaller than \(z\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fceil}{\mathrm{fceil}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)\} \\ +\href{../exec/numerics.html#op-fceil}{\mathrm{fceil}}_N(\pm \infty) &=& \pm \infty \\ +\href{../exec/numerics.html#op-fceil}{\mathrm{fceil}}_N(\pm 0) &=& \pm 0 \\ +\href{../exec/numerics.html#op-fceil}{\mathrm{fceil}}_N(- q) &=& -0 & (\mathrel{\mbox{if}} -1 < -q < 0) \\ +\href{../exec/numerics.html#op-fceil}{\mathrm{fceil}}_N(\pm q) &=& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(i) & (\mathrel{\mbox{if}} \pm q \leq i < \pm q + 1) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ffloor}{\mathrm{ffloor}}_N(z)\)

    +
      +

    • If \(z\) is a NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z\}\).

      • +

    • Else if \(z\) is an infinity, then return \(z\).

      • +

    • Else if \(z\) is a zero, then return \(z\).

      • +

    • Else if \(z\) is greater than \(0\) but smaller than \(1\), then return positive zero.

      • +

    • Else return the largest integral value that is not larger than \(z\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ffloor}{\mathrm{ffloor}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)\} \\ +\href{../exec/numerics.html#op-ffloor}{\mathrm{ffloor}}_N(\pm \infty) &=& \pm \infty \\ +\href{../exec/numerics.html#op-ffloor}{\mathrm{ffloor}}_N(\pm 0) &=& \pm 0 \\ +\href{../exec/numerics.html#op-ffloor}{\mathrm{ffloor}}_N(+ q) &=& +0 & (\mathrel{\mbox{if}} 0 < +q < 1) \\ +\href{../exec/numerics.html#op-ffloor}{\mathrm{ffloor}}_N(\pm q) &=& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(i) & (\mathrel{\mbox{if}} \pm q - 1 < i \leq \pm q) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-ftrunc}{\mathrm{ftrunc}}_N(z)\)

    +
      +

    • If \(z\) is a NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z\}\).

      • +

    • Else if \(z\) is an infinity, then return \(z\).

      • +

    • Else if \(z\) is a zero, then return \(z\).

      • +

    • Else if \(z\) is greater than \(0\) but smaller than \(1\), then return positive zero.

      • +

    • Else if \(z\) is smaller than \(0\) but greater than \(-1\), then return negative zero.

      • +

    • Else return the integral value with the same sign as \(z\) and the largest magnitude that is not larger than the magnitude of \(z\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-ftrunc}{\mathrm{ftrunc}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)\} \\ +\href{../exec/numerics.html#op-ftrunc}{\mathrm{ftrunc}}_N(\pm \infty) &=& \pm \infty \\ +\href{../exec/numerics.html#op-ftrunc}{\mathrm{ftrunc}}_N(\pm 0) &=& \pm 0 \\ +\href{../exec/numerics.html#op-ftrunc}{\mathrm{ftrunc}}_N(+ q) &=& +0 & (\mathrel{\mbox{if}} 0 < +q < 1) \\ +\href{../exec/numerics.html#op-ftrunc}{\mathrm{ftrunc}}_N(- q) &=& -0 & (\mathrel{\mbox{if}} -1 < -q < 0) \\ +\href{../exec/numerics.html#op-ftrunc}{\mathrm{ftrunc}}_N(\pm q) &=& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(\pm i) & (\mathrel{\mbox{if}} +q - 1 < i \leq +q) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fnearest}{\mathrm{fnearest}}_N(z)\)

    +
      +

    • If \(z\) is a NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{z\}\).

      • +

    • Else if \(z\) is an infinity, then return \(z\).

      • +

    • Else if \(z\) is a zero, then return \(z\).

      • +

    • Else if \(z\) is greater than \(0\) but smaller than or equal to \(0.5\), then return positive zero.

      • +

    • Else if \(z\) is smaller than \(0\) but greater than or equal to \(-0.5\), then return negative zero.

      • +

    • Else return the integral value that is nearest to \(z\); if two values are equally near, return the even one.

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fnearest}{\mathrm{fnearest}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)\} \\ +\href{../exec/numerics.html#op-fnearest}{\mathrm{fnearest}}_N(\pm \infty) &=& \pm \infty \\ +\href{../exec/numerics.html#op-fnearest}{\mathrm{fnearest}}_N(\pm 0) &=& \pm 0 \\ +\href{../exec/numerics.html#op-fnearest}{\mathrm{fnearest}}_N(+ q) &=& +0 & (\mathrel{\mbox{if}} 0 < +q \leq 0.5) \\ +\href{../exec/numerics.html#op-fnearest}{\mathrm{fnearest}}_N(- q) &=& -0 & (\mathrel{\mbox{if}} -0.5 \leq -q < 0) \\ +\href{../exec/numerics.html#op-fnearest}{\mathrm{fnearest}}_N(\pm q) &=& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(\pm i) & (\mathrel{\mbox{if}} |i - q| < 0.5) \\ +\href{../exec/numerics.html#op-fnearest}{\mathrm{fnearest}}_N(\pm q) &=& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(\pm i) & (\mathrel{\mbox{if}} |i - q| = 0.5 \wedge i~\mbox{even}) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-feq}{\mathrm{feq}}_N(z_1, z_2)\)

    +
      +

    • If either \(z_1\) or \(z_2\) is a NaN, then return \(0\).

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes, then return \(1\).

      • +

    • Else if both \(z_1\) and \(z_2\) are the same value, then return \(1\).

      • +

    • Else return \(0\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-feq}{\mathrm{feq}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2) &=& 0 \\ +\href{../exec/numerics.html#op-feq}{\mathrm{feq}}_N(z_1, \pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& 0 \\ +\href{../exec/numerics.html#op-feq}{\mathrm{feq}}_N(\pm 0, \mp 0) &=& 1 \\ +\href{../exec/numerics.html#op-feq}{\mathrm{feq}}_N(z_1, z_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(z_1 = z_2) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fne}{\mathrm{fne}}_N(z_1, z_2)\)

    +
      +

    • If either \(z_1\) or \(z_2\) is a NaN, then return \(1\).

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes, then return \(0\).

      • +

    • Else if both \(z_1\) and \(z_2\) are the same value, then return \(0\).

      • +

    • Else return \(1\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fne}{\mathrm{fne}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2) &=& 1 \\ +\href{../exec/numerics.html#op-fne}{\mathrm{fne}}_N(z_1, \pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& 1 \\ +\href{../exec/numerics.html#op-fne}{\mathrm{fne}}_N(\pm 0, \mp 0) &=& 0 \\ +\href{../exec/numerics.html#op-fne}{\mathrm{fne}}_N(z_1, z_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(z_1 \neq z_2) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-flt}{\mathrm{flt}}_N(z_1, z_2)\)

    +
      +

    • If either \(z_1\) or \(z_2\) is a NaN, then return \(0\).

      • +

    • Else if \(z_1\) and \(z_2\) are the same value, then return \(0\).

      • +

    • Else if \(z_1\) is positive infinity, then return \(0\).

      • +

    • Else if \(z_1\) is negative infinity, then return \(1\).

      • +

    • Else if \(z_2\) is positive infinity, then return \(1\).

      • +

    • Else if \(z_2\) is negative infinity, then return \(0\).

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes, then return \(0\).

      • +

    • Else if \(z_1\) is smaller than \(z_2\), then return \(1\).

      • +

    • Else return \(0\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-flt}{\mathrm{flt}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2) &=& 0 \\ +\href{../exec/numerics.html#op-flt}{\mathrm{flt}}_N(z_1, \pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& 0 \\ +\href{../exec/numerics.html#op-flt}{\mathrm{flt}}_N(z, z) &=& 0 \\ +\href{../exec/numerics.html#op-flt}{\mathrm{flt}}_N(+ \infty, z_2) &=& 0 \\ +\href{../exec/numerics.html#op-flt}{\mathrm{flt}}_N(- \infty, z_2) &=& 1 \\ +\href{../exec/numerics.html#op-flt}{\mathrm{flt}}_N(z_1, + \infty) &=& 1 \\ +\href{../exec/numerics.html#op-flt}{\mathrm{flt}}_N(z_1, - \infty) &=& 0 \\ +\href{../exec/numerics.html#op-flt}{\mathrm{flt}}_N(\pm 0, \mp 0) &=& 0 \\ +\href{../exec/numerics.html#op-flt}{\mathrm{flt}}_N(z_1, z_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(z_1 < z_2) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fgt}{\mathrm{fgt}}_N(z_1, z_2)\)

    +
      +

    • If either \(z_1\) or \(z_2\) is a NaN, then return \(0\).

      • +

    • Else if \(z_1\) and \(z_2\) are the same value, then return \(0\).

      • +

    • Else if \(z_1\) is positive infinity, then return \(1\).

      • +

    • Else if \(z_1\) is negative infinity, then return \(0\).

      • +

    • Else if \(z_2\) is positive infinity, then return \(0\).

      • +

    • Else if \(z_2\) is negative infinity, then return \(1\).

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes, then return \(0\).

      • +

    • Else if \(z_1\) is larger than \(z_2\), then return \(1\).

      • +

    • Else return \(0\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fgt}{\mathrm{fgt}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2) &=& 0 \\ +\href{../exec/numerics.html#op-fgt}{\mathrm{fgt}}_N(z_1, \pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& 0 \\ +\href{../exec/numerics.html#op-fgt}{\mathrm{fgt}}_N(z, z) &=& 0 \\ +\href{../exec/numerics.html#op-fgt}{\mathrm{fgt}}_N(+ \infty, z_2) &=& 1 \\ +\href{../exec/numerics.html#op-fgt}{\mathrm{fgt}}_N(- \infty, z_2) &=& 0 \\ +\href{../exec/numerics.html#op-fgt}{\mathrm{fgt}}_N(z_1, + \infty) &=& 0 \\ +\href{../exec/numerics.html#op-fgt}{\mathrm{fgt}}_N(z_1, - \infty) &=& 1 \\ +\href{../exec/numerics.html#op-fgt}{\mathrm{fgt}}_N(\pm 0, \mp 0) &=& 0 \\ +\href{../exec/numerics.html#op-fgt}{\mathrm{fgt}}_N(z_1, z_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(z_1 > z_2) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fle}{\mathrm{fle}}_N(z_1, z_2)\)

    +
      +

    • If either \(z_1\) or \(z_2\) is a NaN, then return \(0\).

      • +

    • Else if \(z_1\) and \(z_2\) are the same value, then return \(1\).

      • +

    • Else if \(z_1\) is positive infinity, then return \(0\).

      • +

    • Else if \(z_1\) is negative infinity, then return \(1\).

      • +

    • Else if \(z_2\) is positive infinity, then return \(1\).

      • +

    • Else if \(z_2\) is negative infinity, then return \(0\).

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes, then return \(1\).

      • +

    • Else if \(z_1\) is smaller than or equal to \(z_2\), then return \(1\).

      • +

    • Else return \(0\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fle}{\mathrm{fle}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2) &=& 0 \\ +\href{../exec/numerics.html#op-fle}{\mathrm{fle}}_N(z_1, \pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& 0 \\ +\href{../exec/numerics.html#op-fle}{\mathrm{fle}}_N(z, z) &=& 1 \\ +\href{../exec/numerics.html#op-fle}{\mathrm{fle}}_N(+ \infty, z_2) &=& 0 \\ +\href{../exec/numerics.html#op-fle}{\mathrm{fle}}_N(- \infty, z_2) &=& 1 \\ +\href{../exec/numerics.html#op-fle}{\mathrm{fle}}_N(z_1, + \infty) &=& 1 \\ +\href{../exec/numerics.html#op-fle}{\mathrm{fle}}_N(z_1, - \infty) &=& 0 \\ +\href{../exec/numerics.html#op-fle}{\mathrm{fle}}_N(\pm 0, \mp 0) &=& 1 \\ +\href{../exec/numerics.html#op-fle}{\mathrm{fle}}_N(z_1, z_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(z_1 \leq z_2) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fge}{\mathrm{fge}}_N(z_1, z_2)\)

    +
      +

    • If either \(z_1\) or \(z_2\) is a NaN, then return \(0\).

      • +

    • Else if \(z_1\) and \(z_2\) are the same value, then return \(1\).

      • +

    • Else if \(z_1\) is positive infinity, then return \(1\).

      • +

    • Else if \(z_1\) is negative infinity, then return \(0\).

      • +

    • Else if \(z_2\) is positive infinity, then return \(0\).

      • +

    • Else if \(z_2\) is negative infinity, then return \(1\).

      • +

    • Else if both \(z_1\) and \(z_2\) are zeroes, then return \(1\).

      • +

    • Else if \(z_1\) is smaller than or equal to \(z_2\), then return \(1\).

      • +

    • Else return \(0\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fge}{\mathrm{fge}}_N(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n), z_2) &=& 0 \\ +\href{../exec/numerics.html#op-fge}{\mathrm{fge}}_N(z_1, \pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& 0 \\ +\href{../exec/numerics.html#op-fge}{\mathrm{fge}}_N(z, z) &=& 1 \\ +\href{../exec/numerics.html#op-fge}{\mathrm{fge}}_N(+ \infty, z_2) &=& 1 \\ +\href{../exec/numerics.html#op-fge}{\mathrm{fge}}_N(- \infty, z_2) &=& 0 \\ +\href{../exec/numerics.html#op-fge}{\mathrm{fge}}_N(z_1, + \infty) &=& 0 \\ +\href{../exec/numerics.html#op-fge}{\mathrm{fge}}_N(z_1, - \infty) &=& 1 \\ +\href{../exec/numerics.html#op-fge}{\mathrm{fge}}_N(\pm 0, \mp 0) &=& 1 \\ +\href{../exec/numerics.html#op-fge}{\mathrm{fge}}_N(z_1, z_2) &=& \href{../exec/numerics.html#aux-bool}{\mathrm{bool}}(z_1 \geq z_2) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fpmin}{\mathrm{fpmin}}_N(z_1, z_2)\)

    +
      +

    • If \(z_2\) is less than \(z_1\) then return \(z_2\).

      • +

    • Else return \(z_1\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fpmin}{\mathrm{fpmin}}_N(z_1, z_2) &=& z_2 & (\mathrel{\mbox{if}} \href{../exec/numerics.html#op-flt}{\mathrm{flt}}_N(z_2, z_1) = 1) \\ +\href{../exec/numerics.html#op-fpmin}{\mathrm{fpmin}}_N(z_1, z_2) &=& z_1 & (\mathrel{\mbox{otherwise}}) +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-fpmax}{\mathrm{fpmax}}_N(z_1, z_2)\)

    +
      +

    • If \(z_1\) is less than \(z_2\) then return \(z_2\).

      • +

    • Else return \(z_1\).

      • +
    +
    +\[\begin{split}\begin{array}{@{}lcll} +\href{../exec/numerics.html#op-fpmax}{\mathrm{fpmax}}_N(z_1, z_2) &=& z_2 & (\mathrel{\mbox{if}} \href{../exec/numerics.html#op-flt}{\mathrm{flt}}_N(z_1, z_2) = 1) \\ +\href{../exec/numerics.html#op-fpmax}{\mathrm{fpmax}}_N(z_1, z_2) &=& z_1 & (\mathrel{\mbox{otherwise}}) +\end{array}\end{split}\]
    +
    +
    +
    +

    Conversions

    +
    +

    \(\href{../exec/numerics.html#op-extend-u}{\mathrm{extend}^{\mathsf{u}}}_{M,N}(i)\)

    +
      +

    • Return \(i\).

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-extend-u}{\mathrm{extend}^{\mathsf{u}}}_{M,N}(i) &=& i \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    In the abstract syntax, unsigned extension just reinterprets the same value.

    +
    +
    +
    +

    \(\href{../exec/numerics.html#op-extend-s}{\mathrm{extend}^{\mathsf{s}}}_{M,N}(i)\)

    +
      +

    • Let \(j\) be the signed interpretation of \(i\) of size \(M\).

      • +

    • Return the two’s complement of \(j\) relative to size \(N\).

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-extend-s}{\mathrm{extend}^{\mathsf{s}}}_{M,N}(i) &=& \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_N^{-1}(\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_M(i)) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-wrap}{\mathrm{wrap}}_{M,N}(i)\)

    +
      +

    • Return \(i\) modulo \(2^N\).

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-wrap}{\mathrm{wrap}}_{M,N}(i) &=& i \mathbin{\mathrm{mod}} 2^N \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-trunc-u}{\mathrm{trunc}^{\mathsf{u}}}_{M,N}(z)\)

    +
      +

    • If \(z\) is a NaN, then the result is undefined.

      • +

    • Else if \(z\) is an infinity, then the result is undefined.

      • +

    • Else if \(z\) is a number and \(\href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(z)\) is a value within range of the target type, then return that value.

      • +

    • Else the result is undefined.

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-trunc-u}{\mathrm{trunc}^{\mathsf{u}}}_{M,N}(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \{\} \\ +\href{../exec/numerics.html#op-trunc-u}{\mathrm{trunc}^{\mathsf{u}}}_{M,N}(\pm \infty) &=& \{\} \\ +\href{../exec/numerics.html#op-trunc-u}{\mathrm{trunc}^{\mathsf{u}}}_{M,N}(\pm q) &=& \href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(\pm q) & (\mathrel{\mbox{if}} -1 < \href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(\pm q) < 2^N) \\ +\href{../exec/numerics.html#op-trunc-u}{\mathrm{trunc}^{\mathsf{u}}}_{M,N}(\pm q) &=& \{\} & (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    This operator is partial. +It is not defined for NaNs, infinities, or values for which the result is out of range.

    +
    +
    +
    +

    \(\href{../exec/numerics.html#op-trunc-s}{\mathrm{trunc}^{\mathsf{s}}}_{M,N}(z)\)

    +
      +

    • If \(z\) is a NaN, then the result is undefined.

      • +

    • Else if \(z\) is an infinity, then the result is undefined.

      • +

    • If \(z\) is a number and \(\href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(z)\) is a value within range of the target type, then return that value.

      • +

    • Else the result is undefined.

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-trunc-s}{\mathrm{trunc}^{\mathsf{s}}}_{M,N}(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \{\} \\ +\href{../exec/numerics.html#op-trunc-s}{\mathrm{trunc}^{\mathsf{s}}}_{M,N}(\pm \infty) &=& \{\} \\ +\href{../exec/numerics.html#op-trunc-s}{\mathrm{trunc}^{\mathsf{s}}}_{M,N}(\pm q) &=& \href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(\pm q) & (\mathrel{\mbox{if}} -2^{N-1} - 1 < \href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(\pm q) < 2^{N-1}) \\ +\href{../exec/numerics.html#op-trunc-s}{\mathrm{trunc}^{\mathsf{s}}}_{M,N}(\pm q) &=& \{\} & (\mathrel{\mbox{otherwise}}) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    This operator is partial. +It is not defined for NaNs, infinities, or values for which the result is out of range.

    +
    +
    +
    +

    \(\href{../exec/numerics.html#op-trunc-sat-u}{\mathrm{trunc\_sat\_u}}_{M,N}(z)\)

    +
      +

    • If \(z\) is a NaN, then return \(0\).

      • +

    • Else if \(z\) is negative infinity, then return \(0\).

      • +

    • Else if \(z\) is positive infinity, then return \(2^N - 1\).

      • +

    • Else, return \(\href{../exec/numerics.html#aux-sat-u}{\mathrm{sat}^{\mathsf{u}}}_N(\href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(z))\).

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-trunc-sat-u}{\mathrm{trunc\_sat\_u}}_{M,N}(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& 0 \\ +\href{../exec/numerics.html#op-trunc-sat-u}{\mathrm{trunc\_sat\_u}}_{M,N}(- \infty) &=& 0 \\ +\href{../exec/numerics.html#op-trunc-sat-u}{\mathrm{trunc\_sat\_u}}_{M,N}(+ \infty) &=& 2^N - 1 \\ +\href{../exec/numerics.html#op-trunc-sat-u}{\mathrm{trunc\_sat\_u}}_{M,N}(z) &=& \href{../exec/numerics.html#aux-sat-u}{\mathrm{sat}^{\mathsf{u}}}_N(\href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(z)) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-trunc-sat-s}{\mathrm{trunc\_sat\_s}}_{M,N}(z)\)

    +
      +

    • If \(z\) is a NaN, then return \(0\).

      • +

    • Else if \(z\) is negative infinity, then return \(-2^{N-1}\).

      • +

    • Else if \(z\) is positive infinity, then return \(2^{N-1} - 1\).

      • +

    • Else, return \(\href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(\href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(z))\).

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-trunc-sat-s}{\mathrm{trunc\_sat\_s}}_{M,N}(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& 0 \\ +\href{../exec/numerics.html#op-trunc-sat-s}{\mathrm{trunc\_sat\_s}}_{M,N}(- \infty) &=& -2^{N-1} \\ +\href{../exec/numerics.html#op-trunc-sat-s}{\mathrm{trunc\_sat\_s}}_{M,N}(+ \infty) &=& 2^{N-1}-1 \\ +\href{../exec/numerics.html#op-trunc-sat-s}{\mathrm{trunc\_sat\_s}}_{M,N}(z) &=& \href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(\href{../exec/numerics.html#aux-trunc}{\mathrm{trunc}}(z)) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-promote}{\mathrm{promote}}_{M,N}(z)\)

    +
      +

    • If \(z\) is a canonical NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\}\) (i.e., a canonical NaN of size \(N\)).

      • +

    • Else if \(z\) is a NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(1)\}\) (i.e., any arithmetic NaN of size \(N\)).

      • +

    • Else, return \(z\).

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-promote}{\mathrm{promote}}_{M,N}(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} & (\mathrel{\mbox{if}} n = \href{../syntax/values.html#aux-canon}{\mathrm{canon}}_N) \\ +\href{../exec/numerics.html#op-promote}{\mathrm{promote}}_{M,N}(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{+ \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(1)\} & (\mathrel{\mbox{otherwise}}) \\ +\href{../exec/numerics.html#op-promote}{\mathrm{promote}}_{M,N}(z) &=& z \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-demote}{\mathrm{demote}}_{M,N}(z)\)

    +
      +

    • If \(z\) is a canonical NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\}\) (i.e., a canonical NaN of size \(N\)).

      • +

    • Else if \(z\) is a NaN, then return an element of \(\href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(1)\}\) (i.e., any NaN of size \(N\)).

      • +

    • Else if \(z\) is an infinity, then return that infinity.

      • +

    • Else if \(z\) is a zero, then return that zero.

      • +

    • Else, return \(\href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(z)\).

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-demote}{\mathrm{demote}}_{M,N}(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{\} & (\mathrel{\mbox{if}} n = \href{../syntax/values.html#aux-canon}{\mathrm{canon}}_N) \\ +\href{../exec/numerics.html#op-demote}{\mathrm{demote}}_{M,N}(\pm \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)) &=& \href{../exec/numerics.html#aux-nans}{\mathrm{nans}}_N\{+ \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(1)\} & (\mathrel{\mbox{otherwise}}) \\ +\href{../exec/numerics.html#op-demote}{\mathrm{demote}}_{M,N}(\pm \infty) &=& \pm \infty \\ +\href{../exec/numerics.html#op-demote}{\mathrm{demote}}_{M,N}(\pm 0) &=& \pm 0 \\ +\href{../exec/numerics.html#op-demote}{\mathrm{demote}}_{M,N}(\pm q) &=& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(\pm q) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-convert-u}{\mathrm{convert}^{\mathsf{u}}}_{M,N}(i)\)

    +
      +

    • Return \(\href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(i)\).

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-convert-u}{\mathrm{convert}^{\mathsf{u}}}_{M,N}(i) &=& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(i) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-convert-s}{\mathrm{convert}^{\mathsf{s}}}_{M,N}(i)\)

    +
      +

    • Let \(j\) be the signed interpretation of \(i\).

      • +

    • Return \(\href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(j)\).

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-convert-s}{\mathrm{convert}^{\mathsf{s}}}_{M,N}(i) &=& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_M(i)) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-reinterpret}{\mathrm{reinterpret}}_{t_1,t_2}(c)\)

    +
      +

    • Let \(d^\ast\) be the bit sequence \(\href{../exec/numerics.html#aux-bits}{\mathrm{bits}}_{t_1}(c)\).

      • +

    • Return the constant \(c'\) for which \(\href{../exec/numerics.html#aux-bits}{\mathrm{bits}}_{t_2}(c') = d^\ast\).

      • +
    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-reinterpret}{\mathrm{reinterpret}}_{t_1,t_2}(c) &=& \href{../exec/numerics.html#aux-bits}{\mathrm{bits}}_{t_2}^{-1}(\href{../exec/numerics.html#aux-bits}{\mathrm{bits}}_{t_1}(c)) \\ +\end{array}\end{split}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-narrow-s}{\mathrm{narrow}^{\mathsf{s}}}_{M,N}(i)\)

    +
      +

    • Let \(j\) be the signed interpretation of \(i\) of size \(M\).

      • +

    • Return \(\href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(j)\).

      • +
    +
    +\[\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-narrow-s}{\mathrm{narrow}^{\mathsf{s}}}_{M,N}(i) &=& \href{../exec/numerics.html#aux-sat-s}{\mathrm{sat}^{\mathsf{s}}}_N(\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_M(i)) +\end{array}\]
    +
    +
    +

    \(\href{../exec/numerics.html#op-narrow-u}{\mathrm{narrow}^{\mathsf{u}}}_{M,N}(i)\)

    +
      +

    • Let \(j\) be the signed interpretation of \(i\) of size \(M\).

      • +

    • Return \(\href{../exec/numerics.html#aux-sat-u}{\mathrm{sat}^{\mathsf{u}}}_N(j)\).

      • +
    +
    +\[\begin{array}{lll@{\qquad}l} +\href{../exec/numerics.html#op-narrow-u}{\mathrm{narrow}^{\mathsf{u}}}_{M,N}(i) &=& \href{../exec/numerics.html#aux-sat-u}{\mathrm{sat}^{\mathsf{u}}}_N(\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}_M(i)) +\end{array}\]
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/exec/runtime.html b/core/exec/runtime.html new file mode 100644 index 00000000..4eb896a6 --- /dev/null +++ b/core/exec/runtime.html @@ -0,0 +1,557 @@ + + + + + + + + + Runtime Structure — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Runtime Structure

    +

    Store, stack, and other runtime structure forming the WebAssembly abstract machine, such as values or module instances, are made precise in terms of additional auxiliary syntax.

    +
    +

    Values

    +

    WebAssembly computations manipulate values of either the four basic number types, i.e., integers and floating-point data of 32 or 64 bit width each, of vectors of 128 bit width, or of reference type.

    +

    In most places of the semantics, values of different types can occur. +In order to avoid ambiguities, values are therefore represented with an abstract syntax that makes their type explicit. +It is convenient to reuse the same notation as for the \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}\) instructions and \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}\) producing them.

    +

    References other than null are represented with additional administrative instructions. +They either are function references, pointing to a specific function address, +or external references pointing to an uninterpreted form of extern address that can be defined by the embedder to represent its own objects.

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2149#1{{}}\mathdef2149{(number)} & \href{../exec/runtime.html#syntax-num}{\mathit{num}} &::=& + \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\href{../syntax/values.html#syntax-int}{\mathit{i32}} \\&&|& + \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\href{../syntax/values.html#syntax-int}{\mathit{i64}} \\&&|& + \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\href{../syntax/values.html#syntax-float}{\mathit{f32}} \\&&|& + \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\href{../syntax/values.html#syntax-float}{\mathit{f64}} \\ +\def\mathdef2149#1{{}}\mathdef2149{(vector)} & \href{../exec/runtime.html#syntax-vec}{\mathit{vec}} &::=& + \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\href{../syntax/values.html#syntax-int}{\mathit{i128}} \\ +\def\mathdef2149#1{{}}\mathdef2149{(reference)} & \href{../exec/runtime.html#syntax-ref}{\mathit{ref}} &::=& + \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t \\&&|& + \href{../exec/runtime.html#syntax-ref}{\mathsf{ref}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} \\&&|& + \href{../exec/runtime.html#syntax-ref.extern}{\mathsf{ref{.}extern}}~\href{../exec/runtime.html#syntax-externaddr}{\mathit{externaddr}} \\ +\def\mathdef2149#1{{}}\mathdef2149{(value)} & \href{../exec/runtime.html#syntax-val}{\mathit{val}} &::=& + \href{../exec/runtime.html#syntax-num}{\mathit{num}} ~|~ \href{../exec/runtime.html#syntax-vec}{\mathit{vec}} ~|~ \href{../exec/runtime.html#syntax-ref}{\mathit{ref}} \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    Future versions of WebAssembly may add additional forms of reference.

    +
    +

    Each value type has an associated default value; +it is the respective value \(0\) for number types and null for reference types.

    +
    +\[\begin{split}\begin{array}{lcl@{\qquad}l} +\href{../exec/runtime.html#default-val}{\mathrm{default}}_t &=& t{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0 & (\mathrel{\mbox{if}} t = \href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}) \\ +\href{../exec/runtime.html#default-val}{\mathrm{default}}_t &=& \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t & (\mathrel{\mbox{if}} t = \href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}) \\ +\end{array}\end{split}\]
    +
    +

    Convention

    +
      +

    • The meta variable \(r\) ranges over reference values where clear from context.

      • +
    +
    +
    +
    +

    Results

    +

    A result is the outcome of a computation. +It is either a sequence of values or a trap.

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2149#1{{}}\mathdef2149{(result)} & \href{../exec/runtime.html#syntax-result}{\mathit{result}} &::=& + \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast \\&&|& + \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} +\end{array}\end{split}\]
    +
    +

    Note

    +

    In the current version of WebAssembly, a result can consist of at most one value.

    +
    +
    +
    +

    Store

    +

    The store represents all global state that can be manipulated by WebAssembly programs. +It consists of the runtime representation of all instances of functions, tables, memories, and globals, element segments, and data segments that have been allocated during the life time of the abstract machine. 1

    +

    It is an invariant of the semantics that no element or data instance is addressed from anywhere else but the owning module instances.

    +

    Syntactically, the store is defined as a record listing the existing instances of each category:

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(store)} & \href{../exec/runtime.html#syntax-store}{\mathit{store}} &::=& \{~ + \begin{array}[t]{l@{~}ll} + \href{../exec/runtime.html#syntax-store}{\mathsf{funcs}} & \href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}}^\ast, \\ + \href{../exec/runtime.html#syntax-store}{\mathsf{tables}} & \href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}}^\ast, \\ + \href{../exec/runtime.html#syntax-store}{\mathsf{mems}} & \href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}}^\ast, \\ + \href{../exec/runtime.html#syntax-store}{\mathsf{globals}} & \href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}}^\ast, \\ + \href{../exec/runtime.html#syntax-store}{\mathsf{elems}} & \href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}}^\ast, \\ + \href{../exec/runtime.html#syntax-store}{\mathsf{datas}} & \href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}}^\ast ~\} \\ + \end{array} +\end{array}\end{split}\]
    +
    +
    1
    +

    In practice, implementations may apply techniques like garbage collection to remove objects from the store that are no longer referenced. +However, such techniques are not semantically observable, +and hence outside the scope of this specification.

    +
    +
    +
    +

    Convention

    +
      +

    • The meta variable \(S\) ranges over stores where clear from context.

      • +
    +
    +
    +
    +

    Addresses

    +

    Function instances, table instances, memory instances, and global instances, element instances, and data instances in the store are referenced with abstract addresses. +These are simply indices into the respective store component. +In addition, an embedder may supply an uninterpreted set of host addresses.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(address)} & \href{../exec/runtime.html#syntax-addr}{\mathit{addr}} &::=& + 0 ~|~ 1 ~|~ 2 ~|~ \dots \\ +\def\mathdef2149#1{{}}\mathdef2149{(function address)} & \href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} &::=& + \href{../exec/runtime.html#syntax-addr}{\mathit{addr}} \\ +\def\mathdef2149#1{{}}\mathdef2149{(table address)} & \href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}} &::=& + \href{../exec/runtime.html#syntax-addr}{\mathit{addr}} \\ +\def\mathdef2149#1{{}}\mathdef2149{(memory address)} & \href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}} &::=& + \href{../exec/runtime.html#syntax-addr}{\mathit{addr}} \\ +\def\mathdef2149#1{{}}\mathdef2149{(global address)} & \href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}} &::=& + \href{../exec/runtime.html#syntax-addr}{\mathit{addr}} \\ +\def\mathdef2149#1{{}}\mathdef2149{(element address)} & \href{../exec/runtime.html#syntax-elemaddr}{\mathit{elemaddr}} &::=& + \href{../exec/runtime.html#syntax-addr}{\mathit{addr}} \\ +\def\mathdef2149#1{{}}\mathdef2149{(data address)} & \href{../exec/runtime.html#syntax-dataaddr}{\mathit{dataaddr}} &::=& + \href{../exec/runtime.html#syntax-addr}{\mathit{addr}} \\ +\def\mathdef2149#1{{}}\mathdef2149{(extern address)} & \href{../exec/runtime.html#syntax-externaddr}{\mathit{externaddr}} &::=& + \href{../exec/runtime.html#syntax-addr}{\mathit{addr}} \\ +\end{array}\end{split}\]
    +

    An embedder may assign identity to exported store objects corresponding to their addresses, +even where this identity is not observable from within WebAssembly code itself +(such as for function instances or immutable globals).

    +
    +

    Note

    +

    Addresses are dynamic, globally unique references to runtime objects, +in contrast to indices, +which are static, module-local references to their original definitions. +A memory address \(\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}\) denotes the abstract address of a memory instance in the store, +not an offset inside a memory instance.

    +

    There is no specific limit on the number of allocations of store objects, +hence logical addresses can be arbitrarily large natural numbers.

    +
    +
    +
    +

    Module Instances

    +

    A module instance is the runtime representation of a module. +It is created by instantiating a module, +and collects runtime representations of all entities that are imported, defined, or exported by the module.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(module instance)} & \href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}} &::=& \{ + \begin{array}[t]{l@{~}ll} + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{types}} & \href{../syntax/types.html#syntax-functype}{\mathit{functype}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcaddrs}} & \href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{tableaddrs}} & \href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{memaddrs}} & \href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{globaladdrs}} & \href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{elemaddrs}} & \href{../exec/runtime.html#syntax-elemaddr}{\mathit{elemaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{dataaddrs}} & \href{../exec/runtime.html#syntax-dataaddr}{\mathit{dataaddr}}^\ast, \\ + \href{../exec/runtime.html#syntax-moduleinst}{\mathsf{exports}} & \href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}}^\ast ~\} \\ + \end{array} +\end{array}\end{split}\]
    +

    Each component references runtime instances corresponding to respective declarations from the original module – whether imported or defined – in the order of their static indices. +Function instances, table instances, memory instances, and global instances are referenced with an indirection through their respective addresses in the store.

    +

    It is an invariant of the semantics that all export instances in a given module instance have different names.

    +
    +
    +

    Function Instances

    +

    A function instance is the runtime representation of a function. +It effectively is a closure of the original function over the runtime module instance of its originating module. +The module instance is used to resolve references to other definitions during execution of the function.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(function instance)} & \href{../exec/runtime.html#syntax-funcinst}{\mathit{funcinst}} &::=& + \{ \href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{module}}~\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{code}}~\href{../syntax/modules.html#syntax-func}{\mathit{func}} \} \\ &&|& + \{ \href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{hostcode}}~\href{../exec/runtime.html#syntax-hostfunc}{\mathit{hostfunc}} \} \\ +\def\mathdef2149#1{{}}\mathdef2149{(host function)} & \href{../exec/runtime.html#syntax-hostfunc}{\mathit{hostfunc}} &::=& \dots \\ +\end{array}\end{split}\]
    +

    A host function is a function expressed outside WebAssembly but passed to a module as an import. +The definition and behavior of host functions are outside the scope of this specification. +For the purpose of this specification, it is assumed that when invoked, +a host function behaves non-deterministically, +but within certain constraints that ensure the integrity of the runtime.

    +
    +

    Note

    +

    Function instances are immutable, and their identity is not observable by WebAssembly code. +However, the embedder might provide implicit or explicit means for distinguishing their addresses.

    +
    +
    +
    +

    Table Instances

    +

    A table instance is the runtime representation of a table. +It records its type and holds a vector of reference values.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(table instance)} & \href{../exec/runtime.html#syntax-tableinst}{\mathit{tableinst}} &::=& + \{ \href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}, \href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}) \} \\ +\end{array}\end{split}\]
    +

    Table elements can be mutated through table instructions, the execution of an active element segment, or by external means provided by the embedder.

    +

    It is an invariant of the semantics that all table elements have a type equal to the element type of \(\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\). +It also is an invariant that the length of the element vector never exceeds the maximum size of \(\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\), if present.

    +
    +
    +

    Memory Instances

    +

    A memory instance is the runtime representation of a linear memory. +It records its type and holds a vector of bytes.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(memory instance)} & \href{../exec/runtime.html#syntax-meminst}{\mathit{meminst}} &::=& + \{ \href{../exec/runtime.html#syntax-meminst}{\mathsf{type}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}, \href{../exec/runtime.html#syntax-meminst}{\mathsf{data}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/values.html#syntax-byte}{\mathit{byte}}) \} \\ +\end{array}\end{split}\]
    +

    The length of the vector always is a multiple of the WebAssembly page size, which is defined to be the constant \(65536\) – abbreviated \(64\,\mathrm{Ki}\).

    +

    The bytes can be mutated through memory instructions, the execution of an active data segment, or by external means provided by the embedder.

    +

    It is an invariant of the semantics that the length of the byte vector, divided by page size, never exceeds the maximum size of \(\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\), if present.

    +
    +
    +

    Global Instances

    +

    A global instance is the runtime representation of a global variable. +It records its type and holds an individual value.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(global instance)} & \href{../exec/runtime.html#syntax-globalinst}{\mathit{globalinst}} &::=& + \{ \href{../exec/runtime.html#syntax-globalinst}{\mathsf{type}}~\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}, \href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}} \} \\ +\end{array}\end{split}\]
    +

    The value of mutable globals can be mutated through variable instructions or by external means provided by the embedder.

    +

    It is an invariant of the semantics that the value has a type equal to the value type of \(\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}\).

    +
    +
    +

    Element Instances

    +

    An element instance is the runtime representation of an element segment. +It holds a vector of references and their common type.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(element instance)} & \href{../exec/runtime.html#syntax-eleminst}{\mathit{eleminst}} &::=& + \{ \href{../exec/runtime.html#syntax-eleminst}{\mathsf{type}}~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}, \href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}) \} \\ +\end{array}\end{split}\]
    +
    +
    +

    Data Instances

    +

    An data instance is the runtime representation of a data segment. +It holds a vector of bytes.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(data instance)} & \href{../exec/runtime.html#syntax-datainst}{\mathit{datainst}} &::=& + \{ \href{../exec/runtime.html#syntax-datainst}{\mathsf{data}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/values.html#syntax-byte}{\mathit{byte}}) \} \\ +\end{array}\end{split}\]
    +
    +
    +

    Export Instances

    +

    An export instance is the runtime representation of an export. +It defines the export’s name and the associated external value.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(export instance)} & \href{../exec/runtime.html#syntax-exportinst}{\mathit{exportinst}} &::=& + \{ \href{../exec/runtime.html#syntax-exportinst}{\mathsf{name}}~\href{../syntax/values.html#syntax-name}{\mathit{name}}, \href{../exec/runtime.html#syntax-exportinst}{\mathsf{value}}~\href{../exec/runtime.html#syntax-externval}{\mathit{externval}} \} \\ +\end{array}\end{split}\]
    +
    +
    +

    External Values

    +

    An external value is the runtime representation of an entity that can be imported or exported. +It is an address denoting either a function instance, table instance, memory instance, or global instances in the shared store.

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2149#1{{}}\mathdef2149{(external value)} & \href{../exec/runtime.html#syntax-externval}{\mathit{externval}} &::=& + \href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} \\&&|& + \href{../exec/runtime.html#syntax-externval}{\mathsf{table}}~\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}} \\&&|& + \href{../exec/runtime.html#syntax-externval}{\mathsf{mem}}~\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}} \\&&|& + \href{../exec/runtime.html#syntax-externval}{\mathsf{global}}~\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}} \\ +\end{array}\end{split}\]
    +
    +

    Conventions

    +

    The following auxiliary notation is defined for sequences of external values. +It filters out entries of a specific kind in an order-preserving fashion:

    +
      +

    • \(\href{../exec/runtime.html#syntax-externval}{\mathrm{funcs}}(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^\ast) = [\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} ~|~ (\href{../exec/runtime.html#syntax-externval}{\mathsf{func}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}) \in \href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^\ast]\)

      • +

    • \(\href{../exec/runtime.html#syntax-externval}{\mathrm{tables}}(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^\ast) = [\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}} ~|~ (\href{../exec/runtime.html#syntax-externval}{\mathsf{table}}~\href{../exec/runtime.html#syntax-tableaddr}{\mathit{tableaddr}}) \in \href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^\ast]\)

      • +

    • \(\href{../exec/runtime.html#syntax-externval}{\mathrm{mems}}(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^\ast) = [\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}} ~|~ (\href{../exec/runtime.html#syntax-externval}{\mathsf{mem}}~\href{../exec/runtime.html#syntax-memaddr}{\mathit{memaddr}}) \in \href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^\ast]\)

      • +

    • \(\href{../exec/runtime.html#syntax-externval}{\mathrm{globals}}(\href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^\ast) = [\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}} ~|~ (\href{../exec/runtime.html#syntax-externval}{\mathsf{global}}~\href{../exec/runtime.html#syntax-globaladdr}{\mathit{globaladdr}}) \in \href{../exec/runtime.html#syntax-externval}{\mathit{externval}}^\ast]\)

      • +
    +
    +
    +
    +

    Stack

    +

    Besides the store, most instructions interact with an implicit stack. +The stack contains three kinds of entries:

    + +

    These entries can occur on the stack in any order during the execution of a program. +Stack entries are described by abstract syntax as follows.

    +
    +

    Note

    +

    It is possible to model the WebAssembly semantics using separate stacks for operands, control constructs, and calls. +However, because the stacks are interdependent, additional book keeping about associated stack heights would be required. +For the purpose of this specification, an interleaved representation is simpler.

    +
    +
    +

    Values

    +

    Values are represented by themselves.

    +
    +
    +

    Labels

    +

    Labels carry an argument arity \(n\) and their associated branch target, which is expressed syntactically as an instruction sequence:

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(label)} & \href{../exec/runtime.html#syntax-label}{\mathit{label}} &::=& + \href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\} \\ +\end{array}\end{split}\]
    +

    Intuitively, \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) is the continuation to execute when the branch is taken, in place of the original control construct.

    +
    +

    Note

    +

    For example, a loop label has the form

    +
    +\[\href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}~\dots~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\}\]
    +

    When performing a branch to this label, this executes the loop, effectively restarting it from the beginning. +Conversely, a simple block label has the form

    +
    +\[\href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\epsilon\}\]
    +

    When branching, the empty continuation ends the targeted block, such that execution can proceed with consecutive instructions.

    +
    +
    +
    +

    Activations and Frames

    +

    Activation frames carry the return arity \(n\) of the respective function, +hold the values of its locals (including arguments) in the order corresponding to their static local indices, +and a reference to the function’s own module instance:

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(activation)} & \mathit{activation} &::=& + \href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}_n\{\href{../exec/runtime.html#syntax-frame}{\mathit{frame}}\} \\ +\def\mathdef2149#1{{}}\mathdef2149{(frame)} & \href{../exec/runtime.html#syntax-frame}{\mathit{frame}} &::=& + \{ \href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast, \href{../exec/runtime.html#syntax-frame}{\mathsf{module}}~\href{../exec/runtime.html#syntax-moduleinst}{\mathit{moduleinst}} \} \\ +\end{array}\end{split}\]
    +

    The values of the locals are mutated by respective variable instructions.

    +
    +
    +

    Conventions

    +
      +

    • The meta variable \(L\) ranges over labels where clear from context.

      • +

    • The meta variable \(F\) ranges over frames where clear from context.

      • +

    • The following auxiliary definition takes a block type and looks up the function type that it denotes in the current frame:

      • +
    +
    +\[\begin{split}\begin{array}{lll} +\href{../exec/runtime.html#exec-expand}{\mathrm{expand}}_F(\href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}}) &=& F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{types}}[\href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}}] \\ +\href{../exec/runtime.html#exec-expand}{\mathrm{expand}}_F([\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}^?]) &=& [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}^?] \\ +\end{array}\end{split}\]
    +
    +
    +
    +

    Administrative Instructions

    +
    +

    Note

    +

    This section is only relevant for the formal notation.

    +
    +

    In order to express the reduction of traps, calls, and control instructions, the syntax of instructions is extended to include the following administrative instructions:

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2149#1{{}}\mathdef2149{(administrative instruction)} & \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}} &::=& + \dots \\ &&|& + \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ &&|& + \href{../exec/runtime.html#syntax-ref}{\mathsf{ref}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} \\ &&|& + \href{../exec/runtime.html#syntax-ref.extern}{\mathsf{ref{.}extern}}~\href{../exec/runtime.html#syntax-externaddr}{\mathit{externaddr}} \\ &&|& + \href{../exec/runtime.html#syntax-invoke}{\mathsf{invoke}}~\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}} \\ &&|& + \href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\ &&|& + \href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}_n\{\href{../exec/runtime.html#syntax-frame}{\mathit{frame}}\}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\ +\end{array}\end{split}\]
    +

    The \(\href{../exec/runtime.html#syntax-trap}{\mathsf{trap}}\) instruction represents the occurrence of a trap. +Traps are bubbled up through nested instruction sequences, ultimately reducing the entire program to a single \(\href{../exec/runtime.html#syntax-trap}{\mathsf{trap}}\) instruction, signalling abrupt termination.

    +

    The \(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref}}\) instruction represents function reference values. Similarly, \(\href{../exec/runtime.html#syntax-ref.extern}{\mathsf{ref{.}extern}}\) represents external references.

    +

    The \(\href{../exec/runtime.html#syntax-invoke}{\mathsf{invoke}}\) instruction represents the imminent invocation of a function instance, identified by its address. +It unifies the handling of different forms of calls.

    +

    The \(\href{../exec/runtime.html#syntax-label}{\mathsf{label}}\) and \(\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}\) instructions model labels and frames “on the stack”. +Moreover, the administrative syntax maintains the nesting structure of the original structured control instruction or function body and their instruction sequences with an \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\) marker. +That way, the end of the inner instruction sequence is known when part of an outer sequence.

    +
    +

    Note

    +

    For example, the reduction rule for \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}\) is:

    +
    +\[\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~[t^n]~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad +\href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\epsilon\}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\]
    +

    This replaces the block with a label instruction, +which can be interpreted as “pushing” the label on the stack. +When \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\) is reached, i.e., the inner instruction sequence has been reduced to the empty sequence – or rather, a sequence of \(n\) \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}\) instructions representing the resulting values – then the \(\href{../exec/runtime.html#syntax-label}{\mathsf{label}}\) instruction is eliminated courtesy of its own reduction rule:

    +
    +\[\href{../exec/runtime.html#syntax-label}{\mathsf{label}}_m\{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n\]
    +

    This can be interpreted as removing the label from the stack and only leaving the locally accumulated operand values.

    +
    +
    +

    Block Contexts

    +

    In order to specify the reduction of branches, the following syntax of block contexts is defined, indexed by the count \(k\) of labels surrounding a hole \([\_]\) that marks the place where the next step of computation is taking place:

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(block contexts)} & \href{../exec/runtime.html#syntax-ctxt-block}{B}^0 &::=& + \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast~[\_]~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast \\ +\def\mathdef2149#1{{}}\mathdef2149{(block contexts)} & \href{../exec/runtime.html#syntax-ctxt-block}{B}^{k+1} &::=& + \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast~\href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\}~\href{../exec/runtime.html#syntax-ctxt-block}{B}^k~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast \\ +\end{array}\end{split}\]
    +

    This definition allows to index active labels surrounding a branch or return instruction.

    +
    +

    Note

    +

    For example, the reduction of a simple branch can be defined as follows:

    +
    +\[\href{../exec/runtime.html#syntax-label}{\mathsf{label}}_0\{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\}~\href{../exec/runtime.html#syntax-ctxt-block}{B}^l[\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l]~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \quad\href{../exec/conventions.html#formal-notation}{\hookrightarrow}\quad \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\]
    +

    Here, the hole \([\_]\) of the context is instantiated with a branch instruction. +When a branch occurs, +this rule replaces the targeted label and associated instruction sequence with the label’s continuation. +The selected label is identified through the label index \(l\), which corresponds to the number of surrounding \(\href{../exec/runtime.html#syntax-label}{\mathsf{label}}\) instructions that must be hopped over – which is exactly the count encoded in the index of a block context.

    +
    +
    +
    +

    Configurations

    +

    A configuration consists of the current store and an executing thread.

    +

    A thread is a computation over instructions +that operates relative to a current frame referring to the module instance in which the computation runs, i.e., where the current function originates from.

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2149#1{{}}\mathdef2149{(configuration)} & \href{../exec/runtime.html#syntax-config}{\mathit{config}} &::=& + \href{../exec/runtime.html#syntax-store}{\mathit{store}}; \href{../exec/runtime.html#syntax-thread}{\mathit{thread}} \\ +\def\mathdef2149#1{{}}\mathdef2149{(thread)} & \href{../exec/runtime.html#syntax-thread}{\mathit{thread}} &::=& + \href{../exec/runtime.html#syntax-frame}{\mathit{frame}}; \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The current version of WebAssembly is single-threaded, +but configurations with multiple threads may be supported in the future.

    +
    +
    +
    +

    Evaluation Contexts

    +

    Finally, the following definition of evaluation context and associated structural rules enable reduction inside instruction sequences and administrative forms as well as the propagation of traps:

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2149#1{{}}\mathdef2149{(evaluation contexts)} & E &::=& + [\_] ~|~ + \href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast~E~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast ~|~ + \href{../exec/runtime.html#syntax-label}{\mathsf{label}}_n\{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\}~E~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{rcl} +S; F; E[\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast] &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S'; F'; E[{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}'}^\ast] \\ + && (\mathrel{\mbox{if}} S; F; \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast \href{../exec/conventions.html#formal-notation}{\hookrightarrow} S'; F'; {\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}'}^\ast) \\ +S; F; \href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}_n\{F'\}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S'; F; \href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}_n\{F''\}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}'^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\ + && (\mathrel{\mbox{if}} S; F'; \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast \href{../exec/conventions.html#formal-notation}{\hookrightarrow} S'; F''; {\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}'}^\ast) \\[1ex] +S; F; E[\href{../exec/runtime.html#syntax-trap}{\mathsf{trap}}] &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} + \qquad (\mathrel{\mbox{if}} E \neq [\_]) \\ +S; F; \href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}_n\{F'\}~\href{../exec/runtime.html#syntax-trap}{\mathsf{trap}}~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} &\href{../exec/conventions.html#formal-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ +\end{array}\end{split}\]
    +

    Reduction terminates when a thread’s instruction sequence has been reduced to a result, +that is, either a sequence of values or to a \(\href{../exec/runtime.html#syntax-trap}{\mathsf{trap}}\).

    +
    +

    Note

    +

    The restriction on evaluation contexts rules out contexts like \([\_]\) and \(\epsilon~[\_]~\epsilon\) for which \(E[\href{../exec/runtime.html#syntax-trap}{\mathsf{trap}}] = \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}}\).

    +

    For an example of reduction under evaluation contexts, consider the following instruction sequence.

    +
    +\[(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_1)~(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_2)~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{neg}}~(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_3)~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}}\]
    +

    This can be decomposed into \(E[(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_2)~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{neg}}]\) where

    +
    +\[E = (\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_1)~[\_]~(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~x_3)~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}}\]
    +

    Moreover, this is the only possible choice of evaluation context where the contents of the hole matches the left-hand side of a reduction rule.

    +
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/genindex.html b/core/genindex.html new file mode 100644 index 00000000..0adb322f --- /dev/null +++ b/core/genindex.html @@ -0,0 +1,1947 @@ + + + + + + + + Index — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + + +

    Index

    + +
    + Symbols + | A + | B + | C + | D + | E + | F + | G + | H + | I + | K + | L + | M + | N + | O + | P + | R + | S + | T + | U + | V + | W + +
    +

    Symbols

    + + +
    + +

    A

    + + + +
    + +

    B

    + + + +
    + +

    C

    + + + +
    + +

    D

    + + + +
    + +

    E

    + + + +
    + +

    F

    + + + +
    + +

    G

    + + + +
    + +

    H

    + + + +
    + +

    I

    + + + +
    + +

    K

    + + +
    + +

    L

    + + + +
    + +

    M

    + + + +
    + +

    N

    + + + +
    + +

    O

    + + + +
    + +

    P

    + + + +
    + +

    R

    + + + +
    + +

    S

    + + + +
    + +

    T

    + + + +
    + +

    U

    + + + +
    + +

    V

    + + + +
    + +

    W

    + + +
    + + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/index.html b/core/index.html new file mode 100644 index 00000000..586df31b --- /dev/null +++ b/core/index.html @@ -0,0 +1,172 @@ + + + + + + + + + WebAssembly Specification — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    WebAssembly Specification

    +
    +
    Release 2.0 + stringref (Draft 2022-04-27)
    +
    +
    +
    Editor: Andreas Rossberg
    +
    +
    +
    Latest Draft: https://webassembly.github.io/stringref/core/
    +
    Issue Tracker: https://github.com/webassembly/stringref/issues/
    +
    +
    + +
    + +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/intro/index.html b/core/intro/index.html new file mode 100644 index 00000000..998f8048 --- /dev/null +++ b/core/intro/index.html @@ -0,0 +1,119 @@ + + + + + + + + + Introduction — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Introduction

    +
    + +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/intro/introduction.html b/core/intro/introduction.html new file mode 100644 index 00000000..614de8bf --- /dev/null +++ b/core/intro/introduction.html @@ -0,0 +1,181 @@ + + + + + + + + + Introduction — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Introduction

    +

    WebAssembly (abbreviated Wasm 1) is a safe, portable, low-level code format +designed for efficient execution and compact representation. +Its main goal is to enable high performance applications on the Web, but it does not make any Web-specific assumptions or provide Web-specific features, so it can be employed in other environments as well.

    +

    WebAssembly is an open standard developed by a W3C Community Group.

    +

    This document describes version 2.0 + stringref (Draft 2022-04-27) of the core WebAssembly standard. +It is intended that it will be superseded by new incremental releases with additional features in the future.

    +
    +

    Design Goals

    +

    The design goals of WebAssembly are the following:

    +
      +

    • Fast, safe, and portable semantics:

      +
        +

      • Fast: executes with near native code performance, taking advantage of capabilities common to all contemporary hardware.

        • +

      • Safe: code is validated and executes in a memory-safe 2, sandboxed environment preventing data corruption or security breaches.

        • +

      • Well-defined: fully and precisely defines valid programs and their behavior in a way that is easy to reason about informally and formally.

        • +

      • Hardware-independent: can be compiled on all modern architectures, desktop or mobile devices and embedded systems alike.

        • +

      • Language-independent: does not privilege any particular language, programming model, or object model.

        • +

      • Platform-independent: can be embedded in browsers, run as a stand-alone VM, or integrated in other environments.

        • +

      • Open: programs can interoperate with their environment in a simple and universal manner.

        • +
      +
      • +

    • Efficient and portable representation:

      +
        +

      • Compact: has a binary format that is fast to transmit by being smaller than typical text or native code formats.

        • +

      • Modular: programs can be split up in smaller parts that can be transmitted, cached, and consumed separately.

        • +

      • Efficient: can be decoded, validated, and compiled in a fast single pass, equally with either just-in-time (JIT) or ahead-of-time (AOT) compilation.

        • +

      • Streamable: allows decoding, validation, and compilation to begin as soon as possible, before all data has been seen.

        • +

      • Parallelizable: allows decoding, validation, and compilation to be split into many independent parallel tasks.

        • +

      • Portable: makes no architectural assumptions that are not broadly supported across modern hardware.

        • +
      +
      • +
    +

    WebAssembly code is also intended to be easy to inspect and debug, especially in environments like web browsers, but such features are beyond the scope of this specification.

    +
    +
    1
    +

    A contraction of “WebAssembly”, not an acronym, hence not using all-caps.

    +
    +
    2
    +

    No program can break WebAssembly’s memory model. Of course, it cannot guarantee that an unsafe language compiling to WebAssembly does not corrupt its own memory layout, e.g. inside WebAssembly’s linear memory.

    +
    +
    +
    +
    +

    Scope

    +

    At its core, WebAssembly is a virtual instruction set architecture (virtual ISA). +As such, it has many use cases and can be embedded in many different environments. +To encompass their variety and enable maximum reuse, the WebAssembly specification is split and layered into several documents.

    +

    This document is concerned with the core ISA layer of WebAssembly. +It defines the instruction set, binary encoding, validation, and execution semantics, as well as a textual representation. +It does not, however, define how WebAssembly programs can interact with a specific environment they execute in, nor how they are invoked from such an environment.

    +

    Instead, this specification is complemented by additional documents defining interfaces to specific embedding environments such as the Web. +These will each define a WebAssembly application programming interface (API) suitable for a given environment.

    +
    +
    +

    Security Considerations

    +

    WebAssembly provides no ambient access to the computing environment in which code is executed. +Any interaction with the environment, such as I/O, access to resources, or operating system calls, can only be performed by invoking functions provided by the embedder and imported into a WebAssembly module. +An embedder can establish security policies suitable for a respective environment by controlling or limiting which functional capabilities it makes available for import. +Such considerations are an embedder’s responsibility and the subject of API definitions for a specific environment.

    +

    Because WebAssembly is designed to be translated into machine code running directly on the host’s hardware, it is potentially vulnerable to side channel attacks on the hardware level. +In environments where this is a concern, an embedder may have to put suitable mitigations into place to isolate WebAssembly computations.

    +
    +
    +

    Dependencies

    +

    WebAssembly depends on two existing standards:

    + +

    However, to make this specification self-contained, relevant aspects of the aforementioned standards are defined and formalized as part of this specification, +such as the binary representation and rounding of floating-point values, and the value range and UTF-8 encoding of Unicode characters.

    +
    +

    Note

    +

    The aforementioned standards are the authoritative source of all respective definitions. +Formalizations given in this specification are intended to match these definitions. +Any discrepancy in the syntax or semantics described is to be considered an error.

    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/intro/overview.html b/core/intro/overview.html new file mode 100644 index 00000000..778a2b7f --- /dev/null +++ b/core/intro/overview.html @@ -0,0 +1,228 @@ + + + + + + + + + Overview — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Overview

    +
    +

    Concepts

    +

    WebAssembly encodes a low-level, assembly-like programming language. +This language is structured around the following concepts.

    +
    +
    Values

    WebAssembly provides only four basic number types. +These are integers and IEEE 754-2019 numbers, +each in 32 and 64 bit width. +32 bit integers also serve as Booleans and as memory addresses. +The usual operations on these types are available, +including the full matrix of conversions between them. +There is no distinction between signed and unsigned integer types. +Instead, integers are interpreted by respective operations +as either unsigned or signed in two’s complement representation.

    +

    In addition to these basic number types, there is a single 128 bit wide +vector type representing different types of packed data. +The supported representations are 4 32-bit, or 2 64-bit +IEEE 754-2019 numbers, or different widths of packed integer values +specifically 2 64-bit integers, 4 32-bit integers, 8 +16-bit integers, or 16 8-bit integers.

    +

    Finally, values can consist of opaque references that represent pointers towards different sorts of entities. +Unlike with other types, their size or representation is not observable.

    +
    +
    +
    +
    Instructions

    The computational model of WebAssembly is based on a stack machine. +Code consists of sequences of instructions that are executed in order. +Instructions manipulate values on an implicit operand stack 1 +and fall into two main categories. +Simple instructions perform basic operations on data. +They pop arguments from the operand stack and push results back to it. +Control instructions alter control flow. +Control flow is structured, meaning it is expressed with well-nested constructs such as blocks, loops, and conditionals. +Branches can only target such constructs.

    +
    +
    +
    +
    Traps

    Under some conditions, certain instructions may produce a trap, +which immediately aborts execution. +Traps cannot be handled by WebAssembly code, +but are reported to the outside environment, +where they typically can be caught.

    +
    +
    +
    +
    Functions

    Code is organized into separate functions. +Each function takes a sequence of values as parameters +and returns a sequence of values as results. +Functions can call each other, including recursively, +resulting in an implicit call stack that cannot be accessed directly. +Functions may also declare mutable local variables that are usable as virtual registers.

    +
    +
    +
    +
    Tables

    A table is an array of opaque values of a particular element type. +It allows programs to select such values indirectly through a dynamic index operand. +Currently, the only available element type is an untyped function reference. +Thereby, a program can call functions indirectly through a dynamic index into a table. +For example, this allows emulating function pointers by way of table indices.

    +
    +
    +
    +
    Linear Memory

    A linear memory is a contiguous, mutable array of raw bytes. +Such a memory is created with an initial size but can be grown dynamically. +A program can load and store values from/to a linear memory at any byte address (including unaligned). +Integer loads and stores can specify a storage size which is smaller than the size of the respective value type. +A trap occurs if an access is not within the bounds of the current memory size.

    +
    +
    +
    +
    Modules

    A WebAssembly binary takes the form of a module +that contains definitions for functions, tables, and linear memories, +as well as mutable or immutable global variables. +Definitions can also be imported, specifying a module/name pair and a suitable type. +Each definition can optionally be exported under one or more names. +In addition to definitions, modules can define initialization data for their memories or tables +that takes the form of segments copied to given offsets. +They can also define a start function that is automatically executed.

    +
    +
    +
    +
    Embedder

    A WebAssembly implementation will typically be embedded into a host environment. +This environment defines how loading of modules is initiated, +how imports are provided (including host-side definitions), and how exports can be accessed. +However, the details of any particular embedding are beyond the scope of this specification, and will instead be provided by complementary, environment-specific API definitions.

    +
    +
    +
    +
    1
    +

    In practice, implementations need not maintain an actual operand stack. Instead, the stack can be viewed as a set of anonymous registers that are implicitly referenced by instructions. The type system ensures that the stack height, and thus any referenced register, is always known statically.

    +
    +
    +
    +
    +

    Semantic Phases

    +

    Conceptually, the semantics of WebAssembly is divided into three phases. +For each part of the language, the specification specifies each of them.

    +
    +
    Decoding

    WebAssembly modules are distributed in a binary format. +Decoding processes that format and converts it into an internal representation of a module. +In this specification, this representation is modelled by abstract syntax, but a real implementation could compile directly to machine code instead.

    +
    +
    +
    +
    Validation

    A decoded module has to be valid. +Validation checks a number of well-formedness conditions to guarantee that the module is meaningful and safe. +In particular, it performs type checking of functions and the instruction sequences in their bodies, ensuring for example that the operand stack is used consistently.

    +
    +
    +
    +
    Execution

    Finally, a valid module can be executed. +Execution can be further divided into two phases:

    +

    Instantiation. +A module instance is the dynamic representation of a module, +complete with its own state and execution stack. +Instantiation executes the module body itself, given definitions for all its imports. +It initializes globals, memories and tables and invokes the module’s start function if defined. +It returns the instances of the module’s exports.

    +

    Invocation. +Once instantiated, further WebAssembly computations can be initiated by invoking an exported function on a module instance. +Given the required arguments, that executes the respective function and returns its results.

    +

    Instantiation and invocation are operations within the embedding environment.

    +
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/objects.inv b/core/objects.inv new file mode 100644 index 0000000000000000000000000000000000000000..6bbef7a86e4231b6f9692858d20e39bfa02d7f4c GIT binary patch literal 10897 zcmZ{}Q*b2?@Fg7U#+lsM6LVtQwlT?#tsC36HNnKT?POw3Jh5%=@B4pMyZf?LU3Ka- zs=6Qg>QoV z{u?$W1-n?;TabF$TA45*d8}Rd>cvxVH5__>ML|9CuLdl|Uj8M*ZA62PkH7fw^XZ4a z;ji?dPzKuKT{k+)BZ=x$!v_Z=!(& zq;lTGQst)Krk0sa-FC#vcTF;2PFY6SN2gEa#^pqZ4M#)O#3uVK-zO0MWk9=@2|$bJwd|tWop;zKny7| zL$VW9CS=v-b(7*I%Smo@vc$tW8tUEzfPo1uOTrcy`lAOA)e`+x&?IF zE6kw-;NDXflD-%dV$$ApQ>c|CIC3;x$dW04L-~sTNS@h>;N%cpN4A^3-AwB&yj(p! zTp{KZi9IGpD~h?jBHnY@&7|aIe-r!b$}j->ske!b@xwG+L25wzXi6g`RCFSB^(J=n1Ch zPv*2(_}wTaUKy{LhFelHG*qrmhV|GS&XcgFD)Wbt18!YcSDd@3WLGyDgH*$=Dg~H5 zx((hNEWj4|224$6>%3?a5vmftc9W7z9Q2b(^YY>@DPn+8bqR%v&FvSDmKA5ZWv~YA znwJVSC-T-Q?fe$d!NKoeciHNi+bVF=8NYH{zp3L8wt~9ID|i=MtA^GLizCJrU!;#S z<|&w?J@IxVPVuWp{=vMfku#K z=}inK8mte!Cpgq8pMjgjmal+nKF%q=3ZdhOU@FW{2^A@-LoE1SNNA7s8jf3xVm>U; ze9sD4Oj_Zy@lcad(-X#lUSz#oX}ip;eXjOU@|H(mPpkCdUf~#ooA)l70PA-L?yer( z0}$0f0k~1~hyxs$HO=~zp1gqbNwC;5K_3wF(6W9POJ1s}VDV57vd`7z3@bF`?Z5xa z?iDVHc!K5PdB9;}cZxJGKS9L4j=@J~DX!CZFdppmp`J;AdWm~c({^r;0Aql5rVSSo z5f-y)^3bR%+X)w)hiH!P&`Wpnd;m616glDp;yXOaa71mu`vUc!cWd#&%fn2BqxGq5 zt1|ySx2Mg>viwMeqtL;`=Rs(!Wt6{0Kzh7waMo(0>9yC)t!BGj6^?*FJr8|5DlG!% z1C5#iOnUP_3{6pU$o9?b!}eM`n^AlaQi551h7ZABoB89Y#JC54<9KmD+6E;dLrYO5 zL4@LiQZ!*GznXZtnDUMnJ9mXo7YmuU-}MP05V=_X-mk_`ZDTPRuAHC5UADe{aPKLe z#|tJQ`fJvXzT8j5%0FxNl34J6>q1F4KssRtVjkJadRaU-Z=@*b)J|aZq!iEe#y&Ge zU1+m2L|(f?zSY zbyClT)|)fe`J<4yb5E-|uz{!fquEp5Zfr5t3^h5RT|SdhQdn)H?w2VCx1e_Oj1JaC z6eGoy>LDPxe=bec>-}LZFe5X|F07%w@;ir3m;MD>ywy@w002?n!Ce`YiDOVDq_H<}g)YLhLc7L^jG4#**VG#&FN?dEJip%y}N{z;!-%-}ED4 zK!3=|BnIc?lN@b1jCb?*n-Aa0yd+Ee@Re#HPq0omypbVdWvs(1R%OO2mw#mFgPI^q6&vK_hH6B(R^1>QO+GIP|Qt)0$oGZoQSLU6*Bd@`yt}&yGo6IWv zm|PNDhj_)5xRjgF^BYiHB6&yivNZL*Bb^X-{2Cq>+!qs^X9V~v`4mxK+EScC??Fgz zy*ckXC6S>(aR5coTbFUyjI-}+2W|9{*gP->);+sc&G!!lSnJun|KD=iZ%Tv|<>)AN z*xl7kW!&iRrxk9A`evS+=tK|>2aX%2a6bvTG8N~Yl2^Rq7_`({Ko2$C2gWXP)|CV*Bg@S`JzRE1|{DyBVovc>BFJOKV}m zxB;GI!E+SL?$ApTRRic1OkYhj+2-2`{kvw2=!mKj&=)W8(FUZWa=XaxUA=eZApB$P2=lBJnDEiNP|zJ7=w#_&K6e!PG(1{d5RsBr2d zW`|F=+=BE9D) zl(Pmo=6)rE_n6C+s-2j6gKRAZ45S;+U`yQ(oogu+8v%UwD7TJ6>mqQmCMA>! 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    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/searchindex.js b/core/searchindex.js new file mode 100644 index 00000000..ed31bc93 --- /dev/null +++ b/core/searchindex.js @@ -0,0 +1 @@ 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,43],_3:13,_4:[13,34],_5:13,_6:13,_7:13,_8:[13,20,34],_9:13,_:[1,6,12,13,15,19,21,28,34,36,38],_e:20,_f32:[28,34],_f32x4:[1,6,12,28,34],_f64:[28,34],_f64x2:[1,6,12,28,34],_f:[1,18,21,28],_high:[6,12,34],_i16x8:[1,6,12,28,34],_i32:[28,34],_i32x4:[1,6,12,28,34],_i64:[28,34],_i8x16:[1,6,12,28,34],_i:[1,3,9,19,26,28,34,36,41,42],_if:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_indirect:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_lane:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_low:[1,6,12,28,34],_m:[18,20,21],_n:[2,13,18,21,31,34,38,39],_null:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_pairwis:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_s:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_sat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],_splat:[1,6,12,28,34],_t:[18,20,21],_tabl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_true:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],_x:18,_y:18,_zero:[1,6,12,28,34],a0:[6,12],a1:[6,12],a2:[6,12],a3:[6,12],a4:[6,12],a5:[6,12],a6:[6,12],a7:[6,12],a8:[6,12],a9:[6,12],a_1:[10,26,32],a_2:26,a_i:[10,26,32],a_n:[10,26,32],aa:[6,12],ab:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],abbrevi:[21,24,33,38],abil:1,abl:[9,13],abort:[16,18,25,28],about:[3,9,16,21,24,39],abov:[0,4,9,18,31,35],abrupt:21,absent:[9,39,41],absolut:34,ac:[6,12],accept:30,access:[0,1,3,9,18,24,25,26,28,29,34,39,42],accord:[3,18,28,35,39],accordingli:[39,41],accumul:[0,21,41],acm:[9,16,39],acronym:24,across:24,activ:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],actual:[0,2,10,12,13,18,19,25,32,42],ad:[1,6,9,12,13,19,20,28],add:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],addit:[0,1,3,4,9,10,12,13,15,21,24,25,28,29,30,32,34,36,39],addition:[0,28],addr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],address:[3,9,17,19,25,28],adher:[9,18],admin:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],administr:[5,17,18],adopt:[3,10,16,26,32,39],advantag:24,ae:[6,12],af:[6,12],affect:[2,18,19,28,35],aforement:24,after:[0,2,13,16,18,28,29,34],afterward:[0,16],again:20,against:[0,18,19,28,43],ahead:[24,35],akin:41,algorithm:[5,22,39,41],align:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],alik:24,all:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],alloc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocdata:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocelem:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocfunc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocglob:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allochostfunc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocmem:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocmodul:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],alloct:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocx:19,allow:[0,1,4,9,10,12,14,15,18,20,21,24,25,28,29,32,34,35,36,38,39,41,43],alon:[9,16,24,39],along:0,alreadi:[4,18,38],also:[1,3,9,10,12,14,16,18,19,20,21,24,25,26,28,29,30,31,32,34,36,38,39,41],alter:25,altern:[10,20,28],alwai:[9,20,21,25,28,35,38,39,43],ambient:24,ambigu:21,amen:[16,39],among:[20,31],an:[0,1,2,3,4,9,10,12,13,15,16,18,19,20,21,24,25,26,28,29,30,31,32,34,36,38,39,41,42,43],analog:34,andnot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],andrea:[9,16,22,39],ani:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],annot:[12,18,28,34,39,41],anonym:[25,36,37],anoth:[28,36,41],anyth:41,anywher:[21,34,37],aot:24,api:[19,24,25],appear:[2,10,18,26,32,34,36,42],append:[19,26,39],appendix:[0,1,2,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],appli:[9,16,18,20,21,32,36,39,43],applic:[4,10,16,20,24,32],approach:[16,39],appropri:[9,16,19,28],ar:[0,1,2,3,4,9,10,12,13,14,15,16,18,19,20,21,24,25,26,28,29,30,31,32,34,35,36,38,39,41,42,43],arbitrari:[1,20,31,32,38],arbitrarili:[21,41],architectur:24,argument:[3,9,12,18,19,20,21,25,28,34],arithmet:[20,31],ariti:[0,18,21],around:[25,34],arrai:[2,3,9,10,12,13,14,15,16,18,19,20,21,25,26,28,29,30,31,32,34,35,36,37,38,39,41,42],articl:[9,16,39],ascii:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ascrib:18,aspect:[0,4,24],assembl:25,assert:[3,16,18,19],assign:[2,21,32,35],associ:[0,2,9,18,19,21,28,30,32],assum:[3,4,9,16,19,20,21,26,32,35,39,41],assumpt:[9,24,39],ast:[6,7,8,10,12,13,14,15,16,19,20,21,26,28,29,30,31,32,34,35,36,37,38,39,43],ast_i:19,atom:[19,26],attach:2,attack:24,attribut:[10,20,32,36],augment:[10,26,32,36],authorit:24,automat:[3,9,25,29,36],aux:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],auxiliari:[0,3,11,15,18,19,20,21,27,29,30,31,34,36,41],avail:[18,24,25,28,29,39],averylonginstructionnameforvectext:34,avgr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],avoid:[1,12,16,21,32],awai:28,axiom:39,b0:[6,12],b1:[6,12],b2:[6,12],b3:[6,12],b4:[6,12],b5:[6,12],b6:[6,12],b7:[6,12],b8:[6,12],b9:[6,12],b:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],b_1:[9,10,15,26],b_2:[9,15,26],b_3:15,b_4:15,b_:12,b_i:10,b_n:10,ba:[6,12],back:[0,18,25,28,41],backslash0asm:13,backslash:38,backward:[13,18,28,34,36],base:[18,20,25,28,29,31,34],basic:[10,21,25,28],bastien:[9,16,39],bb:[6,12],bc:[6,12],bd:[6,12],becaus:[18,19,20,21,24,41],becom:29,been:[0,1,16,19,21,24,29],befor:[4,13,19,24,29,32,36],beforehand:19,begin:[2,3,4,9,10,12,13,14,15,16,18,19,20,21,24,26,28,29,30,31,32,34,35,36,37,38,39,41,42],behav:[9,21,28],behavior:[9,16,18,21,24,28],being:[13,24,28,41],below:[9,19,42],ben:[9,16,39],benjamin:[16,39],besid:[20,21],between:[3,20,25,31,32],beyond:[24,25],bf:[6,12],big:39,bigoplu:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bigwedg:18,biject:20,binari:[0,1,2,3,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bind:[10,32,34,36],binop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],bit:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bitfield:13,bitmask:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],bitselect:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bitwidth:28,bitwis:[20,28],block:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42],blockchar:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],blockcom:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],blockinstr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],blocktyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],bodi:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],book:[16,21,39],bool:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bot:[9,18,41],both:[9,14,15,16,20,26,28,29,34,36,38,39,41,43],bottom:41,bound:[10,13,15,25,26,28,31,32,34,36,43],boundari:1,br:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],br_if:0,br_tabl:0,bracket:[12,28,30,34,35,38],branch:[0,18,21,25,28,34],breach:24,brief:[16,39],bring:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],broadli:24,browser:24,bt:[6,12,18,34],bubbl:21,bytes_:[12,20],c0:[6,12,15],c1:[6,12],c2:[6,12,18],c3:[6,12],c4:[6,12],c5:6,c6:6,c7:6,c8:6,c9:6,c:[3,7,9,15,28,34,35,38,39,42,43],c_0:20,c_1:[18,20],c_2:18,c_3:18,c_:20,c_i:20,c_k:20,ca:6,cach:24,calcul:19,call:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],calle:28,can:[0,1,2,3,9,10,12,13,14,16,18,19,20,21,24,25,26,28,29,30,31,32,34,35,36,38,39,41,42],candid:20,candidatepair:20,cannot:[0,12,19,24,25,28,29,35,37],canon:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],cap:[20,24],capabl:24,carri:[3,21],carriag:35,categori:[8,21,25,28,35],caught:25,caus:28,cb:6,cc:6,ccc:9,cd:6,cdot2:31,cdot64:18,cdot:[3,9,15,16,18,19,20,31,38,41],ce:6,ceil:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],certain:[9,16,20,21,25],certifi:9,cf:6,chang:[0,5,9,13,22,39],channel:24,chapter:35,charact:[4,15,24,31,32,33,38],check:[0,1,13,18,19,25,28,30,34,39,41,42,43],choic:[18,21,36,41],chosen:[20,41],clamp:20,classif:3,classifi:[9,19,30,39,41,42,43],claus:[20,36],clear:[21,30,31],clll:36,cllll:36,close:[10,28,32,42],closest:20,closur:[19,21],clutter:[16,32],clz:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],code:[0,1,2,3,4,5,6,7,8,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],codesec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],codifi:9,coexist:14,coincid:[9,16,18],collect:[21,29,39],collid:12,com:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],combin:[1,20,36,37,41],combinatori:[10,26,32],come:28,comma:38,comment:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,36,37,38,39,40,41,42,43],common:[4,21,24,26],commun:24,compact:24,comparison:28,compat:[13,34,36],compil:[1,2,4,13,24,25,29],complement:[15,20,24,25,28,31],complementari:25,complet:[0,3,10,25,29,32,39],complex:[26,31],compon:[9,13,16,21,26,29,32,39,42],compos:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],composit:[26,36],compound:[9,41],compress:[10,12,13],comput:[4,9,16,18,20,21,24,25,28,30,32],concat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],concaten:[3,9,13,18,19,26,42],concept:23,conceptu:25,concern:[24,28],concis:[16,26,39],conclus:39,concret:[4,26,32,39],condit:[5,9,10,15,18,19,20,25,26,28,32,34,36,39],confer:[9,16,39],config:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],configur:[5,7,16],conform:4,conjunct:20,connect:3,conrad:9,consecut:[0,4,21,36],consequ:[0,9,10,28,29,35,36,41,42],consid:[20,21,24,32,34,35],consider:23,consist:[0,2,9,12,13,16,18,19,20,21,25,28,29,34,35,36],constant:[0,1,2,3,4,5,6,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],constitut:18,constrain:[30,41],constraint:[0,4,9,15,21,39,41],construct:[16,21,25,26,28,29,31,32,36,39,42],constructor:[8,14],consum:[18,24,28,39,41],cont:13,contain:[0,9,10,13,15,16,18,19,21,24,25,28,29,32,34,35,36,38,39,41,42],contemporari:24,content:[2,13,18,19,21,26,29,39,42],context:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,31,33,34,35,36,37,38,40,41,42,43],contigu:25,continu:[18,21,26,28],contract:24,contrast:[21,41],contribut:2,control:[0,1,2,3,4,5,6,7,8,10,11,13,14,15,16,17,19,20,21,22,23,24,25,26,27,29,30,31,32,33,35,36,37,38,39,40,42,43],conveni:[16,20,21,28,32],convent:[0,1,2,3,4,5,6,7,8,9,11,12,13,14,15,17,18,19,20,22,23,24,25,27,33,34,35,36,37,40,41,42,43],convers:[17,18,21,25,28],convert:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],convert_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],convert_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],copi:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],copysign:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],core:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],corollari:9,correct:9,correctli:38,correspond:[3,12,13,14,18,19,20,21,26,29,30,31,32,34,35,38,39,41],corrupt:24,could:25,count:[1,11,18,20,21],cours:24,courtesi:21,cover:9,cpp:9,crash:9,creat:[3,21,25],crucial:16,ctrl:0,ctrl_frame:0,ctrl_stack:0,ctxt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ctz:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],cup:20,current:[0,2,9,10,13,16,18,21,25,28,29,36,39,41],custom:[0,1,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],customsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],cvtop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],d0:[6,12],d1:[6,12],d2:[6,12],d3:6,d4:6,d5:6,d6:6,d7:6,d7ff:[31,35],d800:[15,38],d8:6,d9:6,d:[13,18,20,36,38],d_0:20,d_1:[18,20],d_2:[18,20],d_:20,da:[6,18,36],dan:[9,16,39],data:[1,2,3,4,5,6,7,8,10,11,12,14,15,16,17,20,22,23,24,25,26,27,28,30,31,32,33,34,35,37,38,39,40,43],dataaddr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],datacountsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],dataidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],datainst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],datamod:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],datasec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],datastr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],db:6,dc:6,dd:6,de:6,deal:[10,26],debug:[13,24],debugg:2,decim:38,declar:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],decod:[0,10,13,24,25],decompos:21,decreas:20,dedic:2,deduct:39,def:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],defer:[4,13],defin:[1,2,3,9,10,13,15,16,18,19,20,21,24,25,26,29,30,31,32,34,35,36,38,39,41,42,43],definit:[2,3,9,13,16,18,19,20,21,24,25,26,29,31,35,36,39,41,42],degre:41,delimit:[34,35],delta:28,demot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],denot:[10,13,14,18,20,21,26,28,29,30,31,32,38,39],dens:10,depend:[2,4,13,18,19,20,23,28,29,31,38,39,42],deploy:29,depth:[4,28],derek:[9,16,39],deriv:[3,9,10,16,39],desc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],describ:[0,9,13,16,21,24,26,28,29,31,39,41],descript:[3,7,13,16,29,32,36,39,42],descriptor:[29,34,36],design:[4,9,16,23,39],desktop:24,destin:28,detail:25,detect:0,determin:[0,16,19,20,28,30,31,34,42],determinist:[16,18,20,21],develop:24,devic:[19,24,42],df:6,diagnost:3,differ:[0,3,9,10,12,18,19,20,21,24,25,26,28,29,31,41,42],digit:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],dim:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],dimens:[4,41],dimension:2,dinstr:19,direct:[20,28],directli:[0,1,3,9,15,18,24,25,32,34,36],disallow:35,disambigu:35,discrep:24,disjoint:[9,42],disjunct:20,distinct:[25,31,32],distinguish:[10,13,21,28,29,31,32,34,41],distribut:25,div:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],diverg:[9,18],divid:[3,18,19,20,21,25,28,35,41],dividend:20,divis:[19,20],dmode:19,document:[24,37],documentari:36,doe:[0,3,9,13,18,19,20,24,28,35,38,39,42],dot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],doubl:[30,35],draft:[22,24],drawn:32,drop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],due:[3,18,19,31],dummi:19,dup:0,duplic:[0,28,32,36],dure:[4,9,18,21,29,30,43],dynam:[9,19,21,25,28],e000:[15,31,35,38],e0:[6,15],e1:6,e2:6,e3:6,e4:6,e5:6,e6:6,e7:6,e8:6,e9:6,e:[0,2,9,10,13,18,19,20,21,24,28,31,36,38],e_i:[13,42],ea:[6,18],each:[0,2,3,9,10,12,13,16,18,19,20,21,24,25,26,28,29,32,36,38,39,41,42,43],earlier:[18,36],eas:43,easi:[0,24],easili:[19,42],eb:6,ec:6,ed:6,editor:22,ee:6,ef:6,effect:[0,16,18,21,28,34,35,41,42],effector:35,effici:[24,41],einit:19,einstr:19,either:[0,9,10,12,15,16,18,19,20,21,24,25,26,28,29,30,31,32,35,36,38,41,43],el:[13,36],elem:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,43],elemaddr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],element:[0,1,3,4,7,10,11,14,17,18,20,25,26,27,28,30,33,38,39,40,41],elemexpr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elemidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],eleminst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elemkind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elemlist:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elemmod:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],elemsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elimin:21,ellips:26,els:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],elsewher:39,emb:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],embed:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],embedd:[3,4,9,18,19,21,24,25,29,30],embodi:39,emploi:[24,26],empti:[0,3,9,10,12,13,16,18,19,20,21,26,29,32,34,36,39,42,43],emptyset:[9,13],emul:25,enabl:[4,13,21,24],encapsul:9,enclos:[28,32,35,38],encod:[2,10,12,13,14,15,21,24,25,31,32,38,39],encompass:24,end:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],end_typ:0,endian:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],enforc:[15,28,34,36,39,41],enough:28,enrich:1,ensur:[0,9,18,19,21,25,36],enter:[0,16,28],entir:[16,21,29,36,41,42],entiti:[21,25,29,30],entri:[1,3,13,18,19,21,28,30,32,34,39],enumer:0,environ:[3,4,24,25,29],eof:35,epsilon:[3,8,9,10,12,13,14,16,18,19,20,21,26,32,34,36,37,38,42,43],eq:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],equal:[3,9,10,19,20,21,24,26,41,43],equat:20,equiv:[32,34,36,37],equival:[13,16,29,39],eqz:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],err:18,error:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],error_if:0,escap:38,especi:24,establish:24,et:[13,14,19,36,37,42],ev:3,evalu:[9,16,18,19],even:[0,3,20,21,29],event:4,ever:13,everi:[3,4,9,13,16,18,29,31,39],ex:[3,13,19,36],exact:[20,28],exactli:[10,20,21],exampl:[0,3,9,10,15,16,18,20,21,25,28,29,32,34,35,39,41],exce:[15,21],exceed:[4,18],except:[9,10,12,13,16,20,26,32,35,38,41,42],exclud:20,exclus:[20,35],exec:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],execut:[5,6,9,16,18,19,21,22,24,25,28,30,41],exist:[0,3,9,18,19,20,21,24,34,36,39],exit:[0,16],expand:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],expans:[10,20,26,32,36,38],expect:[0,3,4,9,13,18,19,28,41],experi:2,explan:[16,39],explanatori:0,explicit:[9,12,13,21,26,34,36,38],explicitli:[3,9,16,18,39],expon:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],exportdesc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],exportinst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],exportsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],expr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],express:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23,24,25,26,27,29,30,31,32,33,35,36,37,38,39,40,42,43],extadd:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],extend16:34,extend32:34,extend8:34,extend:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],extend_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],extend_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],extens:[0,5,10,12,13,18,20,28,32,39],extern:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,20,22,23,24,25,26,27,28,29,31,32,33,34,35,36,37,38,39,40,41,42],externaddr:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],externref:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],externtyp:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],externv:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],extmul:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],extra:9,extract:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],f0:[6,15],f1:6,f2:6,f32:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f32x4:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f3:6,f4:6,f5:6,f64:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f64x2:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f6:6,f7:6,f8:6,f9:6,f:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f_:19,fa:6,fab:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fact:[0,18,34,35],fadd:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fail:[18,19],failur:[3,18,19],fall:[18,25,35],fals:0,farther:28,fashion:[21,29,30],fast:24,fb:6,fbia:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fbit:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fc:[6,12],fceil:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fcopysign:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fd:[6,12],fdiv:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fe:[6,15],featur:[4,24],feed:35,feq:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],few:[10,16,32],ff:[6,15,31],ffloor:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fge:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fgt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],field:[13,19,26,36,39,42],file:[10,32,36],fill:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],filter:[21,29,30],finit:9,first:[0,4,19,20,26,28,29,30,36,41],fit:19,fix:[4,26,31],flag:[0,14,20],flat:[0,26],flavor:28,fle:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],floor:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],flow:[25,28],flt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fmax:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fmin:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fmul:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fn:36,fne:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fnearest:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fneg:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fold:[4,33],foldedinstr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],follow:[0,1,2,3,4,9,10,12,13,14,15,16,18,19,20,21,24,25,26,28,29,30,32,34,35,36,38,39,43],font:[10,26,32],foral:[9,20],foreach:0,forev:9,form:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],formal:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,40,41,42,43],format:[0,1,2,3,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,36,37,38,39,40,41,42,43],formed:[25,36,42],former:[0,10,32],formul:39,forth:10,forward:[13,28,29],found:[16,39],four:[21,25,28],fpmax:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fpmin:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],frac:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fraction:38,frame:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],free:[19,29,39],freed:28,frelop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fresh:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],from:[0,3,4,9,10,13,16,19,20,21,24,25,26,28,29,30,31,32,34,35,36,37,39,41,42],front:39,fshape:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fsign:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fsqrt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fsub:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ft:[3,13,18,36,42],ftestop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ftrunc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],full:25,fulli:[4,24,41],func:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],funcaddr:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcbind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcinst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcnamesec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcnamesubsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcref:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],functyp:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],funop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],further:[13,15,16,25,28,41],furthermor:[9,13,16,18,36,38,42],futur:[4,9,12,13,14,18,20,21,24,28,29,30,41,42],g:[0,2,9,19,24,31],gap:12,garbag:21,ge:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],gener:[0,1,9,10,13,16,18,20,26,32,39],geq:[10,12,15,20,26,31,32,38,43],get:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],gi:3,ginit:19,github:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],give:[16,39],given:[2,4,9,10,16,18,19,20,21,24,25,26,28,29,30,32,34,36,38,39,41,43],gl:36,glob:[13,18],global:[0,1,2,4,5,6,7,8,10,11,12,15,16,17,20,22,23,24,25,26,27,28,31,32,33,34,35,38,39,40],globaladdr:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globalbind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globalidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globalinst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globalsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globaltyp:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],go:29,goal:23,gohman:[9,16,39],grammar:[3,11,13,27,28,31,33,34,35,36,38],grave:38,greater:20,group:[2,24,28,34],grow:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],growmem:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],grown:25,growtabl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],gt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],guarante:[3,16,24,25],h:38,ha:[0,1,2,3,9,10,13,16,18,19,20,21,24,25,26,29,31,32,39,41],haa:[9,16,39],had:10,half:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],hand:[3,21],handl:[0,20,21,25,34],happen:19,hardwar:[18,24,28],hat:38,have:[1,4,10,12,13,18,20,21,24,26,28,29,31,32,34,37,39,41,43],head:34,heap:37,heaptyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],height:[0,21,25,28],help:20,henc:[3,20,21,24,38,39],here:[0,3,10,13,18,19,21,35,39,41,43],heterogen:28,hexadecim:[10,31,38],hexdigit:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hexfloat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hexfrac:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hexnum:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hf:18,hfill:19,hh:38,high:[18,24,28],hint:[2,18,28],histori:[5,22],hold:[9,18,20,21,30,39],hole:21,holman:[9,16,39],hookrightarrow:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hop:21,horizont:35,host:[3,21,24,25,29],hostcod:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hostfunc:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],how:[19,24,25,28,29,34,41],howev:[0,2,4,10,13,15,18,19,21,24,25,28,29,31,32,34,36,39,42,43],hspace:34,http:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i128:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i16:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i16x8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i2:20,i32:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i32x4:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i64:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i64x2:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i8x16:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],i:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i_1:18,i_2:18,iab:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iadd:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iaddsat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iaddsat_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iaddsat_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iand:[0,1,2,3,4,5,6,7,8,9,10,11,12,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1,32,33,34,35,36,37,38,39,40,41,42,43],opposit:20,optim:[18,28],option:[1,10,13,25,26,28,30,32,34,36,37,38,39],order:[0,2,3,9,10,12,13,15,16,19,20,21,25,28,29,30,31,32,36,42],organ:[13,25,29],origin:[0,1,9,16,18,20,21],other:[0,3,4,9,10,12,13,15,16,18,19,20,21,24,25,28,29,31,32,34,35,38,39,41,42],otherwis:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],out:[0,4,13,20,21,28,29,30,32,39],outcom:[9,18,21,42],outer:21,outermost:28,output:[20,28,30,41],outsid:[9,10,21,25,28,38,39],outward:28,over:[0,3,4,13,20,21,26,28,29,30,31,32,36,39,42],overflow:38,overlap:[28,35,36],overload:29,overview:[1,22,23],own:[9,19,21,24,25,29,30],p:[20,38],p_1:20,p_2:20,pack:[20,25,28,30,41],page:[3,9,18,19,21,28,29,30,36],pair:[2,3,10,13,18,20,25,29,36],parallel:[1,13,24],paralleliz:24,param:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],paramet:[1,3,4,14,18,19,25,29,30,32,36,37,39,42],parameter:13,parametr:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23,24,25,26,27,29,30,31,32,33,35,36,37,38,39,40,42,43],parenthes:[10,26,31,32,34,35],pars:[3,10,32,34],part:[2,3,16,18,21,24,25,26,28,39,41],parti:13,partial:[18,20],particular:[16,20,24,25,29],particularli:42,pass:[0,3,13,19,21,24,30,42],passiv:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],path:26,pattern:[12,15,30],payload:[20,31,38],per:[1,2,3,16,18,32,41],perform:[0,1,16,18,19,21,24,25,28,41,42],permit:20,phantom:[12,34],phase:23,phrase:[10,34,39],physic:4,pick:[10,20,41],piec:39,pierc:[16,39],place:[13,14,16,19,21,24,28,32,36,39],placehold:20,placement:13,plain:[12,20,32,34,43],plaininstr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],platform:24,pldi:[9,16,39],pm:[20,31,38],pmax:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],pmin:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],point:[1,3,11,17,18,21,24,26,27,28,30,33,41],pointer:25,pointwis:[19,20],polici:24,polymorph:[0,41],pop:[0,16,18,19,25,28,41],pop_ctrl:0,pop_val:0,popcnt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],portabl:24,posit:[8,12,14,15,18,20,31,34,39],possibl:[3,9,10,12,13,14,18,19,20,21,24,26,28,29,30,31,32,35,36,41],post:[5,9,18],potenti:24,power:[20,28],practic:[18,19,21,25],pre:[5,9,18,19,42],preambl:13,preced:[14,20,29,36],preceq:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],precis:[9,16,18,21,24,30],predic:20,prefix:[12,28,41],premis:39,prepend:[0,9,39,41],prescrib:[13,28,41],presenc:[0,13,16,18],present:[0,12,13,14,19,21,29,41],preserv:[9,21,29,30],press:[16,39],presum:38,prevent:[24,28,38],previou:[9,28],previous:36,primari:2,primarili:[19,39],primit:[20,31],printabl:[2,38],privileg:24,proce:[21,39],proceed:[9,16,39],process:[25,30,31,43],produc:[13,16,18,19,20,21,25,28,29,36,39,41],product:[10,15,26,32,35,36,38],program:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],progress:9,project:1,promot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],proof:[9,16,39],prop:9,propag:21,proper:0,properti:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],propos:1,proposit:39,prose:[17,40],prove:9,provid:[1,2,3,10,19,21,24,25,26,28,29,32,38,39,41,43],pseudo:[0,28,34,35],pth:26,pure:0,purg:0,purpos:[0,2,19,21,37],push:[0,16,18,19,21,25,28,41],push_ctrl:0,push_val:0,put:24,q15mulr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],q:[20,38],q_1:20,q_2:20,qquad:[3,9,10,13,14,15,18,19,20,21,31,32,34,35,36,37,38,39,41,42,43],quad:[9,13,16,18,19,21,29,32,34,36,42,43],qualif:20,quiet:[20,31],quot:32,quotat:38,r:[3,9,18,19,20,21,26,38],r_1:26,r_2:26,rang:[1,3,4,12,13,20,21,24,26,28,29,30,31,38,43],rather:21,ration:20,raw:[25,29,31,36,38],rcl:21,rcll:19,re:19,reach:[3,9,18,21],reachabl:0,read:[9,13,16,20,28,39],readabl:32,reader:[16,39],readili:[16,39],real:[20,25],reason:[4,24],recent:[16,41],recogn:35,recommend:[10,20,32],record:[0,13,16,21,26,32,39],rectifi:20,recurs:[19,25,26,32,34,39,41,42],reduc:[16,18,21],reduct:[16,18,21],ref:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],refer:[3,8,9,11,16,17,21,25,27,29,33,36,39,40,42],referenc:[18,19,21,25,28,29,36,37],refin:[0,3],reftyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],regard:[20,34],regardless:[18,28,30],region:28,regist:25,regular:[3,9,34,36],regularli:18,reinterpret:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],reject:4,rel:[9,18,19,20,21,28,34,39,41],relat:[1,9,19,20,28],releas:[5,22,24],relev:[10,21,24,26,32,35,36,39],relop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],rem:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],remain:9,remaind:[0,20],remov:[0,9,16,18,21],render:[2,16,32,39],reorder:1,repeat:[18,34],repeatedli:36,replac:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],report:[4,19,25],repres:[0,2,12,13,16,20,21,25,28,31,34,35,38,39],represent:[0,1,10,15,16,17,21,24,25,26,30,31,38],repurpos:9,requir:[0,3,4,9,10,13,16,18,19,20,21,25,26,28,29,38,39,41,42],reserv:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],resiz:[0,30],resolv:[20,21,29,32,36],resourc:[4,18,24],respect:[0,1,3,9,10,12,13,14,16,18,20,21,24,25,26,28,29,30,31,32,34,36,38,39,41,43],respons:[3,24],rest:[19,35],restart:[21,28],restrict:[4,10,15,21,28,29,32,35,36,42,43],result:[0,1,2,3,4,5,6,7,8,10,11,12,13,15,16,17,18,19,20,22,23,24,25,26,27,28,29,31,32,33,34,35,36,37,38,39,40,41,42,43],resulttyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],resum:28,retriev:28,reus:[21,24,36],revers:0,rewrit:32,right:[0,9,16,18,20,35],rightarrow:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],rlll:19,rllll:19,role:36,root:20,rossberg:[9,16,22,39],rotat:20,rotl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],rotr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],round:[24,36,38],rt:[14,42],rule:[9,10,13,16,18,19,21,22,26,32,34,35,38,39,41,42,43],run:[9,21,24],rundata:19,runelem:19,runtim:[0,1,2,4,5,6,8,10,11,12,13,14,15,16,17,18,20,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s16:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s32:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s64:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s_0:19,s_1:[9,19],s_2:[9,19],s_3:19,s_4:19,s_5:19,s_:19,s_i:[19,26],s_n:19,safe:[24,25],safeti:9,sai:39,said:39,same:[4,9,10,13,14,18,20,21,26,28,29,31,32,34,36,39,41,42,43],san:26,sandbox:24,sat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],sat_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],sat_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],satisfi:[3,9,18],satur:[12,20,28],scalar:[31,32,35,38],schuff:[9,16,39],scope:[9,10,21,23,25,36,39],second:[0,28,36],secondari:[2,19],section:[0,1,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],secur:23,see:36,seen:24,seg:13,segment:[1,4,7,13,18,21,25,27,28,33,39,40,41],select:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],self:[0,24],semant:[0,2,3,9,13,16,18,19,21,22,23,24,39],semicolon:[35,38],sens:3,separ:[0,9,10,12,13,16,20,21,24,25,26,28,32,35,38],seq:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],sequenc:[2,3,5,7,9,10,12,13,15,16,18,19,20,21,25,26,28,29,30,31,32,34,35,36,38,39,40,42],serif:26,serv:[25,29,36],set:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],sever:[12,20,24,28,41],shape:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],share:21,shift:[20,28,34,39,41],shl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],shortcut:28,shorten:26,shorthand:[10,19,20,26,28,32],should:2,show:0,shown:0,shr:[0,1,2,3,4,5,6,7,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0,t2:0,t:[0,3,6,12,13,14,15,20,21,28,30,32,34,36,37,38,39],t_0:41,t_1:[6,9,19,32,36,37,39,42],t_2:[6,9,19,36,37,39,42],t_3:41,t_i:[9,13,19,32,41],t_j:41,t_n:32,ta:[18,36],tab:[13,18],tabl:[0,2,4,5,6,7,8,10,11,15,16,17,20,22,23,24,25,26,27,31,32,33,35,38,39,40],tableaddr:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tablebind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tableidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tableinst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tablesec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tabletyp:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],tableus:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tabul:35,take:[0,1,2,4,9,19,20,21,24,25,28,32],taken:21,target:[16,20,21,25,28],task:24,technic:20,techniqu:21,tee:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],term:[10,16,18,21,26,32,36],termin:[4,9,10,12,15,16,18,21,26,28,29,32,35],ternari:[1,28],test:[1,20,28],testop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],text:[0,1,2,3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,35,36,37,38,39,40,41,42,43],textual:[24,32,38],th:[18,26],than:[1,3,13,18,19,20,21,24,25,28,31,38,41,42,43],thei:[2,4,9,10,12,13,14,18,20,21,24,25,28,29,30,31,32,34,35,36,37,38,39,41,42],them:[0,3,9,16,20,21,25,28,29,31,34,36,39],themselv:[9,15,21,28,35,42],theorem:5,therebi:[16,25,36],therefor:[0,18,21,41],thereof:30,thi:[0,2,3,4,9,10,13,15,16,18,19,20,21,24,25,26,28,29,30,31,32,34,35,38,39,41,42,43],third:[13,28],thisisenough:34,thisshouldbeenough:[12,34],thorough:[16,39],those:[9,10,26,28,32,42],thread:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],three:[16,18,21,25,28],through:[0,3,13,18,21,25,28,29],thu:[10,14,20,25,29,32],ti:[3,20],tild:38,time:[1,4,9,10,18,19,21,24,26,28,29,32],titzer:[9,16,39],togeth:28,token:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,36,37,38,39,40,41,42,43],tool:36,top:[0,10,18,19],toplevel:36,total:15,touch:16,toward:[20,25],track:0,tracker:22,trail:[15,20],transfer:41,translat:24,transmit:24,transpar:30,trap:[0,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],treat:[3,12,26,28],tree:1,tripl:3,trunc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],trunc_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],trunc_sat_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],trunc_sat_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],trunc_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],truncat:[12,20],tt:[3,9,13,36,42],tupl:16,turn:[2,4,13],two:[0,2,10,13,15,16,18,20,24,25,26,28,29,31,35,39,41,43],ty:36,type:[0,2,4,5,6,10,11,12,15,16,17,20,21,22,23,24,25,26,27,28,31,32,33,34,35,38,39,40],typebind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],typedef:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],typeidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],typesec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],typeus:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],typewrit:[10,32],typic:[3,4,16,24,25,28],u16:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u1:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u32:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u64:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ultim:21,unalign:[18,25],unambigu:[14,32],unari:[1,20,28],unchang:9,uncondit:[0,28,41],uncondition:39,unconstrain:41,undefin:[9,20],under:[0,9,18,21,25,30,39,41,42],underflow:0,underli:[18,20,31],underscor:38,understand:[16,39],unicod:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],unifi:21,uniniti:29,uninterpret:[13,15,21,29,31,38],union:30,uniqu:[2,21,29],unit:[28,29,30],univers:[24,43],unknown:[0,13],unless:[9,16,18],unlik:[12,15,25,28,29],unnam:[32,34],unnecessari:[16,32],unop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],unpack:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],unravel:19,unreach:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],unsaf:24,unsign:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],unspecif:3,unspecifi:20,until:[4,13,18],untyp:25,unus:15,unwind:28,up:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],updat:[3,19,26,34,36],upon:29,upper:20,us:[0,1,2,3,4,10,12,13,15,16,18,20,21,24,25,26,28,29,30,31,32,33,34,35,38,39],usabl:25,user:2,usual:[4,10,20,25,28,32],utf8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],utf:[2,15,24,31,32,38],v128:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],v:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],val:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],val_i:19,val_stack:0,val_typ:0,valid:[1,2,3,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,41,42,43],valtyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42],valu:[0,2,4,5,6,7,8,10,11,12,13,16,17,18,20,22,23,24,25,26,27,28,29,32,33,34,35,36,39,40,41,43],vari:[4,12,31],variabl:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23,24,25,26,27,29,30,31,32,33,35,36,37,38,39,40,42,43],variant:[12,15],varieti:24,variou:[0,16,30],vbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vcvtop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vdash:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vechaslongerinstructionnam:12,vechasreallylonginstructionnam:34,vector:[2,8,9,11,13,15,17,19,21,25,27,29,33,40,42],vectyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vee:[9,13,15,18,20,34,36,38],veebar:20,verbatim:34,veri:[13,16],verifi:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],version:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vextmul:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vfbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vfrelop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vfunop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],via:[18,19],vibinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],view:25,viminmaxop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],violat:18,virelop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],virtual:[24,25],visatbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vishiftop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],visual:34,vitestop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],viunop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vm:24,vrelop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vternop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vtestop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vulner:24,vunop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vvbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vvternop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vvtestop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vvunop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],w3c:24,w:18,wa:28,wagner:[9,16,39],wai:[3,9,21,24,25],wasm:[10,24],wat:32,watt:9,we:[29,39,41],web:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],webassembl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],wedg:[3,9,15,18,19,20,35,36,38],well:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],were:0,wf:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],what:[1,39],when:[0,1,2,3,9,10,13,16,18,20,21,26,29,32,36,38,39,41,42,43],where:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],wherea:12,whether:[0,9,13,14,21,28,29,31],which:[0,2,3,4,9,10,12,13,15,16,18,19,20,21,24,25,28,29,30,31,32,34,35,36,38,39,41,42,43],white:[32,33,34,38],whitespac:35,whose:[0,2,9,10,13,18,19,20,31,32,36,39,43],wide:[16,25,39],width:[18,20,21,25,28,30,31,41],wise:[16,18,20,26,28,41],within:[1,9,15,20,21,25,28,29,30,38,43],without:[4,12,13,18,41],word:[9,39],would:[0,13,18,21,41],wrap:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],write:32,written:[9,10,20,26,28,30,32,34,36,38,39],ww:28,x:[1,6,8,10,12,13,19,20,26,28,29,32,34,35,36,39],x_1:[16,21],x_2:[16,21],x_3:[16,21],x_4:16,x_5:16,x_6:16,x_i:18,xor:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],xref:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],y:[6,12,13,29,34,36],yield:[3,18,28],z:[12,18,31,34,35,38],z_1:18,z_k:18,zakai:[9,16,39],zero:[10,12,15,18,19,20,28,29,31]},titles:["Validation Algorithm","Change History","Custom Sections","Embedding","Implementation Limitations","Appendix","Index of Instructions","Index of Semantic Rules","Index of Types","Soundness","Conventions","Binary Format","Instructions","Modules","Types","Values","Conventions","Execution","Instructions","Modules","Numerics","Runtime Structure","WebAssembly Specification","Introduction","Introduction","Overview","Conventions","Structure","Instructions","Modules","Types","Values","Conventions","Text Format","Instructions","Lexical Format","Modules","Types","Values","Conventions","Validation","Instructions","Modules","Types"],titleterms:{"0":1,"16":41,"2":1,"boolean":20,"byte":[3,15,31],"char":3,"const":[18,19,41],"export":[9,13,21,29,36,42],"float":[1,15,20,31,38],"function":[2,3,9,13,14,18,19,21,29,30,36,37,42,43],"import":[13,29,36,42,43],"int":[1,3],"null":[18,19,41],"return":[18,41],"static":7,_0:9,_1:[18,41,42],_2:[18,41,42],_:[18,20,41],_alloc:3,_decod:3,_export:3,_grow:3,_i16x8:18,_if:[18,41],_import:3,_indirect:[18,41],_init:3,_instanti:3,_invok:3,_lane:[18,41],_n:[9,20,41],_null:[18,41],_pairwis:[18,41],_pars:3,_read:3,_s:[18,20,41],_sat:20,_size:3,_splat:[18,41],_t_1:18,_tabl:[18,41],_true:18,_type:3,_u:20,_valid:3,_write:3,_zero:[18,41],abbrevi:[32,34,36,37],activ:[21,42],address:[18,21],administr:[9,21],algorithm:0,all:18,alloc:19,ani:18,appendix:[3,5],ast:[3,9,18,41,42],auxiliari:[10,26],b:[9,42],binari:[4,11],binop:[18,41],bitmask:[18,41],block:[18,21,41,43],blocktyp:[18,41],bodi:42,br:[18,41],bulk:1,c:[18,19,20,41],call:[18,41],chang:1,charact:35,code:[9,13],comment:35,concept:25,condit:3,configur:[9,21],consider:24,constant:[7,41],construct:7,context:[21,32,39],control:[9,12,18,28,34,41],convent:[10,16,21,26,28,29,30,31,32,38,39],convers:[1,20],convert:20,convert_:20,convert_u:20,copi:[18,41],count:13,custom:[2,13],cvtop:[18,41],data:[0,9,13,18,19,21,29,36,41,42],datainst:9,datamod:42,declar:42,demot:20,depend:24,desc:42,design:24,dot:[18,41],drop:[18,41],e:42,elem:[9,18,41,42],element:[9,13,19,21,29,36,42],eleminst:9,elemmod:42,els:[18,41],emb:3,embed:3,empti:41,end:[9,18,41],enter:18,epsilon:41,error:3,evalu:21,exec:[3,9,19,20],execut:[4,7,17],exit:18,exportdesc:42,exportinst:9,expr:42,express:[12,18,28,34,41],extadd:[18,41],extend:20,extend_:20,extend_u:20,extens:[1,7,9],extern:[9,19,21,30,43],externaddr:9,externtyp:[3,43],externv:[3,9,19],extmul:[18,41],extract:[18,41],f:9,fa:9,fab:20,fadd:20,fceil:20,fcopysign:20,fdiv:20,feq:20,ffloor:20,fge:20,fgt:20,fill:[18,41],fle:20,flt:20,fmax:20,fmin:20,fmul:20,fne:20,fnearest:20,fneg:20,fold:34,formal:[16,39],format:[4,11,33,35],fpmax:20,fpmin:20,frame:[9,21],from:18,fsqrt:20,fsub:20,ftrunc:20,func:[3,9,18,19,41,42,43],funcaddr:[3,9],funcinst:9,functyp:[3,9,43],get:[18,41],global:[3,9,13,14,18,19,21,29,30,36,37,41,42,43],globaladdr:3,globalinst:9,globaltyp:[3,42,43],goal:24,grammar:[10,26,32],grow:[18,19,41],half:[18,41],hf:9,histori:1,host:[9,18,19],hostcod:9,hostfunc:3,i32x4:18,i8x16:[18,41],i:[3,20],i_1:20,i_2:20,i_3:20,iab:20,iadd:20,iaddsat:20,iaddsat_:20,iaddsat_u:20,iand:20,iandnot:20,iavgr:20,iavgr_u:20,ibitselect:20,iclz:20,ictz:20,identifi:38,idiv:20,idiv_:20,idiv_u:20,ieq:20,ieqz:20,iextend:20,iextendn_:20,ig:20,ige_:20,ige_u:20,igt:20,igt_:20,igt_u:20,il:20,ile_:20,ile_u:20,ilt:20,ilt_:20,ilt_u:20,imax:20,imax_:20,imax_u:20,imin:20,imin_:20,imin_u:20,implement:4,importdesc:42,imul:20,index:[6,7,8],indic:[13,29,36],ine:20,ineg:20,init:[18,41,42],inot:20,instanc:[3,9,21],instanti:19,instr:[9,18,19,41],instruct:[1,6,9,12,18,19,21,28,34,41,42],integ:[15,20,31,38],interpret:20,introduct:[23,24],invoc:[18,19],invok:9,ior:20,ipopcnt:20,iq15mulrsat:20,iq15mulrsat_:20,irem:20,irem_:20,irem_u:20,irotl:20,irotr:20,ishap:41,ishl:20,ishr:20,ishr_:20,ishr_u:20,isub:20,isubsat:20,isubsat_:20,isubsat_u:20,ixor:20,l:[18,41],l_n:[18,41],label:[9,18,21,34],laneidx:41,lexic:35,limit:[4,9,14,30,37,43],load:[18,41],local:[2,9,18,41,42],loop:[18,41],m:[18,20,41,43],map:2,match:7,mathit:[3,9,18,41,42,43],mathrm:[3,20],mathsf:[9,18,19,20,41,42,43],max:43,mem:[3,19,42,43],memaddr:3,memarg:[18,41],meminst:9,memori:[1,3,9,12,13,14,18,19,21,28,29,30,34,36,37,41,42,43],memtyp:[3,42,43],min:43,mode:42,modul:[2,3,9,13,19,21,29,36,42,43],moduleinst:[3,9],multipl:1,mut:[9,42,43],n:[3,18,20,41,43],name:[2,3,9,15,31,38,42],nan:20,narrow:[18,20,41],narrow_:20,narrow_u:20,non:[1,41],nop:[18,41],notat:[10,16,26,39],number:[14,30,37],numer:[12,18,19,20,28,34,41],offset:42,op:20,opcod:0,oper:20,overview:25,parametr:[12,18,28,34,41],passiv:42,phase:25,point:[15,20,31,38],post:3,pre:3,promot:20,propag:20,prose:[16,39],ref:[3,9,18,19,41],refer:[1,12,14,18,19,28,30,34,37,41],reftyp:43,reinterpret:20,releas:1,relop:[18,41],replac:[18,41],represent:20,result:[9,14,21,30],rightarrow:43,round:20,rule:7,runtim:[3,7,9,19,21],s:[9,20],scope:24,section:[2,13],secur:24,segment:[19,29,36,42],select:[18,41],semant:[7,25],sequenc:[0,41],set:[18,41],shape:[18,41],shuffl:[18,41],sign:[1,20],size:[18,41],sound:9,space:35,specif:22,splat:[18,41],stack:21,start:[13,29,36,42],storag:20,store:[3,7,9,18,21,41],string:38,structur:[0,4,21,27],subsect:2,subtyp:43,swizzl:[18,41],sx:[18,41],syntact:4,syntax:[3,9,18,19,41,42,43],t:[9,18,19,41,42],t_1:[18,20,41,43],t_2:[18,20,41,43],tabl:[1,3,9,12,13,14,18,19,21,28,29,30,34,36,37,41,42,43],tableaddr:3,tableinst:9,tabletyp:[3,42,43],tee:[18,41],testop:[18,41],text:[4,33],theorem:9,thread:9,token:35,trap:[1,9],trunc:20,trunc_:20,trunc_sat_:20,trunc_sat_u:20,trunc_u:20,type:[1,3,7,8,9,13,14,18,19,29,30,36,37,41,42,43],typeidx:43,u32:3,u:20,unop:[18,41],unreach:[18,41],us:36,v128:[18,41],val:[3,9],valid:[0,4,9,40],valtyp:[18,41,43],valu:[1,3,9,14,15,19,21,30,31,37,38,42],variabl:[12,18,28,34,41],vbinop:[18,41],vcvtop:[18,41],vec:[18,41],vector:[1,10,12,14,18,20,26,28,30,31,32,34,37,41],vishiftop:[18,41],vrelop:[18,41],vtestop:41,vunop:[18,41],vvbinop:[18,41],vvternop:[18,41],vvtestop:41,vvunop:[18,41],webassembl:22,white:35,wrap:20,x:[18,41,42],xref:[3,9,18,19,20,41,42,43],y:[18,41],z:20,z_1:20,z_2:20}}) \ No newline at end of file diff --git a/core/syntax/conventions.html b/core/syntax/conventions.html new file mode 100644 index 00000000..87e171b0 --- /dev/null +++ b/core/syntax/conventions.html @@ -0,0 +1,186 @@ + + + + + + + + + Conventions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Conventions

    +

    WebAssembly is a programming language that has multiple concrete representations +(its binary format and the text format). +Both map to a common structure. +For conciseness, this structure is described in the form of an abstract syntax. +All parts of this specification are defined in terms of this abstract syntax.

    +
    +

    Grammar Notation

    +

    The following conventions are adopted in defining grammar rules for abstract syntax.

    +
      +

    • Terminal symbols (atoms) are written in sans-serif font: \(\mathsf{i32}, \mathsf{end}\).

      • +

    • Nonterminal symbols are written in italic font: \(\mathit{valtype}, \mathit{instr}\).

      • +

    • \(A^n\) is a sequence of \(n\geq 0\) iterations of \(A\).

      • +

    • \(A^\ast\) is a possibly empty sequence of iterations of \(A\). +(This is a shorthand for \(A^n\) used where \(n\) is not relevant.)

      • +

    • \(A^+\) is a non-empty sequence of iterations of \(A\). +(This is a shorthand for \(A^n\) where \(n \geq 1\).)

      • +

    • \(A^?\) is an optional occurrence of \(A\). +(This is a shorthand for \(A^n\) where \(n \leq 1\).)

      • +

    • Productions are written \(\mathit{sym} ::= A_1 ~|~ \dots ~|~ A_n\).

      • +

    • Large productions may be split into multiple definitions, indicated by ending the first one with explicit ellipses, \(\mathit{sym} ::= A_1 ~|~ \dots\), and starting continuations with ellipses, \(\mathit{sym} ::= \dots ~|~ A_2\).

      • +

    • Some productions are augmented with side conditions in parentheses, “\((\mathrel{\mbox{if}} \mathit{condition})\)”, that provide a shorthand for a combinatorial expansion of the production into many separate cases.

      • +

    • If the same meta variable or non-terminal symbol appears multiple times in a production, then all those occurrences must have the same instantiation. +(This is a shorthand for a side condition requiring multiple different variables to be equal.)

      • +
    +
    +
    +

    Auxiliary Notation

    +

    When dealing with syntactic constructs the following notation is also used:

    +
      +

    • \(\epsilon\) denotes the empty sequence.

      • +

    • \(|s|\) denotes the length of a sequence \(s\).

      • +

    • \(s[i]\) denotes the \(i\)-th element of a sequence \(s\), starting from \(0\).

      • +

    • \(s[i \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} n]\) denotes the sub-sequence \(s[i]~\dots~s[i+n-1]\) of a sequence \(s\).

      • +

    • \(s \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} [i] = A\) denotes the same sequence as \(s\), +except that the \(i\)-th element is replaced with \(A\).

      • +

    • \(s \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} [i \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} n] = A^n\) denotes the same sequence as \(s\), +except that the sub-sequence \(s[i \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} n]\) is replaced with \(A^n\).

      • +

    • \(\href{../syntax/conventions.html#notation-concat}{\mathrm{concat}}(s^\ast)\) denotes the flat sequence formed by concatenating all sequences \(s_i\) in \(s^\ast\).

      • +
    +

    Moreover, the following conventions are employed:

    +
      +

    • The notation \(x^n\), where \(x\) is a non-terminal symbol, is treated as a meta variable ranging over respective sequences of \(x\) (similarly for \(x^\ast\), \(x^+\), \(x^?\)).

      • +

    • When given a sequence \(x^n\), +then the occurrences of \(x\) in a sequence written \((A_1~x~A_2)^n\) are assumed to be in point-wise correspondence with \(x^n\) +(similarly for \(x^\ast\), \(x^+\), \(x^?\)). +This implicitly expresses a form of mapping syntactic constructions over a sequence.

      • +
    +

    Productions of the following form are interpreted as records that map a fixed set of fields \(\mathsf{field}_i\) to “values” \(A_i\), respectively:

    +
    +\[\mathit{r} ~::=~ \{ \mathsf{field}_1~A_1, \mathsf{field}_2~A_2, \dots \}\]
    +

    The following notation is adopted for manipulating such records:

    +
      +

    • \(r.\mathsf{field}\) denotes the contents of the \(\mathsf{field}\) component of \(r\).

      • +

    • \(r \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \mathsf{field} = A\) denotes the same record as \(r\), +except that the contents of the \(\mathsf{field}\) component is replaced with \(A\).

      • +

    • \(r_1 \href{../syntax/conventions.html#notation-compose}{\oplus} r_2\) denotes the composition of two records with the same fields of sequences by appending each sequence point-wise:

      +
      +\[\{ \mathsf{field}_1\,A_1^\ast, \mathsf{field}_2\,A_2^\ast, \dots \} \href{../syntax/conventions.html#notation-compose}{\oplus} \{ \mathsf{field}_1\,B_1^\ast, \mathsf{field}_2\,B_2^\ast, \dots \} = \{ \mathsf{field}_1\,A_1^\ast~B_1^\ast, \mathsf{field}_2\,A_2^\ast~B_2^\ast, \dots \}\]
      +
      • +

    • \(\href{../syntax/conventions.html#notation-compose}{\bigoplus} r^\ast\) denotes the composition of a sequence of records, respectively; if the sequence is empty, then all fields of the resulting record are empty.

      • +
    +

    The update notation for sequences and records generalizes recursively to nested components accessed by “paths” \(\mathit{pth} ::= ([\dots] \;| \;.\mathsf{field})^+\):

    +
      +

    • \(s \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} [i]\,\mathit{pth} = A\) is short for \(s \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} [i] = (s[i] \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \mathit{pth} = A)\).

      • +

    • \(r \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \mathsf{field}\,\mathit{pth} = A\) is short for \(r \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \mathsf{field} = (r.\mathsf{field} \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \mathit{pth} = A)\).

      • +
    +

    where \(r \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}}~.\mathsf{field} = A\) is shortened to \(r \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \mathsf{field} = A\).

    +
    +
    +

    Vectors

    +

    Vectors are bounded sequences of the form \(A^n\) (or \(A^\ast\)), +where the \(A\) can either be values or complex constructions. +A vector can have at most \(2^{32}-1\) elements.

    +
    +\[\begin{split}\begin{array}{lllll} +\def\mathdef2344#1{{}}\mathdef2344{vector} & \href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(A) &::=& + A^n + & (\mathrel{\mbox{if}} n < 2^{32})\\ +\end{array}\end{split}\]
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/syntax/index.html b/core/syntax/index.html new file mode 100644 index 00000000..1ea446c5 --- /dev/null +++ b/core/syntax/index.html @@ -0,0 +1,164 @@ + + + + + + + + + Structure — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Structure

    +
    + +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/syntax/instructions.html b/core/syntax/instructions.html new file mode 100644 index 00000000..227af43b --- /dev/null +++ b/core/syntax/instructions.html @@ -0,0 +1,634 @@ + + + + + + + + + Instructions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Instructions

    +

    WebAssembly code consists of sequences of instructions. +Its computational model is based on a stack machine in that instructions manipulate values on an implicit operand stack, +consuming (popping) argument values and producing or returning (pushing) result values.

    +

    In addition to dynamic operands from the stack, some instructions also have static immediate arguments, +typically indices or type annotations, +which are part of the instruction itself.

    +

    Some instructions are structured in that they bracket nested sequences of instructions.

    +

    The following sections group instructions into a number of different categories.

    +
    +

    Numeric Instructions

    +

    Numeric instructions provide basic operations over numeric values of specific type. +These operations closely match respective operations available in hardware.

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2422#1{{}}\mathdef2422{width} & \mathit{nn}, \mathit{mm} &::=& + \mathsf{32} ~|~ \mathsf{64} \\ +\def\mathdef2422#1{{}}\mathdef2422{signedness} & \href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} &::=& + \mathsf{u} ~|~ \mathsf{s} \\ +\def\mathdef2422#1{{}}\mathdef2422{instruction} & \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}} &::=& + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\href{../syntax/values.html#syntax-int}{\def\mathdef2461#1{{\mathit{i#1}}}\mathdef2461{\mathit{nn}}} ~|~ + \mathsf{f}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~\href{../syntax/values.html#syntax-float}{\def\mathdef2462#1{{\mathit{f#1}}}\mathdef2462{\mathit{nn}}} \\&&|& + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-iunop}{\mathit{iunop}} ~|~ + \mathsf{f}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-funop}{\mathit{funop}} \\&&|& + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-ibinop}{\mathit{ibinop}} ~|~ + \mathsf{f}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-fbinop}{\mathit{fbinop}} \\&&|& + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-itestop}{\mathit{itestop}} \\&&|& + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-irelop}{\mathit{irelop}} ~|~ + \mathsf{f}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-frelop}{\mathit{frelop}} \\&&|& + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{8\_s} ~|~ + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{16\_s} ~|~ + \mathsf{i64.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{32\_s} \\&&|& + \mathsf{i32.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{wrap}}\mathsf{\_i64} ~|~ + \mathsf{i64.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{\_i32}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_f}\mathit{mm}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\&&|& + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_f}\mathit{mm}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\&&|& + \mathsf{f32.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{demote}}\mathsf{\_f64} ~|~ + \mathsf{f64.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{promote}}\mathsf{\_f32} ~|~ + \mathsf{f}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_i}\mathit{mm}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\&&|& + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{reinterpret}}\mathsf{\_f}\mathit{nn} ~|~ + \mathsf{f}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{reinterpret}}\mathsf{\_i}\mathit{nn} \\&&|& + \dots \\ +\def\mathdef2422#1{{}}\mathdef2422{integer unary operator} & \href{../syntax/instructions.html#syntax-iunop}{\mathit{iunop}} &::=& + \mathsf{clz} ~|~ + \mathsf{ctz} ~|~ + \mathsf{popcnt} \\ +\def\mathdef2422#1{{}}\mathdef2422{integer binary operator} & \href{../syntax/instructions.html#syntax-ibinop}{\mathit{ibinop}} &::=& + \mathsf{add} ~|~ + \mathsf{sub} ~|~ + \mathsf{mul} ~|~ + \mathsf{div\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{rem\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\&&|& + \mathsf{and} ~|~ + \mathsf{or} ~|~ + \mathsf{xor} ~|~ + \mathsf{shl} ~|~ + \mathsf{shr\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{rotl} ~|~ + \mathsf{rotr} \\ +\def\mathdef2422#1{{}}\mathdef2422{floating-point unary operator} & \href{../syntax/instructions.html#syntax-funop}{\mathit{funop}} &::=& + \mathsf{abs} ~|~ + \mathsf{neg} ~|~ + \mathsf{sqrt} ~|~ + \mathsf{ceil} ~|~ + \mathsf{floor} ~|~ + \mathsf{trunc} ~|~ + \mathsf{nearest} \\ +\def\mathdef2422#1{{}}\mathdef2422{floating-point binary operator} & \href{../syntax/instructions.html#syntax-fbinop}{\mathit{fbinop}} &::=& + \mathsf{add} ~|~ + \mathsf{sub} ~|~ + \mathsf{mul} ~|~ + \mathsf{div} ~|~ + \mathsf{min} ~|~ + \mathsf{max} ~|~ + \mathsf{copysign} \\ +\def\mathdef2422#1{{}}\mathdef2422{integer test operator} & \href{../syntax/instructions.html#syntax-itestop}{\mathit{itestop}} &::=& + \mathsf{eqz} \\ +\def\mathdef2422#1{{}}\mathdef2422{integer relational operator} & \href{../syntax/instructions.html#syntax-irelop}{\mathit{irelop}} &::=& + \mathsf{eq} ~|~ + \mathsf{ne} ~|~ + \mathsf{lt\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{gt\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{le\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{ge\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\ +\def\mathdef2422#1{{}}\mathdef2422{floating-point relational operator} & \href{../syntax/instructions.html#syntax-frelop}{\mathit{frelop}} &::=& + \mathsf{eq} ~|~ + \mathsf{ne} ~|~ + \mathsf{lt} ~|~ + \mathsf{gt} ~|~ + \mathsf{le} ~|~ + \mathsf{ge} \\ +\end{array}\end{split}\]
    +

    Numeric instructions are divided by number type. +For each type, several subcategories can be distinguished:

    +
      +

    • Constants: return a static constant.

      • +

    • Unary Operations: consume one operand and produce one result of the respective type.

      • +

    • Binary Operations: consume two operands and produce one result of the respective type.

      • +

    • Tests: consume one operand of the respective type and produce a Boolean integer result.

      • +

    • Comparisons: consume two operands of the respective type and produce a Boolean integer result.

      • +

    • Conversions: consume a value of one type and produce a result of another +(the source type of the conversion is the one after the “\(\mathsf{\_}\)”).

      • +
    +

    Some integer instructions come in two flavors, +where a signedness annotation \(\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\) distinguishes whether the operands are to be interpreted as unsigned or signed integers. +For the other integer instructions, the use of two’s complement for the signed interpretation means that they behave the same regardless of signedness.

    +
    +

    Conventions

    +

    Occasionally, it is convenient to group operators together according to the following grammar shorthands:

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2422#1{{}}\mathdef2422{unary operator} & \href{../syntax/instructions.html#syntax-unop}{\mathit{unop}} &::=& + \href{../syntax/instructions.html#syntax-iunop}{\mathit{iunop}} ~|~ + \href{../syntax/instructions.html#syntax-funop}{\mathit{funop}} ~|~ + \href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}{N}\mathsf{\_s} \\ +\def\mathdef2422#1{{}}\mathdef2422{binary operator} & \href{../syntax/instructions.html#syntax-binop}{\mathit{binop}} &::=& \href{../syntax/instructions.html#syntax-ibinop}{\mathit{ibinop}} ~|~ \href{../syntax/instructions.html#syntax-fbinop}{\mathit{fbinop}} \\ +\def\mathdef2422#1{{}}\mathdef2422{test operator} & \href{../syntax/instructions.html#syntax-testop}{\mathit{testop}} &::=& \href{../syntax/instructions.html#syntax-itestop}{\mathit{itestop}} \\ +\def\mathdef2422#1{{}}\mathdef2422{relational operator} & \href{../syntax/instructions.html#syntax-relop}{\mathit{relop}} &::=& \href{../syntax/instructions.html#syntax-irelop}{\mathit{irelop}} ~|~ \href{../syntax/instructions.html#syntax-frelop}{\mathit{frelop}} \\ +\def\mathdef2422#1{{}}\mathdef2422{conversion operator} & \href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}} &::=& + \href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{wrap}} ~|~ + \href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}} ~|~ + \href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}} ~|~ + \href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat} ~|~ + \href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}} ~|~ + \href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{demote}} ~|~ + \href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{promote}} ~|~ + \href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{reinterpret}} \\ +\end{array}\end{split}\]
    +
    +
    +
    +

    Vector Instructions

    +

    Vector instructions (also known as SIMD instructions, single data multiple value) provide basic operations over values of vector type.

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2422#1{{}}\mathdef2422{ishape} & \href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}} &::=& + \mathsf{i8x16} ~|~ \mathsf{i16x8} ~|~ \mathsf{i32x4} ~|~ \mathsf{i64x2} \\ +\def\mathdef2422#1{{}}\mathdef2422{fshape} & \href{../syntax/instructions.html#syntax-shape}{\mathit{fshape}} &::=& + \mathsf{f32x4} ~|~ \mathsf{f64x2} \\ +\def\mathdef2422#1{{}}\mathdef2422{shape} & \href{../syntax/instructions.html#syntax-shape}{\mathit{shape}} &::=& + \href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}} ~|~ \href{../syntax/instructions.html#syntax-shape}{\mathit{fshape}} \\ +\def\mathdef2422#1{{}}\mathdef2422{half} & \href{../syntax/instructions.html#syntax-half}{\mathit{half}} &::=& + \mathsf{low} ~|~ \mathsf{high} \\ +\def\mathdef2422#1{{}}\mathdef2422{lane index} & \href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} &::=& \href{../syntax/values.html#syntax-int}{\mathit{u8}} \\ +\def\mathdef2422#1{{}}\mathdef2422{instruction} & \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}} &::=& + \dots \\&&|& + \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~\href{../syntax/values.html#syntax-int}{\mathit{i128}} \\&&|& + \mathsf{v128.}\href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}} \\&&|& + \mathsf{v128.}\href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}} \\&&|& + \mathsf{v128.}\href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}} \\&&|& + \mathsf{v128.}\href{../syntax/instructions.html#syntax-vvtestop}{\mathit{vvtestop}} \\&&|& + \mathsf{i8x16.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}^{16} \\&&|& + \mathsf{i8x16.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{swizzle}} \\&&|& + \href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}} \\&&|& + \mathsf{i8x16.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} ~|~ + \mathsf{i16x8.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} \\&&|& + \mathsf{i32x4.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} ~|~ + \mathsf{i64x2.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} \\&&|& + \href{../syntax/instructions.html#syntax-shape}{\mathit{fshape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} \\&&|& + \href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} \\&&|& + \mathsf{i8x16}\mathsf{.}\href{../syntax/instructions.html#syntax-virelop}{\mathit{virelop}} ~|~ + \mathsf{i16x8}\mathsf{.}\href{../syntax/instructions.html#syntax-virelop}{\mathit{virelop}} ~|~ + \mathsf{i32x4}\mathsf{.}\href{../syntax/instructions.html#syntax-virelop}{\mathit{virelop}} \\&&|& + \mathsf{i64x2.}\mathsf{eq} ~|~ + \mathsf{i64x2.}\mathsf{ne} ~|~ + \mathsf{i64x2.}\mathsf{lt\_s} ~|~ + \mathsf{i64x2.}\mathsf{gt\_s} ~|~ + \mathsf{i64x2.}\mathsf{le\_s} ~|~ + \mathsf{i64x2.}\mathsf{ge\_s} \\&&|& + \href{../syntax/instructions.html#syntax-shape}{\mathit{fshape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vfrelop}{\mathit{vfrelop}} \\&&|& + \href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}\mathsf{.}\href{../syntax/instructions.html#syntax-viunop}{\mathit{viunop}} ~|~ + \mathsf{i8x16.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{popcnt}} \\&&|& + \mathsf{i16x8.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{q15mulr\_sat}}\mathsf{\_s} \\ &&|& + \mathsf{i32x4.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{dot}}\mathsf{\_i16x8\_s} \\ &&|& + \href{../syntax/instructions.html#syntax-shape}{\mathit{fshape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vfunop}{\mathit{vfunop}} \\&&|& + \href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vitestop}{\mathit{vitestop}} \\ &&|& + \href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}} \\ &&|& + \mathsf{i8x16.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i16x8\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{i16x8.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i32x4\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\&&|& + \mathsf{i16x8.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_i8x16\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{i32x4.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_i16x8\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\&&|& + \mathsf{i64x2.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_i32x4\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\&&|& + \href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vishiftop}{\mathit{vishiftop}} \\&&|& + \href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vibinop}{\mathit{vibinop}} \\&&|& + \mathsf{i8x16.}\href{../syntax/instructions.html#syntax-viminmaxop}{\mathit{viminmaxop}} ~|~ + \mathsf{i16x8.}\href{../syntax/instructions.html#syntax-viminmaxop}{\mathit{viminmaxop}} ~|~ + \mathsf{i32x4.}\href{../syntax/instructions.html#syntax-viminmaxop}{\mathit{viminmaxop}} \\&&|& + \mathsf{i8x16.}\href{../syntax/instructions.html#syntax-visatbinop}{\mathit{visatbinop}} ~|~ + \mathsf{i16x8.}\href{../syntax/instructions.html#syntax-visatbinop}{\mathit{visatbinop}} \\&&|& + \mathsf{i16x8.}\mathsf{mul} ~|~ + \mathsf{i32x4.}\mathsf{mul} ~|~ + \mathsf{i64x2.}\mathsf{mul} \\&&|& + \mathsf{i8x16.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{avgr}}\mathsf{\_u} ~|~ + \mathsf{i16x8.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{avgr}}\mathsf{\_u} \\&&|& + \mathsf{i16x8.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_i8x16\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{i32x4.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_i16x8\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{i64x2.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_i32x4\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\ &&|& + \mathsf{i16x8.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_i8x16\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{i32x4.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_i16x8\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\ &&|& + \href{../syntax/instructions.html#syntax-shape}{\mathit{fshape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vfbinop}{\mathit{vfbinop}} \\&&|& + \mathsf{i32x4.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}}\mathsf{\_sat\_f32x4\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{i32x4.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}}\mathsf{\_sat\_f64x2\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\mathsf{\_zero} \\&&|& + \mathsf{f32x4.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{convert}}\mathsf{\_i32x4\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{f32x4.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{demote}}\mathsf{\_f64x2\_zero} \\&&|& + \mathsf{f64x2.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{convert}}\mathsf{\_low\_i32x4\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{f64x2.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{promote}}\mathsf{\_low\_f32x4} \\&&|& + \dots \\ +\def\mathdef2422#1{{}}\mathdef2422{vector bitwise unary operator} & \href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}} &::=& + \mathsf{not} \\ +\def\mathdef2422#1{{}}\mathdef2422{vector bitwise binary operator} & \href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}} &::=& + \mathsf{and} ~|~ + \mathsf{andnot} ~|~ + \mathsf{or} ~|~ + \mathsf{xor} \\ +\def\mathdef2422#1{{}}\mathdef2422{vector bitwise ternary operator} & \href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}} &::=& + \mathsf{bitselect} \\ +\def\mathdef2422#1{{}}\mathdef2422{vector bitwise test operator} & \href{../syntax/instructions.html#syntax-vvtestop}{\mathit{vvtestop}} &::=& + \mathsf{any\_true} \\ +\def\mathdef2422#1{{}}\mathdef2422{vector integer test operator} & \href{../syntax/instructions.html#syntax-vitestop}{\mathit{vitestop}} &::=& + \mathsf{all\_true} \\ +\def\mathdef2422#1{{}}\mathdef2422{vector integer relational operator} & \href{../syntax/instructions.html#syntax-virelop}{\mathit{virelop}} &::=& + \mathsf{eq} ~|~ + \mathsf{ne} ~|~ + \mathsf{lt\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{gt\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{le\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{ge\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\ +\def\mathdef2422#1{{}}\mathdef2422{vector floating-point relational operator} & \href{../syntax/instructions.html#syntax-vfrelop}{\mathit{vfrelop}} &::=& + \mathsf{eq} ~|~ + \mathsf{ne} ~|~ + \mathsf{lt} ~|~ + \mathsf{gt} ~|~ + \mathsf{le} ~|~ + \mathsf{ge} \\ +\def\mathdef2422#1{{}}\mathdef2422{vector integer unary operator} & \href{../syntax/instructions.html#syntax-viunop}{\mathit{viunop}} &::=& + \mathsf{abs} ~|~ + \mathsf{neg} \\ +\def\mathdef2422#1{{}}\mathdef2422{vector integer binary operator} & \href{../syntax/instructions.html#syntax-vibinop}{\mathit{vibinop}} &::=& + \mathsf{add} ~|~ + \mathsf{sub} \\ +\def\mathdef2422#1{{}}\mathdef2422{vector integer binary min/max operator} & \href{../syntax/instructions.html#syntax-viminmaxop}{\mathit{viminmaxop}} &::=& + \mathsf{min\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{max\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\ +\def\mathdef2422#1{{}}\mathdef2422{vector integer saturating binary operator} & \href{../syntax/instructions.html#syntax-visatbinop}{\mathit{visatbinop}} &::=& + \mathsf{add\_sat\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} ~|~ + \mathsf{sub\_sat\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\ +\def\mathdef2422#1{{}}\mathdef2422{vector integer shift operator} & \href{../syntax/instructions.html#syntax-vishiftop}{\mathit{vishiftop}} &::=& + \mathsf{shl} ~|~ + \mathsf{shr\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} \\ +\def\mathdef2422#1{{}}\mathdef2422{vector floating-point unary operator} & \href{../syntax/instructions.html#syntax-vfunop}{\mathit{vfunop}} &::=& + \mathsf{abs} ~|~ + \mathsf{neg} ~|~ + \mathsf{sqrt} ~|~ + \mathsf{ceil} ~|~ + \mathsf{floor} ~|~ + \mathsf{trunc} ~|~ + \mathsf{nearest} \\ +\def\mathdef2422#1{{}}\mathdef2422{vector floating-point binary operator} & \href{../syntax/instructions.html#syntax-vfbinop}{\mathit{vfbinop}} &::=& + \mathsf{add} ~|~ + \mathsf{sub} ~|~ + \mathsf{mul} ~|~ + \mathsf{div} ~|~ + \mathsf{min} ~|~ + \mathsf{max} ~|~ + \mathsf{pmin} ~|~ + \mathsf{pmax} \\ +\end{array}\end{split}\]
    +

    Vector instructions have a naming convention involving a prefix that +determines how their operands will be interpreted. +This prefix describes the shape of the operand, +written \(t\mathsf{x}N\), and consisting of a packed numeric type \(t\) and the number of lanes \(N\) of that type. +Operations are performed point-wise on the values of each lane.

    +
    +

    Note

    +

    For example, the shape \(\mathsf{i32x4}\) interprets the operand +as four \(\href{../syntax/values.html#syntax-int}{\mathit{i32}}\) values, packed into an \(\href{../syntax/values.html#syntax-int}{\mathit{i128}}\). +The bitwidth of the numeric type \(t\) times \(N\) always is 128.

    +
    +

    Instructions prefixed with \(\mathsf{v128}\) do not involve a specific interpretation, and treat the \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) as an \(\href{../syntax/values.html#syntax-int}{\mathit{i128}}\) value or a vector of 128 individual bits.

    +

    Vector instructions can be grouped into several subcategories:

    +
      +

    • Constants: return a static constant.

      • +

    • Unary Operations: consume one \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) operand and produce one \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) result.

      • +

    • Binary Operations: consume two \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) operands and produce one \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) result.

      • +

    • Ternary Operations: consume three \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) operands and produce one \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) result.

      • +

    • Tests: consume one \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) operand and produce a Boolean integer result.

      • +

    • Shifts: consume a \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) operand and a \(\href{../syntax/values.html#syntax-int}{\mathit{i32}}\) operand, producing one \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) result.

      • +

    • Splats: consume a value of numeric type and produce a \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) result of a specified shape.

      • +

    • Extract lanes: consume a \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) operand and return the numeric value in a given lane.

      • +

    • Replace lanes: consume a \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) operand and a numeric value for a given lane, and produce a \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) result.

      • +
    +

    Some vector instructions have a signedness annotation \(\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\) which distinguishes whether the elements in the operands are to be interpreted as unsigned or signed integers. +For the other vector instructions, the use of two’s complement for the signed interpretation means that they behave the same regardless of signedness.

    +
    +

    Conventions

    +

    Occasionally, it is convenient to group operators together according to the following grammar shorthands:

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2422#1{{}}\mathdef2422{unary operator} & \href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}} &::=& + \href{../syntax/instructions.html#syntax-viunop}{\mathit{viunop}} ~|~ + \href{../syntax/instructions.html#syntax-vfunop}{\mathit{vfunop}} ~|~ + \href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{popcnt}} \\ +\def\mathdef2422#1{{}}\mathdef2422{binary operator} & \href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}} &::=& + \href{../syntax/instructions.html#syntax-vibinop}{\mathit{vibinop}} ~|~ \href{../syntax/instructions.html#syntax-vfbinop}{\mathit{vfbinop}} \\&&|& + \href{../syntax/instructions.html#syntax-viminmaxop}{\mathit{viminmaxop}} ~|~ \href{../syntax/instructions.html#syntax-visatbinop}{\mathit{visatbinop}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}} ~|~ + \href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{avgr}}\mathsf{\_u} ~|~ + \href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{q15mulr\_sat}}\mathsf{\_s} \\ +\def\mathdef2422#1{{}}\mathdef2422{test operator} & \href{../syntax/instructions.html#syntax-vtestop}{\mathit{vtestop}} &::=& + \href{../syntax/instructions.html#syntax-vitestop}{\mathit{vitestop}} \\ +\def\mathdef2422#1{{}}\mathdef2422{relational operator} & \href{../syntax/instructions.html#syntax-vrelop}{\mathit{vrelop}} &::=& + \href{../syntax/instructions.html#syntax-virelop}{\mathit{virelop}} ~|~ \href{../syntax/instructions.html#syntax-vfrelop}{\mathit{vfrelop}} \\ +\def\mathdef2422#1{{}}\mathdef2422{conversion operator} & \href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}} &::=& + \href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}} ~|~ + \href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}}\mathsf{\_sat} ~|~ + \href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{convert}} ~|~ + \href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{demote}} ~|~ + \href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{promote}} \\ +\end{array}\end{split}\]
    +
    +
    +
    +

    Reference Instructions

    +

    Instructions in this group are concerned with accessing references.

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2422#1{{}}\mathdef2422{instruction} & \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}} &::=& + \dots \\&&|& + \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}is\_null}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~\href{../syntax/modules.html#syntax-funcidx}{\mathit{funcidx}} \\ +\end{array}\end{split}\]
    +

    These instruction produce a null value, check for a null value, or produce a reference to a given function, respectively.

    +
    +
    +

    Parametric Instructions

    +

    Instructions in this group can operate on operands of any value type.

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2422#1{{}}\mathdef2422{instruction} & \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}} &::=& + \dots \\&&|& + \href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{drop}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}~(\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}^\ast)^? \\ +\end{array}\end{split}\]
    +

    The \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{drop}}\) instruction simply throws away a single operand.

    +

    The \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}\) instruction selects one of its first two operands based on whether its third operand is zero or not. +It may include a value type determining the type of these operands. If missing, the operands must be of numeric type.

    +
    +

    Note

    +

    In future versions of WebAssembly, the type annotation on \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}\) may allow for more than a single value being selected at the same time.

    +
    +
    +
    +

    Variable Instructions

    +

    Variable instructions are concerned with access to local or global variables.

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2422#1{{}}\mathdef2422{instruction} & \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}} &::=& + \dots \\&&|& + \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.get}}~\href{../syntax/modules.html#syntax-localidx}{\mathit{localidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.set}}~\href{../syntax/modules.html#syntax-localidx}{\mathit{localidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.tee}}~\href{../syntax/modules.html#syntax-localidx}{\mathit{localidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.get}}~\href{../syntax/modules.html#syntax-globalidx}{\mathit{globalidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.set}}~\href{../syntax/modules.html#syntax-globalidx}{\mathit{globalidx}} \\ +\end{array}\end{split}\]
    +

    These instructions get or set the values of variables, respectively. +The \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.tee}}\) instruction is like \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.set}}\) but also returns its argument.

    +
    +
    +

    Table Instructions

    +

    Instructions in this group are concerned with tables table.

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2422#1{{}}\mathdef2422{instruction} & \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}} &::=& + \dots \\&&|& + \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.size}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.grow}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.fill}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}}~\href{../syntax/modules.html#syntax-elemidx}{\mathit{elemidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem.drop}}~\href{../syntax/modules.html#syntax-elemidx}{\mathit{elemidx}} \\ +\end{array}\end{split}\]
    +

    The \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}\) and \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}\) instructions load or store an element in a table, respectively.

    +

    The \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.size}}\) instruction returns the current size of a table. +The \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.grow}}\) instruction grows table by a given delta and returns the previous size, or \(-1\) if enough space cannot be allocated. +It also takes an initialization value for the newly allocated entries.

    +

    The \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.fill}}\) instruction sets all entries in a range to a given value.

    +

    The \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}\) instruction copies elements from a source table region to a possibly overlapping destination region; the first index denotes the destination. +The \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}\) instruction copies elements from a passive element segment into a table. +The \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem.drop}}\) instruction prevents further use of a passive element segment. This instruction is intended to be used as an optimization hint. After an element segment is dropped its elements can no longer be retrieved, so the memory used by this segment may be freed.

    +

    An additional instruction that accesses a table is the control instruction \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}\).

    +
    +
    +

    Memory Instructions

    +

    Instructions in this group are concerned with linear memory.

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2422#1{{}}\mathdef2422{memory immediate} & \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} &::=& + \{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~\href{../syntax/values.html#syntax-int}{\mathit{u32}}, \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~\href{../syntax/values.html#syntax-int}{\mathit{u32}} \} \\ +\def\mathdef2422#1{{}}\mathdef2422{lane width} & \mathit{ww} &::=& + 8 ~|~ 16 ~|~ 32 ~|~ 64 \\ +\def\mathdef2422#1{{}}\mathdef2422{instruction} & \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}} &::=& + \dots \\&&|& + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} ~|~ + \mathsf{f}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} ~|~ + \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} \\&&|& + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} ~|~ + \mathsf{f}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} ~|~ + \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} \\&&|& + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} ~|~ + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} ~|~ + \mathsf{i64.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} \\&&|& + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} ~|~ + \mathsf{i}\mathit{nn}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{16}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} ~|~ + \mathsf{i64.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{32}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} \\&&|& + \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8x8\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} ~|~ + \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16x4\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} ~|~ + \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32x2\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} \\&&|& + \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_zero}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} ~|~ + \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{64\_zero}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} \\&&|& + \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathit{ww}\mathsf{\_splat}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} \\&&|& + \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathit{ww}\mathsf{\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} ~|~ + \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathit{ww}\mathsf{\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.size}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.grow}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~\href{../syntax/modules.html#syntax-dataidx}{\mathit{dataidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data.drop}}~\href{../syntax/modules.html#syntax-dataidx}{\mathit{dataidx}} \\ +\end{array}\end{split}\]
    +

    Memory is accessed with \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\) and \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\) instructions for the different number types. +They all take a memory immediate \(\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\) that contains an address offset and the expected alignment (expressed as the exponent of a power of 2). +Integer loads and stores can optionally specify a storage size that is smaller than the bit width of the respective value type. +In the case of loads, a sign extension mode \(\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\) is then required to select appropriate behavior.

    +

    Vector loads can specify a shape that is half the bit width of \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\). Each lane is half its usual size, and the sign extension mode \(\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\) then specifies how the smaller lane is extended to the larger lane. +Alternatively, vector loads can perform a splat, such that only a single lane of the specified storage size is loaded, and the result is duplicated to all lanes.

    +

    The static address offset is added to the dynamic address operand, yielding a 33 bit effective address that is the zero-based index at which the memory is accessed. +All values are read and written in little endian byte order. +A trap results if any of the accessed memory bytes lies outside the address range implied by the memory’s current size.

    +
    +

    Note

    +

    Future version of WebAssembly might provide memory instructions with 64 bit address ranges.

    +
    +

    The \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.size}}\) instruction returns the current size of a memory. +The \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.grow}}\) instruction grows memory by a given delta and returns the previous size, or \(-1\) if enough memory cannot be allocated. +Both instructions operate in units of page size.

    +

    The \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}}\) instruction sets all values in a region to a given byte. +The \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}}\) instruction copies data from a source memory region to a possibly overlapping destination region. +The \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}\) instruction copies data from a passive data segment into a memory. +The \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data.drop}}\) instruction prevents further use of a passive data segment. This instruction is intended to be used as an optimization hint. After a data segment is dropped its data can no longer be retrieved, so the memory used by this segment may be freed.

    +
    +

    Note

    +

    In the current version of WebAssembly, +all memory instructions implicitly operate on memory index \(0\). +This restriction may be lifted in future versions.

    +
    +
    +
    +

    Control Instructions

    +

    Instructions in this group affect the flow of control.

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2422#1{{}}\mathdef2422{block type} & \href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}} &::=& + \href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}} ~|~ \href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}^? \\ +\def\mathdef2422#1{{}}\mathdef2422{instruction} & \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}} &::=& + \dots \\&&|& + \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{nop}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}~\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}~\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~\href{../syntax/modules.html#syntax-labelidx}{\mathit{labelidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_if}}~\href{../syntax/modules.html#syntax-labelidx}{\mathit{labelidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/modules.html#syntax-labelidx}{\mathit{labelidx}})~\href{../syntax/modules.html#syntax-labelidx}{\mathit{labelidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call}}~\href{../syntax/modules.html#syntax-funcidx}{\mathit{funcidx}} \\&&|& + \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}}~\href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}} \\ +\end{array}\end{split}\]
    +

    The \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{nop}}\) instruction does nothing.

    +

    The \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}\) instruction causes an unconditional trap.

    +

    The \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}\), \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}\) and \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}\) instructions are structured instructions. +They bracket nested sequences of instructions, called blocks, terminated with, or separated by, \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\) or \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}\) pseudo-instructions. +As the grammar prescribes, they must be well-nested.

    +

    A structured instruction can consume input and produce output on the operand stack according to its annotated block type. +It is given either as a type index that refers to a suitable function type, or as an optional value type inline, which is a shorthand for the function type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}^?]\).

    +

    Each structured control instruction introduces an implicit label. +Labels are targets for branch instructions that reference them with label indices. +Unlike with other index spaces, indexing of labels is relative by nesting depth, +that is, label \(0\) refers to the innermost structured control instruction enclosing the referring branch instruction, +while increasing indices refer to those farther out. +Consequently, labels can only be referenced from within the associated structured control instruction. +This also implies that branches can only be directed outwards, +“breaking” from the block of the control construct they target. +The exact effect depends on that control construct. +In case of \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}\) or \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}\) it is a forward jump, +resuming execution after the matching \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\). +In case of \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}\) it is a backward jump to the beginning of the loop.

    +
    +

    Note

    +

    This enforces structured control flow. +Intuitively, a branch targeting a \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}\) or \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}\) behaves like a \(\mathsf{break}\) statement in most C-like languages, +while a branch targeting a \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}\) behaves like a \(\mathsf{continue}\) statement.

    +
    +

    Branch instructions come in several flavors: +\(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}\) performs an unconditional branch, +\(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_if}}\) performs a conditional branch, +and \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}\) performs an indirect branch through an operand indexing into the label vector that is an immediate to the instruction, or to a default target if the operand is out of bounds. +The \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}\) instruction is a shortcut for an unconditional branch to the outermost block, which implicitly is the body of the current function. +Taking a branch unwinds the operand stack up to the height where the targeted structured control instruction was entered. +However, branches may additionally consume operands themselves, which they push back on the operand stack after unwinding. +Forward branches require operands according to the output of the targeted block’s type, i.e., represent the values produced by the terminated block. +Backward branches require operands according to the input of the targeted block’s type, i.e., represent the values consumed by the restarted block.

    +

    The \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call}}\) instruction invokes another function, consuming the necessary arguments from the stack and returning the result values of the call. +The \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}\) instruction calls a function indirectly through an operand indexing into a table that is denoted by a table index and must have type \(\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}\). +Since it may contain functions of heterogeneous type, +the callee is dynamically checked against the function type indexed by the instruction’s second immediate, and the call is aborted with a trap if it does not match.

    +
    +
    +

    Expressions

    +

    Function bodies, initialization values for globals, and offsets of element or data segments are given as expressions, which are sequences of instructions terminated by an \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\) marker.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2422#1{{}}\mathdef2422{expression} & \href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} &::=& + \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\ +\end{array}\end{split}\]
    +

    In some places, validation restricts expressions to be constant, which limits the set of allowable instructions.

    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/syntax/modules.html b/core/syntax/modules.html new file mode 100644 index 00000000..9b41c91f --- /dev/null +++ b/core/syntax/modules.html @@ -0,0 +1,355 @@ + + + + + + + + + Modules — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Modules

    +

    WebAssembly programs are organized into modules, +which are the unit of deployment, loading, and compilation. +A module collects definitions for types, functions, tables, memories, and globals. +In addition, it can declare imports and exports +and provide initialization in the form of data and element segments, or a start function.

    +
    +\[\begin{split}\begin{array}{lllll} +\def\mathdef2463#1{{}}\mathdef2463{module} & \href{../syntax/modules.html#syntax-module}{\mathit{module}} &::=& \{ & + \href{../syntax/modules.html#syntax-module}{\mathsf{types}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}), \\&&&& + \href{../syntax/modules.html#syntax-module}{\mathsf{funcs}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/modules.html#syntax-func}{\mathit{func}}), \\&&&& + \href{../syntax/modules.html#syntax-module}{\mathsf{tables}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/modules.html#syntax-table}{\mathit{table}}), \\&&&& + \href{../syntax/modules.html#syntax-module}{\mathsf{mems}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/modules.html#syntax-mem}{\mathit{mem}}), \\&&&& + \href{../syntax/modules.html#syntax-module}{\mathsf{globals}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/modules.html#syntax-global}{\mathit{global}}), \\&&&& + \href{../syntax/modules.html#syntax-module}{\mathsf{elems}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}), \\&&&& + \href{../syntax/modules.html#syntax-module}{\mathsf{datas}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/modules.html#syntax-data}{\mathit{data}}), \\&&&& + \href{../syntax/modules.html#syntax-module}{\mathsf{start}}~\href{../syntax/modules.html#syntax-start}{\mathit{start}}^?, \\&&&& + \href{../syntax/modules.html#syntax-module}{\mathsf{imports}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/modules.html#syntax-import}{\mathit{import}}), \\&&&& + \href{../syntax/modules.html#syntax-module}{\mathsf{exports}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/modules.html#syntax-export}{\mathit{export}}) \quad\} \\ +\end{array}\end{split}\]
    +

    Each of the vectors – and thus the entire module – may be empty.

    +
    +

    Indices

    +

    Definitions are referenced with zero-based indices. +Each class of definition has its own index space, as distinguished by the following classes.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2463#1{{}}\mathdef2463{type index} & \href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}} &::=& \href{../syntax/values.html#syntax-int}{\mathit{u32}} \\ +\def\mathdef2463#1{{}}\mathdef2463{function index} & \href{../syntax/modules.html#syntax-funcidx}{\mathit{funcidx}} &::=& \href{../syntax/values.html#syntax-int}{\mathit{u32}} \\ +\def\mathdef2463#1{{}}\mathdef2463{table index} & \href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}} &::=& \href{../syntax/values.html#syntax-int}{\mathit{u32}} \\ +\def\mathdef2463#1{{}}\mathdef2463{memory index} & \href{../syntax/modules.html#syntax-memidx}{\mathit{memidx}} &::=& \href{../syntax/values.html#syntax-int}{\mathit{u32}} \\ +\def\mathdef2463#1{{}}\mathdef2463{global index} & \href{../syntax/modules.html#syntax-globalidx}{\mathit{globalidx}} &::=& \href{../syntax/values.html#syntax-int}{\mathit{u32}} \\ +\def\mathdef2463#1{{}}\mathdef2463{element index} & \href{../syntax/modules.html#syntax-elemidx}{\mathit{elemidx}} &::=& \href{../syntax/values.html#syntax-int}{\mathit{u32}} \\ +\def\mathdef2463#1{{}}\mathdef2463{data index} & \href{../syntax/modules.html#syntax-dataidx}{\mathit{dataidx}} &::=& \href{../syntax/values.html#syntax-int}{\mathit{u32}} \\ +\def\mathdef2463#1{{}}\mathdef2463{local index} & \href{../syntax/modules.html#syntax-localidx}{\mathit{localidx}} &::=& \href{../syntax/values.html#syntax-int}{\mathit{u32}} \\ +\def\mathdef2463#1{{}}\mathdef2463{label index} & \href{../syntax/modules.html#syntax-labelidx}{\mathit{labelidx}} &::=& \href{../syntax/values.html#syntax-int}{\mathit{u32}} \\ +\end{array}\end{split}\]
    +

    The index space for functions, tables, memories and globals includes respective imports declared in the same module. +The indices of these imports precede the indices of other definitions in the same index space.

    +

    Element indices reference element segments and data indices reference data segments.

    +

    The index space for locals is only accessible inside a function and includes the parameters of that function, which precede the local variables.

    +

    Label indices reference structured control instructions inside an instruction sequence.

    +
    +

    Conventions

    +
      +

    • The meta variable \(l\) ranges over label indices.

      • +

    • The meta variables \(x, y\) range over indices in any of the other index spaces.

      • +

    • The notation \(\mathrm{idx}(A)\) denotes the set of indices from index space \(\mathit{idx}\) occurring free in \(A\). We sometimes reinterpret this set as the vector of its elements.

      • +
    +
    +

    Note

    +

    For example, if \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) is \((\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data.drop}}~x) (\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~y)\), then \(\href{../syntax/modules.html#syntax-dataidx}{\mathrm{dataidx}}(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast) = \{x, y\}\), or equivalently, the vector \(x~y\).

    +
    +
    +
    +
    +

    Types

    +

    The \(\href{../syntax/modules.html#syntax-module}{\mathsf{types}}\) component of a module defines a vector of function types.

    +

    All function types used in a module must be defined in this component. +They are referenced by type indices.

    +
    +

    Note

    +

    Future versions of WebAssembly may add additional forms of type definitions.

    +
    +
    +
    +

    Functions

    +

    The \(\href{../syntax/modules.html#syntax-module}{\mathsf{funcs}}\) component of a module defines a vector of functions with the following structure:

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2463#1{{}}\mathdef2463{function} & \href{../syntax/modules.html#syntax-func}{\mathit{func}} &::=& + \{ \href{../syntax/modules.html#syntax-func}{\mathsf{type}}~\href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}}, \href{../syntax/modules.html#syntax-func}{\mathsf{locals}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}), \href{../syntax/modules.html#syntax-func}{\mathsf{body}}~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \} \\ +\end{array}\end{split}\]
    +

    The \(\href{../syntax/modules.html#syntax-func}{\mathsf{type}}\) of a function declares its signature by reference to a type defined in the module. +The parameters of the function are referenced through 0-based local indices in the function’s body; they are mutable.

    +

    The \(\href{../syntax/modules.html#syntax-func}{\mathsf{locals}}\) declare a vector of mutable local variables and their types. +These variables are referenced through local indices in the function’s body. +The index of the first local is the smallest index not referencing a parameter.

    +

    The \(\href{../syntax/modules.html#syntax-func}{\mathsf{body}}\) is an instruction sequence that upon termination must produce a stack matching the function type’s result type.

    +

    Functions are referenced through function indices, +starting with the smallest index not referencing a function import.

    +
    +
    +

    Tables

    +

    The \(\href{../syntax/modules.html#syntax-module}{\mathsf{tables}}\) component of a module defines a vector of tables described by their table type:

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2463#1{{}}\mathdef2463{table} & \href{../syntax/modules.html#syntax-table}{\mathit{table}} &::=& + \{ \href{../syntax/modules.html#syntax-table}{\mathsf{type}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} \} \\ +\end{array}\end{split}\]
    +

    A table is a vector of opaque values of a particular reference type. +The \(\href{../syntax/types.html#syntax-limits}{\mathsf{min}}\) size in the limits of the table type specifies the initial size of that table, while its \(\href{../syntax/types.html#syntax-limits}{\mathsf{max}}\), if present, restricts the size to which it can grow later.

    +

    Tables can be initialized through element segments.

    +

    Tables are referenced through table indices, +starting with the smallest index not referencing a table import. +Most constructs implicitly reference table index \(0\).

    +
    +
    +

    Memories

    +

    The \(\href{../syntax/modules.html#syntax-module}{\mathsf{mems}}\) component of a module defines a vector of linear memories (or memories for short) as described by their memory type:

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2463#1{{}}\mathdef2463{memory} & \href{../syntax/modules.html#syntax-mem}{\mathit{mem}} &::=& + \{ \href{../syntax/modules.html#syntax-mem}{\mathsf{type}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} \} \\ +\end{array}\end{split}\]
    +

    A memory is a vector of raw uninterpreted bytes. +The \(\href{../syntax/types.html#syntax-limits}{\mathsf{min}}\) size in the limits of the memory type specifies the initial size of that memory, while its \(\href{../syntax/types.html#syntax-limits}{\mathsf{max}}\), if present, restricts the size to which it can grow later. +Both are in units of page size.

    +

    Memories can be initialized through data segments.

    +

    Memories are referenced through memory indices, +starting with the smallest index not referencing a memory import. +Most constructs implicitly reference memory index \(0\).

    +
    +

    Note

    +

    In the current version of WebAssembly, at most one memory may be defined or imported in a single module, +and all constructs implicitly reference this memory \(0\). +This restriction may be lifted in future versions.

    +
    +
    +
    +

    Globals

    +

    The \(\href{../syntax/modules.html#syntax-module}{\mathsf{globals}}\) component of a module defines a vector of global variables (or globals for short):

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2463#1{{}}\mathdef2463{global} & \href{../syntax/modules.html#syntax-global}{\mathit{global}} &::=& + \{ \href{../syntax/modules.html#syntax-global}{\mathsf{type}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}, \href{../syntax/modules.html#syntax-global}{\mathsf{init}}~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \} \\ +\end{array}\end{split}\]
    +

    Each global stores a single value of the given global type. +Its \(\href{../syntax/modules.html#syntax-global}{\mathsf{type}}\) also specifies whether a global is immutable or mutable. +Moreover, each global is initialized with an \(\href{../syntax/modules.html#syntax-global}{\mathsf{init}}\) value given by a constant initializer expression.

    +

    Globals are referenced through global indices, +starting with the smallest index not referencing a global import.

    +
    +
    +

    Element Segments

    +

    The initial contents of a table is uninitialized. Element segments can be used to initialize a subrange of a table from a static vector of elements.

    +

    The \(\href{../syntax/modules.html#syntax-module}{\mathsf{elems}}\) component of a module defines a vector of element segments. +Each element segment defines a reference type and a corresponding list of constant element expressions.

    +

    Element segments have a mode that identifies them as either passive, active, or declarative. +A passive element segment’s elements can be copied to a table using the \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}\) instruction. +An active element segment copies its elements into a table during instantiation, as specified by a table index and a constant expression defining an offset into that table. +A declarative element segment is not available at runtime but merely serves to forward-declare references that are formed in code with instructions like \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}\).

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2463#1{{}}\mathdef2463{element segment} & \href{../syntax/modules.html#syntax-elem}{\mathit{elem}} &::=& + \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}), \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathit{elemmode}} \} \\ +\def\mathdef2463#1{{}}\mathdef2463{element segment mode} & \href{../syntax/modules.html#syntax-elemmode}{\mathit{elemmode}} &::=& + \href{../syntax/modules.html#syntax-elemmode}{\mathsf{passive}} \\&&|& + \href{../syntax/modules.html#syntax-elemmode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-elem}{\mathsf{table}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}}, \href{../syntax/modules.html#syntax-elem}{\mathsf{offset}}~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \} \\&&|& + \href{../syntax/modules.html#syntax-elemmode}{\mathsf{declarative}} \\ +\end{array}\end{split}\]
    +

    The \(\href{../syntax/modules.html#syntax-elem}{\mathsf{offset}}\) is given by a constant expression.

    +

    Element segments are referenced through element indices.

    +
    +

    Note

    +

    In the current version of WebAssembly, only tables of element type \(\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}\) can be initialized with an element segment. +This limitation may be lifted in the future.

    +
    +
    +
    +

    Data Segments

    +

    The initial contents of a memory are zero bytes. Data segments can be used to initialize a range of memory from a static vector of bytes.

    +

    The \(\href{../syntax/modules.html#syntax-module}{\mathsf{datas}}\) component of a module defines a vector of data segments.

    +

    Like element segments, data segments have a mode that identifies them as either passive or active. +A passive data segment’s contents can be copied into a memory using the \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}\) instruction. +An active data segment copies its contents into a memory during instantiation, as specified by a memory index and a constant expression defining an offset into that memory.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2463#1{{}}\mathdef2463{data segment} & \href{../syntax/modules.html#syntax-data}{\mathit{data}} &::=& + \{ \href{../syntax/modules.html#syntax-data}{\mathsf{init}}~\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/values.html#syntax-byte}{\mathit{byte}}), \href{../syntax/modules.html#syntax-data}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-datamode}{\mathit{datamode}} \} \\ +\def\mathdef2463#1{{}}\mathdef2463{data segment mode} & \href{../syntax/modules.html#syntax-datamode}{\mathit{datamode}} &::=& + \href{../syntax/modules.html#syntax-datamode}{\mathsf{passive}} \\&&|& + \href{../syntax/modules.html#syntax-datamode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-data}{\mathsf{memory}}~\href{../syntax/modules.html#syntax-memidx}{\mathit{memidx}}, \href{../syntax/modules.html#syntax-data}{\mathsf{offset}}~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \} \\ +\end{array}\end{split}\]
    +

    Data segments are referenced through data indices.

    +
    +

    Note

    +

    In the current version of WebAssembly, at most one memory is allowed in a module. +Consequently, the only valid \(\href{../syntax/modules.html#syntax-memidx}{\mathit{memidx}}\) is \(0\).

    +
    +
    +
    +

    Start Function

    +

    The \(\href{../syntax/modules.html#syntax-module}{\mathsf{start}}\) component of a module declares the function index of a start function that is automatically invoked when the module is instantiated, after tables and memories have been initialized.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2463#1{{}}\mathdef2463{start function} & \href{../syntax/modules.html#syntax-start}{\mathit{start}} &::=& + \{ \href{../syntax/modules.html#syntax-start}{\mathsf{func}}~\href{../syntax/modules.html#syntax-funcidx}{\mathit{funcidx}} \} \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The start function is intended for initializing the state of a module. +The module and its exports are not accessible before this initialization has completed.

    +
    +
    +
    +

    Exports

    +

    The \(\href{../syntax/modules.html#syntax-module}{\mathsf{exports}}\) component of a module defines a set of exports that become accessible to the host environment once the module has been instantiated.

    +
    +\[\begin{split}\begin{array}{llcl} +\def\mathdef2463#1{{}}\mathdef2463{export} & \href{../syntax/modules.html#syntax-export}{\mathit{export}} &::=& + \{ \href{../syntax/modules.html#syntax-export}{\mathsf{name}}~\href{../syntax/values.html#syntax-name}{\mathit{name}}, \href{../syntax/modules.html#syntax-export}{\mathsf{desc}}~\href{../syntax/modules.html#syntax-exportdesc}{\mathit{exportdesc}} \} \\ +\def\mathdef2463#1{{}}\mathdef2463{export description} & \href{../syntax/modules.html#syntax-exportdesc}{\mathit{exportdesc}} &::=& + \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{func}}~\href{../syntax/modules.html#syntax-funcidx}{\mathit{funcidx}} \\&&|& + \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{table}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}} \\&&|& + \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{mem}}~\href{../syntax/modules.html#syntax-memidx}{\mathit{memidx}} \\&&|& + \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{global}}~\href{../syntax/modules.html#syntax-globalidx}{\mathit{globalidx}} \\ +\end{array}\end{split}\]
    +

    Each export is labeled by a unique name. +Exportable definitions are functions, tables, memories, and globals, +which are referenced through a respective descriptor.

    +
    +

    Conventions

    +

    The following auxiliary notation is defined for sequences of exports, filtering out indices of a specific kind in an order-preserving fashion:

    +
      +

    • \(\href{../syntax/modules.html#syntax-exportdesc}{\mathrm{funcs}}(\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast) = [\href{../syntax/modules.html#syntax-funcidx}{\mathit{funcidx}} ~|~ \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{func}}~\href{../syntax/modules.html#syntax-funcidx}{\mathit{funcidx}} \in (\href{../syntax/modules.html#syntax-export}{\mathit{export}}.\href{../syntax/modules.html#syntax-export}{\mathsf{desc}})^\ast]\)

      • +

    • \(\href{../syntax/modules.html#syntax-exportdesc}{\mathrm{tables}}(\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast) = [\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}} ~|~ \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{table}}~\href{../syntax/modules.html#syntax-tableidx}{\mathit{tableidx}} \in (\href{../syntax/modules.html#syntax-export}{\mathit{export}}.\href{../syntax/modules.html#syntax-export}{\mathsf{desc}})^\ast]\)

      • +

    • \(\href{../syntax/modules.html#syntax-exportdesc}{\mathrm{mems}}(\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast) = [\href{../syntax/modules.html#syntax-memidx}{\mathit{memidx}} ~|~ \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{mem}}~\href{../syntax/modules.html#syntax-memidx}{\mathit{memidx}} \in (\href{../syntax/modules.html#syntax-export}{\mathit{export}}.\href{../syntax/modules.html#syntax-export}{\mathsf{desc}})^\ast]\)

      • +

    • \(\href{../syntax/modules.html#syntax-exportdesc}{\mathrm{globals}}(\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast) = [\href{../syntax/modules.html#syntax-globalidx}{\mathit{globalidx}} ~|~ \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{global}}~\href{../syntax/modules.html#syntax-globalidx}{\mathit{globalidx}} \in (\href{../syntax/modules.html#syntax-export}{\mathit{export}}.\href{../syntax/modules.html#syntax-export}{\mathsf{desc}})^\ast]\)

      • +
    +
    +
    +
    +

    Imports

    +

    The \(\href{../syntax/modules.html#syntax-module}{\mathsf{imports}}\) component of a module defines a set of imports that are required for instantiation.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2463#1{{}}\mathdef2463{import} & \href{../syntax/modules.html#syntax-import}{\mathit{import}} &::=& + \{ \href{../syntax/modules.html#syntax-import}{\mathsf{module}}~\href{../syntax/values.html#syntax-name}{\mathit{name}}, \href{../syntax/modules.html#syntax-import}{\mathsf{name}}~\href{../syntax/values.html#syntax-name}{\mathit{name}}, \href{../syntax/modules.html#syntax-import}{\mathsf{desc}}~\href{../syntax/modules.html#syntax-importdesc}{\mathit{importdesc}} \} \\ +\def\mathdef2463#1{{}}\mathdef2463{import description} & \href{../syntax/modules.html#syntax-importdesc}{\mathit{importdesc}} &::=& + \href{../syntax/modules.html#syntax-importdesc}{\mathsf{func}}~\href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}} \\&&|& + \href{../syntax/modules.html#syntax-importdesc}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} \\&&|& + \href{../syntax/modules.html#syntax-importdesc}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} \\&&|& + \href{../syntax/modules.html#syntax-importdesc}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} \\ +\end{array}\end{split}\]
    +

    Each import is labeled by a two-level name space, consisting of a \(\href{../syntax/modules.html#syntax-import}{\mathsf{module}}\) name and a \(\href{../syntax/modules.html#syntax-import}{\mathsf{name}}\) for an entity within that module. +Importable definitions are functions, tables, memories, and globals. +Each import is specified by a descriptor with a respective type that a definition provided during instantiation is required to match.

    +

    Every import defines an index in the respective index space. +In each index space, the indices of imports go before the first index of any definition contained in the module itself.

    +
    +

    Note

    +

    Unlike export names, import names are not necessarily unique. +It is possible to import the same \(\href{../syntax/modules.html#syntax-import}{\mathsf{module}}\)/\(\href{../syntax/modules.html#syntax-import}{\mathsf{name}}\) pair multiple times; +such imports may even have different type descriptions, including different kinds of entities. +A module with such imports can still be instantiated depending on the specifics of how an embedder allows resolving and supplying imports. +However, embedders are not required to support such overloading, +and a WebAssembly module itself cannot implement an overloaded name.

    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/syntax/types.html b/core/syntax/types.html new file mode 100644 index 00000000..76ece205 --- /dev/null +++ b/core/syntax/types.html @@ -0,0 +1,271 @@ + + + + + + + + + Types — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Types

    +

    Various entities in WebAssembly are classified by types. +Types are checked during validation, instantiation, and possibly execution.

    +
    +

    Number Types

    +

    Number types classify numeric values.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2502#1{{}}\mathdef2502{number type} & \href{../syntax/types.html#syntax-numtype}{\mathit{numtype}} &::=& + \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}} ~|~ \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}} ~|~ \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}} ~|~ \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}} \\ +\end{array}\end{split}\]
    +

    The types \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) and \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}\) classify 32 and 64 bit integers, respectively. +Integers are not inherently signed or unsigned, their interpretation is determined by individual operations.

    +

    The types \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\) and \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\) classify 32 and 64 bit floating-point data, respectively. +They correspond to the respective binary floating-point representations, also known as single and double precision, as defined by the IEEE 754-2019 standard (Section 3.3).

    +

    Number types are transparent, meaning that their bit patterns can be observed. +Values of number type can be stored in memories.

    +
    +

    Conventions

    +
      +

    • The notation \(|t|\) denotes the bit width of a number type \(t\). +That is, \(|\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}| = |\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}| = 32\) and \(|\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}| = |\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}| = 64\).

      • +
    +
    +
    +
    +

    Vector Types

    +

    Vector types classify vectors of numeric values processed by vector instructions (also known as SIMD instructions, single instruction multiple data).

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2502#1{{}}\mathdef2502{vector type} & \href{../syntax/types.html#syntax-vectype}{\mathit{vectype}} &::=& + \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}} \\ +\end{array}\end{split}\]
    +

    The type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) corresponds to a 128 bit vector of packed integer or floating-point data. The packed data +can be interpreted as signed or unsigned integers, single or double precision floating-point +values, or a single 128 bit type. The interpretation is determined by individual operations.

    +

    Vector types, like number types are transparent, meaning that their bit patterns can be observed. +Values of vector type can be stored in memories.

    +
    +

    Conventions

    +
      +

    • The notation \(|t|\) for bit width extends to vector types as well, that is, \(|\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}| = 128\).

      • +
    +
    +
    +
    +

    Reference Types

    +

    Reference types classify first-class references to objects in the runtime store.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2502#1{{}}\mathdef2502{reference type} & \href{../syntax/types.html#syntax-reftype}{\mathit{reftype}} &::=& + \href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}} ~|~ \href{../syntax/types.html#syntax-reftype}{\mathsf{externref}} \\ +\end{array}\end{split}\]
    +

    The type \(\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}\) denotes the infinite union of all references to functions, regardless of their function types.

    +

    The type \(\href{../syntax/types.html#syntax-reftype}{\mathsf{externref}}\) denotes the infinite union of all references to objects owned by the embedder and that can be passed into WebAssembly under this type.

    +

    Reference types are opaque, meaning that neither their size nor their bit pattern can be observed. +Values of reference type can be stored in tables.

    +
    +
    +

    Value Types

    +

    Value types classify the individual values that WebAssembly code can compute with and the values that a variable accepts. +They are either number types, vector types, or reference types.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2502#1{{}}\mathdef2502{value type} & \href{../syntax/types.html#syntax-valtype}{\mathit{valtype}} &::=& + \href{../syntax/types.html#syntax-numtype}{\mathit{numtype}} ~|~ \href{../syntax/types.html#syntax-vectype}{\mathit{vectype}} ~|~ \href{../syntax/types.html#syntax-reftype}{\mathit{reftype}} \\ +\end{array}\end{split}\]
    +
    +

    Conventions

    +
      +

    • The meta variable \(t\) ranges over value types or subclasses thereof where clear from context.

      • +
    +
    +
    +
    +

    Result Types

    +

    Result types classify the result of executing instructions or functions, +which is a sequence of values, written with brackets.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2502#1{{}}\mathdef2502{result type} & \href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}} &::=& + [\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}})] \\ +\end{array}\end{split}\]
    +
    +
    +

    Function Types

    +

    Function types classify the signature of functions, +mapping a vector of parameters to a vector of results. +They are also used to classify the inputs and outputs of instructions.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2502#1{{}}\mathdef2502{function type} & \href{../syntax/types.html#syntax-functype}{\mathit{functype}} &::=& + \href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}} \href{../syntax/types.html#syntax-functype}{\rightarrow} \href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}} \\ +\end{array}\end{split}\]
    +
    +
    +

    Limits

    +

    Limits classify the size range of resizeable storage associated with memory types and table types.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2502#1{{}}\mathdef2502{limits} & \href{../syntax/types.html#syntax-limits}{\mathit{limits}} &::=& + \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~\href{../syntax/values.html#syntax-int}{\mathit{u32}}, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~\href{../syntax/values.html#syntax-int}{\mathit{u32}}^? \} \\ +\end{array}\end{split}\]
    +

    If no maximum is given, the respective storage can grow to any size.

    +
    +
    +

    Memory Types

    +

    Memory types classify linear memories and their size range.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2502#1{{}}\mathdef2502{memory type} & \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} &::=& + \href{../syntax/types.html#syntax-limits}{\mathit{limits}} \\ +\end{array}\end{split}\]
    +

    The limits constrain the minimum and optionally the maximum size of a memory. +The limits are given in units of page size.

    +
    +
    +

    Table Types

    +

    Table types classify tables over elements of reference type within a size range.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2502#1{{}}\mathdef2502{table type} & \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} &::=& + \href{../syntax/types.html#syntax-limits}{\mathit{limits}}~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}} \\ +\end{array}\end{split}\]
    +

    Like memories, tables are constrained by limits for their minimum and optionally maximum size. +The limits are given in numbers of entries.

    +
    +

    Note

    +

    In future versions of WebAssembly, additional element types may be introduced.

    +
    +
    +
    +

    Global Types

    +

    Global types classify global variables, which hold a value and can either be mutable or immutable.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2502#1{{}}\mathdef2502{global type} & \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} &::=& + \href{../syntax/types.html#syntax-mut}{\mathit{mut}}~\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}} \\ +\def\mathdef2502#1{{}}\mathdef2502{mutability} & \href{../syntax/types.html#syntax-mut}{\mathit{mut}} &::=& + \href{../syntax/types.html#syntax-mut}{\mathsf{const}} ~|~ + \href{../syntax/types.html#syntax-mut}{\mathsf{var}} \\ +\end{array}\end{split}\]
    +
    +
    +

    External Types

    +

    External types classify imports and external values with their respective types.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2502#1{{}}\mathdef2502{external types} & \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}} &::=& + \href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}} ~|~ + \href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} ~|~ + \href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} ~|~ + \href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} \\ +\end{array}\end{split}\]
    +
    +

    Conventions

    +

    The following auxiliary notation is defined for sequences of external types. +It filters out entries of a specific kind in an order-preserving fashion:

    +
      +

    • \(\href{../syntax/types.html#syntax-externtype}{\mathrm{funcs}}(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast) = [\href{../syntax/types.html#syntax-functype}{\mathit{functype}} ~|~ (\href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}) \in \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast]\)

      • +

    • \(\href{../syntax/types.html#syntax-externtype}{\mathrm{tables}}(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast) = [\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} ~|~ (\href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}) \in \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast]\)

      • +

    • \(\href{../syntax/types.html#syntax-externtype}{\mathrm{mems}}(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast) = [\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} ~|~ (\href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}) \in \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast]\)

      • +

    • \(\href{../syntax/types.html#syntax-externtype}{\mathrm{globals}}(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast) = [\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} ~|~ (\href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}) \in \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast]\)

      • +
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/syntax/values.html b/core/syntax/values.html new file mode 100644 index 00000000..ab13c1fc --- /dev/null +++ b/core/syntax/values.html @@ -0,0 +1,222 @@ + + + + + + + + + Values — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Values

    +

    WebAssembly programs operate on primitive numeric values. +Moreover, in the definition of programs, immutable sequences of values occur to represent more complex data, such as text strings or other vectors.

    +
    +

    Bytes

    +

    The simplest form of value are raw uninterpreted bytes. +In the abstract syntax they are represented as hexadecimal literals.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2541#1{{}}\mathdef2541{byte} & \href{../syntax/values.html#syntax-byte}{\mathit{byte}} &::=& + \def\mathdef2580#1{\mathtt{0x#1}}\mathdef2580{00} ~|~ \dots ~|~ \def\mathdef2581#1{\mathtt{0x#1}}\mathdef2581{FF} \\ +\end{array}\end{split}\]
    +
    +

    Conventions

    +
      +

    • The meta variable \(b\) ranges over bytes.

      • +

    • Bytes are sometimes interpreted as natural numbers \(n < 256\).

      • +
    +
    +
    +
    +

    Integers

    +

    Different classes of integers with different value ranges are distinguished by their bit width \(N\) and by whether they are unsigned or signed.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2541#1{{}}\mathdef2541{unsigned integer} & \href{../syntax/values.html#syntax-int}{\mathit{u}N} &::=& + 0 ~|~ 1 ~|~ \dots ~|~ 2^N{-}1 \\ +\def\mathdef2541#1{{}}\mathdef2541{signed integer} & \href{../syntax/values.html#syntax-int}{\mathit{s}N} &::=& + -2^{N-1} ~|~ \dots ~|~ {-}1 ~|~ 0 ~|~ 1 ~|~ \dots ~|~ 2^{N-1}{-}1 \\ +\def\mathdef2541#1{{}}\mathdef2541{uninterpreted integer} & \href{../syntax/values.html#syntax-int}{\mathit{i}N} &::=& + \href{../syntax/values.html#syntax-int}{\mathit{u}N} \\ +\end{array}\end{split}\]
    +

    The latter class defines uninterpreted integers, whose signedness interpretation can vary depending on context. +In the abstract syntax, they are represented as unsigned values. +However, some operations convert them to signed based on a two’s complement interpretation.

    +
    +

    Note

    +

    The main integer types occurring in this specification are \(\href{../syntax/values.html#syntax-int}{\mathit{u32}}\), \(\href{../syntax/values.html#syntax-int}{\mathit{u64}}\), \(\href{../syntax/values.html#syntax-int}{\mathit{s32}}\), \(\href{../syntax/values.html#syntax-int}{\mathit{s64}}\), \(\href{../syntax/values.html#syntax-int}{\mathit{i8}}\), \(\href{../syntax/values.html#syntax-int}{\mathit{i16}}\), \(\href{../syntax/values.html#syntax-int}{\mathit{i32}}\), \(\href{../syntax/values.html#syntax-int}{\mathit{i64}}\). +However, other sizes occur as auxiliary constructions, e.g., in the definition of floating-point numbers.

    +
    +
    +

    Conventions

    +
      +

    • The meta variables \(m, n, i\) range over integers.

      • +

    • Numbers may be denoted by simple arithmetics, as in the grammar above. +In order to distinguish arithmetics like \(2^N\) from sequences like \((1)^N\), the latter is distinguished with parentheses.

      • +
    +
    +
    +
    +

    Floating-Point

    +

    Floating-point data represents 32 or 64 bit values that correspond to the respective binary formats of the IEEE 754-2019 standard (Section 3.3).

    +

    Every value has a sign and a magnitude. +Magnitudes can either be expressed as normal numbers of the form \(m_0.m_1m_2\dots m_M \cdot2^e\), where \(e\) is the exponent and \(m\) is the significand whose most significant bit \(m_0\) is \(1\), +or as a subnormal number where the exponent is fixed to the smallest possible value and \(m_0\) is \(0\); among the subnormals are positive and negative zero values. +Since the significands are binary values, normals are represented in the form \((1 + m\cdot 2^{-M}) \cdot 2^e\), where \(M\) is the bit width of \(m\); similarly for subnormals.

    +

    Possible magnitudes also include the special values \(\infty\) (infinity) and \(\href{../syntax/values.html#syntax-float}{\mathsf{nan}}\) (NaN, not a number). +NaN values have a payload that describes the mantissa bits in the underlying binary representation. +No distinction is made between signalling and quiet NaNs.

    +
    +\[\begin{split}\begin{array}{llcll} +\def\mathdef2541#1{{}}\mathdef2541{floating-point value} & \href{../syntax/values.html#syntax-float}{\mathit{f}N} &::=& + {+} \href{../syntax/values.html#syntax-float}{\mathit{f}\mathit{Nmag}} ~|~ {-} \href{../syntax/values.html#syntax-float}{\mathit{f}\mathit{Nmag}} \\ +\def\mathdef2541#1{{}}\mathdef2541{floating-point magnitude} & \href{../syntax/values.html#syntax-float}{\mathit{f}\mathit{Nmag}} &::=& + (1 + \href{../syntax/values.html#syntax-int}{\mathit{u}M}\cdot 2^{-M}) \cdot 2^e & (\mathrel{\mbox{if}} -2^{E-1}+2 \leq e \leq 2^{E-1}-1) \\ &&|& + (0 + \href{../syntax/values.html#syntax-int}{\mathit{u}M}\cdot 2^{-M}) \cdot 2^e & (\mathrel{\mbox{if}} e = -2^{E-1}+2) \\ &&|& + \infty \\ &&|& + \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n) & (\mathrel{\mbox{if}} 1 \leq n < 2^M) \\ +\end{array}\end{split}\]
    +

    where \(M = \href{../syntax/values.html#aux-significand}{\mathrm{signif}}(N)\) and \(E = \href{../syntax/values.html#aux-exponent}{\mathrm{expon}}(N)\) with

    +
    +\[\begin{split}\begin{array}{lclllllcl} +\href{../syntax/values.html#aux-significand}{\mathrm{signif}}(32) &=& 23 &&&& +\href{../syntax/values.html#aux-exponent}{\mathrm{expon}}(32) &=& 8 \\ +\href{../syntax/values.html#aux-significand}{\mathrm{signif}}(64) &=& 52 &&&& +\href{../syntax/values.html#aux-exponent}{\mathrm{expon}}(64) &=& 11 \\ +\end{array}\end{split}\]
    +

    A canonical NaN is a floating-point value \(\pm\href{../syntax/values.html#syntax-float}{\mathsf{nan}}(\href{../syntax/values.html#aux-canon}{\mathrm{canon}}_N)\) where \(\href{../syntax/values.html#aux-canon}{\mathrm{canon}}_N\) is a payload whose most significant bit is \(1\) while all others are \(0\):

    +
    +\[\href{../syntax/values.html#aux-canon}{\mathrm{canon}}_N = 2^{\href{../syntax/values.html#aux-significand}{\mathrm{signif}}(N)-1}\]
    +

    An arithmetic NaN is a floating-point value \(\pm\href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n)\) with \(n \geq \href{../syntax/values.html#aux-canon}{\mathrm{canon}}_N\), such that the most significant bit is \(1\) while all others are arbitrary.

    +
    +

    Note

    +

    In the abstract syntax, subnormals are distinguished by the leading 0 of the significand. The exponent of subnormals has the same value as the smallest possible exponent of a normal number. Only in the binary representation the exponent of a subnormal is encoded differently than the exponent of any normal number.

    +
    +
    +

    Conventions

    +
      +

    • The meta variable \(z\) ranges over floating-point values where clear from context.

      • +
    +
    +
    +
    +

    Vectors

    +

    Numeric vectors are 128-bit values that are processed by vector instructions (also known as SIMD instructions, single instruction multiple data). +They are represented in the abstract syntax using \(\href{../syntax/values.html#syntax-int}{\mathit{i128}}\). The interpretation of lane types (integer or floating-point numbers) and lane sizes are determined by the specific instruction operating on them.

    +
    +
    +

    Names

    +

    Names are sequences of characters, which are scalar values as defined by Unicode (Section 2.4).

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef2541#1{{}}\mathdef2541{name} & \href{../syntax/values.html#syntax-name}{\mathit{name}} &::=& + \href{../syntax/values.html#syntax-name}{\mathit{char}}^\ast \qquad\qquad (\mathrel{\mbox{if}} |\href{../binary/values.html#binary-utf8}{\mathrm{utf8}}(\href{../syntax/values.html#syntax-name}{\mathit{char}}^\ast)| < 2^{32}) \\ +\def\mathdef2541#1{{}}\mathdef2541{character} & \href{../syntax/values.html#syntax-name}{\mathit{char}} &::=& + \def\mathdef2582#1{\mathrm{U{+}#1}}\mathdef2582{00} ~|~ \dots ~|~ \def\mathdef2583#1{\mathrm{U{+}#1}}\mathdef2583{D7FF} ~|~ + \def\mathdef2584#1{\mathrm{U{+}#1}}\mathdef2584{E000} ~|~ \dots ~|~ \def\mathdef2585#1{\mathrm{U{+}#1}}\mathdef2585{10FFFF} \\ +\end{array}\end{split}\]
    +

    Due to the limitations of the binary format, +the length of a name is bounded by the length of its UTF-8 encoding.

    +
    +

    Convention

    +
      +

    • Characters (Unicode scalar values) are sometimes used interchangeably with natural numbers \(n < 1114112\).

      • +
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/text/conventions.html b/core/text/conventions.html new file mode 100644 index 00000000..2896d4b5 --- /dev/null +++ b/core/text/conventions.html @@ -0,0 +1,214 @@ + + + + + + + + + Conventions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Conventions

    +

    The textual format for WebAssembly modules is a rendering of their abstract syntax into S-expressions.

    +

    Like the binary format, the text format is defined by an attribute grammar. +A text string is a well-formed description of a module if and only if it is generated by the grammar. +Each production of this grammar has at most one synthesized attribute: the abstract syntax that the respective character sequence expresses. +Thus, the attribute grammar implicitly defines a parsing function. +Some productions also take a context as an inherited attribute +that records bound identifiers.

    +

    Except for a few exceptions, the core of the text grammar closely mirrors the grammar of the abstract syntax. +However, it also defines a number of abbreviations that are “syntactic sugar” over the core syntax.

    +

    The recommended extension for files containing WebAssembly modules in text format is “\(\mathtt{.wat}\)”. +Files with this extension are assumed to be encoded in UTF-8, as per Unicode (Section 2.5).

    +
    +

    Grammar

    +

    The following conventions are adopted in defining grammar rules of the text format. +They mirror the conventions used for abstract syntax and for the binary format. +In order to distinguish symbols of the textual syntax from symbols of the abstract syntax, \(\mathtt{typewriter}\) font is adopted for the former.

    +
      +

    • Terminal symbols are either literal strings of characters enclosed in quotes +or expressed as Unicode scalar values: \(\def\mathdef2625#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2625{module}\), \(\def\mathdef2626#1{\mathrm{U{+}#1}}\mathdef2626{0A}\). +(All characters written literally are unambiguously drawn from the 7-bit ASCII subset of Unicode.)

      • +

    • Nonterminal symbols are written in typewriter font: \(\mathtt{valtype}, \mathtt{instr}\).

      • +

    • \(T^n\) is a sequence of \(n\geq 0\) iterations of \(T\).

      • +

    • \(T^\ast\) is a possibly empty sequence of iterations of \(T\). +(This is a shorthand for \(T^n\) used where \(n\) is not relevant.)

      • +

    • \(T^+\) is a sequence of one or more iterations of \(T\). +(This is a shorthand for \(T^n\) where \(n \geq 1\).)

      • +

    • \(T^?\) is an optional occurrence of \(T\). +(This is a shorthand for \(T^n\) where \(n \leq 1\).)

      • +

    • \(x{:}T\) denotes the same language as the nonterminal \(T\), but also binds the variable \(x\) to the attribute synthesized for \(T\).

      • +

    • Productions are written \(\mathtt{sym} ::= T_1 \Rightarrow A_1 ~|~ \dots ~|~ T_n \Rightarrow A_n\), where each \(A_i\) is the attribute that is synthesized for \(\mathtt{sym}\) in the given case, usually from attribute variables bound in \(T_i\).

      • +

    • Some productions are augmented by side conditions in parentheses, which restrict the applicability of the production. They provide a shorthand for a combinatorial expansion of the production into many separate cases.

      • +

    • If the same meta variable or non-terminal symbol appears multiple times in a production (in the syntax or in an attribute), then all those occurrences must have the same instantiation.

      • +
    +
      +

    • A distinction is made between lexical and syntactic productions. For the latter, arbitrary white space is allowed in any place where the grammar contains spaces. The productions defining lexical syntax and the syntax of values are considered lexical, all others are syntactic.

      • +
    +
    +

    Note

    +

    For example, the textual grammar for number types is given as follows:

    +
    +\[\begin{split}\begin{array}{llcll@{\qquad\qquad}l} +\def\mathdef2586#1{{}}\mathdef2586{number types} & \href{../text/types.html#text-numtype}{\mathtt{numtype}} &::=& + \def\mathdef2627#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2627{i32} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}} \\ &&|& + \def\mathdef2628#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2628{i64} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}} \\ &&|& + \def\mathdef2629#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2629{f32} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}} \\ &&|& + \def\mathdef2630#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2630{f64} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}} \\ +\end{array}\end{split}\]
    +

    The textual grammar for limits is defined as follows:

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef2586#1{{}}\mathdef2586{limits} & \href{../text/types.html#text-limits}{\mathtt{limits}} &::=& + n{:}\href{../text/values.html#text-int}{\def\mathdef2611#1{{\mathtt{u}#1}}\mathdef2611{\mathtt{32}}} &\Rightarrow& \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~\epsilon \} \\ &&|& + n{:}\href{../text/values.html#text-int}{\def\mathdef2611#1{{\mathtt{u}#1}}\mathdef2611{\mathtt{32}}}~~m{:}\href{../text/values.html#text-int}{\def\mathdef2611#1{{\mathtt{u}#1}}\mathdef2611{\mathtt{32}}} &\Rightarrow& \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m \} \\ +\end{array}\end{split}\]
    +

    The variables \(n\) and \(m\) name the attributes of the respective \(\href{../text/values.html#text-int}{\def\mathdef2611#1{{\mathtt{u}#1}}\mathdef2611{\mathtt{32}}}\) nonterminals, which in this case are the actual unsigned integers those parse into. +The attribute of the complete production then is the abstract syntax for the limit, expressed in terms of the former values.

    +
    +
    +
    +

    Abbreviations

    +

    In addition to the core grammar, which corresponds directly to the abstract syntax, the textual syntax also defines a number of abbreviations that can be used for convenience and readability.

    +

    Abbreviations are defined by rewrite rules specifying their expansion into the core syntax:

    +
    +\[\mathit{abbreviation~syntax} \quad\equiv\quad \mathit{expanded~syntax}\]
    +

    These expansions are assumed to be applied, recursively and in order of appearance, before applying the core grammar rules to construct the abstract syntax.

    +
    +
    +

    Contexts

    +

    The text format allows the use of symbolic identifiers in place of indices. +To resolve these identifiers into concrete indices, +some grammar production are indexed by an identifier context \(I\) as a synthesized attribute that records the declared identifiers in each index space. +In addition, the context records the types defined in the module, so that parameter indices can be computed for functions.

    +

    It is convenient to define identifier contexts as records \(I\) with abstract syntax as follows:

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef2586#1{{}}\mathdef2586{(identifier context)} & I &::=& + \begin{array}[t]{l@{~}ll} + \{ & \href{../text/conventions.html#text-context}{\mathsf{types}} & (\href{../text/values.html#text-id}{\mathtt{id}}^?)^\ast, \\ + & \href{../text/conventions.html#text-context}{\mathsf{funcs}} & (\href{../text/values.html#text-id}{\mathtt{id}}^?)^\ast, \\ + & \href{../text/conventions.html#text-context}{\mathsf{tables}} & (\href{../text/values.html#text-id}{\mathtt{id}}^?)^\ast, \\ + & \href{../text/conventions.html#text-context}{\mathsf{mems}} & (\href{../text/values.html#text-id}{\mathtt{id}}^?)^\ast, \\ + & \href{../text/conventions.html#text-context}{\mathsf{globals}} & (\href{../text/values.html#text-id}{\mathtt{id}}^?)^\ast, \\ + & \href{../text/conventions.html#text-context}{\mathsf{elem}} & (\href{../text/values.html#text-id}{\mathtt{id}}^?)^\ast, \\ + & \href{../text/conventions.html#text-context}{\mathsf{data}} & (\href{../text/values.html#text-id}{\mathtt{id}}^?)^\ast, \\ + & \href{../text/conventions.html#text-context}{\mathsf{locals}} & (\href{../text/values.html#text-id}{\mathtt{id}}^?)^\ast, \\ + & \href{../text/conventions.html#text-context}{\mathsf{labels}} & (\href{../text/values.html#text-id}{\mathtt{id}}^?)^\ast, \\ + & \href{../text/conventions.html#text-context}{\mathsf{typedefs}} & \href{../syntax/types.html#syntax-functype}{\mathit{functype}}^\ast ~\} \\ + \end{array} +\end{array}\end{split}\]
    +

    For each index space, such a context contains the list of identifiers assigned to the defined indices. +Unnamed indices are associated with empty (\(\epsilon\)) entries in these lists.

    +

    An identifier context is well-formed if no index space contains duplicate identifiers.

    +
    +

    Conventions

    +

    To avoid unnecessary clutter, empty components are omitted when writing out identifier contexts. +For example, the record \(\{\}\) is shorthand for an identifier context whose components are all empty.

    +
    +
    +
    +

    Vectors

    +

    Vectors are written as plain sequences, but with a restriction on the length of these sequence.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef2586#1{{}}\mathdef2586{vector} & \href{../text/conventions.html#text-vec}{\mathtt{vec}}(\mathtt{A}) &::=& + (x{:}\mathtt{A})^n &\Rightarrow& x^n & (\mathrel{\mbox{if}} n < 2^{32}) \\ +\end{array}\end{split}\]
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/text/index.html b/core/text/index.html new file mode 100644 index 00000000..269f9248 --- /dev/null +++ b/core/text/index.html @@ -0,0 +1,175 @@ + + + + + + + + + Text Format — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Text Format

    +
    + +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/text/instructions.html b/core/text/instructions.html new file mode 100644 index 00000000..4589d9c7 --- /dev/null +++ b/core/text/instructions.html @@ -0,0 +1,857 @@ + + + + + + + + + Instructions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Instructions

    +

    Instructions are syntactically distinguished into plain and structured instructions.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef2670#1{{}}\mathdef2670{instruction} & \href{../text/instructions.html#text-instr}{\mathtt{instr}}_I &::=& + \mathit{in}{:}\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I + &\Rightarrow& \mathit{in} \\ &&|& + \mathit{in}{:}\href{../text/instructions.html#text-blockinstr}{\mathtt{blockinstr}}_I + &\Rightarrow& \mathit{in} \\ +\end{array}\end{split}\]
    +

    In addition, as a syntactic abbreviation, instructions can be written as S-expressions in folded form, to group them visually.

    +
    +

    Labels

    +

    Structured control instructions can be annotated with a symbolic label identifier. +They are the only symbolic identifiers that can be bound locally in an instruction sequence. +The following grammar handles the corresponding update to the identifier context by composing the context with an additional label entry.

    +
    +\[\begin{split}\begin{array}{llcllll} +\def\mathdef2670#1{{}}\mathdef2670{label} & \href{../text/instructions.html#text-label}{\mathtt{label}}_I &::=& + v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& \{\href{../text/conventions.html#text-context}{\mathsf{labels}}~v\} \href{../syntax/conventions.html#notation-compose}{\oplus} I + & (\mathrel{\mbox{if}} v \notin I.\href{../text/conventions.html#text-context}{\mathsf{labels}}) \\ &&|& + \epsilon &\Rightarrow& \{\href{../text/conventions.html#text-context}{\mathsf{labels}}~(\epsilon)\} \href{../syntax/conventions.html#notation-compose}{\oplus} I \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The new label entry is inserted at the beginning of the label list in the identifier context. +This effectively shifts all existing labels up by one, +mirroring the fact that control instructions are indexed relatively not absolutely.

    +
    +
    +
    +

    Control Instructions

    +

    Structured control instructions can bind an optional symbolic label identifier. +The same label identifier may optionally be repeated after the corresponding \(\mathtt{end}\) and \(\mathtt{else}\) pseudo instructions, to indicate the matching delimiters.

    +

    Their block type is given as a type use, analogous to the type of functions. +However, the special case of a type use that is syntactically empty or consists of only a single result is not regarded as an abbreviation for an inline function type, but is parsed directly into an optional value type.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef2670#1{{}}\mathdef2670{block type} & \href{../text/instructions.html#text-blocktype}{\mathtt{blocktype}}_I & +\begin{array}[t]{@{}c@{}} ::= \\ | \\ \end{array} +& +\begin{array}[t]{@{}lcll@{}} + (t{:}\href{../text/types.html#text-functype}{\mathtt{result}})^? &\Rightarrow& t^? \\ + x,I'{:}\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I &\Rightarrow& x & (\mathrel{\mbox{if}} I' = \{\href{../text/conventions.html#text-context}{\mathsf{locals}}~(\epsilon)^\ast\}) \\ +\end{array} \\ +\def\mathdef2670#1{{}}\mathdef2670{block instruction} & \href{../text/instructions.html#text-blockinstr}{\mathtt{blockinstr}}_I &::=& + \def\mathdef2709#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2709{block}~~I'{:}\href{../text/instructions.html#text-label}{\mathtt{label}}_I~~\mathit{bt}{:}\href{../text/instructions.html#text-blocktype}{\mathtt{blocktype}}_I~~(\mathit{in}{:}\href{../text/instructions.html#text-instr}{\mathtt{instr}}_{I'})^\ast~~\def\mathdef2710#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2710{end}~~\href{../text/values.html#text-id}{\mathtt{id}}^? + \\ &&&\qquad \Rightarrow\quad \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~\mathit{bt}~\mathit{in}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} + \qquad\quad~~ (\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \href{../text/instructions.html#text-label}{\mathtt{label}}) \\ &&|& + \def\mathdef2711#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2711{loop}~~I'{:}\href{../text/instructions.html#text-label}{\mathtt{label}}_I~~\mathit{bt}{:}\href{../text/instructions.html#text-blocktype}{\mathtt{blocktype}}_I~~(\mathit{in}{:}\href{../text/instructions.html#text-instr}{\mathtt{instr}}_{I'})^\ast~~\def\mathdef2712#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2712{end}~~\href{../text/values.html#text-id}{\mathtt{id}}^? + \\ &&&\qquad \Rightarrow\quad \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}~\mathit{bt}~\mathit{in}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} + \qquad\qquad (\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \href{../text/instructions.html#text-label}{\mathtt{label}}) \\ &&|& + \def\mathdef2713#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2713{if}~~I'{:}\href{../text/instructions.html#text-label}{\mathtt{label}}_I~~\mathit{bt}{:}\href{../text/instructions.html#text-blocktype}{\mathtt{blocktype}}_I~~(\mathit{in}_1{:}\href{../text/instructions.html#text-instr}{\mathtt{instr}}_{I'})^\ast~~ + \def\mathdef2714#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2714{else}~~\href{../text/values.html#text-id}{\mathtt{id}}_1^?~~(\mathit{in}_2{:}\href{../text/instructions.html#text-instr}{\mathtt{instr}}_{I'})^\ast~~\def\mathdef2715#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2715{end}~~\href{../text/values.html#text-id}{\mathtt{id}}_2^? + \\ &&&\qquad \Rightarrow\quad \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}~\mathit{bt}~\mathit{in}_1^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}~\mathit{in}_2^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} + \qquad (\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}_1^? = \epsilon \vee \href{../text/values.html#text-id}{\mathtt{id}}_1^? = \href{../text/instructions.html#text-label}{\mathtt{label}}, \href{../text/values.html#text-id}{\mathtt{id}}_2^? = \epsilon \vee \href{../text/values.html#text-id}{\mathtt{id}}_2^? = \href{../text/instructions.html#text-label}{\mathtt{label}}) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The side condition stating that the identifier context \(I'\) must only contain unnamed entries in the rule for \(\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}\) block types enforces that no identifier can be bound in any \(\href{../text/types.html#text-functype}{\mathtt{param}}\) declaration for a block type.

    +
    +

    All other control instruction are represented verbatim.

    +
    +\[\begin{split}\begin{array}{llcllll} +\def\mathdef2670#1{{}}\mathdef2670{plain instruction} & \href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I &::=& + \def\mathdef2716#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2716{unreachable} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}} \\ &&|& + \def\mathdef2717#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2717{nop} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{nop}} \\ &&|& + \def\mathdef2718#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2718{br}~~l{:}\href{../text/modules.html#text-labelidx}{\mathtt{labelidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l \\ &&|& + \def\mathdef2719#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2719{br\_if}~~l{:}\href{../text/modules.html#text-labelidx}{\mathtt{labelidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_if}}~l \\ &&|& + \def\mathdef2720#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2720{br\_table}~~l^\ast{:}\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-labelidx}{\mathtt{labelidx}}_I)~~l_N{:}\href{../text/modules.html#text-labelidx}{\mathtt{labelidx}}_I + &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}~l^\ast~l_N \\ &&|& + \def\mathdef2721#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2721{return} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}} \\ &&|& + \def\mathdef2722#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2722{call}~~x{:}\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call}}~x \\ &&|& + \def\mathdef2723#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2723{call\_indirect}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}~~y,I'{:}\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}~x~y + & (\mathrel{\mbox{if}} I' = \{\href{../text/conventions.html#text-context}{\mathsf{locals}}~(\epsilon)^\ast\}) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The side condition stating that the identifier context \(I'\) must only contain unnamed entries in the rule for \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}\) enforces that no identifier can be bound in any \(\href{../text/types.html#text-functype}{\mathtt{param}}\) declaration appearing in the type annotation.

    +
    +
    +

    Abbreviations

    +

    The \(\def\mathdef2724#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2724{else}\) keyword of an \(\def\mathdef2725#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2725{if}\) instruction can be omitted if the following instruction sequence is empty.

    +
    +\[\begin{array}{llclll} +\def\mathdef2670#1{{}}\mathdef2670{block instruction} & + \def\mathdef2726#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2726{if}~~\href{../text/instructions.html#text-label}{\mathtt{label}}~~\href{../text/instructions.html#text-blocktype}{\mathtt{blocktype}}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}^\ast~~\def\mathdef2727#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2727{end} + &\equiv& + \def\mathdef2728#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2728{if}~~\href{../text/instructions.html#text-label}{\mathtt{label}}~~\href{../text/instructions.html#text-blocktype}{\mathtt{blocktype}}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}^\ast~~\def\mathdef2729#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2729{else}~~\def\mathdef2730#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2730{end} +\end{array}\]
    +

    Also, for backwards compatibility, the table index to \(\def\mathdef2731#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2731{call\_indirect}\) can be omitted, defaulting to \(0\).

    +
    +\[\begin{array}{llclll} +\def\mathdef2670#1{{}}\mathdef2670{plain instruction} & + \def\mathdef2732#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2732{call\_indirect}~~\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}} + &\equiv& + \def\mathdef2733#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2733{call\_indirect}~~0~~\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}} +\end{array}\]
    +
    +
    +
    +

    Reference Instructions

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef2670#1{{}}\mathdef2670{instruction} & \href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I &::=& \dots \\ &&|& + \def\mathdef2734#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2734{ref.null}~~t{:}\href{../text/types.html#text-heaptype}{\mathtt{heaptype}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t \\ &&|& + \def\mathdef2735#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2735{ref.is\_null} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}is\_null}} \\ &&|& + \def\mathdef2736#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2736{ref.func}~~x{:}\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~x \\ &&|& +\end{array}\end{split}\]
    +
    +
    +

    Parametric Instructions

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef2670#1{{}}\mathdef2670{instruction} & \href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I &::=& \dots \\ &&|& + \def\mathdef2737#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2737{drop} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{drop}} \\ &&|& + \def\mathdef2738#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2738{select}~((t{:}\href{../text/types.html#text-functype}{\mathtt{result}})^\ast)^? &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}~(t^\ast)^? \\ +\end{array}\end{split}\]
    +
    +
    +

    Variable Instructions

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef2670#1{{}}\mathdef2670{instruction} & \href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I &::=& \dots \\ &&|& + \def\mathdef2739#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2739{local.get}~~x{:}\href{../text/modules.html#text-localidx}{\mathtt{localidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.get}}~x \\ &&|& + \def\mathdef2740#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2740{local.set}~~x{:}\href{../text/modules.html#text-localidx}{\mathtt{localidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.set}}~x \\ &&|& + \def\mathdef2741#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2741{local.tee}~~x{:}\href{../text/modules.html#text-localidx}{\mathtt{localidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.tee}}~x \\ &&|& + \def\mathdef2742#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2742{global.get}~~x{:}\href{../text/modules.html#text-globalidx}{\mathtt{globalidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.get}}~x \\ &&|& + \def\mathdef2743#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2743{global.set}~~x{:}\href{../text/modules.html#text-globalidx}{\mathtt{globalidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.set}}~x \\ +\end{array}\end{split}\]
    +
    +
    +

    Table Instructions

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef2670#1{{}}\mathdef2670{instruction} & \href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I &::=& \dots \\ &&|& + \def\mathdef2744#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2744{table.get}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}~x \\ &&|& + \def\mathdef2745#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2745{table.set}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x \\ &&|& + \def\mathdef2746#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2746{table.size}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.size}}~x \\ &&|& + \def\mathdef2747#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2747{table.grow}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.grow}}~x \\ &&|& + \def\mathdef2748#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2748{table.fill}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.fill}}~x \\ &&|& + \def\mathdef2749#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2749{table.copy}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I~~y{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}~x~y \\ &&|& + \def\mathdef2750#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2750{table.init}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I~~y{:}\href{../text/modules.html#text-elemidx}{\mathtt{elemidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}~x~y \\ &&|& + \def\mathdef2751#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2751{elem.drop}~~x{:}\href{../text/modules.html#text-elemidx}{\mathtt{elemidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem.drop}}~x \\ +\end{array}\end{split}\]
    +
    +

    Abbreviations

    +

    For backwards compatibility, all \(table indices <syntax-tableidx>\) may be omitted from table instructions, defaulting to \(0\).

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef2670#1{{}}\mathdef2670{instruction} & + \def\mathdef2752#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2752{table.get} &\equiv& \def\mathdef2753#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2753{table.get}~~\def\mathdef2754#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2754{0} \\ &&|& + \def\mathdef2755#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2755{table.set} &\equiv& \def\mathdef2756#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2756{table.set}~~\def\mathdef2757#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2757{0} \\ &&|& + \def\mathdef2758#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2758{table.size} &\equiv& \def\mathdef2759#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2759{table.size}~~\def\mathdef2760#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2760{0} \\ &&|& + \def\mathdef2761#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2761{table.grow} &\equiv& \def\mathdef2762#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2762{table.grow}~~\def\mathdef2763#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2763{0} \\ &&|& + \def\mathdef2764#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2764{table.fill} &\equiv& \def\mathdef2765#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2765{table.fill}~~\def\mathdef2766#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2766{0} \\ &&|& + \def\mathdef2767#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2767{table.copy} &\equiv& \def\mathdef2768#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2768{table.copy}~~\def\mathdef2769#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2769{0}~~\def\mathdef2770#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2770{0} \\ &&|& + \def\mathdef2771#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2771{table.init}~~x{:}\href{../text/modules.html#text-elemidx}{\mathtt{elemidx}}_I &\equiv& \def\mathdef2772#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2772{table.init}~~\def\mathdef2773#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2773{0}~~x{:}\href{../text/modules.html#text-elemidx}{\mathtt{elemidx}}_I \\ &&|& +\end{array}\end{split}\]
    +
    +
    +
    +

    Memory Instructions

    +

    The offset and alignment immediates to memory instructions are optional. +The offset defaults to \(\mathtt{0}\), the alignment to the storage size of the respective memory access, which is its natural alignment. +Lexically, an \(\href{../text/instructions.html#text-memarg}{\mathtt{offset}}\) or \(\href{../text/instructions.html#text-memarg}{\mathtt{align}}\) phrase is considered a single keyword token, so no white space is allowed around the \(\def\mathdef2774#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2774{=}\).

    +
    +\[\begin{split}\begin{array}{llcllll} +\def\mathdef2670#1{{}}\mathdef2670{memory argument} & \href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_N &::=& + o{:}\href{../text/instructions.html#text-memarg}{\mathtt{offset}}~~a{:}\href{../text/instructions.html#text-memarg}{\mathtt{align}}_N &\Rightarrow& \{ \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}~n,~\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}~o \} & (\mathrel{\mbox{if}} a = 2^n) \\ +\def\mathdef2670#1{{}}\mathdef2670{memory offset} & \href{../text/instructions.html#text-memarg}{\mathtt{offset}} &::=& + \def\mathdef2775#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2775{offset{=}}o{:}\href{../text/values.html#text-int}{\def\mathdef2695#1{{\mathtt{u}#1}}\mathdef2695{\mathtt{32}}} &\Rightarrow& o \\ &&|& + \epsilon &\Rightarrow& 0 \\ +\def\mathdef2670#1{{}}\mathdef2670{memory alignment} & \href{../text/instructions.html#text-memarg}{\mathtt{align}}_N &::=& + \def\mathdef2776#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2776{align{=}}a{:}\href{../text/values.html#text-int}{\def\mathdef2695#1{{\mathtt{u}#1}}\mathdef2695{\mathtt{32}}} &\Rightarrow& a \\ &&|& + \epsilon &\Rightarrow& N \\ +\def\mathdef2670#1{{}}\mathdef2670{instruction} & \href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I &::=& \dots \\ &&|& + \def\mathdef2777#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2777{i32.load}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_4 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~m \\ &&|& + \def\mathdef2778#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2778{i64.load}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~m \\ &&|& + \def\mathdef2779#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2779{f32.load}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_4 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~m \\ &&|& + \def\mathdef2780#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2780{f64.load}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~m \\ &&|& + \def\mathdef2781#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2781{i32.load8\_s}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_1 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_s}~m \\ &&|& + \def\mathdef2782#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2782{i32.load8\_u}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_1 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_u}~m \\ &&|& + \def\mathdef2783#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2783{i32.load16\_s}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_2 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_s}~m \\ &&|& + \def\mathdef2784#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2784{i32.load16\_u}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_2 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_u}~m \\ &&|& + \def\mathdef2785#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2785{i64.load8\_s}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_1 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_s}~m \\ &&|& + \def\mathdef2786#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2786{i64.load8\_u}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_1 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_u}~m \\ &&|& + \def\mathdef2787#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2787{i64.load16\_s}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_2 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_s}~m \\ &&|& + \def\mathdef2788#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2788{i64.load16\_u}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_2 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_u}~m \\ &&|& + \def\mathdef2789#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2789{i64.load32\_s}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_4 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_s}~m \\ &&|& + \def\mathdef2790#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2790{i64.load32\_u}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_4 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_u}~m \\ &&|& + \def\mathdef2791#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2791{i32.store}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_4 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~m \\ &&|& + \def\mathdef2792#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2792{i64.store}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~m \\ &&|& + \def\mathdef2793#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2793{f32.store}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_4 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~m \\ &&|& + \def\mathdef2794#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2794{f64.store}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~m \\ &&|& + \def\mathdef2795#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2795{i32.store8}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_1 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~m \\ &&|& + \def\mathdef2796#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2796{i32.store16}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_2 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{16}~m \\ &&|& + \def\mathdef2797#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2797{i64.store8}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_1 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8}~m \\ &&|& + \def\mathdef2798#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2798{i64.store16}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_2 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{16}~m \\ &&|& + \def\mathdef2799#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2799{i64.store32}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_4 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{32}~m \\ &&|& + \def\mathdef2800#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2800{memory.size} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.size}} \\ &&|& + \def\mathdef2801#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2801{memory.grow} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.grow}} \\ &&|& + \def\mathdef2802#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2802{memory.fill} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}} \\ &&|& + \def\mathdef2803#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2803{memory.copy} &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}} \\ &&|& + \def\mathdef2804#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2804{memory.init}~~x{:}\href{../text/modules.html#text-dataidx}{\mathtt{dataidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~x \\ &&|& + \def\mathdef2805#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2805{data.drop}~~x{:}\href{../text/modules.html#text-dataidx}{\mathtt{dataidx}}_I &\Rightarrow& \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data.drop}}~x \\ +\end{array}\end{split}\]
    +
    +
    +

    Numeric Instructions

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef2670#1{{}}\mathdef2670{instruction} & \href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I &::=& \dots \\&&|& + \def\mathdef2806#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2806{i32.const}~~n{:}\href{../text/values.html#text-int}{\def\mathdef2703#1{{\mathtt{i}#1}}\mathdef2703{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n \\ &&|& + \def\mathdef2807#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2807{i64.const}~~n{:}\href{../text/values.html#text-int}{\def\mathdef2704#1{{\mathtt{i}#1}}\mathdef2704{\mathtt{64}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n \\ &&|& + \def\mathdef2808#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2808{f32.const}~~z{:}\href{../text/values.html#text-float}{\def\mathdef2707#1{{\mathtt{f}#1}}\mathdef2707{\mathtt{32}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~z \\ &&|& + \def\mathdef2809#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2809{f64.const}~~z{:}\href{../text/values.html#text-float}{\def\mathdef2708#1{{\mathtt{f}#1}}\mathdef2708{\mathtt{64}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~z \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{thisisenough} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef2810#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2810{i32.clz} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{clz}} \\ &&|& + \def\mathdef2811#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2811{i32.ctz} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ctz}} \\ &&|& + \def\mathdef2812#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2812{i32.popcnt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{popcnt}} \\ &&|& + \def\mathdef2813#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2813{i32.add} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}} \\ &&|& + \def\mathdef2814#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2814{i32.sub} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sub}} \\ &&|& + \def\mathdef2815#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2815{i32.mul} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}} \\ &&|& + \def\mathdef2816#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2816{i32.div\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\mathsf{\_s} \\ &&|& + \def\mathdef2817#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2817{i32.div\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\mathsf{\_u} \\ &&|& + \def\mathdef2818#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2818{i32.rem\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rem}}\mathsf{\_s} \\ &&|& + \def\mathdef2819#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2819{i32.rem\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rem}}\mathsf{\_u} \\ &&|& + \def\mathdef2820#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2820{i32.and} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{and}} \\ &&|& + \def\mathdef2821#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2821{i32.or} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{or}} \\ &&|& + \def\mathdef2822#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2822{i32.xor} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{xor}} \\ &&|& + \def\mathdef2823#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2823{i32.shl} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shl}} \\ &&|& + \def\mathdef2824#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2824{i32.shr\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shr}}\mathsf{\_s} \\ &&|& + \def\mathdef2825#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2825{i32.shr\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shr}}\mathsf{\_u} \\ &&|& + \def\mathdef2826#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2826{i32.rotl} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rotl}} \\ &&|& + \def\mathdef2827#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2827{i32.rotr} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rotr}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{thisisenough} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef2828#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2828{i64.clz} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{clz}} \\ &&|& + \def\mathdef2829#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2829{i64.ctz} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ctz}} \\ &&|& + \def\mathdef2830#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2830{i64.popcnt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{popcnt}} \\ &&|& + \def\mathdef2831#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2831{i64.add} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}} \\ &&|& + \def\mathdef2832#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2832{i64.sub} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sub}} \\ &&|& + \def\mathdef2833#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2833{i64.mul} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}} \\ &&|& + \def\mathdef2834#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2834{i64.div\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\mathsf{\_s} \\ &&|& + \def\mathdef2835#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2835{i64.div\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}}\mathsf{\_u} \\ &&|& + \def\mathdef2836#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2836{i64.rem\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rem}}\mathsf{\_s} \\ &&|& + \def\mathdef2837#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2837{i64.rem\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rem}}\mathsf{\_u} \\ &&|& + \def\mathdef2838#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2838{i64.and} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{and}} \\ &&|& + \def\mathdef2839#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2839{i64.or} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{or}} \\ &&|& + \def\mathdef2840#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2840{i64.xor} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{xor}} \\ &&|& + \def\mathdef2841#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2841{i64.shl} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shl}} \\ &&|& + \def\mathdef2842#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2842{i64.shr\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shr}}\mathsf{\_s} \\ &&|& + \def\mathdef2843#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2843{i64.shr\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{shr}}\mathsf{\_u} \\ &&|& + \def\mathdef2844#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2844{i64.rotl} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rotl}} \\ &&|& + \def\mathdef2845#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2845{i64.rotr} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{rotr}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{thisisenough} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef2846#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2846{f32.abs} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{abs}} \\ &&|& + \def\mathdef2847#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2847{f32.neg} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{neg}} \\ &&|& + \def\mathdef2848#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2848{f32.ceil} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ceil}} \\ &&|& + \def\mathdef2849#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2849{f32.floor} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{floor}} \\ &&|& + \def\mathdef2850#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2850{f32.trunc} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}} \\ &&|& + \def\mathdef2851#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2851{f32.nearest} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{nearest}} \\ &&|& + \def\mathdef2852#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2852{f32.sqrt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sqrt}} \\ &&|& + \def\mathdef2853#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2853{f32.add} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}} \\ &&|& + \def\mathdef2854#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2854{f32.sub} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sub}} \\ &&|& + \def\mathdef2855#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2855{f32.mul} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}} \\ &&|& + \def\mathdef2856#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2856{f32.div} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}} \\ &&|& + \def\mathdef2857#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2857{f32.min} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{min}} \\ &&|& + \def\mathdef2858#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2858{f32.max} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{max}} \\ &&|& + \def\mathdef2859#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2859{f32.copysign} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{copysign}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{thisisenough} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef2860#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2860{f64.abs} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{abs}} \\ &&|& + \def\mathdef2861#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2861{f64.neg} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{neg}} \\ &&|& + \def\mathdef2862#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2862{f64.ceil} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ceil}} \\ &&|& + \def\mathdef2863#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2863{f64.floor} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{floor}} \\ &&|& + \def\mathdef2864#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2864{f64.trunc} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}} \\ &&|& + \def\mathdef2865#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2865{f64.nearest} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{nearest}} \\ &&|& + \def\mathdef2866#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2866{f64.sqrt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sqrt}} \\ &&|& + \def\mathdef2867#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2867{f64.add} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}} \\ &&|& + \def\mathdef2868#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2868{f64.sub} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{sub}} \\ &&|& + \def\mathdef2869#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2869{f64.mul} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{mul}} \\ &&|& + \def\mathdef2870#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2870{f64.div} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{div}} \\ &&|& + \def\mathdef2871#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2871{f64.min} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{min}} \\ &&|& + \def\mathdef2872#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2872{f64.max} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{max}} \\ &&|& + \def\mathdef2873#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2873{f64.copysign} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{copysign}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{thisisenough} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef2874#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2874{i32.eqz} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eqz}} \\ &&|& + \def\mathdef2875#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2875{i32.eq} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eq}} \\ &&|& + \def\mathdef2876#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2876{i32.ne} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ne}} \\ &&|& + \def\mathdef2877#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2877{i32.lt\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\mathsf{\_s} \\ &&|& + \def\mathdef2878#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2878{i32.lt\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\mathsf{\_u} \\ &&|& + \def\mathdef2879#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2879{i32.gt\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\mathsf{\_s} \\ &&|& + \def\mathdef2880#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2880{i32.gt\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\mathsf{\_u} \\ &&|& + \def\mathdef2881#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2881{i32.le\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\mathsf{\_s} \\ &&|& + \def\mathdef2882#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2882{i32.le\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\mathsf{\_u} \\ &&|& + \def\mathdef2883#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2883{i32.ge\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\mathsf{\_s} \\ &&|& + \def\mathdef2884#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2884{i32.ge\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\mathsf{\_u} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{thisisenough} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef2885#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2885{i64.eqz} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eqz}} \\ &&|& + \def\mathdef2886#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2886{i64.eq} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eq}} \\ &&|& + \def\mathdef2887#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2887{i64.ne} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ne}} \\ &&|& + \def\mathdef2888#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2888{i64.lt\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\mathsf{\_s} \\ &&|& + \def\mathdef2889#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2889{i64.lt\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}}\mathsf{\_u} \\ &&|& + \def\mathdef2890#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2890{i64.gt\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\mathsf{\_s} \\ &&|& + \def\mathdef2891#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2891{i64.gt\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}}\mathsf{\_u} \\ &&|& + \def\mathdef2892#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2892{i64.le\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\mathsf{\_s} \\ &&|& + \def\mathdef2893#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2893{i64.le\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}}\mathsf{\_u} \\ &&|& + \def\mathdef2894#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2894{i64.ge\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\mathsf{\_s} \\ &&|& + \def\mathdef2895#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2895{i64.ge\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}}\mathsf{\_u} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{thisisenough} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef2896#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2896{f32.eq} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eq}} \\ &&|& + \def\mathdef2897#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2897{f32.ne} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ne}} \\ &&|& + \def\mathdef2898#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2898{f32.lt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}} \\ &&|& + \def\mathdef2899#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2899{f32.gt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}} \\ &&|& + \def\mathdef2900#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2900{f32.le} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}} \\ &&|& + \def\mathdef2901#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2901{f32.ge} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{thisisenough} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef2902#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2902{f64.eq} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{eq}} \\ &&|& + \def\mathdef2903#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2903{f64.ne} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ne}} \\ &&|& + \def\mathdef2904#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2904{f64.lt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{lt}} \\ &&|& + \def\mathdef2905#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2905{f64.gt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{gt}} \\ &&|& + \def\mathdef2906#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2906{f64.le} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{le}} \\ &&|& + \def\mathdef2907#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2907{f64.ge} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{ge}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{thisisenough} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef2908#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2908{i32.wrap\_i64} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{wrap}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}} \\ &&|& + \def\mathdef2909#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2909{i32.trunc\_f32\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_s} \\ &&|& + \def\mathdef2910#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2910{i32.trunc\_f32\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_u} \\ &&|& + \def\mathdef2911#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2911{i32.trunc\_f64\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_s} \\ &&|& + \def\mathdef2912#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2912{i32.trunc\_f64\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_u} \\ &&|& + \def\mathdef2913#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2913{i32.trunc\_sat\_f32\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_s} \\ &&|& + \def\mathdef2914#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2914{i32.trunc\_sat\_f32\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_u} \\ &&|& + \def\mathdef2915#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2915{i32.trunc\_sat\_f64\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_s} \\ &&|& + \def\mathdef2916#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2916{i32.trunc\_sat\_f64\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_u} \\ &&|& + \def\mathdef2917#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2917{i64.extend\_i32\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_s} \\ &&|& + \def\mathdef2918#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2918{i64.extend\_i32\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_u} \\ &&|& + \def\mathdef2919#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2919{i64.trunc\_f32\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_s} \\ &&|& + \def\mathdef2920#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2920{i64.trunc\_f32\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_u} \\ &&|& + \def\mathdef2921#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2921{i64.trunc\_f64\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_s} \\ &&|& + \def\mathdef2922#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2922{i64.trunc\_f64\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_u} \\ &&|& + \def\mathdef2923#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2923{i64.trunc\_sat\_f32\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_s} \\ &&|& + \def\mathdef2924#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2924{i64.trunc\_sat\_f32\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\mathsf{\_u} \\ &&|& + \def\mathdef2925#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2925{i64.trunc\_sat\_f64\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_s} \\ &&|& + \def\mathdef2926#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2926{i64.trunc\_sat\_f64\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_sat\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\mathsf{\_u} \\ &&|& + \def\mathdef2927#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2927{f32.convert\_i32\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_s} \\ &&|& + \def\mathdef2928#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2928{f32.convert\_i32\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_u} \\ &&|& + \def\mathdef2929#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2929{f32.convert\_i64\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}\mathsf{\_s} \\ &&|& + \def\mathdef2930#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2930{f32.convert\_i64\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}\mathsf{\_u} \\ &&|& + \def\mathdef2931#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2931{f32.demote\_f64} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{demote}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}} \\ &&|& + \def\mathdef2932#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2932{f64.convert\_i32\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_s} \\ &&|& + \def\mathdef2933#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2933{f64.convert\_i32\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\mathsf{\_u} \\ &&|& + \def\mathdef2934#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2934{f64.convert\_i64\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}\mathsf{\_s} \\ &&|& + \def\mathdef2935#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2935{f64.convert\_i64\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}\mathsf{\_u} \\ &&|& + \def\mathdef2936#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2936{f64.promote\_f32} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{promote}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}} \\ &&|& + \def\mathdef2937#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2937{i32.reinterpret\_f32} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{reinterpret}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}} \\ &&|& + \def\mathdef2938#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2938{i64.reinterpret\_f64} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{reinterpret}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}} \\ &&|& + \def\mathdef2939#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2939{f32.reinterpret\_i32} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{reinterpret}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}} \\ &&|& + \def\mathdef2940#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2940{f64.reinterpret\_i64} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{reinterpret}}\mathsf{\_}\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}} \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{thisisenough} && \phantom{thisshouldbeenough} \\[-2ex] &&|& + \def\mathdef2941#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2941{i32.extend8\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{8\_s} \\ &&|& + \def\mathdef2942#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2942{i32.extend16\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{16\_s} \\ &&|& + \def\mathdef2943#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2943{i64.extend8\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{8\_s} \\ &&|& + \def\mathdef2944#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2944{i64.extend16\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{16\_s} \\ &&|& + \def\mathdef2945#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2945{i64.extend32\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{extend}}\mathsf{32\_s} \\ +\end{array}\end{split}\]
    +
    +
    +

    Vector Instructions

    +

    Vector memory instructions have optional offset and alignment immediates, like the memory instructions.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef2670#1{{}}\mathdef2670{instruction} & \href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I &::=& \dots \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\ &&|& + \def\mathdef2946#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2946{v128.load}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_{16} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~m \\ &&|& + \def\mathdef2947#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2947{v128.load8x8\_s}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8x8\_s}~m \\ &&|& + \def\mathdef2948#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2948{v128.load8x8\_u}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8x8\_u}~m \\ &&|& + \def\mathdef2949#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2949{v128.load16x4\_s}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16x4\_s}~m \\ &&|& + \def\mathdef2950#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2950{v128.load16x4\_u}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16x4\_u}~m \\ &&|& + \def\mathdef2951#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2951{v128.load32x2\_s}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32x2\_s}~m \\ &&|& + \def\mathdef2952#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2952{v128.load32x2\_u}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32x2\_u}~m \\ &&|& + \def\mathdef2953#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2953{v128.load8\_splat}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_1 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_splat}~m \\ &&|& + \def\mathdef2954#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2954{v128.load16\_splat}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_2 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_splat}~m \\ &&|& + \def\mathdef2955#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2955{v128.load32\_splat}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_4 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_splat}~m \\ &&|& + \def\mathdef2956#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2956{v128.load64\_splat}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{64\_splat}~m \\ &&|& + \def\mathdef2957#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2957{v128.load32\_zero}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_4 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_zero}~m \\ &&|& + \def\mathdef2958#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2958{v128.load64\_zero}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8 &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{64\_zero}~m \\ &&|& + \def\mathdef2959#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2959{v128.store}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_{16} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~m \\ &&|& + \def\mathdef2960#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2960{v128.load8\_lane}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_1~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{8\_lane}~m~laneidx \\ &&|& + \def\mathdef2961#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2961{v128.load16\_lane}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_2~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{16\_lane}~m~laneidx \\ &&|& + \def\mathdef2962#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2962{v128.load32\_lane}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_4~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{32\_lane}~m~laneidx \\ &&|& + \def\mathdef2963#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2963{v128.load64\_lane}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}\mathsf{64\_lane}~m~laneidx \\ &&|& + \def\mathdef2964#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2964{v128.store8\_lane}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_1~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{8\_lane}~m~laneidx \\ &&|& + \def\mathdef2965#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2965{v128.store16\_lane}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_2~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{16\_lane}~m~laneidx \\ &&|& + \def\mathdef2966#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2966{v128.store32\_lane}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_4~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{32\_lane}~m~laneidx \\ &&|& + \def\mathdef2967#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2967{v128.store64\_lane}~~m{:}\href{../text/instructions.html#text-memarg}{\mathtt{memarg}}_8~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}\mathsf{64\_lane}~m~laneidx \\ +\end{array}\end{split}\]
    +

    Vector constant instructions have a mandatory shape descriptor, which determines how the following values are parsed.

    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef2968#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2968{v128.const}~~\def\mathdef2969#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2969{i8x16}~~(n{:}\href{../text/values.html#text-int}{\def\mathdef2701#1{{\mathtt{i}#1}}\mathdef2701{\mathtt{8}}})^{16} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{i128}^{-1}(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{i8}(n)^{16}) \\ &&|& + \def\mathdef2970#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2970{v128.const}~~\def\mathdef2971#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2971{i16x8}~~(n{:}\href{../text/values.html#text-int}{\def\mathdef2702#1{{\mathtt{i}#1}}\mathdef2702{\mathtt{16}}})^{8} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{i128}^{-1}(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{i16}(n)^8) \\ &&|& + \def\mathdef2972#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2972{v128.const}~~\def\mathdef2973#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2973{i32x4}~~(n{:}\href{../text/values.html#text-int}{\def\mathdef2703#1{{\mathtt{i}#1}}\mathdef2703{\mathtt{32}}})^{4} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{i128}^{-1}(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{i32}(n)^4) \\ &&|& + \def\mathdef2974#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2974{v128.const}~~\def\mathdef2975#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2975{i64x2}~~(n{:}\href{../text/values.html#text-int}{\def\mathdef2704#1{{\mathtt{i}#1}}\mathdef2704{\mathtt{64}}})^{2} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{i128}^{-1}(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{i64}(n)^2) \\ &&|& + \def\mathdef2976#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2976{v128.const}~~\def\mathdef2977#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2977{f32x4}~~(z{:}\href{../text/values.html#text-float}{\def\mathdef2707#1{{\mathtt{f}#1}}\mathdef2707{\mathtt{32}}})^{4} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{i128}^{-1}(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{f32}(z)^4) \\ &&|& + \def\mathdef2978#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2978{v128.const}~~\def\mathdef2979#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2979{f64x2}~~(z{:}\href{../text/values.html#text-float}{\def\mathdef2708#1{{\mathtt{f}#1}}\mathdef2708{\mathtt{64}}})^{2} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{i128}^{-1}(\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{f64}(z)^2) +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef2980#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2980{i8x16.shuffle}~~(laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}})^{16} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}~laneidx^{16} \\ &&|& + \def\mathdef2981#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2981{i8x16.swizzle} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{swizzle}} +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef2982#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2982{i8x16.splat} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}\\ &&|& + \def\mathdef2983#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2983{i16x8.splat} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}\\ &&|& + \def\mathdef2984#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2984{i32x4.splat} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}\\ &&|& + \def\mathdef2985#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2985{i64x2.splat} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}\\ &&|& + \def\mathdef2986#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2986{f32x4.splat} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}\\ &&|& + \def\mathdef2987#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2987{f64x2.splat} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef2988#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2988{i8x16.extract\_lane\_s}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_s}~laneidx \\ &&|& + \def\mathdef2989#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2989{i8x16.extract\_lane\_u}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_u}~laneidx \\ &&|& + \def\mathdef2990#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2990{i8x16.replace\_lane}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~laneidx \\ &&|& + \def\mathdef2991#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2991{i16x8.extract\_lane\_s}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_s}~laneidx \\ &&|& + \def\mathdef2992#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2992{i16x8.extract\_lane\_u}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_u}~laneidx \\ &&|& + \def\mathdef2993#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2993{i16x8.replace\_lane}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~laneidx \\ &&|& + \def\mathdef2994#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2994{i32x4.extract\_lane}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~laneidx \\ &&|& + \def\mathdef2995#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2995{i32x4.replace\_lane}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~laneidx \\ &&|& + \def\mathdef2996#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2996{i64x2.extract\_lane}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~laneidx \\ &&|& + \def\mathdef2997#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2997{i64x2.replace\_lane}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~laneidx \\ &&|& + \def\mathdef2998#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2998{f32x4.extract\_lane}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~laneidx \\ &&|& + \def\mathdef2999#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2999{f32x4.replace\_lane}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~laneidx \\ &&|& + \def\mathdef3000#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3000{f64x2.extract\_lane}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~laneidx \\ &&|& + \def\mathdef3001#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3001{f64x2.replace\_lane}~~laneidx{:}\href{../text/values.html#text-int}{\def\mathdef2693#1{{\mathtt{u}#1}}\mathdef2693{\mathtt{8}}} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~laneidx \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3002#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3002{i8x16.eq} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}}\\ &&|& + \def\mathdef3003#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3003{i8x16.ne} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}}\\ &&|& + \def\mathdef3004#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3004{i8x16.lt\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_s}\\ &&|& + \def\mathdef3005#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3005{i8x16.lt\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_u}\\ &&|& + \def\mathdef3006#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3006{i8x16.gt\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_s}\\ &&|& + \def\mathdef3007#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3007{i8x16.gt\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_u}\\ &&|& + \def\mathdef3008#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3008{i8x16.le\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_s}\\ &&|& + \def\mathdef3009#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3009{i8x16.le\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_u}\\ &&|& + \def\mathdef3010#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3010{i8x16.ge\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_s}\\ &&|& + \def\mathdef3011#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3011{i8x16.ge\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_u}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3012#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3012{i16x8.eq} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}}\\ &&|& + \def\mathdef3013#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3013{i16x8.ne} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}}\\ &&|& + \def\mathdef3014#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3014{i16x8.lt\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_s}\\ &&|& + \def\mathdef3015#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3015{i16x8.lt\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_u}\\ &&|& + \def\mathdef3016#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3016{i16x8.gt\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_s}\\ &&|& + \def\mathdef3017#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3017{i16x8.gt\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_u}\\ &&|& + \def\mathdef3018#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3018{i16x8.le\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_s}\\ &&|& + \def\mathdef3019#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3019{i16x8.le\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_u}\\ &&|& + \def\mathdef3020#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3020{i16x8.ge\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_s}\\ &&|& + \def\mathdef3021#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3021{i16x8.ge\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_u}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3022#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3022{i32x4.eq} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}}\\ &&|& + \def\mathdef3023#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3023{i32x4.ne} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}}\\ &&|& + \def\mathdef3024#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3024{i32x4.lt\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_s}\\ &&|& + \def\mathdef3025#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3025{i32x4.lt\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_u}\\ &&|& + \def\mathdef3026#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3026{i32x4.gt\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_s}\\ &&|& + \def\mathdef3027#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3027{i32x4.gt\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_u}\\ &&|& + \def\mathdef3028#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3028{i32x4.le\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_s}\\ &&|& + \def\mathdef3029#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3029{i32x4.le\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_u}\\ &&|& + \def\mathdef3030#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3030{i32x4.ge\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_s}\\ &&|& + \def\mathdef3031#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3031{i32x4.ge\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_u}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3032#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3032{i64x2.eq} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}}\\ &&|& + \def\mathdef3033#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3033{i64x2.ne} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}}\\ &&|& + \def\mathdef3034#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3034{i64x2.lt\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\mathsf{\_s}\\ &&|& + \def\mathdef3035#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3035{i64x2.gt\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\mathsf{\_s}\\ &&|& + \def\mathdef3036#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3036{i64x2.le\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\mathsf{\_s}\\ &&|& + \def\mathdef3037#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3037{i64x2.ge\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\mathsf{\_s}\\ &&|& +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3038#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3038{f32x4.eq} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}}\\ &&|& + \def\mathdef3039#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3039{f32x4.ne} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}}\\ &&|& + \def\mathdef3040#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3040{f32x4.lt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\\ &&|& + \def\mathdef3041#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3041{f32x4.gt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\\ &&|& + \def\mathdef3042#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3042{f32x4.le} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\\ &&|& + \def\mathdef3043#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3043{f32x4.ge} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3044#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3044{f64x2.eq} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{eq}}\\ &&|& + \def\mathdef3045#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3045{f64x2.ne} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ne}}\\ &&|& + \def\mathdef3046#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3046{f64x2.lt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{lt}}\\ &&|& + \def\mathdef3047#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3047{f64x2.gt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{gt}}\\ &&|& + \def\mathdef3048#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3048{f64x2.le} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{le}}\\ &&|& + \def\mathdef3049#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3049{f64x2.ge} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{ge}}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3050#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3050{v128.not} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{not}}\\ &&|& + \def\mathdef3051#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3051{v128.and} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{and}}\\ &&|& + \def\mathdef3052#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3052{v128.andnot} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{andnot}}\\ &&|& + \def\mathdef3053#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3053{v128.or} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{or}}\\ &&|& + \def\mathdef3054#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3054{v128.xor} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{xor}}\\ &&|& + \def\mathdef3055#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3055{v128.bitselect} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitselect}}\\ &&|& + \def\mathdef3056#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3056{v128.any\_true} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{any\_true}} +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3057#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3057{i8x16.abs} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}}\\ &&|& + \def\mathdef3058#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3058{i8x16.neg} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}}\\ &&|& + \def\mathdef3059#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3059{i8x16.all\_true} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}}\\ &&|& + \def\mathdef3060#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3060{i8x16.bitmask} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}\\ &&|& + \def\mathdef3061#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3061{i8x16.narrow\_i16x8\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i16x8\_s}\\ &&|& + \def\mathdef3062#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3062{i8x16.narrow\_i16x8\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i16x8\_u}\\ &&|& + \def\mathdef3063#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3063{i8x16.shl} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shl}}\\ &&|& + \def\mathdef3064#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3064{i8x16.shr\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_s}\\ &&|& + \def\mathdef3065#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3065{i8x16.shr\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_u}\\ &&|& + \def\mathdef3066#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3066{i8x16.add} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\\ &&|& + \def\mathdef3067#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3067{i8x16.add\_sat\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\mathsf{\_sat\_s}\\ &&|& + \def\mathdef3068#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3068{i8x16.add\_sat\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\mathsf{\_sat\_u}\\ &&|& + \def\mathdef3069#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3069{i8x16.sub} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\\ &&|& + \def\mathdef3070#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3070{i8x16.sub\_sat\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\mathsf{\_sat\_s}\\ &&|& + \def\mathdef3071#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3071{i8x16.sub\_sat\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\mathsf{\_sat\_u}\\ &&|& + \def\mathdef3072#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3072{i8x16.min\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_s}\\ &&|& + \def\mathdef3073#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3073{i8x16.min\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_u}\\ &&|& + \def\mathdef3074#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3074{i8x16.max\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_s}\\ &&|& + \def\mathdef3075#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3075{i8x16.max\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_u}\\ &&|& + \def\mathdef3076#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3076{i8x16.avgr\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{avgr}}\mathsf{\_u}\\ &&|& + \def\mathdef3077#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3077{i8x16.popcnt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i8x16}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{popcnt}}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3078#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3078{i16x8.abs} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}}\\ &&|& + \def\mathdef3079#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3079{i16x8.neg} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}}\\ &&|& + \def\mathdef3080#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3080{i16x8.all\_true} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}}\\ &&|& + \def\mathdef3081#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3081{i16x8.bitmask} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}\\ &&|& + \def\mathdef3082#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3082{i16x8.narrow\_i32x4\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i32x4\_s}\\ &&|& + \def\mathdef3083#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3083{i16x8.narrow\_i32x4\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_i32x4\_u}\\ &&|& + \def\mathdef3084#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3084{i16x8.extend\_low\_i8x16\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i8x16\_s}\\ &&|& + \def\mathdef3085#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3085{i16x8.extend\_high\_i8x16\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i8x16\_s}\\ &&|& + \def\mathdef3086#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3086{i16x8.extend\_low\_i8x16\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i8x16\_u}\\ &&|& + \def\mathdef3087#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3087{i16x8.extend\_high\_i8x16\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i8x16\_u}\\ &&|& + \def\mathdef3088#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3088{i16x8.shl} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shl}}\\ &&|& + \def\mathdef3089#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3089{i16x8.shr\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_s}\\ &&|& + \def\mathdef3090#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3090{i16x8.shr\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_u}\\ &&|& + \def\mathdef3091#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3091{i16x8.add} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\\ &&|& + \def\mathdef3092#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3092{i16x8.add\_sat\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\mathsf{\_sat\_s}\\ &&|& + \def\mathdef3093#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3093{i16x8.add\_sat\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\mathsf{\_sat\_u}\\ &&|& + \def\mathdef3094#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3094{i16x8.sub} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\\ &&|& + \def\mathdef3095#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3095{i16x8.sub\_sat\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\mathsf{\_sat\_s}\\ &&|& + \def\mathdef3096#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3096{i16x8.sub\_sat\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\mathsf{\_sat\_u}\\ &&|& + \def\mathdef3097#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3097{i16x8.mul} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}}\\ &&|& + \def\mathdef3098#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3098{i16x8.min\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_s}\\ &&|& + \def\mathdef3099#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3099{i16x8.min\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_u}\\ &&|& + \def\mathdef3100#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3100{i16x8.max\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_s}\\ &&|& + \def\mathdef3101#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3101{i16x8.max\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_u}\\ &&|& + \def\mathdef3102#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3102{i16x8.avgr\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{avgr}}\mathsf{\_u}\\ &&|& + \def\mathdef3103#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3103{i16x8.q15mulr\_sat\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{q15mulr\_sat}}\mathsf{\_s}\\ &&|& + \def\mathdef3104#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3104{i16x8.extmul\_low\_i8x16\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i8x16\_s}\\ &&|& + \def\mathdef3105#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3105{i16x8.extmul\_high\_i8x16\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i8x16\_s}\\ &&|& + \def\mathdef3106#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3106{i16x8.extmul\_low\_i8x16\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i8x16\_u}\\ &&|& + \def\mathdef3107#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3107{i16x8.extmul\_high\_i8x16\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i8x16\_u}\\ &&|& + \def\mathdef3108#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3108{i16x8.extadd\_pairwise\_i8x16\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_i8x16\_s}\\ &&|& + \def\mathdef3109#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3109{i16x8.extadd\_pairwise\_i8x16\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i16x8}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_i8x16\_u}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} + \phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3110#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3110{i32x4.abs} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}}\\ &&|& + \def\mathdef3111#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3111{i32x4.neg} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}}\\ &&|& + \def\mathdef3112#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3112{i32x4.all\_true} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}}\\ &&|& + \def\mathdef3113#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3113{i32x4.bitmask} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}\\ &&|& + \def\mathdef3114#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3114{i32x4.extadd\_pairwise\_i16x8\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_i16x8\_s}\\ &&|& + \def\mathdef3115#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3115{i32x4.extend\_low\_i16x8\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i16x8\_s}\\ &&|& + \def\mathdef3116#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3116{i32x4.extend\_high\_i16x8\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i16x8\_s}\\ &&|& + \def\mathdef3117#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3117{i32x4.extend\_low\_i16x8\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i16x8\_u}\\ &&|& + \def\mathdef3118#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3118{i32x4.extend\_high\_i16x8\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i16x8\_u}\\ &&|& + \def\mathdef3119#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3119{i32x4.shl} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shl}}\\ &&|& + \def\mathdef3120#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3120{i32x4.shr\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_s}\\ &&|& + \def\mathdef3121#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3121{i32x4.shr\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_u}\\ &&|& + \def\mathdef3122#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3122{i32x4.add} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\\ &&|& + \def\mathdef3123#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3123{i32x4.sub} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\\ &&|& + \def\mathdef3124#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3124{i32x4.mul} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}}\\ &&|& + \def\mathdef3125#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3125{i32x4.min\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_s}\\ &&|& + \def\mathdef3126#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3126{i32x4.min\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\mathsf{\_u}\\ &&|& + \def\mathdef3127#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3127{i32x4.max\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_s}\\ &&|& + \def\mathdef3128#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3128{i32x4.max\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\mathsf{\_u}\\ &&|& + \def\mathdef3129#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3129{i32x4.dot\_i16x8\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{dot}}\mathsf{\_i16x8\_s}\\ &&|& + \def\mathdef3130#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3130{i32x4.extmul\_low\_i16x8\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i16x8\_s}\\ &&|& + \def\mathdef3131#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3131{i32x4.extmul\_high\_i16x8\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i16x8\_s}\\ &&|& + \def\mathdef3132#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3132{i32x4.extmul\_low\_i16x8\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i16x8\_u}\\ &&|& + \def\mathdef3133#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3133{i32x4.extmul\_high\_i16x8\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i16x8\_u}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} + \phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3134#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3134{i64x2.abs} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}}\\ &&|& + \def\mathdef3135#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3135{i64x2.neg} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}}\\ &&|& + \def\mathdef3136#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3136{i64x2.all\_true} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{all\_true}}\\ &&|& + \def\mathdef3137#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3137{i64x2.bitmask} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}\\ &&|& + \def\mathdef3138#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3138{i64x2.extend\_low\_i32x4\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i32x4\_s} \\ &&|& + \def\mathdef3139#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3139{i64x2.extend\_high\_i32x4\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i32x4\_s} \\ &&|& + \def\mathdef3140#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3140{i64x2.extend\_low\_i32x4\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_low\_i32x4\_u} \\ &&|& + \def\mathdef3141#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3141{i64x2.extend\_high\_i32x4\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extend}}\mathsf{\_high\_i32x4\_u} \\ &&|& + \def\mathdef3142#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3142{i64x2.shl} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shl}}\\ &&|& + \def\mathdef3143#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3143{i64x2.shr\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_s}\\ &&|& + \def\mathdef3144#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3144{i64x2.shr\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shr}}\mathsf{\_u}\\ &&|& + \def\mathdef3145#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3145{i64x2.add} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\\ &&|& + \def\mathdef3146#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3146{i64x2.sub} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\\ &&|& + \def\mathdef3147#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3147{i64x2.mul} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}}\\ &&|& + \def\mathdef3148#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3148{i64x2.extmul\_low\_i32x4\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i32x4\_s}\\ &&|& + \def\mathdef3149#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3149{i64x2.extmul\_high\_i32x4\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i32x4\_s}\\ &&|& + \def\mathdef3150#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3150{i64x2.extmul\_low\_i32x4\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_low\_i32x4\_u}\\ &&|& + \def\mathdef3151#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3151{i64x2.extmul\_high\_i32x4\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_high\_i32x4\_u}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3152#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3152{f32x4.abs} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}}\\ &&|& + \def\mathdef3153#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3153{f32x4.neg} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}}\\ &&|& + \def\mathdef3154#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3154{f32x4.sqrt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sqrt}}\\ &&|& + \def\mathdef3155#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3155{f32x4.add} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\\ &&|& + \def\mathdef3156#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3156{f32x4.sub} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\\ &&|& + \def\mathdef3157#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3157{f32x4.mul} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}}\\ &&|& + \def\mathdef3158#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3158{f32x4.div} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{div}}\\ &&|& + \def\mathdef3159#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3159{f32x4.min} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\\ &&|& + \def\mathdef3160#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3160{f32x4.max} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\\ &&|& + \def\mathdef3161#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3161{f32x4.pmin} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{pmin}}\\ &&|& + \def\mathdef3162#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3162{f32x4.pmax} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{pmax}}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3163#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3163{f64x2.abs} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{abs}}\\ &&|& + \def\mathdef3164#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3164{f64x2.neg} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{neg}}\\ &&|& + \def\mathdef3165#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3165{f64x2.sqrt} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sqrt}}\\ &&|& + \def\mathdef3166#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3166{f64x2.add} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{add}}\\ &&|& + \def\mathdef3167#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3167{f64x2.sub} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{sub}}\\ &&|& + \def\mathdef3168#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3168{f64x2.mul} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{mul}}\\ &&|& + \def\mathdef3169#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3169{f64x2.div} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{div}}\\ &&|& + \def\mathdef3170#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3170{f64x2.min} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{min}}\\ &&|& + \def\mathdef3171#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3171{f64x2.max} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{max}}\\ &&|& + \def\mathdef3172#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3172{f64x2.pmin} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{pmin}}\\ &&|& + \def\mathdef3173#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3173{f64x2.pmax} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{pmax}}\\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\phantom{\def\mathdef2670#1{{}}\mathdef2670{instruction}} & \phantom{\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}_I} &\phantom{::=}& \phantom{averylonginstructionnameforvectext} && \phantom{vechasreallylonginstructionnames} \\[-2ex] &&|& + \def\mathdef3174#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3174{i32x4.trunc\_sat\_f32x4\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}}\mathsf{\_sat\_f32x4\_s}\\ &&|& + \def\mathdef3175#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3175{i32x4.trunc\_sat\_f32x4\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}}\mathsf{\_sat\_f32x4\_u}\\ &&|& + \def\mathdef3176#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3176{i32x4.trunc\_sat\_f64x2\_s\_zero} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}}\mathsf{\_sat\_f64x2\_s\_zero}\\ &&|& + \def\mathdef3177#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3177{i32x4.trunc\_sat\_f64x2\_u\_zero} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{trunc}}\mathsf{\_sat\_f64x2\_u\_zero}\\ &&|& + \def\mathdef3178#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3178{f32x4.convert\_i32x4\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_i32x4\_s}\\ &&|& + \def\mathdef3179#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3179{f32x4.convert\_i32x4\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{convert}}\mathsf{\_i32x4\_u}\\ &&|& + \def\mathdef3180#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3180{f64x2.convert\_low\_i32x4\_s} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{convert}}\mathsf{\_low\_i32x4\_s}\\ &&|& + \def\mathdef3181#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3181{f64x2.convert\_low\_i32x4\_u} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{convert}}\mathsf{\_low\_i32x4\_u}\\ &&|& + \def\mathdef3182#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3182{f32x4.demote\_f64x2\_zero} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32x4}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{demote}}\mathsf{\_f64x2\_zero}\\ &&|& + \def\mathdef3183#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3183{f64x2.promote\_low\_f32x4} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64x2}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{promote}}\mathsf{\_low\_f32x4}\\ &&|& +\end{array}\end{split}\]
    +
    +
    +

    Folded Instructions

    +

    Instructions can be written as S-expressions by grouping them into folded form. In that notation, an instruction is wrapped in parentheses and optionally includes nested folded instructions to indicate its operands.

    +

    In the case of block instructions, the folded form omits the \(\def\mathdef3184#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3184{end}\) delimiter. +For \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}\) instructions, both branches have to be wrapped into nested S-expressions, headed by the keywords \(\def\mathdef3185#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3185{then}\) and \(\def\mathdef3186#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3186{else}\).

    +

    The set of all phrases defined by the following abbreviations recursively forms the auxiliary syntactic class \(\href{../text/instructions.html#text-foldedinstr}{\mathtt{foldedinstr}}\). +Such a folded instruction can appear anywhere a regular instruction can.

    +
    +\[\begin{split}\begin{array}{lllll} +\def\mathdef2670#1{{}}\mathdef2670{instruction} & + \def\mathdef3187#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3187{(}~\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}}~~\href{../text/instructions.html#text-foldedinstr}{\mathtt{foldedinstr}}^\ast~\def\mathdef3188#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3188{)} + &\equiv\quad \href{../text/instructions.html#text-foldedinstr}{\mathtt{foldedinstr}}^\ast~~\href{../text/instructions.html#text-plaininstr}{\mathtt{plaininstr}} \\ & + \def\mathdef3189#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3189{(}~\def\mathdef3190#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3190{block}~~\href{../text/instructions.html#text-label}{\mathtt{label}}~~\href{../text/instructions.html#text-blocktype}{\mathtt{blocktype}}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}^\ast~\def\mathdef3191#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3191{)} + &\equiv\quad \def\mathdef3192#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3192{block}~~\href{../text/instructions.html#text-label}{\mathtt{label}}~~\href{../text/instructions.html#text-blocktype}{\mathtt{blocktype}}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}^\ast~~\def\mathdef3193#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3193{end} \\ & + \def\mathdef3194#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3194{(}~\def\mathdef3195#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3195{loop}~~\href{../text/instructions.html#text-label}{\mathtt{label}}~~\href{../text/instructions.html#text-blocktype}{\mathtt{blocktype}}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}^\ast~\def\mathdef3196#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3196{)} + &\equiv\quad \def\mathdef3197#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3197{loop}~~\href{../text/instructions.html#text-label}{\mathtt{label}}~~\href{../text/instructions.html#text-blocktype}{\mathtt{blocktype}}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}^\ast~~\def\mathdef3198#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3198{end} \\ & + \def\mathdef3199#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3199{(}~\def\mathdef3200#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3200{if}~~\href{../text/instructions.html#text-label}{\mathtt{label}}~~\href{../text/instructions.html#text-blocktype}{\mathtt{blocktype}}~~\href{../text/instructions.html#text-foldedinstr}{\mathtt{foldedinstr}}^\ast + &\hspace{-3ex} \def\mathdef3201#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3201{(}~\def\mathdef3202#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3202{then}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}_1^\ast~\def\mathdef3203#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3203{)}~~\def\mathdef3204#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3204{(}~\def\mathdef3205#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3205{else}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}_2^\ast~\def\mathdef3206#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3206{)}^?~~\def\mathdef3207#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3207{)} + \quad\equiv \\ &\qquad + \href{../text/instructions.html#text-foldedinstr}{\mathtt{foldedinstr}}^\ast~~\def\mathdef3208#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3208{if}~~\href{../text/instructions.html#text-label}{\mathtt{label}}~~\href{../text/instructions.html#text-blocktype}{\mathtt{blocktype}} &\hspace{-1ex} \href{../text/instructions.html#text-instr}{\mathtt{instr}}_1^\ast~~\def\mathdef3209#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3209{else}~~(\href{../text/instructions.html#text-instr}{\mathtt{instr}}_2^\ast)^?~\def\mathdef3210#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3210{end} \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    For example, the instruction sequence

    +
    +\[\mathtt{(local.get~\$x)~(i32.const~2)~i32.add~(i32.const~3)~i32.mul}\]
    +

    can be folded into

    +
    +\[\mathtt{(i32.mul~(i32.add~(local.get~\$x)~(i32.const~2))~(i32.const~3))}\]
    +

    Folded instructions are solely syntactic sugar, +no additional syntactic or type-based checking is implied.

    +
    +
    +
    +

    Expressions

    +

    Expressions are written as instruction sequences. +No explicit \(\def\mathdef3211#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3211{end}\) keyword is included, since they only occur in bracketed positions.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef2670#1{{}}\mathdef2670{expression} & \href{../text/instructions.html#text-expr}{\mathtt{expr}}_I &::=& + (\mathit{in}{:}\href{../text/instructions.html#text-instr}{\mathtt{instr}}_I)^\ast &\Rightarrow& \mathit{in}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \\ +\end{array}\end{split}\]
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/text/lexical.html b/core/text/lexical.html new file mode 100644 index 00000000..bbd962da --- /dev/null +++ b/core/text/lexical.html @@ -0,0 +1,193 @@ + + + + + + + + + Lexical Format — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Lexical Format

    +
    +

    Characters

    +

    The text format assigns meaning to source text, which consists of a sequence of characters. +Characters are assumed to be represented as valid Unicode (Section 2.4) scalar values.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef3212#1{{}}\mathdef3212{source} & \href{../text/lexical.html#text-source}{\mathtt{source}} &::=& + \href{../text/lexical.html#text-char}{\mathtt{char}}^\ast \\ +\def\mathdef3212#1{{}}\mathdef3212{character} & \href{../text/lexical.html#text-char}{\mathtt{char}} &::=& + \def\mathdef3251#1{\mathrm{U{+}#1}}\mathdef3251{00} ~|~ \dots ~|~ \def\mathdef3252#1{\mathrm{U{+}#1}}\mathdef3252{D7FF} ~|~ \def\mathdef3253#1{\mathrm{U{+}#1}}\mathdef3253{E000} ~|~ \dots ~|~ \def\mathdef3254#1{\mathrm{U{+}#1}}\mathdef3254{10FFFF} \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    While source text may contain any Unicode character in comments or string literals, +the rest of the grammar is formed exclusively from the characters supported by the 7-bit ASCII subset of Unicode.

    +
    +
    +
    +

    Tokens

    +

    The character stream in the source text is divided, from left to right, into a sequence of tokens, as defined by the following grammar.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef3212#1{{}}\mathdef3212{token} & \href{../text/lexical.html#text-token}{\mathtt{token}} &::=& + \href{../text/lexical.html#text-keyword}{\mathtt{keyword}} ~|~ \href{../text/values.html#text-int}{\def\mathdef3233#1{{\mathtt{u}#1}}\mathdef3233{N}} ~|~ \href{../text/values.html#text-int}{\def\mathdef3239#1{{\mathtt{s}#1}}\mathdef3239{N}} ~|~ \href{../text/values.html#text-float}{\def\mathdef3247#1{{\mathtt{f}#1}}\mathdef3247{N}} ~|~ \href{../text/values.html#text-string}{\mathtt{string}} ~|~ \href{../text/values.html#text-id}{\mathtt{id}} ~|~ + \def\mathdef3255#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3255{(} ~|~ \def\mathdef3256#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3256{)} ~|~ \href{../text/lexical.html#text-reserved}{\mathtt{reserved}} \\ +\def\mathdef3212#1{{}}\mathdef3212{keyword} & \href{../text/lexical.html#text-keyword}{\mathtt{keyword}} &::=& + (\def\mathdef3257#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3257{a} ~|~ \dots ~|~ \def\mathdef3258#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3258{z})~\href{../text/values.html#text-idchar}{\mathtt{idchar}}^\ast + \qquad (\mbox{if occurring as a literal terminal in the grammar}) \\ +\def\mathdef3212#1{{}}\mathdef3212{reserved} & \href{../text/lexical.html#text-reserved}{\mathtt{reserved}} &::=& + \href{../text/values.html#text-idchar}{\mathtt{idchar}}^+ \\ +\end{array}\end{split}\]
    +

    Tokens are formed from the input character stream according to the longest match rule. +That is, the next token always consists of the longest possible sequence of characters that is recognized by the above lexical grammar. +Tokens can be separated by white space, +but except for strings, they cannot themselves contain whitespace.

    +

    The set of keyword tokens is defined implicitly, by all occurrences of a terminal symbol in literal form, such as \(\def\mathdef3259#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3259{keyword}\), in a syntactic production of this chapter.

    +

    Any token that does not fall into any of the other categories is considered reserved, and cannot occur in source text.

    +
    +

    Note

    +

    The effect of defining the set of reserved tokens is that all tokens must be separated by either parentheses or white space. +For example, \(\def\mathdef3260#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3260{0\$x}\) is a single reserved token. +Consequently, it is not recognized as two separate tokens \(\def\mathdef3261#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3261{0}\) and \(\def\mathdef3262#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3262{\$x}\), but instead disallowed. +This property of tokenization is not affected by the fact that the definition of reserved tokens overlaps with other token classes.

    +
    +
    +
    +

    White Space

    +

    White space is any sequence of literal space characters, formatting characters, or comments. +The allowed formatting characters correspond to a subset of the ASCII format effectors, namely, horizontal tabulation (\(\def\mathdef3263#1{\mathrm{U{+}#1}}\mathdef3263{09}\)), line feed (\(\def\mathdef3264#1{\mathrm{U{+}#1}}\mathdef3264{0A}\)), and carriage return (\(\def\mathdef3265#1{\mathrm{U{+}#1}}\mathdef3265{0D}\)).

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef3212#1{{}}\mathdef3212{white space} & \href{../text/lexical.html#text-space}{\mathtt{space}} &::=& + (\def\mathdef3266#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3266{~~} ~|~ \href{../text/lexical.html#text-format}{\mathtt{format}} ~|~ \href{../text/lexical.html#text-comment}{\mathtt{comment}})^\ast \\ +\def\mathdef3212#1{{}}\mathdef3212{format} & \href{../text/lexical.html#text-format}{\mathtt{format}} &::=& + \def\mathdef3267#1{\mathrm{U{+}#1}}\mathdef3267{09} ~|~ \def\mathdef3268#1{\mathrm{U{+}#1}}\mathdef3268{0A} ~|~ \def\mathdef3269#1{\mathrm{U{+}#1}}\mathdef3269{0D} \\ +\end{array}\end{split}\]
    +

    The only relevance of white space is to separate tokens. It is otherwise ignored.

    +
    +
    +

    Comments

    +

    A comment can either be a line comment, started with a double semicolon \(\def\mathdef3232#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3232{{;}{;}}\) and extending to the end of the line, +or a block comment, enclosed in delimiters \(\def\mathdef3230#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3230{{(}{;}} \dots \def\mathdef3231#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3231{{;}{)}}\). +Block comments can be nested.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef3212#1{{}}\mathdef3212{comment} & \href{../text/lexical.html#text-comment}{\mathtt{comment}} &::=& + \href{../text/lexical.html#text-comment}{\mathtt{linecomment}} ~|~ \href{../text/lexical.html#text-comment}{\mathtt{blockcomment}} \\ +\def\mathdef3212#1{{}}\mathdef3212{line comment} & \href{../text/lexical.html#text-comment}{\mathtt{linecomment}} &::=& + \def\mathdef3232#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3232{{;}{;}}~~\href{../text/lexical.html#text-comment}{\mathtt{linechar}}^\ast~~(\def\mathdef3270#1{\mathrm{U{+}#1}}\mathdef3270{0A} ~|~ \mathtt{eof}) \\ +\def\mathdef3212#1{{}}\mathdef3212{line character} & \href{../text/lexical.html#text-comment}{\mathtt{linechar}} &::=& + c{:}\href{../text/lexical.html#text-char}{\mathtt{char}} & (\mathrel{\mbox{if}} c \neq \def\mathdef3271#1{\mathrm{U{+}#1}}\mathdef3271{0A}) \\ +\def\mathdef3212#1{{}}\mathdef3212{block comment} & \href{../text/lexical.html#text-comment}{\mathtt{blockcomment}} &::=& + \def\mathdef3230#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3230{{(}{;}}~~\href{../text/lexical.html#text-comment}{\mathtt{blockchar}}^\ast~~\def\mathdef3231#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3231{{;}{)}} \\ +\def\mathdef3212#1{{}}\mathdef3212{block character} & \href{../text/lexical.html#text-comment}{\mathtt{blockchar}} &::=& + c{:}\href{../text/lexical.html#text-char}{\mathtt{char}} & (\mathrel{\mbox{if}} c \neq \def\mathdef3272#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3272{;} \wedge c \neq \def\mathdef3273#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3273{(}) \\ &&|& + \def\mathdef3274#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3274{;} & (\mathrel{\mbox{if}}~\mbox{the next character is not}~\def\mathdef3275#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3275{)}) \\ &&|& + \def\mathdef3276#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3276{(} & (\mathrel{\mbox{if}}~\mbox{the next character is not}~\def\mathdef3277#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3277{;}) \\ &&|& + \href{../text/lexical.html#text-comment}{\mathtt{blockcomment}} \\ +\end{array}\end{split}\]
    +

    Here, the pseudo token \(\mathtt{eof}\) indicates the end of the input. +The look-ahead restrictions on the productions for \(\href{../text/lexical.html#text-comment}{\mathtt{blockchar}}\) disambiguate the grammar such that only well-bracketed uses of block comment delimiters are allowed.

    +
    +

    Note

    +

    Any formatting and control characters are allowed inside comments.

    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/text/modules.html b/core/text/modules.html new file mode 100644 index 00000000..838660a9 --- /dev/null +++ b/core/text/modules.html @@ -0,0 +1,617 @@ + + + + + + + + + Modules — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Modules

    +
    +

    Indices

    +

    Indices can be given either in raw numeric form or as symbolic identifiers when bound by a respective construct. +Such identifiers are looked up in the suitable space of the identifier context \(I\).

    +
    +\[\begin{split}\begin{array}{llcllllllll} +\def\mathdef3278#1{{}}\mathdef3278{type index} & \href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I &::=& + x{:}\href{../text/values.html#text-int}{\def\mathdef3303#1{{\mathtt{u}#1}}\mathdef3303{\mathtt{32}}} &\Rightarrow& x \\&&|& + v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{types}}[x] = v) \\ +\def\mathdef3278#1{{}}\mathdef3278{function index} & \href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I &::=& + x{:}\href{../text/values.html#text-int}{\def\mathdef3303#1{{\mathtt{u}#1}}\mathdef3303{\mathtt{32}}} &\Rightarrow& x \\&&|& + v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{funcs}}[x] = v) \\ +\def\mathdef3278#1{{}}\mathdef3278{table index} & \href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I &::=& + x{:}\href{../text/values.html#text-int}{\def\mathdef3303#1{{\mathtt{u}#1}}\mathdef3303{\mathtt{32}}} &\Rightarrow& x \\&&|& + v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{tables}}[x] = v) \\ +\def\mathdef3278#1{{}}\mathdef3278{memory index} & \href{../text/modules.html#text-memidx}{\mathtt{memidx}}_I &::=& + x{:}\href{../text/values.html#text-int}{\def\mathdef3303#1{{\mathtt{u}#1}}\mathdef3303{\mathtt{32}}} &\Rightarrow& x \\&&|& + v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{mems}}[x] = v) \\ +\def\mathdef3278#1{{}}\mathdef3278{global index} & \href{../text/modules.html#text-globalidx}{\mathtt{globalidx}}_I &::=& + x{:}\href{../text/values.html#text-int}{\def\mathdef3303#1{{\mathtt{u}#1}}\mathdef3303{\mathtt{32}}} &\Rightarrow& x \\&&|& + v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{globals}}[x] = v) \\ +\def\mathdef3278#1{{}}\mathdef3278{element index} & \href{../text/modules.html#text-elemidx}{\mathtt{elemidx}}_I &::=& + x{:}\href{../text/values.html#text-int}{\def\mathdef3303#1{{\mathtt{u}#1}}\mathdef3303{\mathtt{32}}} &\Rightarrow& x \\&&|& + v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{elem}}[x] = v) \\ +\def\mathdef3278#1{{}}\mathdef3278{data index} & \href{../text/modules.html#text-dataidx}{\mathtt{dataidx}}_I &::=& + x{:}\href{../text/values.html#text-int}{\def\mathdef3303#1{{\mathtt{u}#1}}\mathdef3303{\mathtt{32}}} &\Rightarrow& x \\&&|& + v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{data}}[x] = v) \\ +\def\mathdef3278#1{{}}\mathdef3278{local index} & \href{../text/modules.html#text-localidx}{\mathtt{localidx}}_I &::=& + x{:}\href{../text/values.html#text-int}{\def\mathdef3303#1{{\mathtt{u}#1}}\mathdef3303{\mathtt{32}}} &\Rightarrow& x \\&&|& + v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{locals}}[x] = v) \\ +\def\mathdef3278#1{{}}\mathdef3278{label index} & \href{../text/modules.html#text-labelidx}{\mathtt{labelidx}}_I &::=& + l{:}\href{../text/values.html#text-int}{\def\mathdef3303#1{{\mathtt{u}#1}}\mathdef3303{\mathtt{32}}} &\Rightarrow& l \\&&|& + v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& l & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{labels}}[l] = v) \\ +\end{array}\end{split}\]
    +
    +
    +

    Types

    +

    Type definitions can bind a symbolic type identifier.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{type definition} & \href{../text/modules.html#text-typedef}{\mathtt{type}} &::=& + \def\mathdef3317#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3317{(}~\def\mathdef3318#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3318{type}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{ft}{:}\href{../text/types.html#text-functype}{\mathtt{functype}}~\def\mathdef3319#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3319{)} + &\Rightarrow& \mathit{ft} \\ +\end{array}\end{split}\]
    +
    +
    +

    Type Uses

    +

    A type use is a reference to a type definition. +It may optionally be augmented by explicit inlined parameter and result declarations. +That allows binding symbolic identifiers to name the local indices of parameters. +If inline declarations are given, then their types must match the referenced function type.

    +
    +\[\begin{split}\begin{array}{llcllll} +\def\mathdef3278#1{{}}\mathdef3278{type use} & \href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I &::=& + \def\mathdef3320#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3320{(}~\def\mathdef3321#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3321{type}~~x{:}\href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I~\def\mathdef3322#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3322{)} + \quad\Rightarrow\quad x, I' \\ &&& \qquad + (\mathrel{\mbox{if}} \begin{array}[t]{@{}l@{}} + I.\href{../text/conventions.html#text-context}{\mathsf{typedefs}}[x] = [t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] \wedge + I' = \{\href{../text/conventions.html#text-context}{\mathsf{locals}}~(\epsilon)^n\}) \\ + \end{array} \\[1ex] &&|& + \def\mathdef3323#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3323{(}~\def\mathdef3324#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3324{type}~~x{:}\href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I~\def\mathdef3325#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3325{)} + ~~(t_1{:}\href{../text/types.html#text-functype}{\mathtt{param}})^\ast~~(t_2{:}\href{../text/types.html#text-functype}{\mathtt{result}})^\ast + \quad\Rightarrow\quad x, I' \\ &&& \qquad + (\mathrel{\mbox{if}} \begin{array}[t]{@{}l@{}} + I.\href{../text/conventions.html#text-context}{\mathsf{typedefs}}[x] = [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] \wedge + I' = \{\href{../text/conventions.html#text-context}{\mathsf{locals}}~\mathrm{id}(\href{../text/types.html#text-functype}{\mathtt{param}})^\ast\} ~\href{../text/conventions.html#text-context-wf}{\mbox{well-formed}}) \\ + \end{array} \\ +\end{array}\end{split}\]
    +

    The synthesized attribute of a \(\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}\) is a pair consisting of both the used type index and the updated identifier context including possible parameter identifiers. +The following auxiliary function extracts optional identifiers from parameters:

    +
    +\[\begin{split}\begin{array}{lcl@{\qquad\qquad}l} +\mathrm{id}(\def\mathdef3326#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3326{(}~\def\mathdef3327#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3327{param}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3328#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3328{)}) &=& \href{../text/values.html#text-id}{\mathtt{id}}^? \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    Both productions overlap for the case that the function type is \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\). +However, in that case, they also produce the same results, so that the choice is immaterial.

    +

    The well-formedness condition on \(I'\) ensures that the parameters do not contain duplicate identifier.

    +
    +
    +

    Abbreviations

    +

    A \(\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}\) may also be replaced entirely by inline parameter and result declarations. +In that case, a type index is automatically inserted:

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{type use} & + (t_1{:}\href{../text/types.html#text-functype}{\mathtt{param}})^\ast~~(t_2{:}\href{../text/types.html#text-functype}{\mathtt{result}})^\ast &\equiv& + \def\mathdef3329#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3329{(}~\def\mathdef3330#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3330{type}~~x~\def\mathdef3331#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3331{)}~~\href{../text/types.html#text-functype}{\mathtt{param}}^\ast~~\href{../text/types.html#text-functype}{\mathtt{result}}^\ast \\ +\end{array}\end{split}\]
    +

    where \(x\) is the smallest existing type index whose definition in the current module is the function type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\). +If no such index exists, then a new type definition of the form

    +
    +\[\def\mathdef3332#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3332{(}~\def\mathdef3333#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3333{type}~~\def\mathdef3334#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3334{(}~\def\mathdef3335#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3335{func}~~\href{../text/types.html#text-functype}{\mathtt{param}}^\ast~~\href{../text/types.html#text-functype}{\mathtt{result}}^\ast~\def\mathdef3336#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3336{)}~\def\mathdef3337#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3337{)}\]
    +

    is inserted at the end of the module.

    +

    Abbreviations are expanded in the order they appear, such that previously inserted type definitions are reused by consecutive expansions.

    +
    +
    +
    +

    Imports

    +

    The descriptors in imports can bind a symbolic function, table, memory, or global identifier.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{import} & \href{../text/modules.html#text-import}{\mathtt{import}}_I &::=& + \def\mathdef3338#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3338{(}~\def\mathdef3339#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3339{import}~~\mathit{mod}{:}\href{../text/values.html#text-name}{\mathtt{name}}~~\mathit{nm}{:}\href{../text/values.html#text-name}{\mathtt{name}}~~d{:}\href{../text/modules.html#text-importdesc}{\mathtt{importdesc}}_I~\def\mathdef3340#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3340{)} \\ &&& \qquad + \Rightarrow\quad \{ \href{../syntax/modules.html#syntax-import}{\mathsf{module}}~\mathit{mod}, \href{../syntax/modules.html#syntax-import}{\mathsf{name}}~\mathit{nm}, \href{../syntax/modules.html#syntax-import}{\mathsf{desc}}~d \} \\[1ex] +\def\mathdef3278#1{{}}\mathdef3278{import description} & \href{../text/modules.html#text-importdesc}{\mathtt{importdesc}}_I &::=& + \def\mathdef3341#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3341{(}~\def\mathdef3342#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3342{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x,I'{:}\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I~\def\mathdef3343#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3343{)} + &\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{func}}~x \\ &&|& + \def\mathdef3344#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3344{(}~\def\mathdef3345#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3345{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{tt}{:}\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef3346#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3346{)} + &\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{table}}~\mathit{tt} \\ &&|& + \def\mathdef3347#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3347{(}~\def\mathdef3348#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3348{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{mt}{:}\href{../text/types.html#text-memtype}{\mathtt{memtype}}~\def\mathdef3349#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3349{)} + &\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{mem}}~~\mathit{mt} \\ &&|& + \def\mathdef3350#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3350{(}~\def\mathdef3351#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3351{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{gt}{:}\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}~\def\mathdef3352#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3352{)} + &\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{global}}~\mathit{gt} \\ +\end{array}\end{split}\]
    +
    +

    Abbreviations

    +

    As an abbreviation, imports may also be specified inline with function, table, memory, or global definitions; see the respective sections.

    +
    +
    +
    +

    Functions

    +

    Function definitions can bind a symbolic function identifier, and local identifiers for its parameters and locals.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{function} & \href{../text/modules.html#text-func}{\mathtt{func}}_I &::=& + \def\mathdef3353#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3353{(}~\def\mathdef3354#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3354{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x,I'{:}\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I~~ + (t{:}\href{../text/modules.html#text-local}{\mathtt{local}})^\ast~~(\mathit{in}{:}\href{../text/instructions.html#text-instr}{\mathtt{instr}}_{I''})^\ast~\def\mathdef3355#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3355{)} \\ &&& \qquad + \Rightarrow\quad \{ \href{../syntax/modules.html#syntax-func}{\mathsf{type}}~x, \href{../syntax/modules.html#syntax-func}{\mathsf{locals}}~t^\ast, \href{../syntax/modules.html#syntax-func}{\mathsf{body}}~\mathit{in}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \} \\ &&& \qquad\qquad\qquad + (\mathrel{\mbox{if}} I'' = I' \href{../syntax/conventions.html#notation-compose}{\oplus} \{\href{../text/conventions.html#text-context}{\mathsf{locals}}~\mathrm{id}(\href{../text/modules.html#text-local}{\mathtt{local}})^\ast\} ~\href{../text/conventions.html#text-context-wf}{\mbox{well-formed}}) \\[1ex] +\def\mathdef3278#1{{}}\mathdef3278{local} & \href{../text/modules.html#text-local}{\mathtt{local}} &::=& + \def\mathdef3356#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3356{(}~\def\mathdef3357#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3357{local}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~t{:}\href{../text/types.html#text-valtype}{\mathtt{valtype}}~\def\mathdef3358#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3358{)} + \quad\Rightarrow\quad t \\ +\end{array}\end{split}\]
    +

    The definition of the local identifier context \(I''\) uses the following auxiliary function to extract optional identifiers from locals:

    +
    +\[\begin{split}\begin{array}{lcl@{\qquad\qquad}l} +\mathrm{id}(\def\mathdef3359#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3359{(}~\def\mathdef3360#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3360{local}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3361#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3361{)}) &=& \href{../text/values.html#text-id}{\mathtt{id}}^? \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The well-formedness condition on \(I''\) ensures that parameters and locals do not contain duplicate identifiers.

    +
    +
    +

    Abbreviations

    +

    Multiple anonymous locals may be combined into a single declaration:

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{local} & + \def\mathdef3362#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3362{(}~~\def\mathdef3363#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3363{local}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}^\ast~~\def\mathdef3364#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3364{)} &\equiv& + (\def\mathdef3365#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3365{(}~~\def\mathdef3366#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3366{local}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}~~\def\mathdef3367#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3367{)})^\ast \\ +\end{array}\end{split}\]
    +

    Functions can be defined as imports or exports inline:

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{module field} & + \def\mathdef3368#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3368{(}~\def\mathdef3369#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3369{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3370#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3370{(}~\def\mathdef3371#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3371{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef3372#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3372{)}~~\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}~\def\mathdef3373#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3373{)} \quad\equiv \\ & \qquad + \def\mathdef3374#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3374{(}~\def\mathdef3375#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3375{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef3376#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3376{(}~\def\mathdef3377#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3377{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}~\def\mathdef3378#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3378{)}~\def\mathdef3379#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3379{)} \\[1ex] & + \def\mathdef3380#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3380{(}~\def\mathdef3381#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3381{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3382#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3382{(}~\def\mathdef3383#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3383{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef3384#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3384{)}~~\dots~\def\mathdef3385#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3385{)} \quad\equiv \\ & \qquad + \def\mathdef3386#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3386{(}~\def\mathdef3387#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3387{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef3388#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3388{(}~\def\mathdef3389#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3389{func}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3390#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3390{)}~\def\mathdef3391#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3391{)}~~ + \def\mathdef3392#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3392{(}~\def\mathdef3393#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3393{func}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef3394#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3394{)} + \\ & \qquad\qquad + (\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The latter abbreviation can be applied repeatedly, if “\(\dots\)” contains additional export clauses. +Consequently, a function declaration can contain any number of exports, possibly followed by an import.

    +
    +
    +
    +
    +

    Tables

    +

    Table definitions can bind a symbolic table identifier.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{table} & \href{../text/modules.html#text-table}{\mathtt{table}}_I &::=& + \def\mathdef3395#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3395{(}~\def\mathdef3396#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3396{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{tt}{:}\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef3397#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3397{)} + &\Rightarrow& \{ \href{../syntax/modules.html#syntax-table}{\mathsf{type}}~\mathit{tt} \} \\ +\end{array}\end{split}\]
    +
    +

    Abbreviations

    +

    An element segment can be given inline with a table definition, in which case its offset is \(0\) and the limits of the table type are inferred from the length of the given segment:

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{module field} & + \def\mathdef3398#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3398{(}~\def\mathdef3399#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3399{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~~\def\mathdef3400#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3400{(}~\def\mathdef3401#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3401{elem}~~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}^n{:}\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-elemexpr}{\mathtt{elemexpr}})~\def\mathdef3402#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3402{)}~~\def\mathdef3403#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3403{)} \quad\equiv \\ & \qquad + \def\mathdef3404#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3404{(}~\def\mathdef3405#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3405{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~n~~n~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~\def\mathdef3406#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3406{)} \\ & \qquad + \def\mathdef3407#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3407{(}~\def\mathdef3408#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3408{elem}~~\def\mathdef3409#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3409{(}~\def\mathdef3410#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3410{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3411#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3411{)}~~\def\mathdef3412#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3412{(}~\def\mathdef3413#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3413{i32.const}~~\def\mathdef3414#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3414{0}~\def\mathdef3415#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3415{)}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-elemexpr}{\mathtt{elemexpr}})~\def\mathdef3416#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3416{)} + \\ & \qquad\qquad + (\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\ +\end{array}\end{split}\]
    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{module field} & + \def\mathdef3417#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3417{(}~\def\mathdef3418#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3418{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~~\def\mathdef3419#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3419{(}~\def\mathdef3420#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3420{elem}~~x^n{:}\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}})~\def\mathdef3421#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3421{)} \quad\equiv \\ & \qquad + \def\mathdef3422#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3422{(}~\def\mathdef3423#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3423{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~n~~n~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~\def\mathdef3424#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3424{)} \\ & \qquad + \def\mathdef3425#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3425{(}~\def\mathdef3426#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3426{elem}~~\def\mathdef3427#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3427{(}~\def\mathdef3428#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3428{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3429#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3429{)}~~\def\mathdef3430#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3430{(}~\def\mathdef3431#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3431{i32.const}~~\def\mathdef3432#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3432{0}~\def\mathdef3433#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3433{)}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}})~\def\mathdef3434#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3434{)} + \\ & \qquad\qquad + (\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\ +\end{array}\end{split}\]
    +

    Tables can be defined as imports or exports inline:

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{module field} & + \def\mathdef3435#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3435{(}~\def\mathdef3436#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3436{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3437#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3437{(}~\def\mathdef3438#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3438{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef3439#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3439{)}~~\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef3440#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3440{)} \quad\equiv \\ & \qquad + \def\mathdef3441#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3441{(}~\def\mathdef3442#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3442{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef3443#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3443{(}~\def\mathdef3444#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3444{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef3445#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3445{)}~\def\mathdef3446#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3446{)} \\[1ex] & + \def\mathdef3447#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3447{(}~\def\mathdef3448#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3448{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3449#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3449{(}~\def\mathdef3450#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3450{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef3451#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3451{)}~~\dots~\def\mathdef3452#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3452{)} \quad\equiv \\ & \qquad + \def\mathdef3453#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3453{(}~\def\mathdef3454#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3454{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef3455#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3455{(}~\def\mathdef3456#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3456{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3457#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3457{)}~\def\mathdef3458#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3458{)}~~ + \def\mathdef3459#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3459{(}~\def\mathdef3460#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3460{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef3461#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3461{)} + \\ & \qquad\qquad + (\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The latter abbreviation can be applied repeatedly, if “\(\dots\)” contains additional export clauses. +Consequently, a table declaration can contain any number of exports, possibly followed by an import.

    +
    +
    +
    +
    +

    Memories

    +

    Memory definitions can bind a symbolic memory identifier.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{memory} & \href{../text/modules.html#text-mem}{\mathtt{mem}}_I &::=& + \def\mathdef3462#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3462{(}~\def\mathdef3463#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3463{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{mt}{:}\href{../text/types.html#text-memtype}{\mathtt{memtype}}~\def\mathdef3464#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3464{)} + &\Rightarrow& \{ \href{../syntax/modules.html#syntax-mem}{\mathsf{type}}~\mathit{mt} \} \\ +\end{array}\end{split}\]
    +
    +

    Abbreviations

    +

    A data segment can be given inline with a memory definition, in which case its offset is \(0\) the limits of the memory type are inferred from the length of the data, rounded up to page size:

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{module field} & + \def\mathdef3465#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3465{(}~\def\mathdef3466#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3466{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3467#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3467{(}~\def\mathdef3468#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3468{data}~~b^n{:}\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef3469#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3469{)}~~\def\mathdef3470#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3470{)} \quad\equiv \\ & \qquad + \def\mathdef3471#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3471{(}~\def\mathdef3472#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3472{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~m~~m~\def\mathdef3473#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3473{)} \\ & \qquad + \def\mathdef3474#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3474{(}~\def\mathdef3475#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3475{data}~~\def\mathdef3476#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3476{(}~\def\mathdef3477#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3477{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3478#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3478{)}~~\def\mathdef3479#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3479{(}~\def\mathdef3480#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3480{i32.const}~~\def\mathdef3481#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3481{0}~\def\mathdef3482#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3482{)}~~\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef3483#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3483{)} + \\ & \qquad\qquad + (\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}, m = \mathrm{ceil}(n / 64\mathrm{Ki})) \\ +\end{array}\end{split}\]
    +

    Memories can be defined as imports or exports inline:

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{module field} & + \def\mathdef3484#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3484{(}~\def\mathdef3485#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3485{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3486#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3486{(}~\def\mathdef3487#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3487{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef3488#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3488{)}~~\href{../text/types.html#text-memtype}{\mathtt{memtype}}~\def\mathdef3489#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3489{)} \quad\equiv \\ & \qquad + \def\mathdef3490#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3490{(}~\def\mathdef3491#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3491{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef3492#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3492{(}~\def\mathdef3493#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3493{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-memtype}{\mathtt{memtype}}~\def\mathdef3494#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3494{)}~\def\mathdef3495#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3495{)} + \\[1ex] & + \def\mathdef3496#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3496{(}~\def\mathdef3497#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3497{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3498#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3498{(}~\def\mathdef3499#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3499{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef3500#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3500{)}~~\dots~\def\mathdef3501#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3501{)} \quad\equiv \\ & \qquad + \def\mathdef3502#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3502{(}~\def\mathdef3503#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3503{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef3504#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3504{(}~\def\mathdef3505#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3505{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3506#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3506{)}~\def\mathdef3507#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3507{)}~~ + \def\mathdef3508#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3508{(}~\def\mathdef3509#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3509{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef3510#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3510{)} + \\ & \qquad\qquad + (\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The latter abbreviation can be applied repeatedly, if “\(\dots\)” contains additional export clauses. +Consequently, a memory declaration can contain any number of exports, possibly followed by an import.

    +
    +
    +
    +
    +

    Globals

    +

    Global definitions can bind a symbolic global identifier.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{global} & \href{../text/modules.html#text-global}{\mathtt{global}}_I &::=& + \def\mathdef3511#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3511{(}~\def\mathdef3512#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3512{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{gt}{:}\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3513#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3513{)} + &\Rightarrow& \{ \href{../syntax/modules.html#syntax-global}{\mathsf{type}}~\mathit{gt}, \href{../syntax/modules.html#syntax-global}{\mathsf{init}}~e \} \\ +\end{array}\end{split}\]
    +
    +

    Abbreviations

    +

    Globals can be defined as imports or exports inline:

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{module field} & + \def\mathdef3514#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3514{(}~\def\mathdef3515#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3515{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3516#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3516{(}~\def\mathdef3517#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3517{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef3518#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3518{)}~~\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}~\def\mathdef3519#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3519{)} \quad\equiv \\ & \qquad + \def\mathdef3520#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3520{(}~\def\mathdef3521#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3521{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef3522#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3522{(}~\def\mathdef3523#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3523{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}~\def\mathdef3524#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3524{)}~\def\mathdef3525#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3525{)} + \\[1ex] & + \def\mathdef3526#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3526{(}~\def\mathdef3527#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3527{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3528#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3528{(}~\def\mathdef3529#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3529{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef3530#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3530{)}~~\dots~\def\mathdef3531#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3531{)} \quad\equiv \\ & \qquad + \def\mathdef3532#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3532{(}~\def\mathdef3533#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3533{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef3534#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3534{(}~\def\mathdef3535#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3535{global}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3536#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3536{)}~\def\mathdef3537#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3537{)}~~ + \def\mathdef3538#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3538{(}~\def\mathdef3539#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3539{global}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef3540#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3540{)} + \\ & \qquad\qquad + (\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The latter abbreviation can be applied repeatedly, if “\(\dots\)” contains additional export clauses. +Consequently, a global declaration can contain any number of exports, possibly followed by an import.

    +
    +
    +
    +
    +

    Exports

    +

    The syntax for exports mirrors their abstract syntax directly.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{export} & \href{../text/modules.html#text-export}{\mathtt{export}}_I &::=& + \def\mathdef3541#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3541{(}~\def\mathdef3542#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3542{export}~~\mathit{nm}{:}\href{../text/values.html#text-name}{\mathtt{name}}~~d{:}\href{../text/modules.html#text-exportdesc}{\mathtt{exportdesc}}_I~\def\mathdef3543#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3543{)} + &\Rightarrow& \{ \href{../syntax/modules.html#syntax-export}{\mathsf{name}}~\mathit{nm}, \href{../syntax/modules.html#syntax-export}{\mathsf{desc}}~d \} \\ +\def\mathdef3278#1{{}}\mathdef3278{export description} & \href{../text/modules.html#text-exportdesc}{\mathtt{exportdesc}}_I &::=& + \def\mathdef3544#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3544{(}~\def\mathdef3545#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3545{func}~~x{:}\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I~\def\mathdef3546#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3546{)} + &\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{func}}~x \\ &&|& + \def\mathdef3547#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3547{(}~\def\mathdef3548#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3548{table}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I~\def\mathdef3549#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3549{)} + &\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{table}}~x \\ &&|& + \def\mathdef3550#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3550{(}~\def\mathdef3551#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3551{memory}~~x{:}\href{../text/modules.html#text-memidx}{\mathtt{memidx}}_I~\def\mathdef3552#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3552{)} + &\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{mem}}~x \\ &&|& + \def\mathdef3553#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3553{(}~\def\mathdef3554#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3554{global}~~x{:}\href{../text/modules.html#text-globalidx}{\mathtt{globalidx}}_I~\def\mathdef3555#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3555{)} + &\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{global}}~x \\ +\end{array}\end{split}\]
    +
    +

    Abbreviations

    +

    As an abbreviation, exports may also be specified inline with function, table, memory, or global definitions; see the respective sections.

    +
    +
    +
    +

    Start Function

    +

    A start function is defined in terms of its index.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{start function} & \href{../text/modules.html#text-start}{\mathtt{start}}_I &::=& + \def\mathdef3556#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3556{(}~\def\mathdef3557#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3557{start}~~x{:}\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I~\def\mathdef3558#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3558{)} + &\Rightarrow& \{ \href{../syntax/modules.html#syntax-start}{\mathsf{func}}~x \} \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    At most one start function may occur in a module, +which is ensured by a suitable side condition on the \(\href{../text/modules.html#text-module}{\mathtt{module}}\) grammar.

    +
    +
    +
    +

    Element Segments

    +

    Element segments allow for an optional table index to identify the table to initialize.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{element segment} & \href{../text/modules.html#text-elem}{\mathtt{elem}}_I &::=& + \def\mathdef3559#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3559{(}~\def\mathdef3560#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3560{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~(et, y^\ast){:}\href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}_I~\def\mathdef3561#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3561{)} \\ &&& \qquad + \Rightarrow\quad \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~et, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~y^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{passive}} \} \\ &&|& + \def\mathdef3562#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3562{(}~\def\mathdef3563#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3563{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x{:}\href{../text/modules.html#text-tableuse}{\mathtt{tableuse}}_I~~\def\mathdef3564#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3564{(}~\def\mathdef3565#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3565{offset}~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3566#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3566{)}~~(et, y^\ast){:}\href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}_I~\def\mathdef3567#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3567{)} \\ &&& \qquad + \Rightarrow\quad \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~et, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~y^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-elem}{\mathsf{table}}~x, \href{../syntax/modules.html#syntax-elem}{\mathsf{offset}}~e \} \} \\ &&& + \def\mathdef3568#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3568{(}~\def\mathdef3569#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3569{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3570#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3570{declare}~~(et, y^\ast){:}\href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}_I~\def\mathdef3571#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3571{)} \\ &&& \qquad + \Rightarrow\quad \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~et, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~y^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{declarative}} \} \\ +\def\mathdef3278#1{{}}\mathdef3278{element list} & \href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}_I &::=& + t{:}\href{../text/types.html#text-reftype}{\mathtt{reftype}}~~y^\ast{:}\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-elemexpr}{\mathtt{elemexpr}}_I) \qquad\Rightarrow\quad ( \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~t, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~y^\ast ) \\ +\def\mathdef3278#1{{}}\mathdef3278{element expression} & \href{../text/modules.html#text-elemexpr}{\mathtt{elemexpr}}_I &::=& + \def\mathdef3572#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3572{(}~\def\mathdef3573#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3573{item}~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3574#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3574{)} + \quad\Rightarrow\quad e \\ +\def\mathdef3278#1{{}}\mathdef3278{table use} & \href{../text/modules.html#text-tableuse}{\mathtt{tableuse}}_I &::=& + \def\mathdef3575#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3575{(}~\def\mathdef3576#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3576{table}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I ~\def\mathdef3577#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3577{)} + \quad\Rightarrow\quad x \\ +\end{array}\end{split}\]
    +
    +

    Abbreviations

    +

    As an abbreviation, a single instruction may occur in place of the offset of an active element segment or as an element expression:

    +
    +\[\begin{split}\begin{array}{llcll} +\def\mathdef3278#1{{}}\mathdef3278{element offset} & + \def\mathdef3578#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3578{(}~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef3579#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3579{)} &\equiv& + \def\mathdef3580#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3580{(}~\def\mathdef3581#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3581{offset}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef3582#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3582{)} \\ +\def\mathdef3278#1{{}}\mathdef3278{element item} & + \def\mathdef3583#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3583{(}~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef3584#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3584{)} &\equiv& + \def\mathdef3585#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3585{(}~\def\mathdef3586#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3586{item}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef3587#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3587{)} \\ +\end{array}\end{split}\]
    +

    Also, the element list may be written as just a sequence of function indices:

    +
    +\[\begin{array}{llcll} +\def\mathdef3278#1{{}}\mathdef3278{element list} & + \def\mathdef3588#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3588{func}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I) &\equiv& + \def\mathdef3589#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3589{funcref}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\def\mathdef3590#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3590{(}~\def\mathdef3591#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3591{ref.func}~~\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I~\def\mathdef3592#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3592{)}) +\end{array}\]
    +

    A table use can be omitted, defaulting to \(\mathtt{0}\). +Furthermore, for backwards compatibility with earlier versions of WebAssembly, if the table use is omitted, the \(\def\mathdef3593#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3593{func}\) keyword can be omitted as well.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{table use} & + \epsilon &\equiv& \def\mathdef3594#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3594{(}~\def\mathdef3595#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3595{table}~~\def\mathdef3596#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3596{0}~\def\mathdef3597#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3597{)} \\ +\def\mathdef3278#1{{}}\mathdef3278{element segment} & + \def\mathdef3598#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3598{(}~\def\mathdef3599#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3599{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3600#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3600{(}~\def\mathdef3601#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3601{offset}~~\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3602#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3602{)}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I)~\def\mathdef3603#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3603{)} + &\equiv& + \def\mathdef3604#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3604{(}~\def\mathdef3605#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3605{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3606#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3606{(}~\def\mathdef3607#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3607{table}~~\def\mathdef3608#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3608{0}~\def\mathdef3609#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3609{)}~~\def\mathdef3610#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3610{(}~\def\mathdef3611#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3611{offset}~~\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3612#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3612{)}~~\def\mathdef3613#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3613{func}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I)~\def\mathdef3614#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3614{)} +\end{array}\end{split}\]
    +

    As another abbreviation, element segments may also be specified inline with table definitions; see the respective section.

    +
    +
    +
    +

    Data Segments

    +

    Data segments allow for an optional memory index to identify the memory to initialize. +The data is written as a string, which may be split up into a possibly empty sequence of individual string literals.

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{data segment} & \href{../text/modules.html#text-data}{\mathtt{data}}_I &::=& + \def\mathdef3615#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3615{(}~\def\mathdef3616#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3616{data}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~b^\ast{:}\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef3617#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3617{)} \\ &&& \qquad + \Rightarrow\quad \{ \href{../syntax/modules.html#syntax-data}{\mathsf{init}}~b^\ast, \href{../syntax/modules.html#syntax-data}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-datamode}{\mathsf{passive}} \} \\ &&|& + \def\mathdef3618#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3618{(}~\def\mathdef3619#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3619{data}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x{:}\href{../text/modules.html#text-memuse}{\mathtt{memuse}}_I~~\def\mathdef3620#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3620{(}~\def\mathdef3621#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3621{offset}~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3622#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3622{)}~~b^\ast{:}\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef3623#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3623{)} \\ &&& \qquad + \Rightarrow\quad \{ \href{../syntax/modules.html#syntax-data}{\mathsf{init}}~b^\ast, \href{../syntax/modules.html#syntax-data}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-datamode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-data}{\mathsf{memory}}~x', \href{../syntax/modules.html#syntax-data}{\mathsf{offset}}~e \} \} \\ +\def\mathdef3278#1{{}}\mathdef3278{data string} & \href{../text/modules.html#text-datastring}{\mathtt{datastring}} &::=& + (b^\ast{:}\href{../text/values.html#text-string}{\mathtt{string}})^\ast \quad\Rightarrow\quad \href{../syntax/conventions.html#notation-concat}{\mathrm{concat}}((b^\ast)^\ast) \\ +\def\mathdef3278#1{{}}\mathdef3278{memory use} & \href{../text/modules.html#text-memuse}{\mathtt{memuse}}_I &::=& + \def\mathdef3624#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3624{(}~\def\mathdef3625#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3625{memory}~~x{:}\href{../text/modules.html#text-memidx}{\mathtt{memidx}}_I ~\def\mathdef3626#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3626{)} + \quad\Rightarrow\quad x \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    In the current version of WebAssembly, the only valid memory index is 0 +or a symbolic memory identifier resolving to the same value.

    +
    +
    +

    Abbreviations

    +

    As an abbreviation, a single instruction may occur in place of the offset of an active data segment:

    +
    +\[\begin{array}{llcll} +\def\mathdef3278#1{{}}\mathdef3278{data offset} & + \def\mathdef3627#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3627{(}~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef3628#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3628{)} &\equiv& + \def\mathdef3629#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3629{(}~\def\mathdef3630#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3630{offset}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef3631#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3631{)} +\end{array}\]
    +

    Also, a memory use can be omitted, defaulting to \(\mathtt{0}\).

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3278#1{{}}\mathdef3278{memory use} & + \epsilon &\equiv& \def\mathdef3632#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3632{(}~\def\mathdef3633#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3633{memory}~~\def\mathdef3634#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3634{0}~\def\mathdef3635#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3635{)} \\ +\end{array}\end{split}\]
    +

    As another abbreviation, data segments may also be specified inline with memory definitions; see the respective section.

    +
    +
    +
    +

    Modules

    +

    A module consists of a sequence of fields that can occur in any order. +All definitions and their respective bound identifiers scope over the entire module, including the text preceding them.

    +

    A module may optionally bind an identifier that names the module. +The name serves a documentary role only.

    +
    +

    Note

    +

    Tools may include the module name in the name section of the binary format.

    +
    +
    +\[\begin{split}\begin{array}{lll} +\def\mathdef3278#1{{}}\mathdef3278{module} & \href{../text/modules.html#text-module}{\mathtt{module}} & +\begin{array}[t]{@{}cllll} +::=& + \def\mathdef3636#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3636{(}~\def\mathdef3637#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3637{module}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~(m{:}\href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}_I)^\ast~\def\mathdef3638#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3638{)} + \quad\Rightarrow\quad \href{../syntax/conventions.html#notation-compose}{\bigoplus} m^\ast \\ + &\qquad (\mathrel{\mbox{if}} I = \href{../syntax/conventions.html#notation-compose}{\bigoplus} \mathrm{idc}(\href{../text/modules.html#text-modulefield}{\mathtt{modulefield}})^\ast ~\href{../text/conventions.html#text-context-wf}{\mbox{well-formed}}) \\ +\end{array} \\[1ex] +\def\mathdef3278#1{{}}\mathdef3278{module field} & \href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}_I & +\begin{array}[t]{@{}clll} +::=& + \mathit{ty}{:}\href{../text/modules.html#text-typedef}{\mathtt{type}} &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{types}}~\mathit{ty}\} \\ |& + \mathit{im}{:}\href{../text/modules.html#text-import}{\mathtt{import}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{imports}}~\mathit{im}\} \\ |& + \mathit{fn}{:}\href{../text/modules.html#text-func}{\mathtt{func}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{funcs}}~\mathit{fn}\} \\ |& + \mathit{ta}{:}\href{../text/modules.html#text-table}{\mathtt{table}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{tables}}~\mathit{ta}\} \\ |& + \mathit{me}{:}\href{../text/modules.html#text-mem}{\mathtt{mem}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{mems}}~\mathit{me}\} \\ |& + \mathit{gl}{:}\href{../text/modules.html#text-global}{\mathtt{global}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{globals}}~\mathit{gl}\} \\ |& + \mathit{ex}{:}\href{../text/modules.html#text-export}{\mathtt{export}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{exports}}~\mathit{ex}\} \\ |& + \mathit{st}{:}\href{../text/modules.html#text-start}{\mathtt{start}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{start}}~\mathit{st}\} \\ |& + \mathit{el}{:}\href{../text/modules.html#text-elem}{\mathtt{elem}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{elems}}~\mathit{el}\} \\ |& + \mathit{da}{:}\href{../text/modules.html#text-data}{\mathtt{data}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{datas}}~\mathit{da}\} \\ +\end{array} +\end{array}\end{split}\]
    +

    The following restrictions are imposed on the composition of modules: \(m_1 \href{../syntax/conventions.html#notation-compose}{\oplus} m_2\) is defined if and only if

    +
      +

    • \(m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{start}} = \epsilon \vee m_2.\href{../syntax/modules.html#syntax-module}{\mathsf{start}} = \epsilon\)

      • +

    • \(m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{funcs}} = m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{tables}} = m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{mems}} = m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{globals}} = \epsilon \vee m_2.\href{../syntax/modules.html#syntax-module}{\mathsf{imports}} = \epsilon\)

      • +
    +
    +

    Note

    +

    The first condition ensures that there is at most one start function. +The second condition enforces that all imports must occur before any regular definition of a function, table, memory, or global, +thereby maintaining the ordering of the respective index spaces.

    +

    The well-formedness condition on \(I\) in the grammar for \(\href{../text/modules.html#text-module}{\mathtt{module}}\) ensures that no namespace contains duplicate identifiers.

    +
    +

    The definition of the initial identifier context \(I\) uses the following auxiliary definition which maps each relevant definition to a singular context with one (possibly empty) identifier:

    +
    +\[\begin{split}\begin{array}{@{}lcl@{\qquad\qquad}l} +\mathrm{idc}(\def\mathdef3639#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3639{(}~\def\mathdef3640#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3640{type}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\mathit{ft}{:}\href{../text/types.html#text-functype}{\mathtt{functype}}~\def\mathdef3641#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3641{)}) &=& + \{\href{../text/conventions.html#text-context}{\mathsf{types}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?), \href{../text/conventions.html#text-context}{\mathsf{typedefs}}~\mathit{ft}\} \\ +\mathrm{idc}(\def\mathdef3642#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3642{(}~\def\mathdef3643#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3643{func}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3644#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3644{)}) &=& + \{\href{../text/conventions.html#text-context}{\mathsf{funcs}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\ +\mathrm{idc}(\def\mathdef3645#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3645{(}~\def\mathdef3646#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3646{table}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3647#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3647{)}) &=& + \{\href{../text/conventions.html#text-context}{\mathsf{tables}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\ +\mathrm{idc}(\def\mathdef3648#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3648{(}~\def\mathdef3649#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3649{memory}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3650#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3650{)}) &=& + \{\href{../text/conventions.html#text-context}{\mathsf{mems}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\ +\mathrm{idc}(\def\mathdef3651#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3651{(}~\def\mathdef3652#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3652{global}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3653#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3653{)}) &=& + \{\href{../text/conventions.html#text-context}{\mathsf{globals}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\ +\mathrm{idc}(\def\mathdef3654#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3654{(}~\def\mathdef3655#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3655{elem}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3656#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3656{)}) &=& + \{\href{../text/conventions.html#text-context}{\mathsf{elem}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\ +\mathrm{idc}(\def\mathdef3657#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3657{(}~\def\mathdef3658#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3658{data}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3659#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3659{)}) &=& + \{\href{../text/conventions.html#text-context}{\mathsf{data}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\ +\mathrm{idc}(\def\mathdef3660#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3660{(}~\def\mathdef3661#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3661{import}~\dots~\def\mathdef3662#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3662{(}~\def\mathdef3663#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3663{func}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3664#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3664{)}~\def\mathdef3665#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3665{)}) &=& + \{\href{../text/conventions.html#text-context}{\mathsf{funcs}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\ +\mathrm{idc}(\def\mathdef3666#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3666{(}~\def\mathdef3667#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3667{import}~\dots~\def\mathdef3668#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3668{(}~\def\mathdef3669#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3669{table}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3670#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3670{)}~\def\mathdef3671#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3671{)}) &=& + \{\href{../text/conventions.html#text-context}{\mathsf{tables}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\ +\mathrm{idc}(\def\mathdef3672#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3672{(}~\def\mathdef3673#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3673{import}~\dots~\def\mathdef3674#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3674{(}~\def\mathdef3675#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3675{memory}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3676#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3676{)}~\def\mathdef3677#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3677{)}) &=& + \{\href{../text/conventions.html#text-context}{\mathsf{mems}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\ +\mathrm{idc}(\def\mathdef3678#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3678{(}~\def\mathdef3679#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3679{import}~\dots~\def\mathdef3680#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3680{(}~\def\mathdef3681#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3681{global}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3682#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3682{)}~\def\mathdef3683#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3683{)}) &=& + \{\href{../text/conventions.html#text-context}{\mathsf{globals}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\ +\mathrm{idc}(\def\mathdef3684#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3684{(}~\dots~\def\mathdef3685#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3685{)}) &=& + \{\} \\ +\end{array}\end{split}\]
    +
    +

    Abbreviations

    +

    In a source file, the toplevel \(\mathtt{(module}~\dots\mathtt{)}\) surrounding the module body may be omitted.

    +
    +\[\begin{array}{llcll} +\def\mathdef3278#1{{}}\mathdef3278{module} & + \href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}^\ast &\equiv& + \def\mathdef3686#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3686{(}~\def\mathdef3687#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3687{module}~~\href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}^\ast~\def\mathdef3688#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3688{)} +\end{array}\]
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/text/types.html b/core/text/types.html new file mode 100644 index 00000000..45e17456 --- /dev/null +++ b/core/text/types.html @@ -0,0 +1,215 @@ + + + + + + + + + Types — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Types

    +
    +

    Number Types

    +
    +\[\begin{split}\begin{array}{llcll@{\qquad\qquad}l} +\def\mathdef3689#1{{}}\mathdef3689{number type} & \href{../text/types.html#text-numtype}{\mathtt{numtype}} &::=& + \def\mathdef3728#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3728{i32} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}} \\ &&|& + \def\mathdef3729#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3729{i64} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}} \\ &&|& + \def\mathdef3730#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3730{f32} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}} \\ &&|& + \def\mathdef3731#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3731{f64} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}} \\ +\end{array}\end{split}\]
    +
    +
    +

    Vector Types

    +
    +\[\begin{split}\begin{array}{llcll@{\qquad\qquad}l} +\def\mathdef3689#1{{}}\mathdef3689{vector type} & \href{../text/types.html#text-vectype}{\mathtt{vectype}} &::=& + \def\mathdef3732#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3732{v128} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}} \\ +\end{array}\end{split}\]
    +
    +
    +

    Reference Types

    +
    +\[\begin{split}\begin{array}{llcll@{\qquad\qquad}l} +\def\mathdef3689#1{{}}\mathdef3689{reference type} & \href{../text/types.html#text-reftype}{\mathtt{reftype}} &::=& + \def\mathdef3733#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3733{funcref} &\Rightarrow& \href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}} \\ &&|& + \def\mathdef3734#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3734{externref} &\Rightarrow& \href{../syntax/types.html#syntax-reftype}{\mathsf{externref}} \\ +\def\mathdef3689#1{{}}\mathdef3689{heap type} & \href{../text/types.html#text-heaptype}{\mathtt{heaptype}} &::=& + \def\mathdef3735#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3735{func} &\Rightarrow& \href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}} \\ &&|& + \def\mathdef3736#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3736{extern} &\Rightarrow& \href{../syntax/types.html#syntax-reftype}{\mathsf{externref}} \\ +\end{array}\end{split}\]
    +
    +
    +

    Value Types

    +
    +\[\begin{split}\begin{array}{llcll@{\qquad\qquad}l} +\def\mathdef3689#1{{}}\mathdef3689{value type} & \href{../text/types.html#text-valtype}{\mathtt{valtype}} &::=& + t{:}\href{../text/types.html#text-numtype}{\mathtt{numtype}} &\Rightarrow& t \\ &&|& + t{:}\href{../text/types.html#text-vectype}{\mathtt{vectype}} &\Rightarrow& t \\ &&|& + t{:}\href{../text/types.html#text-reftype}{\mathtt{reftype}} &\Rightarrow& t \\ +\end{array}\end{split}\]
    +
    +
    +

    Function Types

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef3689#1{{}}\mathdef3689{function type} & \href{../text/types.html#text-functype}{\mathtt{functype}} &::=& + \def\mathdef3737#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3737{(}~\def\mathdef3738#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3738{func}~~t_1^\ast{:\,}\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/types.html#text-functype}{\mathtt{param}})~~t_2^\ast{:\,}\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/types.html#text-functype}{\mathtt{result}})~\def\mathdef3739#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3739{)} + &\Rightarrow& [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] \\ +\def\mathdef3689#1{{}}\mathdef3689{parameter} & \href{../text/types.html#text-functype}{\mathtt{param}} &::=& + \def\mathdef3740#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3740{(}~\def\mathdef3741#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3741{param}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~t{:}\href{../text/types.html#text-valtype}{\mathtt{valtype}}~\def\mathdef3742#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3742{)} + &\Rightarrow& t \\ +\def\mathdef3689#1{{}}\mathdef3689{result} & \href{../text/types.html#text-functype}{\mathtt{result}} &::=& + \def\mathdef3743#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3743{(}~\def\mathdef3744#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3744{result}~~t{:}\href{../text/types.html#text-valtype}{\mathtt{valtype}}~\def\mathdef3745#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3745{)} + &\Rightarrow& t \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    The optional identifier names for parameters in a function type only have documentation purpose. +They cannot be referenced from anywhere.

    +
    +
    +

    Abbreviations

    +

    Multiple anonymous parameters or results may be combined into a single declaration:

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3689#1{{}}\mathdef3689{parameter} & + \def\mathdef3746#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3746{(}~~\def\mathdef3747#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3747{param}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}^\ast~~\def\mathdef3748#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3748{)} &\equiv& + (\def\mathdef3749#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3749{(}~~\def\mathdef3750#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3750{param}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}~~\def\mathdef3751#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3751{)})^\ast \\ +\def\mathdef3689#1{{}}\mathdef3689{result} & + \def\mathdef3752#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3752{(}~~\def\mathdef3753#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3753{result}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}^\ast~~\def\mathdef3754#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3754{)} &\equiv& + (\def\mathdef3755#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3755{(}~~\def\mathdef3756#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3756{result}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}~~\def\mathdef3757#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3757{)})^\ast \\ +\end{array}\end{split}\]
    +
    +
    +
    +

    Limits

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3689#1{{}}\mathdef3689{limits} & \href{../text/types.html#text-limits}{\mathtt{limits}} &::=& + n{:}\href{../text/values.html#text-int}{\def\mathdef3714#1{{\mathtt{u}#1}}\mathdef3714{\mathtt{32}}} &\Rightarrow& \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~\epsilon \} \\ &&|& + n{:}\href{../text/values.html#text-int}{\def\mathdef3714#1{{\mathtt{u}#1}}\mathdef3714{\mathtt{32}}}~~m{:}\href{../text/values.html#text-int}{\def\mathdef3714#1{{\mathtt{u}#1}}\mathdef3714{\mathtt{32}}} &\Rightarrow& \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m \} \\ +\end{array}\end{split}\]
    +
    +
    +

    Memory Types

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef3689#1{{}}\mathdef3689{memory type} & \href{../text/types.html#text-memtype}{\mathtt{memtype}} &::=& + \mathit{lim}{:}\href{../text/types.html#text-limits}{\mathtt{limits}} &\Rightarrow& \mathit{lim} \\ +\end{array}\end{split}\]
    +
    +
    +

    Table Types

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3689#1{{}}\mathdef3689{table type} & \href{../text/types.html#text-tabletype}{\mathtt{tabletype}} &::=& + \mathit{lim}{:}\href{../text/types.html#text-limits}{\mathtt{limits}}~~\mathit{et}{:}\href{../text/types.html#text-reftype}{\mathtt{reftype}} &\Rightarrow& \mathit{lim}~\mathit{et} \\ +\end{array}\end{split}\]
    +
    +
    +

    Global Types

    +
    +\[\begin{split}\begin{array}{llclll} +\def\mathdef3689#1{{}}\mathdef3689{global type} & \href{../text/types.html#text-globaltype}{\mathtt{globaltype}} &::=& + t{:}\href{../text/types.html#text-valtype}{\mathtt{valtype}} &\Rightarrow& \href{../syntax/types.html#syntax-mut}{\mathsf{const}}~t \\ &&|& + \def\mathdef3758#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3758{(}~\def\mathdef3759#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3759{mut}~~t{:}\href{../text/types.html#text-valtype}{\mathtt{valtype}}~\def\mathdef3760#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3760{)} &\Rightarrow& \href{../syntax/types.html#syntax-mut}{\mathsf{var}}~t \\ +\end{array}\end{split}\]
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/text/values.html b/core/text/values.html new file mode 100644 index 00000000..be60f715 --- /dev/null +++ b/core/text/values.html @@ -0,0 +1,294 @@ + + + + + + + + + Values — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Values

    +

    The grammar productions in this section define lexical syntax, +hence no white space is allowed.

    +
    +

    Integers

    +

    All integers can be written in either decimal or hexadecimal notation. +In both cases, digits can optionally be separated by underscores.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad}l} +\def\mathdef3761#1{{}}\mathdef3761{sign} & \href{../text/values.html#text-sign}{\mathtt{sign}} &::=& + \epsilon \Rightarrow {+} ~~|~~ + \def\mathdef3800#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3800{+} \Rightarrow {+} ~~|~~ + \def\mathdef3801#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3801{-} \Rightarrow {-} \\ +\def\mathdef3761#1{{}}\mathdef3761{decimal digit} & \href{../text/values.html#text-digit}{\mathtt{digit}} &::=& + \def\mathdef3802#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3802{0} \Rightarrow 0 ~~|~~ \dots ~~|~~ \def\mathdef3803#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3803{9} \Rightarrow 9 \\ +\def\mathdef3761#1{{}}\mathdef3761{hexadecimal digit} & \href{../text/values.html#text-hexdigit}{\mathtt{hexdigit}} &::=& + d{:}\href{../text/values.html#text-digit}{\mathtt{digit}} \Rightarrow d \\ &&|& + \def\mathdef3804#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3804{A} \Rightarrow 10 ~~|~~ \dots ~~|~~ \def\mathdef3805#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3805{F} \Rightarrow 15 \\ &&|& + \def\mathdef3806#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3806{a} \Rightarrow 10 ~~|~~ \dots ~~|~~ \def\mathdef3807#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3807{f} \Rightarrow 15 +\\[1ex] +\def\mathdef3761#1{{}}\mathdef3761{decimal number} & \href{../text/values.html#text-num}{\mathtt{num}} &::=& + d{:}\href{../text/values.html#text-digit}{\mathtt{digit}} &\Rightarrow& d \\ &&|& + n{:}\href{../text/values.html#text-num}{\mathtt{num}}~~\def\mathdef3808#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3808{\_}^?~~d{:}\href{../text/values.html#text-digit}{\mathtt{digit}} &\Rightarrow& 10\cdot n + d \\ +\def\mathdef3761#1{{}}\mathdef3761{hexadecimal number} & \href{../text/values.html#text-hexnum}{\mathtt{hexnum}} &::=& + h{:}\href{../text/values.html#text-hexdigit}{\mathtt{hexdigit}} &\Rightarrow& h \\ &&|& + n{:}\href{../text/values.html#text-hexnum}{\mathtt{hexnum}}~~\def\mathdef3809#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3809{\_}^?~~h{:}\href{../text/values.html#text-hexdigit}{\mathtt{hexdigit}} &\Rightarrow& 16\cdot n + h \\ +\end{array}\end{split}\]
    +

    The allowed syntax for integer literals depends on size and signedness. +Moreover, their value must lie within the range of the respective type.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad}l} +\def\mathdef3761#1{{}}\mathdef3761{unsigned integer} & \href{../text/values.html#text-int}{\def\mathdef3782#1{{\mathtt{u}#1}}\mathdef3782{N}} &::=& + n{:}\href{../text/values.html#text-num}{\mathtt{num}} &\Rightarrow& n & (\mathrel{\mbox{if}} n < 2^N) \\ &&|& + \def\mathdef3810#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3810{0x}~~n{:}\href{../text/values.html#text-hexnum}{\mathtt{hexnum}} &\Rightarrow& n & (\mathrel{\mbox{if}} n < 2^N) \\ +\def\mathdef3761#1{{}}\mathdef3761{signed integer} & \href{../text/values.html#text-int}{\def\mathdef3788#1{{\mathtt{s}#1}}\mathdef3788{N}} &::=& + {\pm}{:}\href{../text/values.html#text-sign}{\mathtt{sign}}~~n{:}\href{../text/values.html#text-num}{\mathtt{num}} &\Rightarrow& \pm n & (\mathrel{\mbox{if}} -2^{N-1} \leq \pm n < 2^{N-1}) \\ &&|& + {\pm}{:}\href{../text/values.html#text-sign}{\mathtt{sign}}~~\def\mathdef3811#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3811{0x}~~n{:}\href{../text/values.html#text-hexnum}{\mathtt{hexnum}} &\Rightarrow& \pm n & (\mathrel{\mbox{if}} -2^{N-1} \leq \pm n < 2^{N-1}) \\ +\end{array}\end{split}\]
    +

    Uninterpreted integers can be written as either signed or unsigned, and are normalized to unsigned in the abstract syntax.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef3761#1{{}}\mathdef3761{uninterpreted integers} & \href{../text/values.html#text-int}{\def\mathdef3791#1{{\mathtt{i}#1}}\mathdef3791{N}} &::=& + n{:}\href{../text/values.html#text-int}{\def\mathdef3782#1{{\mathtt{u}#1}}\mathdef3782{N}} &\Rightarrow& n \\ &&|& + i{:}\href{../text/values.html#text-int}{\def\mathdef3788#1{{\mathtt{s}#1}}\mathdef3788{N}} &\Rightarrow& n & (\mathrel{\mbox{if}} i = \href{../exec/numerics.html#aux-signed}{\mathrm{signed}}(n)) \\ +\end{array}\end{split}\]
    +
    +
    +

    Floating-Point

    +

    Floating-point values can be represented in either decimal or hexadecimal notation.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef3761#1{{}}\mathdef3761{decimal floating-point fraction} & \href{../text/values.html#text-frac}{\mathtt{frac}} &::=& + d{:}\href{../text/values.html#text-digit}{\mathtt{digit}} &\Rightarrow& d/10 \\ &&|& + d{:}\href{../text/values.html#text-digit}{\mathtt{digit}}~~\def\mathdef3812#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3812{\_}^?~~p{:}\href{../text/values.html#text-frac}{\mathtt{frac}} &\Rightarrow& (d+p/10)/10 \\ +\def\mathdef3761#1{{}}\mathdef3761{hexadecimal floating-point fraction} & \href{../text/values.html#text-hexfrac}{\mathtt{hexfrac}} &::=& + h{:}\href{../text/values.html#text-hexdigit}{\mathtt{hexdigit}} &\Rightarrow& h/16 \\ &&|& + h{:}\href{../text/values.html#text-hexdigit}{\mathtt{hexdigit}}~~\def\mathdef3813#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3813{\_}^?~~p{:}\href{../text/values.html#text-hexfrac}{\mathtt{hexfrac}} &\Rightarrow& (h+p/16)/16 \\ +\def\mathdef3761#1{{}}\mathdef3761{decimal floating-point number} & \href{../text/values.html#text-float}{\mathtt{float}} &::=& + p{:}\href{../text/values.html#text-num}{\mathtt{num}}~\def\mathdef3814#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3814{.}^? + &\Rightarrow& p \\ &&|& + p{:}\href{../text/values.html#text-num}{\mathtt{num}}~\def\mathdef3815#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3815{.}~q{:}\href{../text/values.html#text-frac}{\mathtt{frac}} + &\Rightarrow& p+q \\ &&|& + p{:}\href{../text/values.html#text-num}{\mathtt{num}}~\def\mathdef3816#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3816{.}^?~(\def\mathdef3817#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3817{E}~|~\def\mathdef3818#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3818{e})~{\pm}{:}\href{../text/values.html#text-sign}{\mathtt{sign}}~e{:}\href{../text/values.html#text-num}{\mathtt{num}} + &\Rightarrow& p\cdot 10^{\pm e} \\ &&|& + p{:}\href{../text/values.html#text-num}{\mathtt{num}}~\def\mathdef3819#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3819{.}~q{:}\href{../text/values.html#text-frac}{\mathtt{frac}}~(\def\mathdef3820#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3820{E}~|~\def\mathdef3821#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3821{e})~{\pm}{:}\href{../text/values.html#text-sign}{\mathtt{sign}}~e{:}\href{../text/values.html#text-num}{\mathtt{num}} + &\Rightarrow& (p+q)\cdot 10^{\pm e} \\ +\def\mathdef3761#1{{}}\mathdef3761{hexadecimal floating-point number} & \href{../text/values.html#text-hexfloat}{\mathtt{hexfloat}} &::=& + \def\mathdef3822#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3822{0x}~p{:}\href{../text/values.html#text-hexnum}{\mathtt{hexnum}}~\def\mathdef3823#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3823{.}^? + &\Rightarrow& p \\ &&|& + \def\mathdef3824#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3824{0x}~p{:}\href{../text/values.html#text-hexnum}{\mathtt{hexnum}}~\def\mathdef3825#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3825{.}~q{:}\href{../text/values.html#text-hexfrac}{\mathtt{hexfrac}} + &\Rightarrow& p+q \\ &&|& + \def\mathdef3826#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3826{0x}~p{:}\href{../text/values.html#text-hexnum}{\mathtt{hexnum}}~\def\mathdef3827#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3827{.}^?~(\def\mathdef3828#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3828{P}~|~\def\mathdef3829#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3829{p})~{\pm}{:}\href{../text/values.html#text-sign}{\mathtt{sign}}~e{:}\href{../text/values.html#text-num}{\mathtt{num}} + &\Rightarrow& p\cdot 2^{\pm e} \\ &&|& + \def\mathdef3830#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3830{0x}~p{:}\href{../text/values.html#text-hexnum}{\mathtt{hexnum}}~\def\mathdef3831#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3831{.}~q{:}\href{../text/values.html#text-hexfrac}{\mathtt{hexfrac}}~(\def\mathdef3832#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3832{P}~|~\def\mathdef3833#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3833{p})~{\pm}{:}\href{../text/values.html#text-sign}{\mathtt{sign}}~e{:}\href{../text/values.html#text-num}{\mathtt{num}} + &\Rightarrow& (p+q)\cdot 2^{\pm e} +\end{array}\end{split}\]
    +

    The value of a literal must not lie outside the representable range of the corresponding IEEE 754-2019 type +(that is, a numeric value must not overflow to \(\pm\mbox{infinity}\)), +but it may be rounded to the nearest representable value.

    +
    +

    Note

    +

    Rounding can be prevented by using hexadecimal notation with no more significant bits than supported by the required type.

    +
    +

    Floating-point values may also be written as constants for infinity or canonical NaN (not a number). +Furthermore, arbitrary NaN values may be expressed by providing an explicit payload value.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef3761#1{{}}\mathdef3761{floating-point value} & \href{../text/values.html#text-float}{\def\mathdef3796#1{{\mathtt{f}#1}}\mathdef3796{N}} &::=& + {\pm}{:}\href{../text/values.html#text-sign}{\mathtt{sign}}~z{:}\href{../text/values.html#text-float}{\def\mathdef3797#1{{\mathtt{f}#1}}\mathdef3797{N}\mathtt{mag}} &\Rightarrow& \pm z \\ +\def\mathdef3761#1{{}}\mathdef3761{floating-point magnitude} & \href{../text/values.html#text-float}{\def\mathdef3797#1{{\mathtt{f}#1}}\mathdef3797{N}\mathtt{mag}} &::=& + z{:}\href{../text/values.html#text-float}{\mathtt{float}} &\Rightarrow& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(z) & (\mathrel{\mbox{if}} \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(z) \neq \pm \infty) \\ &&|& + z{:}\href{../text/values.html#text-hexfloat}{\mathtt{hexfloat}} &\Rightarrow& \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(z) & (\mathrel{\mbox{if}} \href{../exec/numerics.html#aux-ieee}{\mathrm{float}}_N(z) \neq \pm \infty) \\ &&|& + \def\mathdef3834#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3834{inf} &\Rightarrow& \infty \\ &&|& + \def\mathdef3835#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3835{nan} &\Rightarrow& \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(2^{\href{../syntax/values.html#aux-significand}{\mathrm{signif}}(N)-1}) \\ &&|& + \def\mathdef3836#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3836{nan{:}0x}~n{:}\href{../text/values.html#text-hexnum}{\mathtt{hexnum}} &\Rightarrow& \href{../syntax/values.html#syntax-float}{\mathsf{nan}}(n) & (\mathrel{\mbox{if}} 1 \leq n < 2^{\href{../syntax/values.html#aux-significand}{\mathrm{signif}}(N)}) \\ +\end{array}\end{split}\]
    +
    +
    +

    Strings

    +

    Strings denote sequences of bytes that can represent both textual and binary data. +They are enclosed in quotation marks +and may contain any character other than ASCII control characters, quotation marks (\(\def\mathdef3837#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3837{"}\)), or backslash (\(\def\mathdef3838#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3838{\backslash}\)), +except when expressed with an escape sequence.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef3761#1{{}}\mathdef3761{string} & \href{../text/values.html#text-string}{\mathtt{string}} &::=& + \def\mathdef3839#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3839{"}~(b^\ast{:}\href{../text/values.html#text-string}{\mathtt{stringelem}})^\ast~\def\mathdef3840#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3840{"} + &\Rightarrow& \href{../syntax/conventions.html#notation-concat}{\mathrm{concat}}((b^\ast)^\ast) + & (\mathrel{\mbox{if}} |\href{../syntax/conventions.html#notation-concat}{\mathrm{concat}}((b^\ast)^\ast)| < 2^{32}) \\ +\def\mathdef3761#1{{}}\mathdef3761{string element} & \href{../text/values.html#text-string}{\mathtt{stringelem}} &::=& + c{:}\href{../text/values.html#text-string}{\mathtt{stringchar}} &\Rightarrow& \href{../binary/values.html#binary-utf8}{\mathrm{utf8}}(c) \\ &&|& + \def\mathdef3841#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3841{\backslash}~n{:}\href{../text/values.html#text-hexdigit}{\mathtt{hexdigit}}~m{:}\href{../text/values.html#text-hexdigit}{\mathtt{hexdigit}} + &\Rightarrow& 16\cdot n+m \\ +\end{array}\end{split}\]
    +

    Each character in a string literal represents the byte sequence corresponding to its UTF-8 Unicode (Section 2.5) encoding, +except for hexadecimal escape sequences \(\mbox{‘}\backslash hh\mbox{’}\), which represent raw bytes of the respective value.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l} +\def\mathdef3761#1{{}}\mathdef3761{string character} & \href{../text/values.html#text-string}{\mathtt{stringchar}} &::=& + c{:}\href{../text/lexical.html#text-char}{\mathtt{char}} &\Rightarrow& c \qquad + & (\mathrel{\mbox{if}} c \geq \def\mathdef3842#1{\mathrm{U{+}#1}}\mathdef3842{20} \wedge c \neq \def\mathdef3843#1{\mathrm{U{+}#1}}\mathdef3843{7F} \wedge c \neq \def\mathdef3844#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3844{"} \wedge c \neq \def\mathdef3845#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3845{\backslash}) \\ &&|& + \def\mathdef3846#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3846{\backslash t} &\Rightarrow& \def\mathdef3847#1{\mathrm{U{+}#1}}\mathdef3847{09} \\ &&|& + \def\mathdef3848#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3848{\backslash n} &\Rightarrow& \def\mathdef3849#1{\mathrm{U{+}#1}}\mathdef3849{0A} \\ &&|& + \def\mathdef3850#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3850{\backslash r} &\Rightarrow& \def\mathdef3851#1{\mathrm{U{+}#1}}\mathdef3851{0D} \\ &&|& + \def\mathdef3852#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3852{\backslash{"}} &\Rightarrow& \def\mathdef3853#1{\mathrm{U{+}#1}}\mathdef3853{22} \\ &&|& + \def\mathdef3854#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3854{\backslash{'}} &\Rightarrow& \def\mathdef3855#1{\mathrm{U{+}#1}}\mathdef3855{27} \\ &&|& + \def\mathdef3856#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3856{\backslash\backslash} &\Rightarrow& \def\mathdef3857#1{\mathrm{U{+}#1}}\mathdef3857{5C} \\ &&|& + \def\mathdef3858#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3858{\backslash u\{}~n{:}\href{../text/values.html#text-hexnum}{\mathtt{hexnum}}~\def\mathdef3859#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3859{\}} + &\Rightarrow& \def\mathdef3860#1{\mathrm{U{+}#1}}\mathdef3860{(n)} & (\mathrel{\mbox{if}} n < \def\mathdef3861#1{\mathtt{0x#1}}\mathdef3861{D800} \vee \def\mathdef3862#1{\mathtt{0x#1}}\mathdef3862{E000} \leq n < \def\mathdef3863#1{\mathtt{0x#1}}\mathdef3863{110000}) \\ +\end{array}\end{split}\]
    +
    +
    +

    Names

    +

    Names are strings denoting a literal character sequence. +A name string must form a valid UTF-8 encoding as defined by Unicode (Section 2.5) and is interpreted as a string of Unicode scalar values.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad}l} +\def\mathdef3761#1{{}}\mathdef3761{name} & \href{../text/values.html#text-name}{\mathtt{name}} &::=& + b^\ast{:}\href{../text/values.html#text-string}{\mathtt{string}} &\Rightarrow& c^\ast & (\mathrel{\mbox{if}} b^\ast = \href{../binary/values.html#binary-utf8}{\mathrm{utf8}}(c^\ast)) \\ +\end{array}\end{split}\]
    +
    +

    Note

    +

    Presuming the source text is itself encoded correctly, +strings that do not contain any uses of hexadecimal byte escapes are always valid names.

    +
    +
    +
    +

    Identifiers

    +

    Indices can be given in both numeric and symbolic form. +Symbolic identifiers that stand in lieu of indices start with \(\def\mathdef3864#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3864{\$}\), followed by any sequence of printable ASCII characters that does not contain a space, quotation mark, comma, semicolon, or bracket.

    +
    +\[\begin{split}\begin{array}{llclll@{\qquad}l} +\def\mathdef3761#1{{}}\mathdef3761{identifier} & \href{../text/values.html#text-id}{\mathtt{id}} &::=& + \def\mathdef3865#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3865{\$}~\href{../text/values.html#text-idchar}{\mathtt{idchar}}^+ \\ +\def\mathdef3761#1{{}}\mathdef3761{identifier character} & \href{../text/values.html#text-idchar}{\mathtt{idchar}} &::=& + \def\mathdef3866#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3866{0} ~~|~~ \dots ~~|~~ \def\mathdef3867#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3867{9} \\ &&|& + \def\mathdef3868#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3868{A} ~~|~~ \dots ~~|~~ \def\mathdef3869#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3869{Z} \\ &&|& + \def\mathdef3870#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3870{a} ~~|~~ \dots ~~|~~ \def\mathdef3871#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3871{z} \\ &&|& + \def\mathdef3872#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3872{!} ~~|~~ + \def\mathdef3873#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3873{\#} ~~|~~ + \def\mathdef3874#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3874{\$} ~~|~~ + \def\mathdef3875#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3875{\%} ~~|~~ + \def\mathdef3876#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3876{\&} ~~|~~ + \def\mathdef3877#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3877{'} ~~|~~ + \def\mathdef3878#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3878{*} ~~|~~ + \def\mathdef3879#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3879{+} ~~|~~ + \def\mathdef3880#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3880{-} ~~|~~ + \def\mathdef3881#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3881{.} ~~|~~ + \def\mathdef3882#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3882{/} \\ &&|& + \def\mathdef3883#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3883{:} ~~|~~ + \def\mathdef3884#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3884{<} ~~|~~ + \def\mathdef3885#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3885{=} ~~|~~ + \def\mathdef3886#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3886{>} ~~|~~ + \def\mathdef3887#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3887{?} ~~|~~ + \def\mathdef3888#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3888{@} ~~|~~ + \def\mathdef3889#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3889{\backslash} ~~|~~ + \def\mathdef3890#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3890{\hat{~~}} ~~|~~ + \def\mathdef3891#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3891{\_} ~~|~~ + \def\mathdef3892#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3892{\grave{~~}} ~~|~~ + \def\mathdef3893#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3893{|} ~~|~~ + \def\mathdef3894#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3894{\tilde{~~}} \\ +\end{array}\end{split}\]
    +
    +

    Conventions

    +

    The expansion rules of some abbreviations require insertion of a fresh identifier. +That may be any syntactically valid identifier that does not already occur in the given source text.

    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/valid/conventions.html b/core/valid/conventions.html new file mode 100644 index 00000000..f2b18f4f --- /dev/null +++ b/core/valid/conventions.html @@ -0,0 +1,270 @@ + + + + + + + + + Conventions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Conventions

    +

    Validation checks that a WebAssembly module is well-formed. +Only valid modules can be instantiated.

    +

    Validity is defined by a type system over the abstract syntax of a module and its contents. +For each piece of abstract syntax, there is a typing rule that specifies the constraints that apply to it. +All rules are given in two equivalent forms:

    +
      +

    1. In prose, describing the meaning in intuitive form.

      2. +

    2. In formal notation, describing the rule in mathematical form. 1

      3. +
    +
    +

    Note

    +

    The prose and formal rules are equivalent, +so that understanding of the formal notation is not required to read this specification. +The formalism offers a more concise description in notation that is used widely in programming languages semantics and is readily amenable to mathematical proof.

    +
    +

    In both cases, the rules are formulated in a declarative manner. +That is, they only formulate the constraints, they do not define an algorithm. +The skeleton of a sound and complete algorithm for type-checking instruction sequences according to this specification is provided in the appendix.

    +
    +

    Contexts

    +

    Validity of an individual definition is specified relative to a context, +which collects relevant information about the surrounding module and the definitions in scope:

    +
      +

    • Types: the list of types defined in the current module.

      • +

    • Functions: the list of functions declared in the current module, represented by their function type.

      • +

    • Tables: the list of tables declared in the current module, represented by their table type.

      • +

    • Memories: the list of memories declared in the current module, represented by their memory type.

      • +

    • Globals: the list of globals declared in the current module, represented by their global type.

      • +

    • Element Segments: the list of element segments declared in the current module, represented by their element type.

      • +

    • Data Segments: the list of data segments declared in the current module, each represented by an \(\mathrel{\mbox{ok}}\) entry.

      • +

    • Locals: the list of locals declared in the current function (including parameters), represented by their value type.

      • +

    • Labels: the stack of labels accessible from the current position, represented by their result type.

      • +

    • Return: the return type of the current function, represented as an optional result type that is absent when no return is allowed, as in free-standing expressions.

      • +

    • References: the list of function indices that occur in the module outside functions and can hence be used to form references inside them.

      • +
    +

    In other words, a context contains a sequence of suitable types for each index space, +describing each defined entry in that space. +Locals, labels and return type are only used for validating instructions in function bodies, and are left empty elsewhere. +The label stack is the only part of the context that changes as validation of an instruction sequence proceeds.

    +

    More concretely, contexts are defined as records \(C\) with abstract syntax:

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef3895#1{{}}\mathdef3895{(context)} & C &::=& + \begin{array}[t]{l@{~}ll} + \{ & \href{../valid/conventions.html#context}{\mathsf{types}} & \href{../syntax/types.html#syntax-functype}{\mathit{functype}}^\ast, \\ + & \href{../valid/conventions.html#context}{\mathsf{funcs}} & \href{../syntax/types.html#syntax-functype}{\mathit{functype}}^\ast, \\ + & \href{../valid/conventions.html#context}{\mathsf{tables}} & \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}^\ast, \\ + & \href{../valid/conventions.html#context}{\mathsf{mems}} & \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}^\ast, \\ + & \href{../valid/conventions.html#context}{\mathsf{globals}} & \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}^\ast, \\ + & \href{../valid/conventions.html#context}{\mathsf{elems}} & \href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}^\ast, \\ + & \href{../valid/conventions.html#context}{\mathsf{datas}} & {\mathrel{\mbox{ok}}}^\ast, \\ + & \href{../valid/conventions.html#context}{\mathsf{locals}} & \href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}^\ast, \\ + & \href{../valid/conventions.html#context}{\mathsf{labels}} & \href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}}^\ast, \\ + & \href{../valid/conventions.html#context}{\mathsf{return}} & \href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}}^?, \\ + & \href{../valid/conventions.html#context}{\mathsf{refs}} & \href{../syntax/modules.html#syntax-funcidx}{\mathit{funcidx}}^\ast ~\} \\ + \end{array} +\end{array}\end{split}\]
    +

    In addition to field access written \(C.\mathsf{field}\) the following notation is adopted for manipulating contexts:

    +
      +

    • When spelling out a context, empty fields are omitted.

      • +

    • \(C,\mathsf{field}\,A^\ast\) denotes the same context as \(C\) but with the elements \(A^\ast\) prepended to its \(\mathsf{field}\) component sequence.

      • +
    +
    +

    Note

    +

    We use indexing notation like \(C.\href{../valid/conventions.html#context}{\mathsf{labels}}[i]\) to look up indices in their respective index space in the context. +Context extension notation \(C,\mathsf{field}\,A\) is primarily used to locally extend relative index spaces, such as label indices. +Accordingly, the notation is defined to append at the front of the respective sequence, introducing a new relative index \(0\) and shifting the existing ones.

    +
    +
    +
    +

    Prose Notation

    +

    Validation is specified by stylised rules for each relevant part of the abstract syntax. +The rules not only state constraints defining when a phrase is valid, +they also classify it with a type. +The following conventions are adopted in stating these rules.

    +
      +

    • A phrase \(A\) is said to be “valid with type \(T\)” +if and only if all constraints expressed by the respective rules are met. +The form of \(T\) depends on what \(A\) is.

      +
      +

      Note

      +

      For example, if \(A\) is a function, +then \(T\) is a function type; +for an \(A\) that is a global, +\(T\) is a global type; +and so on.

      +
      +
      • +

    • The rules implicitly assume a given context \(C\).

      • +

    • In some places, this context is locally extended to a context \(C'\) with additional entries. +The formulation “Under context \(C'\), … statement …” is adopted to express that the following statement must apply under the assumptions embodied in the extended context.

      • +
    +
    +
    +

    Formal Notation

    +
    +

    Note

    +

    This section gives a brief explanation of the notation for specifying typing rules formally. +For the interested reader, a more thorough introduction can be found in respective text books. 2

    +
    +

    The proposition that a phrase \(A\) has a respective type \(T\) is written \(A : T\). +In general, however, typing is dependent on a context \(C\). +To express this explicitly, the complete form is a judgement \(C \vdash A : T\), +which says that \(A : T\) holds under the assumptions encoded in \(C\).

    +

    The formal typing rules use a standard approach for specifying type systems, rendering them into deduction rules. +Every rule has the following general form:

    +
    +\[\frac{ + \mathit{premise}_1 \qquad \mathit{premise}_2 \qquad \dots \qquad \mathit{premise}_n +}{ + \mathit{conclusion} +}\]
    +

    Such a rule is read as a big implication: if all premises hold, then the conclusion holds. +Some rules have no premises; they are axioms whose conclusion holds unconditionally. +The conclusion always is a judgment \(C \vdash A : T\), +and there is one respective rule for each relevant construct \(A\) of the abstract syntax.

    +
    +

    Note

    +

    For example, the typing rule for the \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}\) instruction can be given as an axiom:

    +
    +\[\frac{ +}{ + C \vdash \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] +}\]
    +

    The instruction is always valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\)] +(saying that it consumes two \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) values and produces one), +independent of any side conditions.

    +

    An instruction like \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.get}}\) can be typed as follows:

    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{locals}}[x] = t +}{ + C \vdash \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.get}}~x : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +}\]
    +

    Here, the premise enforces that the immediate local index \(x\) exists in the context. +The instruction produces a value of its respective type \(t\) +(and does not consume any values). +If \(C.\href{../valid/conventions.html#context}{\mathsf{locals}}[x]\) does not exist then the premise does not hold, +and the instruction is ill-typed.

    +

    Finally, a structured instruction requires +a recursive rule, where the premise is itself a typing judgement:

    +
    +\[\frac{ + C \vdash \href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}} : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] + \qquad + C,\href{../exec/runtime.html#syntax-label}{\mathsf{label}}\,[t_2^\ast] \vdash \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}{ + C \vdash \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +

    A \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}\) instruction is only valid when the instruction sequence in its body is. +Moreover, the result type must match the block’s annotation \(\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}\). +If so, then the \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}\) instruction has the same type as the body. +Inside the body an additional label of the corresponding result type is available, +which is expressed by extending the context \(C\) with the additional label information for the premise.

    +
    +
    +
    1
    +

    The semantics is derived from the following article: +Andreas Haas, Andreas Rossberg, Derek Schuff, Ben Titzer, Dan Gohman, Luke Wagner, Alon Zakai, JF Bastien, Michael Holman. Bringing the Web up to Speed with WebAssembly. Proceedings of the 38th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2017). ACM 2017.

    +
    +
    2
    +

    For example: Benjamin Pierce. Types and Programming Languages. The MIT Press 2002

    +
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/valid/index.html b/core/valid/index.html new file mode 100644 index 00000000..cf58ab56 --- /dev/null +++ b/core/valid/index.html @@ -0,0 +1,152 @@ + + + + + + + + + Validation — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Validation

    +
    + +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/valid/instructions.html b/core/valid/instructions.html new file mode 100644 index 00000000..388e27c0 --- /dev/null +++ b/core/valid/instructions.html @@ -0,0 +1,1354 @@ + + + + + + + + + Instructions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Instructions

    +

    Instructions are classified by stack types \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\) that describe how instructions manipulate the operand stack.

    +
    +\[\begin{split}\begin{array}{llll} +\def\mathdef3973#1{{}}\mathdef3973{stack type} & \href{../syntax/types.html#syntax-stacktype}{\mathit{stacktype}} &::=& + [\href{../syntax/types.html#syntax-opdtype}{\mathit{opdtype}}^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-opdtype}{\mathit{opdtype}}^\ast] \\ +\def\mathdef3973#1{{}}\mathdef3973{operand type} & \href{../syntax/types.html#syntax-opdtype}{\mathit{opdtype}} &::=& + \href{../syntax/types.html#syntax-valtype}{\mathit{valtype}} ~|~ \bot \\ +\end{array}\end{split}\]
    +

    The types describe the required input stack with operand types \(t_1^\ast\) that an instruction pops off +and the provided output stack with result values of types \(t_2^\ast\) that it pushes back. +Stack types are akin to function types, +except that they allow individual operands to be classified as \(\bot\) (bottom), indicating that the type is unconstrained. +As an auxiliary notion, an operand type \(t_1\) matches another operand type \(t_2\), if \(t_1\) is either \(\bot\) or equal to \(t_2\). +This is extended to stack types in a point-wise manner.

    +
    +\[\frac{ +}{ + \vdash t \leq t +} +\qquad +\frac{ +}{ + \vdash \bot \leq t +}\]
    +
    +\[\frac{ + (\vdash t \leq t')^\ast +}{ + \vdash [t^\ast] \leq [{t'}^\ast] +}\]
    +
    +

    Note

    +

    For example, the instruction \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}\) has type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\), +consuming two \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) values and producing one.

    +
    +

    Typing extends to instruction sequences \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\). +Such a sequence has a function type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\) if the accumulative effect of executing the instructions is consuming values of types \(t_1^\ast\) off the operand stack and pushing new values of types \(t_2^\ast\).

    +

    For some instructions, the typing rules do not fully constrain the type, +and therefore allow for multiple types. +Such instructions are called polymorphic. +Two degrees of polymorphism can be distinguished:

    +
      +

    • value-polymorphic: +the value type \(t\) of one or several individual operands is unconstrained. +That is the case for all parametric instructions like \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{drop}}\) and \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}\).

      • +

    • stack-polymorphic: +the entire (or most of the) function type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\) of the instruction is unconstrained. +That is the case for all control instructions that perform an unconditional control transfer, such as \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}\), \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}\), \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}\), and \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}\).

      • +
    +

    In both cases, the unconstrained types or type sequences can be chosen arbitrarily, as long as they meet the constraints imposed for the surrounding parts of the program.

    +
    +

    Note

    +

    For example, the \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}\) instruction is valid with type \([t~t~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t]\), for any possible number type \(t\). Consequently, both instruction sequences

    +
    +\[(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1)~~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~2)~~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~3)~~\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}{}\]
    +

    and

    +
    +\[(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1.0)~~(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~2.0)~~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~3)~~\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}{}\]
    +

    are valid, with \(t\) in the typing of \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}\) being instantiated to \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) or \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\), respectively.

    +

    The \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}\) instruction is valid with type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\) for any possible sequences of value types \(t_1^\ast\) and \(t_2^\ast\). +Consequently,

    +
    +\[\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}~~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}\]
    +

    is valid by assuming type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\) for the \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}\) instruction. +In contrast,

    +
    +\[\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}~~(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0)~~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}\]
    +

    is invalid, because there is no possible type to pick for the \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}\) instruction that would make the sequence well-typed.

    +
    +

    The Appendix describes a type checking algorithm that efficiently implements validation of instruction sequences as prescribed by the rules given here.

    +
    +

    Numeric Instructions

    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\)

    +
      +

    • The instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +}\]
    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}\)

    +
      +

    • The instruction is valid with type \([t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} t\mathsf{.}\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}} : [t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +}\]
    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}\)

    +
      +

    • The instruction is valid with type \([t~t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} t\mathsf{.}\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}} : [t~t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +}\]
    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-testop}{\mathit{testop}}\)

    +
      +

    • The instruction is valid with type \([t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} t\mathsf{.}\href{../syntax/instructions.html#syntax-testop}{\mathit{testop}} : [t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] +}\]
    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-relop}{\mathit{relop}}\)

    +
      +

    • The instruction is valid with type \([t~t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} t\mathsf{.}\href{../syntax/instructions.html#syntax-relop}{\mathit{relop}} : [t~t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] +}\]
    +
    +
    +

    \(t_2\mathsf{.}\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}\mathsf{\_}t_1\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?\)

    +
      +

    • The instruction is valid with type \([t_1] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} t_2\mathsf{.}\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}\mathsf{\_}t_1\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^? : [t_1] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2] +}\]
    +
    +
    +
    +

    Reference Instructions

    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t\)

    +
      +

    • The instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +}\]
    +
    +

    Note

    +

    In future versions of WebAssembly, there may be reference types for which no null reference is allowed.

    +
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}is\_null}}\)

    +
      +

    • The instruction is valid with type \([t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\), for any reference type \(t\).

      • +
    +
    +\[\frac{ + t = \href{../syntax/types.html#syntax-reftype}{\mathit{reftype}} +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}is\_null}} : [t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~x\)

    +
      +

    • The function \(C.\href{../valid/conventions.html#context}{\mathsf{funcs}}[x]\) must be defined in the context.

      • +

    • The function index \(x\) must be contained in \(C.\href{../valid/conventions.html#context}{\mathsf{refs}}\).

      • +

    • The instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{funcs}}[x] = \href{../syntax/types.html#syntax-functype}{\mathit{functype}} + \qquad + x \in C.\href{../valid/conventions.html#context}{\mathsf{refs}} +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~x : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}] +}\]
    +
    +
    +
    +

    Vector Instructions

    +

    Vector instructions can have a prefix to describe the shape of the operand. Packed numeric types, \(\href{../exec/runtime.html#syntax-storagetype}{\mathsf{i8}}\) and \(\href{../exec/runtime.html#syntax-storagetype}{\mathsf{i16}}\), are not value type, we define an auxiliary function to map such packed types into value types:

    +
    +\[\begin{split}\begin{array}{lll@{\qquad}l} +\href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(\mathsf{i8x16}) &=& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}} \\ +\href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(\mathsf{i16x8}) &=& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}} \\ +\href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(t\mathsf{x}N) &=& t +\end{array}\end{split}\]
    +

    We also define an auxiliary function to get number of packed numeric types in a \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\), dimension:

    +
    +\[\begin{array}{lll@{\qquad}l} +\href{../valid/instructions.html#aux-dim}{\mathrm{dim}}(t\mathsf{x}N) &=& N +\end{array}\]
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\)

    +
      +

    • The instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvtestop}{\mathit{vvtestop}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\mathsf{.}\href{../syntax/instructions.html#syntax-vvtestop}{\mathit{vvtestop}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] +}\]
    +
    +
    +

    \(\mathsf{i8x16.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{swizzle}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \mathsf{i8x16.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{swizzle}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\mathsf{i8x16.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}^{16}\)

    +
      +

    • For all \(\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}_i\), in \(\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}^{16}\), \(\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}_i\) must be smaller than \(32\).

      • +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ + (\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} < 32)^{16} +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \mathsf{i8x16.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}^{16} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}\)

    +
      +

    • Let \(t\) be \(\href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}})\).

      • +

    • The instruction is valid with type \([t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}} : [\href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}})] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    +
      +

    • The lane index \(\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\) must be smaller than \(\href{../valid/instructions.html#aux-dim}{\mathrm{dim}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}})\).

      • +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}})]\).

      • +
    +
    +\[\frac{ + \href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} < \href{../valid/instructions.html#aux-dim}{\mathrm{dim}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}) +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} t\mathsf{x}N\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}})] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    +
      +

    • The lane index \(\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\) must be smaller than \(\href{../valid/instructions.html#aux-dim}{\mathrm{dim}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}})\).

      • +

    • Let \(t\) be \(\href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}})\).

      • +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ + \href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} < \href{../valid/instructions.html#aux-dim}{\mathrm{dim}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}) +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../valid/instructions.html#aux-unpacked}{\mathrm{unpacked}}(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}})] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vrelop}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vrelop}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vishiftop}{\mathit{vishiftop}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vishiftop}{\mathit{vishiftop}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vtestop}{\mathit{vtestop}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vtestop}{\mathit{vtestop}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}^?\mathsf{\_}\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?\mathsf{\_zero}^?\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{.}\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}^?\mathsf{\_}\href{../syntax/instructions.html#syntax-shape}{\mathit{shape}}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?\mathsf{\_zero}^? : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_1\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_}\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_2\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_1\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}\mathsf{\_}\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_2\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_1\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{dot}}\mathsf{\_}\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_2\mathsf{\_s}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_1\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{dot}}\mathsf{\_}\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_2\mathsf{\_s} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_1\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_}\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_2\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_1\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extmul}}\mathsf{\_}\href{../syntax/instructions.html#syntax-half}{\mathit{half}}\mathsf{\_}\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_2\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_1\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_}\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_2\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}\)

    +
      +

    • The instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_1\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extadd\_pairwise}}\mathsf{\_}\href{../syntax/instructions.html#syntax-shape}{\mathit{ishape}}_2\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +
    +

    Parametric Instructions

    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{drop}}\)

    +
      +

    • The instruction is valid with type \([t] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\), for any value type \(t\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{drop}} : [t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +

    Note

    +

    Both \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{drop}}\) and \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}\) without annotation are value-polymorphic instructions.

    +
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}~(t^\ast)^?\)

    +
      +

    • If \(t^\ast\) is present, then:

      +
        +

      • The length of \(t^\ast\) must be \(1\).

        • +

      • Then the instruction is valid with type \([t^\ast~t^\ast~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t^\ast]\).

        • +
      +
      • +

    • Else:

      +
        +

      • The instruction is valid with type \([t~t~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t]\), for any operand type \(t\) that matches some number type or vector type.

        • +
      +
      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}~t : [t~t~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +} +\qquad +\frac{ + \vdash t \leq \href{../syntax/types.html#syntax-numtype}{\mathit{numtype}} +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}} : [t~t~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +} +\qquad +\frac{ + \vdash t \leq \href{../syntax/types.html#syntax-vectype}{\mathit{vectype}} +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}} : [t~t~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +}\]
    +
    +

    Note

    +

    In future versions of WebAssembly, \(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}\) may allow more than one value per choice.

    +
    +
    +
    +
    +

    Variable Instructions

    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.get}}~x\)

    +
      +

    • The local \(C.\href{../valid/conventions.html#context}{\mathsf{locals}}[x]\) must be defined in the context.

      • +

    • Let \(t\) be the value type \(C.\href{../valid/conventions.html#context}{\mathsf{locals}}[x]\).

      • +

    • Then the instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{locals}}[x] = t +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.get}}~x : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.set}}~x\)

    +
      +

    • The local \(C.\href{../valid/conventions.html#context}{\mathsf{locals}}[x]\) must be defined in the context.

      • +

    • Let \(t\) be the value type \(C.\href{../valid/conventions.html#context}{\mathsf{locals}}[x]\).

      • +

    • Then the instruction is valid with type \([t] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{locals}}[x] = t +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.set}}~x : [t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.tee}}~x\)

    +
      +

    • The local \(C.\href{../valid/conventions.html#context}{\mathsf{locals}}[x]\) must be defined in the context.

      • +

    • Let \(t\) be the value type \(C.\href{../valid/conventions.html#context}{\mathsf{locals}}[x]\).

      • +

    • Then the instruction is valid with type \([t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{locals}}[x] = t +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local.tee}}~x : [t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.get}}~x\)

    +
      +

    • The global \(C.\href{../valid/conventions.html#context}{\mathsf{globals}}[x]\) must be defined in the context.

      • +

    • Let \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t\) be the global type \(C.\href{../valid/conventions.html#context}{\mathsf{globals}}[x]\).

      • +

    • Then the instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{globals}}[x] = \href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.get}}~x : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.set}}~x\)

    +
      +

    • The global \(C.\href{../valid/conventions.html#context}{\mathsf{globals}}[x]\) must be defined in the context.

      • +

    • Let \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t\) be the global type \(C.\href{../valid/conventions.html#context}{\mathsf{globals}}[x]\).

      • +

    • The mutability \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}\) must be \(\href{../syntax/types.html#syntax-mut}{\mathsf{var}}\).

      • +

    • Then the instruction is valid with type \([t] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{globals}}[x] = \href{../syntax/types.html#syntax-mut}{\mathsf{var}}~t +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.set}}~x : [t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +
    +

    Table Instructions

    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}~x\)

    +
      +

    • The table \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\) must be defined in the context.

      • +

    • Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t\) be the table type \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x] = \href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.get}}~x : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x\)

    +
      +

    • The table \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\) must be defined in the context.

      • +

    • Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t\) be the table type \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~t] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x] = t +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.set}}~x : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.size}}~x\)

    +
      +

    • The table \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\) must be defined in the context.

      • +

    • Then the instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x] = \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.size}}~x : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.grow}}~x\)

    +
      +

    • The table \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\) must be defined in the context.

      • +

    • Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t\) be the table type \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\).

      • +

    • Then the instruction is valid with type \([t~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x] = \href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.grow}}~x : [t~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.fill}}~x\)

    +
      +

    • The table \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\) must be defined in the context.

      • +

    • Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t\) be the table type \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~t~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x] = \href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.fill}}~x : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~t~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}~x~y\)

    +
      +

    • The table \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\) must be defined in the context.

      • +

    • Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_1~t_1\) be the table type \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\).

      • +

    • The table \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[y]\) must be defined in the context.

      • +

    • Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_2~t_2\) be the table type \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[y]\).

      • +

    • The reference type \(t_1\) must be the same as \(t_2\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x] = \href{../syntax/types.html#syntax-limits}{\mathit{limits}}_1~t + \qquad + C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x] = \href{../syntax/types.html#syntax-limits}{\mathit{limits}}_2~t +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.copy}}~x~y : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}~x~y\)

    +
      +

    • The table \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\) must be defined in the context.

      • +

    • Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t_1\) be the table type \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\).

      • +

    • The element segment \(C.\href{../valid/conventions.html#context}{\mathsf{elems}}[y]\) must be defined in the context.

      • +

    • Let \(t_2\) be the reference type \(C.\href{../valid/conventions.html#context}{\mathsf{elems}}[y]\).

      • +

    • The reference type \(t_1\) must be the same as \(t_2\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x] = \href{../syntax/types.html#syntax-limits}{\mathit{limits}}_1~t + \qquad + C.\href{../valid/conventions.html#context}{\mathsf{elems}}[y] = t +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table.init}}~x~y : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem.drop}}~x\)

    +
      +

    • The element segment \(C.\href{../valid/conventions.html#context}{\mathsf{elems}}[x]\) must be defined in the context.

      • +

    • Then the instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{elems}}[x] = t +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem.drop}}~x : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +
    +

    Memory Instructions

    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • The alignment \(2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}}\) must not be larger than the bit width of \(t\) divided by \(8\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} + \qquad + 2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}} \leq |t|/8 +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} t\mathsf{.load}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +}\]
    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • The alignment \(2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}}\) must not be larger than \(N/8\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} + \qquad + 2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}} \leq N/8 +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} t\mathsf{.load}N\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t] +}\]
    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • The alignment \(2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}}\) must not be larger than the bit width of \(t\) divided by \(8\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~t] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} + \qquad + 2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}} \leq |t|/8 +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} t\mathsf{.store}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +

    \(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}{N}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • The alignment \(2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}}\) must not be larger than \(N/8\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~t] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} + \qquad + 2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}} \leq N/8 +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} t\mathsf{.store}N~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~t] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +

    \(\mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{x}M\_\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • The alignment \(2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}}\) must not be larger than \(N/8 \cdot M\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} + \qquad + 2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}} \leq N/8 \cdot M +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \mathsf{v128.}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{x}M\_\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_splat}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • The alignment \(2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}}\) must not be larger than \(N/8\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} + \qquad + 2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}} \leq N/8 +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_splat}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_zero}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • The alignment \(2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}}\) must not be larger than \(N/8\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} + \qquad + 2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}} \leq N/8 +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_zero}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    +
      +

    • The lane index \(\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\) must be smaller than \(128/N\).

      • +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • The alignment \(2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}}\) must not be larger than \(N/8\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ + \href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} < 128/N + \qquad + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} + \qquad + 2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}} < N/8 +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] +}\]
    +
    +
    +

    \(\mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}{N}\mathsf{\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\)

    +
      +

    • The lane index \(\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}}\) must be smaller than \(128/N\).

      • +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • The alignment \(2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}}\) must not be larger than \(N/8\).

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}]\).

      • +
    +
    +\[\frac{ + \href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} < 128/N + \qquad + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} + \qquad + 2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}} < N/8 +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \mathsf{v128.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}{N}\mathsf{\_lane}~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~\href{../syntax/instructions.html#syntax-laneidx}{\mathit{laneidx}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.size}}\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • Then the instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.size}} : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.grow}}\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.grow}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}}\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.fill}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}}\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.copy}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~x\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0]\) must be defined in the context.

      • +

    • The data segment \(C.\href{../valid/conventions.html#context}{\mathsf{datas}}[x]\) must be defined in the context.

      • +

    • Then the instruction is valid with type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[0] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} + \qquad + C.\href{../valid/conventions.html#context}{\mathsf{datas}}[x] = {\mathrel{\mbox{ok}}} +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory.init}}~x : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data.drop}}~x\)

    +
      +

    • The data segment \(C.\href{../valid/conventions.html#context}{\mathsf{datas}}[x]\) must be defined in the context.

      • +

    • Then the instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{datas}}[x] = {\mathrel{\mbox{ok}}} +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data.drop}}~x : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +
    +

    Control Instructions

    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{nop}}\)

    +
      +

    • The instruction is valid with type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{nop}} : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}\)

    +
      +

    • The instruction is valid with type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\), for any sequences of value types \(t_1^\ast\) and \(t_2^\ast\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}} : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +
    +

    Note

    +

    The \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}\) instruction is stack-polymorphic.

    +
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\)

    +
      +

    • The block type must be valid as some function type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +

    • Let \(C'\) be the same context as \(C\), but with the result type \([t_2^\ast]\) prepended to the \(\href{../valid/conventions.html#context}{\mathsf{labels}}\) vector.

      • +

    • Under context \(C'\), +the instruction sequence \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) must be valid with type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +

    • Then the compound instruction is valid with type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +
    +
    +\[\frac{ + C \href{../valid/types.html#valid-blocktype}{\vdash} \href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}} : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] + \qquad + C,\href{../valid/conventions.html#context}{\mathsf{labels}}\,[t_2^\ast] \href{../valid/instructions.html#valid-instr-seq}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +
    +

    Note

    +

    The notation \(C,\href{../valid/conventions.html#context}{\mathsf{labels}}\,[t^\ast]\) inserts the new label type at index \(0\), shifting all others.

    +
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}~\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\)

    +
      +

    • The block type must be valid as some function type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +

    • Let \(C'\) be the same context as \(C\), but with the result type \([t_1^\ast]\) prepended to the \(\href{../valid/conventions.html#context}{\mathsf{labels}}\) vector.

      • +

    • Under context \(C'\), +the instruction sequence \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) must be valid with type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +

    • Then the compound instruction is valid with type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +
    +
    +\[\frac{ + C \href{../valid/types.html#valid-blocktype}{\vdash} \href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}} : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] + \qquad + C,\href{../valid/conventions.html#context}{\mathsf{labels}}\,[t_1^\ast] \href{../valid/instructions.html#valid-instr-seq}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}~\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +
    +

    Note

    +

    The notation \(C,\href{../valid/conventions.html#context}{\mathsf{labels}}\,[t^\ast]\) inserts the new label type at index \(0\), shifting all others.

    +
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}~\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_1^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_2^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\)

    +
      +

    • The block type must be valid as some function type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +

    • Let \(C'\) be the same context as \(C\), but with the result type \([t_2^\ast]\) prepended to the \(\href{../valid/conventions.html#context}{\mathsf{labels}}\) vector.

      • +

    • Under context \(C'\), +the instruction sequence \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_1^\ast\) must be valid with type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +

    • Under context \(C'\), +the instruction sequence \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_2^\ast\) must be valid with type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +

    • Then the compound instruction is valid with type \([t_1^\ast~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +
    +
    +\[\frac{ + C \href{../valid/types.html#valid-blocktype}{\vdash} \href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}} : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] + \qquad + C,\href{../valid/conventions.html#context}{\mathsf{labels}}\,[t_2^\ast] \href{../valid/instructions.html#valid-instr-seq}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_1^\ast : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] + \qquad + C,\href{../valid/conventions.html#context}{\mathsf{labels}}\,[t_2^\ast] \href{../valid/instructions.html#valid-instr-seq}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_2^\ast : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}~\href{../syntax/instructions.html#syntax-blocktype}{\mathit{blocktype}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_1^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_2^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} : [t_1^\ast~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +
    +

    Note

    +

    The notation \(C,\href{../valid/conventions.html#context}{\mathsf{labels}}\,[t^\ast]\) inserts the new label type at index \(0\), shifting all others.

    +
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l\)

    +
      +

    • The label \(C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l]\) must be defined in the context.

      • +

    • Let \([t^\ast]\) be the result type \(C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l]\).

      • +

    • Then the instruction is valid with type \([t_1^\ast~t^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\), for any sequences of value types \(t_1^\ast\) and \(t_2^\ast\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l] = [t^\ast] +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l : [t_1^\ast~t^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +
    +

    Note

    +

    The label index space in the context \(C\) contains the most recent label first, so that \(C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l]\) performs a relative lookup as expected.

    +

    The \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}\) instruction is stack-polymorphic.

    +
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_if}}~l\)

    +
      +

    • The label \(C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l]\) must be defined in the context.

      • +

    • Let \([t^\ast]\) be the result type \(C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l]\).

      • +

    • Then the instruction is valid with type \([t^\ast~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t^\ast]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l] = [t^\ast] +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_if}}~l : [t^\ast~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t^\ast] +}\]
    +
    +

    Note

    +

    The label index space in the context \(C\) contains the most recent label first, so that \(C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l]\) performs a relative lookup as expected.

    +
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}~l^\ast~l_N\)

    +
      +

    • The label \(C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l_N]\) must be defined in the context.

      • +

    • For all \(l_i\) in \(l^\ast\), +the label \(C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l_i]\) must be defined in the context.

      • +

    • There must be a result type \([t^\ast]\), such that:

      +
        +

      • For each operand type \(t_j\) in \(t^\ast\) and corresponding type \(t'_{Nj}\) in \(C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l_N]\), \(t_j\) matches \(t'_{Nj}\).

        • +

      • For all \(l_i\) in \(l^\ast\), +and for each operand type \(t_j\) in \(t^\ast\) and corresponding type \(t'_{ij}\) in \(C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l_i]\), \(t_j\) matches \(t'_{ij}\).

        • +
      +
      • +

    • Then the instruction is valid with type \([t_1^\ast~t^\ast~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\), for any sequences of value types \(t_1^\ast\) and \(t_2^\ast\).

      • +
    +
    +\[\frac{ + (\vdash [t^\ast] \leq C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l])^\ast + \qquad + \vdash [t^\ast] \leq C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l_N] +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}~l^\ast~l_N : [t_1^\ast~t^\ast~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +
    +

    Note

    +

    The label index space in the context \(C\) contains the most recent label first, so that \(C.\href{../valid/conventions.html#context}{\mathsf{labels}}[l_i]\) performs a relative lookup as expected.

    +

    The \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}\) instruction is stack-polymorphic.

    +
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}\)

    +
      +

    • The return type \(C.\href{../valid/conventions.html#context}{\mathsf{return}}\) must not be absent in the context.

      • +

    • Let \([t^\ast]\) be the result type of \(C.\href{../valid/conventions.html#context}{\mathsf{return}}\).

      • +

    • Then the instruction is valid with type \([t_1^\ast~t^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\), for any sequences of value types \(t_1^\ast\) and \(t_2^\ast\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{return}} = [t^\ast] +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}} : [t_1^\ast~t^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +
    +

    Note

    +

    The \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}\) instruction is stack-polymorphic.

    +

    \(C.\href{../valid/conventions.html#context}{\mathsf{return}}\) is absent (set to \(\epsilon\)) when validating an expression that is not a function body. +This differs from it being set to the empty result type (\([\epsilon]\)), +which is the case for functions not returning anything.

    +
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call}}~x\)

    +
      +

    • The function \(C.\href{../valid/conventions.html#context}{\mathsf{funcs}}[x]\) must be defined in the context.

      • +

    • Then the instruction is valid with type \(C.\href{../valid/conventions.html#context}{\mathsf{funcs}}[x]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{funcs}}[x] = [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call}}~x : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +
    +
    +

    \(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}~x~y\)

    +
      +

    • The table \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\) must be defined in the context.

      • +

    • Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t\) be the table type \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\).

      • +

    • The reference type \(t\) must be \(\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}\).

      • +

    • The type \(C.\href{../valid/conventions.html#context}{\mathsf{types}}[y]\) must be defined in the context.

      • +

    • Let \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\) be the function type \(C.\href{../valid/conventions.html#context}{\mathsf{types}}[y]\).

      • +

    • Then the instruction is valid with type \([t_1^\ast~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x] = \href{../syntax/types.html#syntax-limits}{\mathit{limits}}~\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}} + \qquad + C.\href{../valid/conventions.html#context}{\mathsf{types}}[y] = [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}{ + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}~x~y : [t_1^\ast~\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +
    +
    +
    +

    Instruction Sequences

    +

    Typing of instruction sequences is defined recursively.

    +
    +

    Empty Instruction Sequence: \(\epsilon\)

    +
      +

    • The empty instruction sequence is valid with type \([t^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t^\ast]\), +for any sequence of operand types \(t^\ast\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-instr-seq}{\vdash} \epsilon : [t^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t^\ast] +}\]
    +
    +
    +

    Non-empty Instruction Sequence: \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_N\)

    +
      +

    • The instruction sequence \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) must be valid with type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\), +for some sequences of value types \(t_1^\ast\) and \(t_2^\ast\).

      • +

    • The instruction \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_N\) must be valid with type \([t^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_3^\ast]\), +for some sequences of value types \(t^\ast\) and \(t_3^\ast\).

      • +

    • There must be a sequence of value types \(t_0^\ast\), +such that \(t_2^\ast = t_0^\ast~{t'}^\ast\) where the type sequence \({t'}^\ast\) is as long as \(t^\ast\).

      • +

    • For each operand type \(t'_i\) in \({t'}^\ast\) and corresponding type \(t_i\) in \(t^\ast\), \(t'_i\) matches \(t_i\).

      • +

    • Then the combined instruction sequence is valid with type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_0^\ast~t_3^\ast]\).

      • +
    +
    +\[\frac{ + C \href{../valid/instructions.html#valid-instr-seq}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_0^\ast~{t'}^\ast] + \qquad + \vdash [{t'}^\ast] \leq [t^\ast] + \qquad + C \href{../valid/instructions.html#valid-instr}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_N : [t^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_3^\ast] +}{ + C \href{../valid/instructions.html#valid-instr-seq}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}_N : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_0^\ast~t_3^\ast] +}\]
    +
    +
    +
    +

    Expressions

    +

    Expressions \(\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}\) are classified by result types of the form \([t^\ast]\).

    +
    +

    \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\)

    +
      +

    • The instruction sequence \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) must be valid with some stack type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [{t'}^\ast]\).

      • +

    • For each operand type \(t'_i\) in \({t'}^\ast\) and corresponding value type type \(t_i\) in \(t^\ast\), \(t'_i\) matches \(t_i\).

      • +

    • Then the expression is valid with result type \([t^\ast]\).

      • +
    +
    +\[\frac{ + C \href{../valid/instructions.html#valid-instr-seq}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [{t'}^\ast] + \qquad + \vdash [{t'}^\ast] \leq [t^\ast] +}{ + C \href{../valid/instructions.html#valid-expr}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} : [t^\ast] +}\]
    +
    +
    +

    Constant Expressions

    +
      +

    • In a constant expression \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}\) all instructions in \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast\) must be constant.

      • +

    • A constant instruction \(\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}\) must be:

      +
        +

      • either of the form \(t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\),

        • +

      • or of the form \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}\),

        • +

      • or of the form \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~x\),

        • +

      • or of the form \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.get}}~x\), in which case \(C.\href{../valid/conventions.html#context}{\mathsf{globals}}[x]\) must be a global type of the form \(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~t\).

        • +
      +
      • +
    +
    +\[\frac{ + (C \href{../valid/instructions.html#valid-constant}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}} \href{../valid/instructions.html#valid-constant}{\mathrel{\mbox{const}}})^\ast +}{ + C \href{../valid/instructions.html#valid-constant}{\vdash} \href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \href{../valid/instructions.html#valid-constant}{\mathrel{\mbox{const}}} +}\]
    +
    +\[\frac{ +}{ + C \href{../valid/instructions.html#valid-constant}{\vdash} t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c \href{../valid/instructions.html#valid-constant}{\mathrel{\mbox{const}}} +} +\qquad +\frac{ +}{ + C \href{../valid/instructions.html#valid-constant}{\vdash} \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}} \href{../valid/instructions.html#valid-constant}{\mathrel{\mbox{const}}} +} +\qquad +\frac{ +}{ + C \href{../valid/instructions.html#valid-constant}{\vdash} \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~x \href{../valid/instructions.html#valid-constant}{\mathrel{\mbox{const}}} +}\]
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{globals}}[x] = \href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~t +}{ + C \href{../valid/instructions.html#valid-constant}{\vdash} \href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.get}}~x \href{../valid/instructions.html#valid-constant}{\mathrel{\mbox{const}}} +}\]
    +
    +

    Note

    +

    Currently, constant expressions occurring as initializers of globals are further constrained in that contained \(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global.get}}\) instructions are only allowed to refer to imported globals. +This is enforced in the validation rule for modules by constraining the context \(C\) accordingly.

    +

    The definition of constant expression may be extended in future versions of WebAssembly.

    +
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/valid/modules.html b/core/valid/modules.html new file mode 100644 index 00000000..bd150cca --- /dev/null +++ b/core/valid/modules.html @@ -0,0 +1,618 @@ + + + + + + + + + Modules — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Modules

    +

    Modules are valid when all the components they contain are valid. +Furthermore, most definitions are themselves classified with a suitable type.

    +
    +

    Functions

    +

    Functions \(\href{../syntax/modules.html#syntax-func}{\mathit{func}}\) are classified by function types of the form \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

    +
    +

    \(\{ \href{../syntax/modules.html#syntax-func}{\mathsf{type}}~x, \href{../syntax/modules.html#syntax-func}{\mathsf{locals}}~t^\ast, \href{../syntax/modules.html#syntax-func}{\mathsf{body}}~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \}\)

    +
      +

    • The type \(C.\href{../valid/conventions.html#context}{\mathsf{types}}[x]\) must be defined in the context.

      • +

    • Let \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\) be the function type \(C.\href{../valid/conventions.html#context}{\mathsf{types}}[x]\).

      • +

    • Let \(C'\) be the same context as \(C\), +but with:

      +
        +

      • \(\href{../valid/conventions.html#context}{\mathsf{locals}}\) set to the sequence of value types \(t_1^\ast~t^\ast\), concatenating parameters and locals,

        • +

      • \(\href{../valid/conventions.html#context}{\mathsf{labels}}\) set to the singular sequence containing only result type \([t_2^\ast]\).

        • +

      • \(\href{../valid/conventions.html#context}{\mathsf{return}}\) set to the result type \([t_2^\ast]\).

        • +
      +
      • +

    • Under the context \(C'\), +the expression \(\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}\) must be valid with type \([t_2^\ast]\).

      • +

    • Then the function definition is valid with type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{types}}[x] = [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] + \qquad + C,\href{../valid/conventions.html#context}{\mathsf{locals}}\,t_1^\ast~t^\ast,\href{../valid/conventions.html#context}{\mathsf{labels}}~[t_2^\ast],\href{../valid/conventions.html#context}{\mathsf{return}}~[t_2^\ast] \href{../valid/instructions.html#valid-expr}{\vdash} \href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} : [t_2^\ast] +}{ + C \href{../valid/modules.html#valid-func}{\vdash} \{ \href{../syntax/modules.html#syntax-func}{\mathsf{type}}~x, \href{../syntax/modules.html#syntax-func}{\mathsf{locals}}~t^\ast, \href{../syntax/modules.html#syntax-func}{\mathsf{body}}~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \} : [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +
    +
    +
    +

    Tables

    +

    Tables \(\href{../syntax/modules.html#syntax-table}{\mathit{table}}\) are classified by table types.

    +
    +

    \(\{ \href{../syntax/modules.html#syntax-table}{\mathsf{type}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} \}\)

    +
      +

    • The table type \(\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\) must be valid.

      • +

    • Then the table definition is valid with type \(\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\).

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-tabletype}{\vdash} \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} \mathrel{\mbox{ok}} +}{ + C \href{../valid/modules.html#valid-table}{\vdash} \{ \href{../syntax/modules.html#syntax-table}{\mathsf{type}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} \} : \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} +}\]
    +
    +
    +
    +

    Memories

    +

    Memories \(\href{../syntax/modules.html#syntax-mem}{\mathit{mem}}\) are classified by memory types.

    +
    +

    \(\{ \href{../syntax/modules.html#syntax-mem}{\mathsf{type}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} \}\)

    +
      +

    • The memory type \(\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\) must be valid.

      • +

    • Then the memory definition is valid with type \(\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\).

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-memtype}{\vdash} \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} \mathrel{\mbox{ok}} +}{ + C \href{../valid/modules.html#valid-mem}{\vdash} \{ \href{../syntax/modules.html#syntax-mem}{\mathsf{type}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} \} : \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} +}\]
    +
    +
    +
    +

    Globals

    +

    Globals \(\href{../syntax/modules.html#syntax-global}{\mathit{global}}\) are classified by global types of the form \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t\).

    +
    +

    \(\{ \href{../syntax/modules.html#syntax-global}{\mathsf{type}}~\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t, \href{../syntax/modules.html#syntax-global}{\mathsf{init}}~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \}\)

    +
      +

    • The global type \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t\) must be valid.

      • +

    • The expression \(\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}\) must be valid with result type \([t]\).

      • +

    • The expression \(\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}\) must be constant.

      • +

    • Then the global definition is valid with type \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t\).

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-globaltype}{\vdash} \href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t \mathrel{\mbox{ok}} + \qquad + C \href{../valid/instructions.html#valid-expr}{\vdash} \href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} : [t] + \qquad + C \href{../valid/instructions.html#valid-constant}{\vdash} \href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \href{../valid/instructions.html#valid-constant}{\mathrel{\mbox{const}}} +}{ + C \href{../valid/modules.html#valid-global}{\vdash} \{ \href{../syntax/modules.html#syntax-global}{\mathsf{type}}~\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t, \href{../syntax/modules.html#syntax-global}{\mathsf{init}}~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \} : \href{../syntax/types.html#syntax-mut}{\mathit{mut}}~t +}\]
    +
    +
    +
    +

    Element Segments

    +

    Element segments \(\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}\) are classified by the reference type of their elements.

    +
    +

    \(\{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~t, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~e^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathit{elemmode}} \}\)

    +
      +

    • For each \(e_i\) in \(e^\ast\),

      +
        +

      • The expression \(e_i\) must be valid.

        • +

      • The expression \(e_i\) must be constant.

        • +
      +
      • +

    • The element mode \(\href{../syntax/modules.html#syntax-elemmode}{\mathit{elemmode}}\) must be valid with reference type \(t\).

      • +

    • Then the element segment is valid with reference type \(t\).

      • +
    +
    +\[\frac{ + (C \href{../valid/instructions.html#valid-expr}{\vdash} e \mathrel{\mbox{ok}})^\ast + \qquad + (C \href{../valid/instructions.html#valid-constant}{\vdash} e \href{../valid/instructions.html#valid-constant}{\mathrel{\mbox{const}}})^\ast + \qquad + C \href{../valid/modules.html#valid-elemmode}{\vdash} \href{../syntax/modules.html#syntax-elemmode}{\mathit{elemmode}} : t +}{ + C \href{../valid/modules.html#valid-elem}{\vdash} \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~t, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~e^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathit{elemmode}} \} : t +}\]
    +
    +
    +

    \(\href{../syntax/modules.html#syntax-elemmode}{\mathsf{passive}}\)

    + +
    +\[\frac{ +}{ + C \href{../valid/modules.html#valid-elemmode}{\vdash} \href{../syntax/modules.html#syntax-elemmode}{\mathsf{passive}} : \href{../syntax/types.html#syntax-reftype}{\mathit{reftype}} +}\]
    +
    +
    +

    \(\href{../syntax/modules.html#syntax-elemmode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-elem}{\mathsf{table}}~x, \href{../syntax/modules.html#syntax-elem}{\mathsf{offset}}~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \}\)

    +
      +

    • The table \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\) must be defined in the context.

      • +

    • Let \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t\) be the table type \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\).

      • +

    • The expression \(\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}\) must be valid with result type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\).

      • +

    • The expression \(\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}\) must be constant.

      • +

    • Then the element mode is valid with reference type \(t\).

      • +
    +
    +\[\begin{split}\frac{ + \begin{array}{@{}c@{}} + C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x] = \href{../syntax/types.html#syntax-limits}{\mathit{limits}}~t + \\ + C \href{../valid/instructions.html#valid-expr}{\vdash} \href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] + \qquad + C \href{../valid/instructions.html#valid-constant}{\vdash} \href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \href{../valid/instructions.html#valid-constant}{\mathrel{\mbox{const}}} + \end{array} +}{ + C \href{../valid/modules.html#valid-elemmode}{\vdash} \href{../syntax/modules.html#syntax-elemmode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-elem}{\mathsf{table}}~x, \href{../syntax/modules.html#syntax-elem}{\mathsf{offset}}~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \} : t +}\end{split}\]
    +
    +
    +

    \(\href{../syntax/modules.html#syntax-elemmode}{\mathsf{declarative}}\)

    + +
    +\[\frac{ +}{ + C \href{../valid/modules.html#valid-elemmode}{\vdash} \href{../syntax/modules.html#syntax-elemmode}{\mathsf{declarative}} : \href{../syntax/types.html#syntax-reftype}{\mathit{reftype}} +}\]
    +
    +
    +
    +

    Data Segments

    +

    Data segments \(\href{../syntax/modules.html#syntax-data}{\mathit{data}}\) are not classified by any type but merely checked for well-formedness.

    +
    +

    \(\{ \href{../syntax/modules.html#syntax-data}{\mathsf{init}}~b^\ast, \href{../syntax/modules.html#syntax-data}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-datamode}{\mathit{datamode}} \}\)

    +
      +

    • The data mode \(\href{../syntax/modules.html#syntax-datamode}{\mathit{datamode}}\) must be valid.

      • +

    • Then the data segment is valid.

      • +
    +
    +\[\frac{ + C \href{../valid/modules.html#valid-datamode}{\vdash} \href{../syntax/modules.html#syntax-datamode}{\mathit{datamode}} \mathrel{\mbox{ok}} +}{ + C \href{../valid/modules.html#valid-data}{\vdash} \{ \href{../syntax/modules.html#syntax-data}{\mathsf{init}}~b^\ast, \href{../syntax/modules.html#syntax-data}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-datamode}{\mathit{datamode}} \} \mathrel{\mbox{ok}} +}\]
    +
    +
    +

    \(\href{../syntax/modules.html#syntax-datamode}{\mathsf{passive}}\)

    +
      +

    • The data mode is valid.

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/modules.html#valid-datamode}{\vdash} \href{../syntax/modules.html#syntax-datamode}{\mathsf{passive}} \mathrel{\mbox{ok}} +}\]
    +
    +
    +

    \(\href{../syntax/modules.html#syntax-datamode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-data}{\mathsf{memory}}~x, \href{../syntax/modules.html#syntax-data}{\mathsf{offset}}~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \}\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[x]\) must be defined in the context.

      • +

    • The expression \(\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}\) must be valid with result type \([\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}]\).

      • +

    • The expression \(\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}\) must be constant.

      • +

    • Then the data mode is valid.

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[x] = \href{../syntax/types.html#syntax-limits}{\mathit{limits}} + \qquad + C \href{../valid/instructions.html#valid-expr}{\vdash} \href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} : [\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}] + \qquad + C \href{../valid/instructions.html#valid-constant}{\vdash} \href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \href{../valid/instructions.html#valid-constant}{\mathrel{\mbox{const}}} +}{ + C \href{../valid/modules.html#valid-datamode}{\vdash} \href{../syntax/modules.html#syntax-datamode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-data}{\mathsf{memory}}~x, \href{../syntax/modules.html#syntax-data}{\mathsf{offset}}~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}} \} \mathrel{\mbox{ok}} +}\]
    +
    +
    +
    +

    Start Function

    +

    Start function declarations \(\href{../syntax/modules.html#syntax-start}{\mathit{start}}\) are not classified by any type.

    +
    +

    \(\{ \href{../syntax/modules.html#syntax-start}{\mathsf{func}}~x \}\)

    +
      +

    • The function \(C.\href{../valid/conventions.html#context}{\mathsf{funcs}}[x]\) must be defined in the context.

      • +

    • The type of \(C.\href{../valid/conventions.html#context}{\mathsf{funcs}}[x]\) must be \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\).

      • +

    • Then the start function is valid.

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{funcs}}[x] = [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [] +}{ + C \href{../valid/modules.html#valid-start}{\vdash} \{ \href{../syntax/modules.html#syntax-start}{\mathsf{func}}~x \} \mathrel{\mbox{ok}} +}\]
    +
    +
    +
    +

    Exports

    +

    Exports \(\href{../syntax/modules.html#syntax-export}{\mathit{export}}\) and export descriptions \(\href{../syntax/modules.html#syntax-exportdesc}{\mathit{exportdesc}}\) are classified by their external type.

    +
    +

    \(\{ \href{../syntax/modules.html#syntax-export}{\mathsf{name}}~\href{../syntax/values.html#syntax-name}{\mathit{name}}, \href{../syntax/modules.html#syntax-export}{\mathsf{desc}}~\href{../syntax/modules.html#syntax-exportdesc}{\mathit{exportdesc}} \}\)

    +
      +

    • The export description \(\href{../syntax/modules.html#syntax-exportdesc}{\mathit{exportdesc}}\) must be valid with external type \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}\).

      • +

    • Then the export is valid with external type \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}\).

      • +
    +
    +\[\frac{ + C \href{../valid/modules.html#valid-exportdesc}{\vdash} \href{../syntax/modules.html#syntax-exportdesc}{\mathit{exportdesc}} : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}} +}{ + C \href{../valid/modules.html#valid-export}{\vdash} \{ \href{../syntax/modules.html#syntax-export}{\mathsf{name}}~\href{../syntax/values.html#syntax-name}{\mathit{name}}, \href{../syntax/modules.html#syntax-export}{\mathsf{desc}}~\href{../syntax/modules.html#syntax-exportdesc}{\mathit{exportdesc}} \} : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}} +}\]
    +
    +
    +

    \(\href{../syntax/modules.html#syntax-exportdesc}{\mathsf{func}}~x\)

    +
      +

    • The function \(C.\href{../valid/conventions.html#context}{\mathsf{funcs}}[x]\) must be defined in the context.

      • +

    • Then the export description is valid with external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~C.\href{../valid/conventions.html#context}{\mathsf{funcs}}[x]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{funcs}}[x] = \href{../syntax/types.html#syntax-functype}{\mathit{functype}} +}{ + C \href{../valid/modules.html#valid-exportdesc}{\vdash} \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{func}}~x : \href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}} +}\]
    +
    +
    +

    \(\href{../syntax/modules.html#syntax-exportdesc}{\mathsf{table}}~x\)

    +
      +

    • The table \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\) must be defined in the context.

      • +

    • Then the export description is valid with external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{tables}}[x] = \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} +}{ + C \href{../valid/modules.html#valid-exportdesc}{\vdash} \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{table}}~x : \href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} +}\]
    +
    +
    +

    \(\href{../syntax/modules.html#syntax-exportdesc}{\mathsf{mem}}~x\)

    +
      +

    • The memory \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}[x]\) must be defined in the context.

      • +

    • Then the export description is valid with external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~C.\href{../valid/conventions.html#context}{\mathsf{mems}}[x]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{mems}}[x] = \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} +}{ + C \href{../valid/modules.html#valid-exportdesc}{\vdash} \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{mem}}~x : \href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} +}\]
    +
    +
    +

    \(\href{../syntax/modules.html#syntax-exportdesc}{\mathsf{global}}~x\)

    +
      +

    • The global \(C.\href{../valid/conventions.html#context}{\mathsf{globals}}[x]\) must be defined in the context.

      • +

    • Then the export description is valid with external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~C.\href{../valid/conventions.html#context}{\mathsf{globals}}[x]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{globals}}[x] = \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} +}{ + C \href{../valid/modules.html#valid-exportdesc}{\vdash} \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{global}}~x : \href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} +}\]
    +
    +
    +
    +

    Imports

    +

    Imports \(\href{../syntax/modules.html#syntax-import}{\mathit{import}}\) and import descriptions \(\href{../syntax/modules.html#syntax-importdesc}{\mathit{importdesc}}\) are classified by external types.

    +
    +

    \(\{ \href{../syntax/modules.html#syntax-import}{\mathsf{module}}~\href{../syntax/values.html#syntax-name}{\mathit{name}}_1, \href{../syntax/modules.html#syntax-import}{\mathsf{name}}~\href{../syntax/values.html#syntax-name}{\mathit{name}}_2, \href{../syntax/modules.html#syntax-import}{\mathsf{desc}}~\href{../syntax/modules.html#syntax-importdesc}{\mathit{importdesc}} \}\)

    +
      +

    • The import description \(\href{../syntax/modules.html#syntax-importdesc}{\mathit{importdesc}}\) must be valid with type \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}\).

      • +

    • Then the import is valid with type \(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}\).

      • +
    +
    +\[\frac{ + C \href{../valid/modules.html#valid-importdesc}{\vdash} \href{../syntax/modules.html#syntax-importdesc}{\mathit{importdesc}} : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}} +}{ + C \href{../valid/modules.html#valid-import}{\vdash} \{ \href{../syntax/modules.html#syntax-import}{\mathsf{module}}~\href{../syntax/values.html#syntax-name}{\mathit{name}}_1, \href{../syntax/modules.html#syntax-import}{\mathsf{name}}~\href{../syntax/values.html#syntax-name}{\mathit{name}}_2, \href{../syntax/modules.html#syntax-import}{\mathsf{desc}}~\href{../syntax/modules.html#syntax-importdesc}{\mathit{importdesc}} \} : \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}} +}\]
    +
    +
    +

    \(\href{../syntax/modules.html#syntax-importdesc}{\mathsf{func}}~x\)

    +
      +

    • The function \(C.\href{../valid/conventions.html#context}{\mathsf{types}}[x]\) must be defined in the context.

      • +

    • Let \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\) be the function type \(C.\href{../valid/conventions.html#context}{\mathsf{types}}[x]\).

      • +

    • Then the import description is valid with type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~[t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{types}}[x] = [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}{ + C \href{../valid/modules.html#valid-importdesc}{\vdash} \href{../syntax/modules.html#syntax-importdesc}{\mathsf{func}}~x : \href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~[t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] +}\]
    +
    +
    +

    \(\href{../syntax/modules.html#syntax-importdesc}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\)

    +
      +

    • The table type \(\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\) must be valid.

      • +

    • Then the import description is valid with type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\).

      • +
    +
    +\[\frac{ + \href{../valid/modules.html#valid-table}{\vdash} \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} \mathrel{\mbox{ok}} +}{ + C \href{../valid/modules.html#valid-importdesc}{\vdash} \href{../syntax/modules.html#syntax-importdesc}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} : \href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} +}\]
    +
    +
    +

    \(\href{../syntax/modules.html#syntax-importdesc}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\)

    +
      +

    • The memory type \(\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\) must be valid.

      • +

    • Then the import description is valid with type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\).

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-memtype}{\vdash} \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} \mathrel{\mbox{ok}} +}{ + C \href{../valid/modules.html#valid-importdesc}{\vdash} \href{../syntax/modules.html#syntax-importdesc}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} : \href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} +}\]
    +
    +
    +

    \(\href{../syntax/modules.html#syntax-importdesc}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}\)

    +
      +

    • The global type \(\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}\) must be valid.

      • +

    • Then the import description is valid with type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}\).

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-globaltype}{\vdash} \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} \mathrel{\mbox{ok}} +}{ + C \href{../valid/modules.html#valid-importdesc}{\vdash} \href{../syntax/modules.html#syntax-importdesc}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} : \href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} +}\]
    +
    +
    +
    +

    Modules

    +

    Modules are classified by their mapping from the external types of their imports to those of their exports.

    +

    A module is entirely closed, +that is, its components can only refer to definitions that appear in the module itself. +Consequently, no initial context is required. +Instead, the context \(C\) for validation of the module’s content is constructed from the definitions in the module.

    +
      +

    • Let \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}\) be the module to validate.

      • +

    • Let \(C\) be a context where:

      +
        +

      • \(C.\href{../valid/conventions.html#context}{\mathsf{types}}\) is \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{types}}\),

        • +

      • \(C.\href{../valid/conventions.html#context}{\mathsf{funcs}}\) is \(\href{../syntax/types.html#syntax-externtype}{\mathrm{funcs}}(\mathit{it}^\ast)\) concatenated with \(\mathit{ft}^\ast\), +with the import’s external types \(\mathit{it}^\ast\) and the internal function types \(\mathit{ft}^\ast\) as determined below,

        • +

      • \(C.\href{../valid/conventions.html#context}{\mathsf{tables}}\) is \(\href{../syntax/types.html#syntax-externtype}{\mathrm{tables}}(\mathit{it}^\ast)\) concatenated with \(\mathit{tt}^\ast\), +with the import’s external types \(\mathit{it}^\ast\) and the internal table types \(\mathit{tt}^\ast\) as determined below,

        • +

      • \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}\) is \(\href{../syntax/types.html#syntax-externtype}{\mathrm{mems}}(\mathit{it}^\ast)\) concatenated with \(\mathit{mt}^\ast\), +with the import’s external types \(\mathit{it}^\ast\) and the internal memory types \(\mathit{mt}^\ast\) as determined below,

        • +

      • \(C.\href{../valid/conventions.html#context}{\mathsf{globals}}\) is \(\href{../syntax/types.html#syntax-externtype}{\mathrm{globals}}(\mathit{it}^\ast)\) concatenated with \(\mathit{gt}^\ast\), +with the import’s external types \(\mathit{it}^\ast\) and the internal global types \(\mathit{gt}^\ast\) as determined below,

        • +

      • \(C.\href{../valid/conventions.html#context}{\mathsf{elems}}\) is \({\mathit{rt}}^\ast\) as determined below,

        • +

      • \(C.\href{../valid/conventions.html#context}{\mathsf{datas}}\) is \({\mathrel{\mbox{ok}}}^n\), where \(n\) is the length of the vector \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{datas}}\),

        • +

      • \(C.\href{../valid/conventions.html#context}{\mathsf{locals}}\) is empty,

        • +

      • \(C.\href{../valid/conventions.html#context}{\mathsf{labels}}\) is empty,

        • +

      • \(C.\href{../valid/conventions.html#context}{\mathsf{return}}\) is empty.

        • +

      • \(C.\href{../valid/conventions.html#context}{\mathsf{refs}}\) is the set \(\href{../syntax/modules.html#syntax-funcidx}{\mathrm{funcidx}}(\href{../syntax/modules.html#syntax-module}{\mathit{module}} \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../syntax/modules.html#syntax-module}{\mathsf{funcs}} = \epsilon \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../syntax/modules.html#syntax-module}{\mathsf{start}} = \epsilon)\), i.e., the set of function indices occurring in the module, except in its functions or start function.

        • +
      +
      • +

    • Let \(C'\) be the context where:

      +
        +

      • \(C'.\href{../valid/conventions.html#context}{\mathsf{globals}}\) is the sequence \(\href{../syntax/types.html#syntax-externtype}{\mathrm{globals}}(\mathit{it}^\ast)\),

        • +

      • \(C'.\href{../valid/conventions.html#context}{\mathsf{funcs}}\) is the same as \(C.\href{../valid/conventions.html#context}{\mathsf{funcs}}\),

        • +

      • \(C'.\href{../valid/conventions.html#context}{\mathsf{refs}}\) is the same as \(C.\href{../valid/conventions.html#context}{\mathsf{refs}}\),

        • +

      • all other fields are empty.

        • +
      +
      • +

    • Under the context \(C\):

      +
        +

      • For each \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{types}}\), +the function type \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}_i\) must be valid.

        • +

      • For each \(\href{../syntax/modules.html#syntax-func}{\mathit{func}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{funcs}}\), +the definition \(\href{../syntax/modules.html#syntax-func}{\mathit{func}}_i\) must be valid with a function type \(\mathit{ft}_i\).

        • +

      • For each \(\href{../syntax/modules.html#syntax-table}{\mathit{table}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{tables}}\), +the definition \(\href{../syntax/modules.html#syntax-table}{\mathit{table}}_i\) must be valid with a table type \(\mathit{tt}_i\).

        • +

      • For each \(\href{../syntax/modules.html#syntax-mem}{\mathit{mem}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{mems}}\), +the definition \(\href{../syntax/modules.html#syntax-mem}{\mathit{mem}}_i\) must be valid with a memory type \(\mathit{mt}_i\).

        • +

      • For each \(\href{../syntax/modules.html#syntax-global}{\mathit{global}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{globals}}\):

        +
          +

        • Under the context \(C'\), +the definition \(\href{../syntax/modules.html#syntax-global}{\mathit{global}}_i\) must be valid with a global type \(\mathit{gt}_i\).

          • +
        +
        • +

      • For each \(\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{elems}}\), +the segment \(\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}_i\) must be valid with reference type \(\mathit{rt}_i\).

        • +

      • For each \(\href{../syntax/modules.html#syntax-data}{\mathit{data}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{datas}}\), +the segment \(\href{../syntax/modules.html#syntax-data}{\mathit{data}}_i\) must be valid.

        • +

      • If \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{start}}\) is non-empty, +then \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{start}}\) must be valid.

        • +

      • For each \(\href{../syntax/modules.html#syntax-import}{\mathit{import}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{imports}}\), +the segment \(\href{../syntax/modules.html#syntax-import}{\mathit{import}}_i\) must be valid with an external type \(\mathit{it}_i\).

        • +

      • For each \(\href{../syntax/modules.html#syntax-export}{\mathit{export}}_i\) in \(\href{../syntax/modules.html#syntax-module}{\mathit{module}}.\href{../syntax/modules.html#syntax-module}{\mathsf{exports}}\), +the segment \(\href{../syntax/modules.html#syntax-export}{\mathit{export}}_i\) must be valid with external type \(\mathit{et}_i\).

        • +
      +
      • +

    • The length of \(C.\href{../valid/conventions.html#context}{\mathsf{mems}}\) must not be larger than \(1\).

      • +

    • All export names \(\href{../syntax/modules.html#syntax-export}{\mathit{export}}_i.\href{../syntax/modules.html#syntax-export}{\mathsf{name}}\) must be different.

      • +

    • Let \(\mathit{ft}^\ast\) be the concatenation of the internal function types \(\mathit{ft}_i\), in index order.

      • +

    • Let \(\mathit{tt}^\ast\) be the concatenation of the internal table types \(\mathit{tt}_i\), in index order.

      • +

    • Let \(\mathit{mt}^\ast\) be the concatenation of the internal memory types \(\mathit{mt}_i\), in index order.

      • +

    • Let \(\mathit{gt}^\ast\) be the concatenation of the internal global types \(\mathit{gt}_i\), in index order.

      • +

    • Let \(\mathit{rt}^\ast\) be the concatenation of the reference types \(\mathit{rt}_i\), in index order.

      • +

    • Let \(\mathit{it}^\ast\) be the concatenation of external types \(\mathit{it}_i\) of the imports, in index order.

      • +

    • Let \(\mathit{et}^\ast\) be the concatenation of external types \(\mathit{et}_i\) of the exports, in index order.

      • +

    • Then the module is valid with external types \(\mathit{it}^\ast \href{../syntax/types.html#syntax-functype}{\rightarrow} \mathit{et}^\ast\).

      • +
    +
    +\[\begin{split}\frac{ + \begin{array}{@{}c@{}} + (\href{../valid/types.html#valid-functype}{\vdash} \href{../syntax/types.html#syntax-functype}{\mathit{type}} \mathrel{\mbox{ok}})^\ast + \quad + (C \href{../valid/modules.html#valid-func}{\vdash} \href{../syntax/modules.html#syntax-func}{\mathit{func}} : \mathit{ft})^\ast + \quad + (C \href{../valid/modules.html#valid-table}{\vdash} \href{../syntax/modules.html#syntax-table}{\mathit{table}} : \mathit{tt})^\ast + \quad + (C \href{../valid/modules.html#valid-mem}{\vdash} \href{../syntax/modules.html#syntax-mem}{\mathit{mem}} : \mathit{mt})^\ast + \quad + (C' \href{../valid/modules.html#valid-global}{\vdash} \href{../syntax/modules.html#syntax-global}{\mathit{global}} : \mathit{gt})^\ast + \\ + (C \href{../valid/modules.html#valid-elem}{\vdash} \href{../syntax/modules.html#syntax-elem}{\mathit{elem}} : \mathit{rt})^\ast + \quad + (C \href{../valid/modules.html#valid-data}{\vdash} \href{../syntax/modules.html#syntax-data}{\mathit{data}} \mathrel{\mbox{ok}})^n + \quad + (C \href{../valid/modules.html#valid-start}{\vdash} \href{../syntax/modules.html#syntax-start}{\mathit{start}} \mathrel{\mbox{ok}})^? + \quad + (C \href{../valid/modules.html#valid-import}{\vdash} \href{../syntax/modules.html#syntax-import}{\mathit{import}} : \mathit{it})^\ast + \quad + (C \href{../valid/modules.html#valid-export}{\vdash} \href{../syntax/modules.html#syntax-export}{\mathit{export}} : \mathit{et})^\ast + \\ + \mathit{ift}^\ast = \href{../syntax/types.html#syntax-externtype}{\mathrm{funcs}}(\mathit{it}^\ast) + \qquad + \mathit{itt}^\ast = \href{../syntax/types.html#syntax-externtype}{\mathrm{tables}}(\mathit{it}^\ast) + \qquad + \mathit{imt}^\ast = \href{../syntax/types.html#syntax-externtype}{\mathrm{mems}}(\mathit{it}^\ast) + \qquad + \mathit{igt}^\ast = \href{../syntax/types.html#syntax-externtype}{\mathrm{globals}}(\mathit{it}^\ast) + \\ + x^\ast = \href{../syntax/modules.html#syntax-funcidx}{\mathrm{funcidx}}(\href{../syntax/modules.html#syntax-module}{\mathit{module}} \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../syntax/modules.html#syntax-module}{\mathsf{funcs}} = \epsilon \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../syntax/modules.html#syntax-module}{\mathsf{start}} = \epsilon) + \\ + C = \{ \href{../valid/conventions.html#context}{\mathsf{types}}~\href{../syntax/types.html#syntax-functype}{\mathit{type}}^\ast, \href{../valid/conventions.html#context}{\mathsf{funcs}}~\mathit{ift}^\ast\,\mathit{ft}^\ast, \href{../valid/conventions.html#context}{\mathsf{tables}}~\mathit{itt}^\ast\,\mathit{tt}^\ast, \href{../valid/conventions.html#context}{\mathsf{mems}}~\mathit{imt}^\ast\,\mathit{mt}^\ast, \href{../valid/conventions.html#context}{\mathsf{globals}}~\mathit{igt}^\ast\,\mathit{gt}^\ast, \href{../valid/conventions.html#context}{\mathsf{elems}}~\mathit{rt}^\ast, \href{../valid/conventions.html#context}{\mathsf{datas}}~{\mathrel{\mbox{ok}}}^n, \href{../valid/conventions.html#context}{\mathsf{refs}}~x^\ast \} + \\ + C' = \{ \href{../valid/conventions.html#context}{\mathsf{globals}}~\mathit{igt}^\ast, \href{../valid/conventions.html#context}{\mathsf{funcs}}~(C.\href{../valid/conventions.html#context}{\mathsf{funcs}}), \href{../valid/conventions.html#context}{\mathsf{refs}}~(C.\href{../valid/conventions.html#context}{\mathsf{refs}}) \} + \qquad + |C.\href{../valid/conventions.html#context}{\mathsf{mems}}| \leq 1 + \qquad + (\href{../syntax/modules.html#syntax-export}{\mathit{export}}.\href{../syntax/modules.html#syntax-export}{\mathsf{name}})^\ast ~\mathrm{disjoint} + \\ + \href{../syntax/modules.html#syntax-module}{\mathit{module}} = \{ + \begin{array}[t]{@{}l@{}} + \href{../syntax/modules.html#syntax-module}{\mathsf{types}}~\href{../syntax/types.html#syntax-functype}{\mathit{type}}^\ast, + \href{../syntax/modules.html#syntax-module}{\mathsf{funcs}}~\href{../syntax/modules.html#syntax-func}{\mathit{func}}^\ast, + \href{../syntax/modules.html#syntax-module}{\mathsf{tables}}~\href{../syntax/modules.html#syntax-table}{\mathit{table}}^\ast, + \href{../syntax/modules.html#syntax-module}{\mathsf{mems}}~\href{../syntax/modules.html#syntax-mem}{\mathit{mem}}^\ast, + \href{../syntax/modules.html#syntax-module}{\mathsf{globals}}~\href{../syntax/modules.html#syntax-global}{\mathit{global}}^\ast, \\ + \href{../syntax/modules.html#syntax-module}{\mathsf{elems}}~\href{../syntax/modules.html#syntax-elem}{\mathit{elem}}^\ast, + \href{../syntax/modules.html#syntax-module}{\mathsf{datas}}~\href{../syntax/modules.html#syntax-data}{\mathit{data}}^n, + \href{../syntax/modules.html#syntax-module}{\mathsf{start}}~\href{../syntax/modules.html#syntax-start}{\mathit{start}}^?, + \href{../syntax/modules.html#syntax-module}{\mathsf{imports}}~\href{../syntax/modules.html#syntax-import}{\mathit{import}}^\ast, + \href{../syntax/modules.html#syntax-module}{\mathsf{exports}}~\href{../syntax/modules.html#syntax-export}{\mathit{export}}^\ast \} + \end{array} + \end{array} +}{ + \href{../valid/modules.html#valid-module}{\vdash} \href{../syntax/modules.html#syntax-module}{\mathit{module}} : \mathit{it}^\ast \href{../syntax/types.html#syntax-functype}{\rightarrow} \mathit{et}^\ast +}\end{split}\]
    +
    +

    Note

    +

    Most definitions in a module – particularly functions – are mutually recursive. +Consequently, the definition of the context \(C\) in this rule is recursive: +it depends on the outcome of validation of the function, table, memory, and global definitions contained in the module, +which itself depends on \(C\). +However, this recursion is just a specification device. +All types needed to construct \(C\) can easily be determined from a simple pre-pass over the module that does not perform any actual validation.

    +

    Globals, however, are not recursive. +The effect of defining the limited context \(C'\) for validating the module’s globals is that their initialization expressions can only access functions and imported globals and nothing else.

    +
    +
    +

    Note

    +

    The restriction on the number of memories may be lifted in future versions of WebAssembly.

    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/core/valid/types.html b/core/valid/types.html new file mode 100644 index 00000000..380c829f --- /dev/null +++ b/core/valid/types.html @@ -0,0 +1,371 @@ + + + + + + + + + Types — WebAssembly 2.0 + stringref (Draft 2022-04-27) + + + + + + + + + + + + + + + + + + + +
    + + +
    +
    + + +
    + +
    +

    Types

    +

    Most types are universally valid. +However, restrictions apply to limits, which must be checked during validation. +Moreover, block types are converted to plain function types for ease of processing.

    +
    +

    Limits

    +

    Limits must have meaningful bounds that are within a given range.

    +
    +

    \(\{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m^? \}\)

    +
      +

    • The value of \(n\) must not be larger than \(k\).

      • +

    • If the maximum \(m^?\) is not empty, then:

      +
        +

      • Its value must not be larger than \(k\).

        • +

      • Its value must not be smaller than \(n\).

        • +
      +
      • +

    • Then the limit is valid within range \(k\).

      • +
    +
    +\[\frac{ + n \leq k + \qquad + (m \leq k)^? + \qquad + (n \leq m)^? +}{ + \href{../valid/types.html#valid-limits}{\vdash} \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m^? \} : k +}\]
    +
    +
    +
    +

    Block Types

    +

    Block types may be expressed in one of two forms, both of which are converted to plain function types by the following rules.

    +
    +

    \(\href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}}\)

    +
      +

    • The type \(C.\href{../valid/conventions.html#context}{\mathsf{types}}[\href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}}]\) must be defined in the context.

      • +

    • Then the block type is valid as function type \(C.\href{../valid/conventions.html#context}{\mathsf{types}}[\href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}}]\).

      • +
    +
    +\[\frac{ + C.\href{../valid/conventions.html#context}{\mathsf{types}}[\href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}}] = \href{../syntax/types.html#syntax-functype}{\mathit{functype}} +}{ + C \href{../valid/types.html#valid-blocktype}{\vdash} \href{../syntax/modules.html#syntax-typeidx}{\mathit{typeidx}} : \href{../syntax/types.html#syntax-functype}{\mathit{functype}} +}\]
    +
    +
    +

    \([\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}^?]\)

    +
      +

    • The block type is valid as function type \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}^?]\).

      • +
    +
    +\[\frac{ +}{ + C \href{../valid/types.html#valid-blocktype}{\vdash} [\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}^?] : [] \href{../syntax/types.html#syntax-functype}{\rightarrow} [\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}^?] +}\]
    +
    +
    +
    +

    Function Types

    +

    Function types are always valid.

    +
    +

    \([t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^m]\)

    +
      +

    • The function type is valid.

      • +
    +
    +\[\frac{ +}{ + \href{../valid/types.html#valid-functype}{\vdash} [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] \mathrel{\mbox{ok}} +}\]
    +
    +
    +
    +

    Table Types

    +
    +

    \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}\)

    +
      +

    • The limits \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}\) must be valid within range \(2^{32}-1\).

      • +

    • Then the table type is valid.

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-limits}{\vdash} \href{../syntax/types.html#syntax-limits}{\mathit{limits}} : 2^{32} - 1 +}{ + \href{../valid/types.html#valid-tabletype}{\vdash} \href{../syntax/types.html#syntax-limits}{\mathit{limits}}~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}} \mathrel{\mbox{ok}} +}\]
    +
    +
    +
    +

    Memory Types

    +
    +

    \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}\)

    +
      +

    • The limits \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}\) must be valid within range \(2^{16}\).

      • +

    • Then the memory type is valid.

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-limits}{\vdash} \href{../syntax/types.html#syntax-limits}{\mathit{limits}} : 2^{16} +}{ + \href{../valid/types.html#valid-memtype}{\vdash} \href{../syntax/types.html#syntax-limits}{\mathit{limits}} \mathrel{\mbox{ok}} +}\]
    +
    +
    +
    +

    Global Types

    +
    +

    \(\href{../syntax/types.html#syntax-mut}{\mathit{mut}}~\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}}\)

    +
      +

    • The global type is valid.

      • +
    +
    +\[\frac{ +}{ + \href{../valid/types.html#valid-globaltype}{\vdash} \href{../syntax/types.html#syntax-mut}{\mathit{mut}}~\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}} \mathrel{\mbox{ok}} +}\]
    +
    +
    +
    +

    External Types

    +
    +

    \(\href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\)

    +
      +

    • The function type \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\) must be valid.

      • +

    • Then the external type is valid.

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-functype}{\vdash} \href{../syntax/types.html#syntax-functype}{\mathit{functype}} \mathrel{\mbox{ok}} +}{ + \href{../valid/types.html#valid-externtype}{\vdash} \href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}} \mathrel{\mbox{ok}} +}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\)

    +
      +

    • The table type \(\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}\) must be valid.

      • +

    • Then the external type is valid.

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-tabletype}{\vdash} \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} \mathrel{\mbox{ok}} +}{ + \href{../valid/types.html#valid-externtype}{\vdash} \href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} \mathrel{\mbox{ok}} +}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\)

    +
      +

    • The memory type \(\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}\) must be valid.

      • +

    • Then the external type is valid.

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-memtype}{\vdash} \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} \mathrel{\mbox{ok}} +}{ + \href{../valid/types.html#valid-externtype}{\vdash} \href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} \mathrel{\mbox{ok}} +}\]
    +
    +
    +

    \(\href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}\)

    +
      +

    • The global type \(\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}\) must be valid.

      • +

    • Then the external type is valid.

      • +
    +
    +\[\frac{ + \href{../valid/types.html#valid-globaltype}{\vdash} \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} \mathrel{\mbox{ok}} +}{ + \href{../valid/types.html#valid-externtype}{\vdash} \href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} \mathrel{\mbox{ok}} +}\]
    +
    +
    +
    +

    Import Subtyping

    +

    When instantiating a module, +external values must be provided whose types are matched against the respective external types classifying each import. +In some cases, this allows for a simple form of subtyping, as defined here.

    +
    +

    Limits

    +

    Limits \(\{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n_1, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m_1^? \}\) match limits \(\{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n_2, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m_2^? \}\) if and only if:

    +
      +

    • \(n_1\) is larger than or equal to \(n_2\).

      • +

    • Either:

      +
        +

      • \(m_2^?\) is empty.

        • +
      +
      • +

    • Or:

      +
        +

      • Both \(m_1^?\) and \(m_2^?\) are non-empty.

        • +

      • \(m_1\) is smaller than or equal to \(m_2\).

        • +
      +
      • +
    +
    +\[\begin{split}~\\[-1ex] +\frac{ + n_1 \geq n_2 +}{ + \href{../exec/modules.html#match-limits}{\vdash} \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n_1, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m_1^? \} \href{../exec/modules.html#match-limits}{\leq} \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n_2, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~\epsilon \} +} +\quad +\frac{ + n_1 \geq n_2 + \qquad + m_1 \leq m_2 +}{ + \href{../exec/modules.html#match-limits}{\vdash} \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n_1, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m_1 \} \href{../exec/modules.html#match-limits}{\leq} \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n_2, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m_2 \} +}\end{split}\]
    +
    +
    +

    Functions

    +

    An external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}_1\) matches \(\href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}_2\) if and only if:

    +
      +

    • Both \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}_1\) and \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}_2\) are the same.

      • +
    +
    +\[\begin{split}~\\[-1ex] +\frac{ +}{ + \href{../exec/modules.html#match-externtype}{\vdash} \href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}} \href{../exec/modules.html#match-externtype}{\leq} \href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}} +}\end{split}\]
    +
    +
    +

    Tables

    +

    An external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_1~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}_1)\) matches \(\href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_2~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}_2)\) if and only if:

    +
      +

    • Limits \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_1\) match \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_2\).

      • +

    • Both \(\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}_1\) and \(\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}_2\) are the same.

      • +
    +
    +\[\frac{ + \href{../exec/modules.html#match-limits}{\vdash} \href{../syntax/types.html#syntax-limits}{\mathit{limits}}_1 \href{../exec/modules.html#match-limits}{\leq} \href{../syntax/types.html#syntax-limits}{\mathit{limits}}_2 +}{ + \href{../exec/modules.html#match-externtype}{\vdash} \href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_1~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}) \href{../exec/modules.html#match-externtype}{\leq} \href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_2~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}}) +}\]
    +
    +
    +

    Memories

    +

    An external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_1\) matches \(\href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_2\) if and only if:

    +
      +

    • Limits \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_1\) match \(\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_2\).

      • +
    +
    +\[\frac{ + \href{../exec/modules.html#match-limits}{\vdash} \href{../syntax/types.html#syntax-limits}{\mathit{limits}}_1 \href{../exec/modules.html#match-limits}{\leq} \href{../syntax/types.html#syntax-limits}{\mathit{limits}}_2 +}{ + \href{../exec/modules.html#match-externtype}{\vdash} \href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_1 \href{../exec/modules.html#match-externtype}{\leq} \href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-limits}{\mathit{limits}}_2 +}\]
    +
    +
    +

    Globals

    +

    An external type \(\href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}_1\) matches \(\href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}_2\) if and only if:

    +
      +

    • Both \(\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}_1\) and \(\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}_2\) are the same.

      • +
    +
    +\[\begin{split}~\\[-1ex] +\frac{ +}{ + \href{../exec/modules.html#match-externtype}{\vdash} \href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} \href{../exec/modules.html#match-externtype}{\leq} \href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} +}\end{split}\]
    +
    +
    +
    + + +
    + +
    +
    +
    +
    +
    + ©2022, WebAssembly Community Group. + +
    + + + + + + \ No newline at end of file diff --git a/index.html b/index.html new file mode 100644 index 00000000..37eed976 --- /dev/null +++ b/index.html @@ -0,0 +1,74 @@ + + + + + + + WebAssembly Specifications + + + + + + +
    +
    + +

    WebAssembly Specifications

    + +

    +To support the embedding of WebAssembly into different environments, its specification is split into layers that are specified in separate documents. +

    + +

    Core specification

    + +

    Defines the semantics of WebAssembly modules independent from a concrete embedding. + The WebAssembly core is specified in a single document:

    + +
      +
    • +

      WebAssembly: + defines the structure of WebAssembly modules, their instruction set, and their representation + in binary and text format, as well as the semantics of validation, + instantiation, and execution. +

      + +
      • +
    + +

    Embedder specifications

    + +

    Define application programming interfaces (APIs) enabling the use of WebAssembly modules in concrete embedding environments. + Currently, two APIs are specified:

    + +
      +

    • JavaScript Embedding: defines JavaScript classes and objects for accessing WebAssembly from within JavaScript, including methods for validation, compilation, instantiation, and classes for representing and manipulating imports and exports as JavaScript objects.

      + +
      • + +

    • Web Embedding: defines extensions to the JavaScript API made available specifically in web browsers, in particular, an interface for streaming compilation and instantiation from origin-bound Response types.

      + +
      • +
    + +

    + Source for these documents is available + here. +

    + +
    +
    + + + diff --git a/js-api/index.html b/js-api/index.html new file mode 100644 index 00000000..0dfdf601 --- /dev/null +++ b/js-api/index.html @@ -0,0 +1,4177 @@ + + + + + WebAssembly JavaScript Interface + + + + + + + + + + + + + + + +
    +

    +

    WebAssembly JavaScript Interface

    +

    Editor’s Draft,

    +
    + More details about this document +
    +
    +
    This version: +
    https://webassembly.github.io/spec/js-api/ +
    Latest published version: +
    https://www.w3.org/TR/wasm-js-api-2/ +
    Feedback: +
    Inline In Spec +
    Editor: +
    Ms2ger (Igalia) +
    Issue Tracking: +
    GitHub Issues +
    +
    +
    +
    +

    Copyright © 2022 W3C® (MIT, ERCIM, Keio, Beihang). W3C liability, trademark and permissive document license rules apply.

    +
    +
    +
    +

    Abstract

    +

    This document provides an explicit JavaScript API for interacting with WebAssembly.

    + This is part of a collection of related documents: +the Core WebAssembly Specification, +the WebAssembly JS Interface, +and the WebAssembly Web API. +
    +

    Status of this document

    +
    +

    This is a public copy of the editors’ draft. + It is provided for discussion only and may change at any moment. + Its publication here does not imply endorsement of its contents by W3C. + Don’t cite this document other than as work in progress.

    +

    GitHub Issues are preferred for discussion of this specification. + All issues and comments are archived.

    +

    This document was produced by the WebAssembly Working Group.

    +

    This document was produced by a group operating under + the W3C Patent Policy. + W3C maintains a public list of any patent disclosures made in connection with the deliverables of the group; + that page also includes instructions for disclosing a patent. + An individual who has actual knowledge of a patent which the individual believes contains Essential Claim(s) must disclose the information in accordance with section 6 of the W3C Patent Policy.

    +

    This document is governed by the 2 November 2021 W3C Process Document.

    +

    +
    +
    + +
    +

    This API provides a way to access WebAssembly [WEBASSEMBLY] through a bridge to explicitly construct modules from JavaScript [ECMASCRIPT].

    +

    1. Sample API Usage

    +

    This section is non-normative.

    +

    Given demo.wat (encoded to demo.wasm):

    +
    (module
+    (import "js" "import1" (func $i1))
+    (import "js" "import2" (func $i2))
+    (func $main (call $i1))
+    (start $main)
+    (func (export "f") (call $i2))
+)
+
    +

    and the following JavaScript, run in a browser:

    +
    var importObj = {js: {
+    import1: () => console.log("hello,"),
+    import2: () => console.log("world!")
+}};
+fetch('demo.wasm').then(response =>
+    response.arrayBuffer()
+).then(buffer =>
+    WebAssembly.instantiate(buffer, importObj)
+).then(({module, instance}) =>
+    instance.exports.f()
+);
+
    +

    2. Notation

    +

    This specification depends on the Infra Standard. [INFRA]

    +

    The WebAssembly sequence type is equivalent to the list type defined there; values of one +are treated as values of the other transparently.

    +

    3. Internal storage

    +

    3.1. Interaction of the WebAssembly Store with JavaScript

    +

    Note: WebAssembly semantics are defined in terms of an abstract store, representing the state of the WebAssembly abstract machine. WebAssembly operations take a store and return an updated store.

    +

    Each agent has an associated store. When a new agent is created, its associated store is set to the result of store_init().

    +

    Note: In this specification, no WebAssembly-related objects, memory or addresses can be shared among agents in an agent cluster. In a future version of WebAssembly, this may change.

    +

    Elements of the WebAssembly store may be identified with JavaScript values. In particular, each WebAssembly memory instance with a corresponding Memory object is identified with a JavaScript Data Block; modifications to this Data Block are identified to updating the agent’s store to a store which reflects those changes, and vice versa.

    +

    3.2. WebAssembly JS Object Caches

    +

    Note: There are several WebAssembly objects that may have a corresponding JavaScript object. The correspondence is stored in a per-agent mapping from WebAssembly addresses to JavaScript objects. +This mapping is used to ensure that, for a given agent, there exists at most one JavaScript object for a particular WebAssembly address. However, this property does not hold for shared objects.

    +

    Each agent is associated with the following ordered maps:

    + +

    4. The WebAssembly Namespace

    +
    dictionary WebAssemblyInstantiatedSource {
+    required Module module;
+    required Instance instance;
+};
+
+[Exposed=(Window,Worker,Worklet)]
+namespace WebAssembly {
+    boolean validate(BufferSource bytes);
+    Promise<Module> compile(BufferSource bytes);
+
+    Promise<WebAssemblyInstantiatedSource> instantiate(
+        BufferSource bytes, optional object importObject);
+
+    Promise<Instance> instantiate(
+        Module moduleObject, optional object importObject);
+};
+
    +
    + To compile a WebAssembly module from source bytes bytes, perform the following steps: +
      +
    1. +

      Let module be module_decode(bytes). If module is error, return error.

      +
    2. +

      If module_validate(module) is error, return error.

      +
    3. +

      Return module.

      +
    +
    +
    + The validate(bytes) method, when invoked, performs the following steps: +
      +
    1. +

      Let stableBytes be a copy of the bytes held by the buffer bytes.

      +
    2. +

      Compile stableBytes as a WebAssembly module and store the results as module.

      +
    3. +

      If module is error, return false.

      +
    4. +

      Return true.

      +
    +
    +

    A Module object represents a single WebAssembly module. Each Module object has the following internal slots:

    +
      +
    • +

      [[Module]] : a WebAssembly module

      +
    • +

      [[Bytes]] : the source bytes of [[Module]].

      +
    +
    + To construct a WebAssembly module object from a module module and source bytes bytes, perform the following steps: +
      +
    1. +

      Let moduleObject be a new Module object.

      +
    2. +

      Set moduleObject.[[Module]] to module.

      +
    3. +

      Set moduleObject.[[Bytes]] to bytes.

      +
    4. +

      Return moduleObject.

      +
    +
    +
    + To asynchronously compile a WebAssembly module from source bytes bytes, using optional task source taskSource, perform the following steps: +
      +
    1. +

      Let promise be a new promise.

      +
    2. +

      Run the following steps in parallel:

      +
        +
      1. +

        Compile the WebAssembly module bytes and store the result as module.

        +
      2. +

        Queue a task to perform the following steps. If taskSource was provided, queue the task on that task source.

        +
          +
        1. +

          If module is error, reject promise with a CompileError exception.

          +
        2. +

          Otherwise,

          +
            +
          1. +

            Construct a WebAssembly module object from module and bytes, and let moduleObject be the result.

            +
          2. +

            Resolve promise with moduleObject.

            +
          +
        +
      +
    3. +

      Return promise.

      +
    +
    +
    + The compile(bytes) method, when invoked, performs the following steps: +
      +
    1. +

      Let stableBytes be a copy of the bytes held by the buffer bytes.

      +
    2. +

      Asynchronously compile a WebAssembly module from stableBytes and return the result.

      +
    +
    +
    + To read the imports from a WebAssembly module module from imports object importObject, perform the following steps: +
      +
    1. +

      If module.imports is not empty, and importObject is undefined, throw a TypeError exception.

      +
    2. +

      Let imports be « ».

      +
    3. +

      For each (moduleName, componentName, externtype) of module_imports(module),

      +
        +
      1. +

        Let o be ? Get(importObject, moduleName).

        +
      2. +

        If Type(o) is not Object, throw a TypeError exception.

        +
      3. +

        Let v be ? Get(o, componentName).

        +
      4. +

        If externtype is of the form func functype,

        +
          +
        1. +

          If IsCallable(v) is false, throw a LinkError exception.

          +
        2. +

          If v has a [[FunctionAddress]] internal slot, and therefore is an Exported Function,

          +
            +
          1. +

            Let funcaddr be the value of v’s [[FunctionAddress]] internal slot.

            +
          +
        3. +

          Otherwise,

          +
            +
          1. +

            Create a host function from v and functype, and let funcaddr be the result.

            +
          2. +

            Let index be the number of external functions in imports. This value index is known as the index of the host function funcaddr.

            +
          +
        4. +

          Let externfunc be the external value func funcaddr.

          +
        5. +

          Append externfunc to imports.

          +
        +
      5. +

        If externtype is of the form global mut valtype,

        +
          +
        1. +

          If Type(v) is Number or BigInt,

          +
            +
          1. +

            If valtype is i64 and Type(v) is Number,

            +
              +
            1. +

              Throw a LinkError exception.

              +
            +
          2. +

            If valtype is not i64 and Type(v) is BigInt,

            +
              +
            1. +

              Throw a LinkError exception.

              +
            +
          3. +

            If valtype is v128,

            +
              +
            1. +

              Throw a LinkError exception.

              +
            +
          4. +

            Let value be ToWebAssemblyValue(v, valtype).

            +
          5. +

            Let store be the surrounding agent's associated store.

            +
          6. +

            Let (store, globaladdr) be global_alloc(store, const valtype, value).

            +
          7. +

            Set the surrounding agent's associated store to store.

            +
          +
        2. +

          Otherwise, if v implements Global,

          +
            +
          1. +

            Let globaladdr be v.[[Global]].

            +
          +
        3. +

          Otherwise,

          +
            +
          1. +

            Throw a LinkError exception.

            +
          +
        4. +

          Let externglobal be global globaladdr.

          +
        5. +

          Append externglobal to imports.

          +
        +
      6. +

        If externtype is of the form mem memtype,

        +
          +
        1. +

          If v does not implement Memory, throw a LinkError exception.

          +
        2. +

          Let externmem be the external value mem v.[[Memory]].

          +
        3. +

          Append externmem to imports.

          +
        +
      7. +

        If externtype is of the form table tabletype,

        +
          +
        1. +

          If v does not implement Table, throw a LinkError exception.

          +
        2. +

          Let tableaddr be v.[[Table]].

          +
        3. +

          Let externtable be the external value table tableaddr.

          +
        4. +

          Append externtable to imports.

          +
        +
      +
    4. +

      Return imports.

      +
    +

    Note: This algorithm only verifies the right kind of JavaScript values are passed. +The verification of WebAssembly type requirements is deferred to the +"instantiate the core of a WebAssembly module" algorithm.

    +
    +
    + To create an exports object from a WebAssembly module module and instance instance, perform the following steps: +
      +
    1. +

      Let exportsObject be ! ObjectCreate(null).

      +
    2. +

      For each (name, externtype) of module_exports(module),

      +
        +
      1. +

        Let externval be instance_export(instance, name).

        +
      2. +

        Assert: externval is not error.

        +
      3. +

        If externtype is of the form func functype,

        +
          +
        1. +

          Assert: externval is of the form func funcaddr.

          +
        2. +

          Let func funcaddr be externval.

          +
        3. +

          Let func be the result of creating a new Exported Function from funcaddr.

          +
        4. +

          Let value be func.

          +
        +
      4. +

        If externtype is of the form global mut globaltype,

        +
          +
        1. +

          Assert: externval is of the form global globaladdr.

          +
        2. +

          Let global globaladdr be externval.

          +
        3. +

          Let global be a new Global object created from globaladdr.

          +
        4. +

          Let value be global.

          +
        +
      5. +

        If externtype is of the form mem memtype,

        +
          +
        1. +

          Assert: externval is of the form mem memaddr.

          +
        2. +

          Let mem memaddr be externval.

          +
        3. +

          Let memory be a new Memory object created from memaddr.

          +
        4. +

          Let value be memory.

          +
        +
      6. +

        If externtype is of the form table tabletype,

        +
          +
        1. +

          Assert: externval is of the form table tableaddr.

          +
        2. +

          Let table tableaddr be externval.

          +
        3. +

          Let table be a new Table object created from tableaddr.

          +
        4. +

          Let value be table.

          +
        +
      7. +

        Let status be ! CreateDataProperty(exportsObject, name, value).

        +
      8. +

        Assert: status is true.

        +
      +

      Note: the validity and uniqueness checks performed during WebAssembly module validation ensure that each property name is valid and no properties are defined twice.

      +
    3. +

      Perform ! SetIntegrityLevel(exportsObject, "frozen").

      +
    4. +

      Return exportsObject.

      +
    +
    +
    + To initialize an instance object instanceObject from a WebAssembly module module and instance instance, perform the following steps: +
      +
    1. +

      Create an exports object from module and instance and let exportsObject be the result.

      +
    2. +

      Set instanceObject.[[Instance]] to instance.

      +
    3. +

      Set instanceObject.[[Exports]] to exportsObject.

      +
    +
    +
    + To instantiate the core of a WebAssembly module from a module module and imports imports, perform the following steps: +
      +
    1. +

      Let store be the surrounding agent's associated store.

      +
    2. +

      Let result be module_instantiate(store, module, imports).

      +
    3. +

      If result is error, throw an appropriate exception type:

      +
        +
      • +

        A LinkError exception for most cases which occur during linking.

        +
      • +

        If the error came when running the start function, throw a RuntimeError for most errors which occur from WebAssembly, or the error object propagated from inner ECMAScript code.

        +
      • +

        Another error type if appropriate, for example an out-of-memory exception, as documented in the WebAssembly error mapping.

        +
      +
    4. +

      Let (store, instance) be result.

      +
    5. +

      Set the surrounding agent's associated store to store.

      +
    6. +

      Return instance.

      +
    +
    +
    + To asynchronously instantiate a WebAssembly module from a Module moduleObject and imports importObject, perform the following steps: +
      +
    1. +

      Let promise be a new promise.

      +
    2. +

      Let module be moduleObject.[[Module]].

      +
    3. +

      Read the imports of module with imports importObject, and let imports be the result. +If this operation throws an exception, catch it, reject promise with the exception, and return promise.

      +
    4. +

      Queue a task to perform the following steps:

      +
        +
      1. +

        Instantiate the core of a WebAssembly module module with imports, and let instance be the result. +If this throws an exception, catch it, reject promise with the exception, and terminate these substeps.

        +
      2. +

        Let instanceObject be a new Instance.

        +
      3. +

        Initialize instanceObject from module and instance. +If this throws an exception, catch it, reject promise with the exception, and terminate these substeps.

        +
      4. +

        Resolve promise with instanceObject.

        +
      +
    5. +

      Return promise.

      +
    +
    +
    + To instantiate a WebAssembly module from a Module moduleObject and imports importObject, perform the following steps: +
      +
    1. +

      Let module be moduleObject.[[Module]].

      +
    2. +

      Read the imports of module with imports importObject, and let imports be the result.

      +
    3. +

      Instantiate the core of a WebAssembly module module with imports, and let instance be the result.

      +
    4. +

      Let instanceObject be a new Instance.

      +
    5. +

      Initialize instanceObject from module and instance.

      +
    6. +

      Return instanceObject.

      +
    +
    +
    + To instantiate a promise of a module promiseOfModule with imports importObject, perform the following steps: +
      +
    1. +

      Let promise be a new promise.

      +
    2. +

      Upon fulfillment of promiseOfModule with value module:

      +
        +
      1. +

        Instantiate the WebAssembly module module importing importObject, and let instance be the result. If this throws an exception, catch it, reject promise with the exception, and abort these substeps.

        +
      2. +

        Let result be the WebAssemblyInstantiatedSource value «[ "module" → module, "instance" → instance ]».

        +
      3. +

        Resolve promise with result.

        +
      +
    3. +

      Upon rejection of promiseOfModule with reason reason:

      +
        +
      1. +

        Reject promise with reason.

        +
      +
    4. +

      Return promise.

      +
    +

    Note: It would be valid to perform certain parts of the instantiation in parallel, but several parts need to happen in the event loop, including JavaScript operations to access the importObject and execution of the start function.

    +
    +
    + The instantiate(bytes, importObject) method, when invoked, performs the following steps: +
      +
    1. +

      Let stableBytes be a copy of the bytes held by the buffer bytes.

      +
    2. +

      Asynchronously compile a WebAssembly module from stableBytes and let promiseOfModule be the result.

      +
    3. +

      Instantiate promiseOfModule with imports importObject and return the result.

      +
    +
    +
    + The instantiate(moduleObject, importObject) method, when invoked, performs the following steps: +
      +
    1. +

      Asynchronously instantiate the WebAssembly module moduleObject importing importObject, and return the result.

      +
    +
    +

    Note: A follow-on streaming API is documented in the WebAssembly Web API.

    +

    4.1. Modules

    +
    enum ImportExportKind {
+  "function",
+  "table",
+  "memory",
+  "global"
+};
+
+dictionary ModuleExportDescriptor {
+  required USVString name;
+  required ImportExportKind kind;
+  // Note: Other fields such as signature may be added in the future.
+};
+
+dictionary ModuleImportDescriptor {
+  required USVString module;
+  required USVString name;
+  required ImportExportKind kind;
+};
+
+[LegacyNamespace=WebAssembly, Exposed=(Window,Worker,Worklet)]
+interface Module {
+  constructor(BufferSource bytes);
+  static sequence<ModuleExportDescriptor> exports(Module moduleObject);
+  static sequence<ModuleImportDescriptor> imports(Module moduleObject);
+  static sequence<ArrayBuffer> customSections(Module moduleObject, DOMString sectionName);
+};
+
    +
    + The string value of the extern type type is +
      +
    • +

      "function" if type is of the form func functype

      +
    • +

      "table" if type is of the form table tabletype

      +
    • +

      "memory" if type is of the form mem memtype

      +
    • +

      "global" if type is of the form global globaltype

      +
    +
    +
    + The exports(moduleObject) method, when invoked, performs the following steps: +
      +
    1. +

      Let module be moduleObject.[[Module]].

      +
    2. +

      Let exports be « ».

      +
    3. +

      For each (name, type) of module_exports(module),

      +
        +
      1. +

        Let kind be the string value of the extern type type.

        +
      2. +

        Let obj be «[ "name" → name, "kind" → kind ]».

        +
      3. +

        Append obj to exports.

        +
      +
    4. +

      Return exports.

      +
    +
    +
    + The imports(moduleObject) method, when invoked, performs the following steps: +
      +
    1. +

      Let module be moduleObject.[[Module]].

      +
    2. +

      Let imports be « ».

      +
    3. +

      For each (moduleName, name, type) of module_imports(module),

      +
        +
      1. +

        Let kind be the string value of the extern type type.

        +
      2. +

        Let obj be «[ "module" → moduleName, "name" → name, "kind" → kind ]».

        +
      3. +

        Append obj to imports.

        +
      +
    4. +

      Return imports.

      +
    +
    +
    + The customSections(moduleObject, sectionName) method, when invoked, performs the following steps: +
      +
    1. +

      Let bytes be moduleObject.[[Bytes]].

      +
    2. +

      Let customSections be « ».

      +
    3. +

      For each custom section customSection of bytes, interpreted according to the module grammar,

      +
        +
      1. +

        Let name be the name of customSection, decoded as UTF-8.

        +
      2. +

        Assert: name is not failure (moduleObject.[[Module]] is valid).

        +
      3. +

        If name equals sectionName as string values,

        +
          +
        1. +

          Append a new ArrayBuffer containing a copy of the bytes in bytes for the range matched by this customsec production to customSections.

          +
        +
      +
    4. +

      Return customSections.

      +
    +
    +
    + The Module(bytes) constructor, when invoked, performs the follwing steps: +
      +
    1. +

      Let stableBytes be a copy of the bytes held by the buffer bytes.

      +
    2. +

      Compile the WebAssembly module stableBytes and store the result as module.

      +
    3. +

      If module is error, throw a CompileError exception.

      +
    4. +

      Set this.[[Module]] to module.

      +
    5. +

      Set this.[[Bytes]] to stableBytes.

      +
    +
    +

    4.2. Instances

    +
    [LegacyNamespace=WebAssembly, Exposed=(Window,Worker,Worklet)]
+interface Instance {
+  constructor(Module module, optional object importObject);
+  readonly attribute object exports;
+};
+
    +
    + The Instance(module, importObject) constructor, when invoked, runs the following steps: +
      +
    1. +

      Let module be module.[[Module]].

      +
    2. +

      Read the imports of module with imports importObject, and let imports be the result.

      +
    3. +

      Instantiate the core of a WebAssembly module module with imports, and let instance be the result.

      +
    4. +

      Initialize this from module and instance.

      +
    +
    +
    The getter of the exports attribute of Instance returns this.[[Exports]].
    +

    4.3. Memories

    +
    dictionary MemoryDescriptor {
+  required [EnforceRange] unsigned long initial;
+  [EnforceRange] unsigned long maximum;
+};
+
+[LegacyNamespace=WebAssembly, Exposed=(Window,Worker,Worklet)]
+interface Memory {
+  constructor(MemoryDescriptor descriptor);
+  unsigned long grow([EnforceRange] unsigned long delta);
+  readonly attribute ArrayBuffer buffer;
+};
+
    +

    A Memory object represents a single memory instance which can be simultaneously referenced by multiple Instance objects. Each Memory object has the following internal slots:

    + +
    + To create a memory buffer from a memory address memaddr, perform the following steps: +
      +
    1. +

      Let block be a Data Block which is identified with the underlying memory of memaddr.

      +
    2. +

      Let buffer be a new ArrayBuffer whose [[ArrayBufferData]] is block and [[ArrayBufferByteLength]] is set to the length of block.

      +
    3. +

      Set buffer.[[ArrayBufferDetachKey]] to "WebAssembly.Memory".

      +
    4. +

      Return buffer.

      +
    +
    +
    + To initialize a memory object memory from a memory address memaddr, perform the following steps: +
      +
    1. +

      Let map be the surrounding agent's associated Memory object cache.

      +
    2. +

      Assert: map[memaddr] doesn’t exist.

      +
    3. +

      Let buffer be the result of creating a memory buffer from memaddr.

      +
    4. +

      Set memory.[[Memory]] to memaddr.

      +
    5. +

      Set memory.[[BufferObject]] to buffer.

      +
    6. +

      Set map[memaddr] to memory.

      +
    +
    +
    + To create a memory object from a memory address memaddr, perform the following steps: +
      +
    1. +

      Let map be the surrounding agent's associated Memory object cache.

      +
    2. +

      If map[memaddr] exists,

      +
        +
      1. +

        Return map[memaddr].

        +
      +
    3. +

      Let memory be a new Memory.

      +
    4. +

      Initialize memory from memaddr.

      +
    5. +

      Return memory.

      +
    +
    +
    + The Memory(descriptor) constructor, when invoked, performs the following steps: +
      +
    1. +

      Let initial be descriptor["initial"].

      +
    2. +

      If descriptor["maximum"] exists, let maximum be descriptor["maximum"]; otherwise, let maximum be empty.

      +
    3. +

      If maximum is not empty and maximum < initial, throw a RangeError exception.

      +
    4. +

      Let memtype be { min initial, max maximum }.

      +
    5. +

      Let store be the surrounding agent's associated store.

      +
    6. +

      Let (store, memaddr) be mem_alloc(store, memtype). If allocation fails, throw a RangeError exception.

      +
    7. +

      Set the surrounding agent's associated store to store.

      +
    8. +

      Initialize this from memaddr.

      +
    +
    +
    + To reset the Memory buffer of memaddr, perform the following steps: +
      +
    1. +

      Let map be the surrounding agent's associated Memory object cache.

      +
    2. +

      Assert: map[memaddr] exists.

      +
    3. +

      Let memory be map[memaddr].

      +
    4. +

      Perform ! DetachArrayBuffer(memory.[[BufferObject]], "WebAssembly.Memory").

      +
    5. +

      Let buffer be the result of creating a memory buffer from memaddr.

      +
    6. +

      Set memory.[[BufferObject]] to buffer.

      +
    +
    +
    + The grow(delta) method, when invoked, performs the following steps: +
      +
    1. +

      Let store be the surrounding agent's associated store.

      +
    2. +

      Let memaddr be this.[[Memory]].

      +
    3. +

      Let ret be the mem_size(store, memaddr).

      +
    4. +

      Let store be mem_grow(store, memaddr, delta).

      +
    5. +

      If store is error, throw a RangeError exception.

      +
    6. +

      Set the surrounding agent's associated store to store.

      +
    7. +

      Reset the memory buffer of memaddr.

      +
    8. +

      Return ret.

      +
    +
    +

    Immediately after a WebAssembly memory.grow instruction executes, perform the following steps:

    +
    +
      +
    1. +

      If the top of the stack is not i32.const (−1),

      +
        +
      1. +

        Let frame be the current frame.

        +
      2. +

        Assert: due to validation, frame.module.memaddrs[0] exists.

        +
      3. +

        Let memaddr be the memory address frame.module.memaddrs[0].

        +
      4. +

        Reset the memory buffer of memaddr.

        +
      +
    +
    +
    The getter of the buffer attribute of Memory returns this.[[BufferObject]].
    +

    4.4. Tables

    +
    enum TableKind {
+  "externref",
+  "anyfunc",
+  // Note: More values may be added in future iterations,
+  // e.g., typed function references, typed GC references
+};
+
+dictionary TableDescriptor {
+  required TableKind element;
+  required [EnforceRange] unsigned long initial;
+  [EnforceRange] unsigned long maximum;
+};
+
+[LegacyNamespace=WebAssembly, Exposed=(Window,Worker,Worklet)]
+interface Table {
+  constructor(TableDescriptor descriptor, optional any value);
+  unsigned long grow([EnforceRange] unsigned long delta, optional any value);
+  any get([EnforceRange] unsigned long index);
+  undefined set([EnforceRange] unsigned long index, optional any value);
+  readonly attribute unsigned long length;
+};
+
    +

    A Table object represents a single table instance which can be simultaneously referenced by +multiple Instance objects. +Each Table object has a [[Table]] internal slot, which is a table address.

    +
    + To initialize a table object table from a table address tableaddr, perform the following steps: +
      +
    1. +

      Let map be the surrounding agent's associated Table object cache.

      +
    2. +

      Assert: map[tableaddr] doesn’t exist.

      +
    3. +

      Set table.[[Table]] to tableaddr.

      +
    4. +

      Set map[tableaddr] to table.

      +
    +
    +
    + To create a table object from a table address tableaddr, perform the following steps: +
      +
    1. +

      Let map be the surrounding agent's associated Table object cache.

      +
    2. +

      If map[tableaddr] exists,

      +
        +
      1. +

        Return map[tableaddr].

        +
      +
    3. +

      Let table be a new Table.

      +
    4. +

      Initialize table from tableaddr.

      +
    5. +

      Return table.

      +
    +
    +
    + The Table(descriptor, value) constructor, when invoked, performs the following steps: +
      +
    1. +

      Let elementType be ToValueType(descriptor["element"]).

      +
    2. +

      If elementType is not a reftype,

      +
        +
      1. +

        Throw a TypeError exception.

        +
      +
    3. +

      Let initial be descriptor["initial"].

      +
    4. +

      If descriptor["maximum"] exists, let maximum be descriptor["maximum"]; otherwise, let maximum be empty.

      +
    5. +

      If maximum is not empty and maximum < initial, throw a RangeError exception.

      +
    6. +

      If value is missing,

      +
        +
      1. +

        Let ref be DefaultValue(elementType).

        +
      +
    7. +

      Otherwise,

      +
        +
      1. +

        Let ref be ? ToWebAssemblyValue(value, elementType).

        +
      +
    8. +

      Let type be the table type {min initial, ma𝗑 maximum} elementType.

      +
    9. +

      Let store be the surrounding agent's associated store.

      +
    10. +

      Let (store, tableaddr) be table_alloc(store, type, ref).

      +
    11. +

      Set the surrounding agent's associated store to store.

      +
    12. +

      Initialize this from tableaddr.

      +
    +
    +
    + The grow(delta, value) method, when invoked, performs the following steps: +
      +
    1. +

      Let tableaddr be this.[[Table]].

      +
    2. +

      Let store be the surrounding agent's associated store.

      +
    3. +

      Let initialSize be table_size(store, tableaddr).

      +
    4. +

      Let (limits, elementType) be table_type(tableaddr).

      +
    5. +

      If value is missing,

      +
        +
      1. +

        Let ref be DefaultValue(elementType).

        +
      +
    6. +

      Otherwise,

      +
        +
      1. +

        Let ref be ? ToWebAssemblyValue(value, elementType).

        +
      +
    7. +

      Let result be table_grow(store, tableaddr, delta, ref).

      +
    8. +

      If result is error, throw a RangeError exception.

      +

      Note: The above exception can happen due to either insufficient memory or an invalid size parameter.

      +
    9. +

      Set the surrounding agent's associated store to result.

      +
    10. +

      Return initialSize.

      +
    +
    +
    + The getter of the length attribute of Table, when invoked, performs the following steps: +
      +
    1. +

      Let tableaddr be this.[[Table]].

      +
    2. +

      Let store be the surrounding agent's associated store.

      +
    3. +

      Return table_size(store, tableaddr).

      +
    +
    +
    + The get(index) method, when invoked, performs the following steps: +
      +
    1. +

      Let tableaddr be this.[[Table]].

      +
    2. +

      Let store be the surrounding agent's associated store.

      +
    3. +

      Let result be table_read(store, tableaddr, index).

      +
    4. +

      If result is error, throw a RangeError exception.

      +
    5. +

      Return ToJSValue(result).

      +
    +
    +
    + The set(index, value) method, when invoked, performs the following steps: +
      +
    1. +

      Let tableaddr be this.[[Table]].

      +
    2. +

      Let (limits, elementType) be table_type(tableaddr).

      +
    3. +

      If value is missing,

      +
        +
      1. +

        Let ref be DefaultValue(elementType).

        +
      +
    4. +

      Otherwise,

      +
        +
      1. +

        Let ref be ? ToWebAssemblyValue(value, elementType).

        +
      +
    5. +

      Let store be the surrounding agent's associated store.

      +
    6. +

      Let store be table_write(store, tableaddr, index, ref).

      +
    7. +

      If store is error, throw a RangeError exception.

      +
    8. +

      Set the surrounding agent's associated store to store.

      +
    +
    +

    4.5. Globals

    +
    enum ValueType {
+  "i32",
+  "i64",
+  "f32",
+  "f64",
+  "v128",
+  "externref",
+  "anyfunc",
+};
+
    +

    Note: this type may be extended with additional cases in future versions of WebAssembly.

    +
    dictionary GlobalDescriptor {
+  required ValueType value;
+  boolean mutable = false;
+};
+
+[LegacyNamespace=WebAssembly, Exposed=(Window,Worker,Worklet)]
+interface Global {
+  constructor(GlobalDescriptor descriptor, optional any v);
+  any valueOf();
+  attribute any value;
+};
+
    +

    A Global object represents a single global instance which can be simultaneously referenced by multiple Instance objects. Each Global object has one internal slot:

    + +
    + To initialize a global object global from a global address globaladdr, perform the following steps: +
      +
    1. +

      Let map be the surrounding agent's associated Global object cache.

      +
    2. +

      Assert: map[globaladdr] doesn’t exist.

      +
    3. +

      Set global.[[Global]] to globaladdr.

      +
    4. +

      Set map[globaladdr] to global.

      +
    +
    +
    + To create a global object from a global address globaladdr, perform the following steps: +
      +
    1. +

      Let map be the current agent's associated Global object cache.

      +
    2. +

      If map[globaladdr] exists,

      +
        +
      1. +

        Return map[globaladdr].

        +
      +
    3. +

      Let global be a new Global.

      +
    4. +

      Initialize global from globaladdr.

      +
    5. +

      Return global.

      +
    +
    +
    + The algorithm ToValueType(s) performs the following steps: +
      +
    1. +

      If s equals "i32", return i32.

      +
    2. +

      If s equals "i64", return i64.

      +
    3. +

      If s equals "f32", return f32.

      +
    4. +

      If s equals "f64", return f64.

      +
    5. +

      If s equals "v128", return v128.

      +
    6. +

      If s equals "anyfunc", return funcref.

      +
    7. +

      If s equals "externref", return externref.

      +
    8. +

      Assert: This step is not reached.

      +
    +
    +
    + The algorithm DefaultValue(valuetype) performs the following steps: +
      +
    1. +

      If valuetype equals i32, return i32.const 0.

      +
    2. +

      If valuetype equals i64, return i64.const 0.

      +
    3. +

      If valuetype equals f32, return f32.const 0.

      +
    4. +

      If valuetype equals f64, return f64.const 0.

      +
    5. +

      If valuetype equals funcref, return ref.null funcref.

      +
    6. +

      If valuetype equals externref, return ToWebAssemblyValue(undefined, valuetype).

      +
    7. +

      Assert: This step is not reached.

      +
    +
    +
    + The Global(descriptor, v) constructor, when invoked, performs the following steps: +
      +
    1. +

      Let mutable be descriptor["mutable"].

      +
    2. +

      Let valuetype be ToValueType(descriptor["value"]).

      +
    3. +

      If valuetype is v128,

      +
        +
      1. +

        Throw a LinkError exception.

        +
      +
    4. +

      If v is missing,

      +
        +
      1. +

        Let value be DefaultValue(valuetype).

        +
      +
    5. +

      Otherwise,

      +
        +
      1. +

        Let value be ToWebAssemblyValue(v, valuetype).

        +
      +
    6. +

      If mutable is true, let globaltype be var valuetype; otherwise, let globaltype be const valuetype.

      +
    7. +

      Let store be the current agent’s associated store.

      +
    8. +

      Let (store, globaladdr) be global_alloc(store, globaltype, value).

      +
    9. +

      Set the current agent’s associated store to store.

      +
    10. +

      Initialize this from globaladdr.

      +
    +
    +
    + The algorithm GetGlobalValue(Global global) performs the following steps: +
      +
    1. +

      Let store be the current agent’s associated store.

      +
    2. +

      Let globaladdr be global.[[Global]].

      +
    3. +

      Let globaltype be global_type(store, globaladdr).

      +
    4. +

      If globaltype is of the form mut v128, throw a TypeError.

      +
    5. +

      Let value be global_read(store, globaladdr).

      +
    6. +

      Return ToJSValue(value).

      +
    +
    +
    + The getter of the value attribute of Global, when invoked, performs the following steps: +
      +
    1. +

      Return GetGlobalValue(this).

      +
    +

    The setter of the value attribute of Global, when invoked, performs the following steps:

    +
      +
    1. +

      Let store be the current agent’s associated store.

      +
    2. +

      Let globaladdr be this.[[Global]].

      +
    3. +

      Let mut valuetype be global_type(store, globaladdr).

      +
    4. +

      If valuetype is v128, throw a TypeError.

      +
    5. +

      If mut is const, throw a TypeError.

      +
    6. +

      Let value be ToWebAssemblyValue(the given value, valuetype).

      +
    7. +

      Let store be global_write(store, globaladdr, value).

      +
    8. +

      If store is error, throw a RangeError exception.

      +
    9. +

      Set the current agent’s associated store to store.

      +
    +
    +
    + The valueOf() method, when invoked, performs the following steps: +
      +
    1. +

      Return GetGlobalValue(this).

      +
    +
    +

    4.6. Exported Functions

    +

    A WebAssembly function is made available in JavaScript as an Exported Function. +Exported Functions are Built-in Function Objects which are not constructors, and which have a [[FunctionAddress]] internal slot. +This slot holds a function address relative to the surrounding agent's associated store.

    +
    + The name of the WebAssembly function funcaddr is found by performing the following steps: +
      +
    1. +

      Let store be the surrounding agent's associated store.

      +
    2. +

      Let funcinst be store.funcs[funcaddr].

      +
    3. +

      If funcinst is of the form {type functype, hostcode hostfunc},

      +
        +
      1. +

        Assert: hostfunc is a JavaScript object and IsCallable(hostfunc) is true.

        +
      2. +

        Let index be the index of the host function funcaddr.

        +
      +
    4. +

      Otherwise,

      +
        +
      1. +

        Let moduleinst be funcinst.module.

        +
      2. +

        Assert: funcaddr is contained in moduleinst.funcaddrs.

        +
      3. +

        Let index be the index of moduleinst.funcaddrs where funcaddr is found.

        +
      +
    5. +

      Return ! ToString(index).

      +
    +
    +
    + To create a new Exported Function from a WebAssembly function address funcaddr, perform the following steps: +
      +
    1. +

      Let map be the surrounding agent's associated Exported Function cache.

      +
    2. +

      If map[funcaddr] exists,

      +
        +
      1. +

        Return map[funcaddr].

        +
      +
    3. +

      Let steps be "call the Exported Function funcaddr with arguments."

      +
    4. +

      Let realm be the current Realm.

      +
    5. +

      Let store be the surrounding agent's associated store.

      +
    6. +

      Let functype be func_type(store, funcaddr).

      +
    7. +

      Let [paramTypes] → [resultTypes] be functype.

      +
    8. +

      Let arity be paramTypes’s size.

      +
    9. +

      Let name be the name of the WebAssembly function funcaddr.

      +
    10. +

      Let function be ! CreateBuiltinFunction(steps, arity, name, « [[FunctionAddress]] », realm).

      +
    11. +

      Set function.[[FunctionAddress]] to funcaddr.

      +
    12. +

      Set map[funcaddr] to function.

      +
    13. +

      Return function.

      +
    +
    +
    + To call an Exported Function with function address funcaddr and a list of JavaScript arguments argValues, perform the following steps: +
      +
    1. +

      Let store be the surrounding agent's associated store.

      +
    2. +

      Let functype be func_type(store, funcaddr).

      +
    3. +

      Let [parameters] → [results] be functype.

      +
    4. +

      If parameters or results contain v128, throw a TypeError.

      +

      Note: the above error is thrown each time the [[Call]] method is invoked.

      +
    5. +

      Let args be « ».

      +
    6. +

      Let i be 0.

      +
    7. +

      For each t of parameters,

      +
        +
      1. +

        If argValues’s size > i, let arg be argValues[i].

        +
      2. +

        Otherwise, let arg be undefined.

        +
      3. +

        Append ToWebAssemblyValue(arg, t) to args.

        +
      4. +

        Set i to i + 1.

        +
      +
    8. +

      Let (store, ret) be the result of func_invoke(store, funcaddr, args).

      +
    9. +

      Set the surrounding agent's associated store to store.

      +
    10. +

      If ret is error, throw an exception. This exception should be a WebAssembly RuntimeError exception, unless otherwise indicated by the WebAssembly error mapping.

      +
    11. +

      Let outArity be the size of ret.

      +
    12. +

      If outArity is 0, return undefined.

      +
    13. +

      Otherwise, if outArity is 1, return ToJSValue(ret[0]).

      +
    14. +

      Otherwise,

      +
        +
      1. +

        Let values be « ».

        +
      2. +

        For each r of ret,

        +
          +
        1. +

          Append ToJSValue(r) to values.

          +
        +
      3. +

        Return CreateArrayFromList(values).

        +
      +
    +
    +

    Note: Calling an Exported Function executes in the [[Realm]] of the callee Exported Function, as per the definition of built-in function objects.

    +

    Note: Exported Functions do not have a [[Construct]] method and thus it is not possible to call one with the new operator.

    +
    + To run a host function from the JavaScript object func, type functype, and list of WebAssembly values arguments, perform the following steps: +
      +
    1. +

      Let [parameters] → [results] be functype.

      +
    2. +

      If parameters or results contain v128, throw a TypeError.

      +
    3. +

      Let jsArguments be « ».

      +
    4. +

      For each arg of arguments,

      +
        +
      1. +

        Append ! ToJSValue(arg) to jsArguments.

        +
      +
    5. +

      Let ret be ? Call(func, undefined, jsArguments).

      +
    6. +

      Let resultsSize be results’s size.

      +
    7. +

      If resultsSize is 0, return « ».

      +
    8. +

      Otherwise, if resultsSize is 1, return « ? ToWebAssemblyValue(ret, results[0]) ».

      +
    9. +

      Otherwise,

      +
        +
      1. +

        Let method be ? GetMethod(ret, @@iterator).

        +
      2. +

        If method is undefined, throw a TypeError.

        +
      3. +

        Let values be ? IterableToList(ret, method).

        +
      4. +

        Let wasmValues be a new, empty list.

        +
      5. +

        If values’s size is not resultsSize, throw a TypeError exception.

        +
      6. +

        For each value and resultType in values and results, paired linearly,

        +
          +
        1. +

          Append ToWebAssemblyValue(value, resultType) to wasmValues.

          +
        +
      7. +

        Return wasmValues.

        +
      +
    +
    +
    + To create a host function from the JavaScript object func and type functype, perform the following steps: +
      +
    1. +

      Assert: IsCallable(func).

      +
    2. +

      Let stored settings be the incumbent settings object.

      +
    3. +

      Let hostfunc be a host function which performs the following steps when called with arguments arguments:

      +
        +
      1. +

        Let realm be func’s associated Realm.

        +
      2. +

        Let relevant settings be realm’s settings object.

        +
      3. +

        Prepare to run script with relevant settings.

        +
      4. +

        Prepare to run a callback with stored settings.

        +
      5. +

        Let result be the result of running a host function from func, functype, and arguments.

        +
      6. +

        Clean up after running a callback with stored settings.

        +
      7. +

        Clean up after running script with relevant settings.

        +
      8. +

        Assert: result.[[Type]] is throw or normal.

        +
      9. +

        If result.[[Type]] is throw, then trigger a WebAssembly trap, and propagate result.[[Value]] to the enclosing JavaScript.

        +
      10. +

        Otherwise, return result.[[Value]].

        +
      +
    4. +

      Let store be the surrounding agent's associated store.

      +
    5. +

      Let (store, funcaddr) be func_alloc(store, functype, hostfunc).

      +
    6. +

      Set the surrounding agent's associated store to store.

      +
    7. +

      Return funcaddr.

      +
    +
    +
    + The algorithm ToJSValue(w) coerces a WebAssembly value to a JavaScript value by performing the following steps: +
      +
    1. +

      Assert: w is not of the form v128.const v128.

      +
    2. +

      If w is of the form i64.const i64,

      +
        +
      1. +

        Let v be signed_64(i64).

        +
      2. +

        Return a BigInt representing the mathematical value v.

        +
      +
    3. +

      If w is of the form i32.const i32, return the Number value for signed_32(i32).

      +
    4. +

      If w is of the form f32.const f32, return the Number value for f32.

      +
    5. +

      If w is of the form f64.const f64, return the Number value for f64.

      +
    6. +

      If w is of the form ref.null t, return null.

      +
    7. +

      If w is of the form ref.func funcaddr, return the result of creating a new Exported Function from funcaddr.

      +
    8. +

      If w is of the form ref.extern externaddr, return the result of retrieving an extern value from externaddr.

      +
    +

    Note: Number values which are equal to NaN may have various observable NaN payloads; see NumberToRawBytes for details.

    +
    +
    +

    For retrieving an extern value from an extern address externaddr, perform the following steps:

    +
      +
    1. +

      Let map be the surrounding agent's associated extern value cache.

      +
    2. +

      Assert: map[externaddr] exists.

      +
    3. +

      Return map[externaddr].

      +
    +
    +
    + The algorithm ToWebAssemblyValue(v, type) coerces a JavaScript value to a WebAssembly value by performing the following steps: +
      +
    1. +

      Assert: type is not v128.

      +
    2. +

      If type is i64,

      +
        +
      1. +

        Let i64 be ? ToBigInt64(v).

        +
      2. +

        Return i64.const i64.

        +
      +
    3. +

      If type is i32,

      +
        +
      1. +

        Let i32 be ? ToInt32(v).

        +
      2. +

        Return i32.const i32.

        +
      +
    4. +

      If type is f32,

      +
        +
      1. +

        Let f32 be ? ToNumber(v) rounded to the nearest representable value using IEEE 754-2008 round to nearest, ties to even mode.

        +
      2. +

        Return f32.const f32.

        +
      +
    5. +

      If type is f64,

      +
        +
      1. +

        Let f64 be ? ToNumber(v).

        +
      2. +

        Return f64.const f64.

        +
      +
    6. +

      If type is funcref,

      +
        +
      1. +

        If v is null,

        +
          +
        1. +

          Return ref.null funcref.

          +
        +
      2. +

        If v is an Exported Function,

        +
          +
        1. +

          Let funcaddr be the value of v’s [[FunctionAddress]] internal slot.

          +
        2. +

          Return ref.func funcaddr.

          +
        +
      3. +

        Throw a TypeError.

        +
      +
    7. +

      If type is externref,

      +
        +
      1. +

        If v is null,

        +
          +
        1. +

          Return ref.null externref.

          +
        +
      2. +

        Let map be the surrounding agent's associated extern value cache.

        +
      3. +

        If a extern address externaddr exists such that map[externaddr] is the same as v,

        +
          +
        1. +

          Return ref.extern externaddr.

          +
        +
      4. +

        Let extern address externaddr be the smallest address such that map[externaddr] exists is false.

        +
      5. +

        Set map[externaddr] to v.

        +
      6. +

        Return ref.extern externaddr.

        +
      +
    8. +

      Assert: This step is not reached.

      +
    +
    +

    4.7. Error Objects

    +

    WebAssembly defines the following Error classes: CompileError, LinkError, and RuntimeError.

    +
    + When the namespace object for the WebAssembly namespace is created, the following steps must be run: +
      +
    1. +

      Let namespaceObject the namespace object.

      +
    2. +

      For each error of « "CompileError", "LinkError", "RuntimeError" »,

      +
        +
      1. +

        Let constructor be a new object, implementing the NativeError Object Structure, with NativeError set to error.

        +
      2. +

        ! CreateMethodProperty(namespaceObject, error, constructor).

        +
      +
    +
    +

    Note: This defines CompileError, LinkError, and RuntimeError classes on the WebAssembly namespace, which are produced by the APIs defined in this specification. +They expose the same interface as native JavaScript errors like TypeError and RangeError.

    +

    Note: It is not currently possible to define this behavior using Web IDL.

    +

    5. Error Condition Mappings to JavaScript

    +

    Running WebAssembly programs encounter certain events which halt execution of the WebAssembly code. +WebAssembly code (currently) +has no way to catch these conditions and thus an exception will necessarily +propagate to the enclosing non-WebAssembly caller (whether it is a browser, +JavaScript or another runtime system) where it is handled like a normal JavaScript exception.

    +

    If WebAssembly calls JavaScript via import and the JavaScript throws an +exception, the exception is propagated through the WebAssembly activation to the +enclosing caller.

    +

    Because JavaScript exceptions can be handled, and JavaScript can continue to +call WebAssembly exports after a trap has been handled, traps do not, in +general, prevent future execution.

    +

    5.1. Stack Overflow

    +

    Whenever a stack overflow occurs in +WebAssembly code, the same class of exception is thrown as for a stack overflow in +JavaScript. The particular exception here is implementation-defined in both cases.

    +

    Note: ECMAScript doesn’t specify any sort of behavior on stack overflow; implementations have been observed to throw RangeError, InternalError or Error. Any is valid here.

    +

    5.2. Out of Memory

    +

    Whenever validation, compilation or instantiation run out of memory, the +same class of exception is thrown as for out of memory conditions in JavaScript. +The particular exception here is implementation-defined in both cases.

    +

    Note: ECMAScript doesn’t specify any sort of behavior on out-of-memory conditions; implementations have been observed to throw OOMError and to crash. Either is valid here.

    +
    + A failed allocation of a large table or memory may either result in + + In a future revision, we may reconsider more reliable and recoverable errors for allocations of large amounts of memory. +

    See Issue 879 for further discussion.

    +
    +

    6. Implementation-defined Limits

    +

    The WebAssembly core specification allows an implementation to define limits on the syntactic structure of the module. +While each embedding of WebAssembly may choose to define its own limits, for predictability the standard WebAssembly JavaScript Interface described in this document defines the following exact limits. +An implementation must reject a module that exceeds one of the following limits with a CompileError: +In practice, an implementation may run out of resources for valid modules below these limits.

    +
      +
    • The maximum size of a module is 1073741824 bytes (1 GiB). +
    • The maximum number of types defined in the types section is 1000000. +
    • The maximum number of functions defined in a module is 1000000. +
    • The maximum number of imports declared in a module is 100000. +
    • The maximum number of exports declared in a module is 100000. +
    • The maximum number of globals defined in a module is 1000000. +
    • The maximum number of data segments defined in a module is 100000. +
    • The maximum number of tables, including declared or imported tables, is 100000. +
    • The maximum size of a table is 10000000. +
    • The maximum number of table entries in any table initialization is 10000000. +
    • The maximum number of memories, including declared or imported memories, is 1. +
    • The maximum number of parameters to any function or block is 1000. +
    • The maximum number of return values for any function or block is 1000. +
    • The maximum size of a function body, including locals declarations, is 7654321 bytes. +
    • The maximum number of locals declared in a function, including implicitly declared as parameters, is 50000. +
    +

    An implementation must throw a RuntimeError if one of the following limits is exceeded during runtime: +In practice, an implementation may run out of resources for valid modules below these limits.

    +
      +
    • The maximum size of a table is 10000000. +
    • The maximum number of pages of a memory is 65536. +
    +

    7. Security and Privacy Considerations

    +

    This section is non-normative.

    +

    This document defines a host environment for WebAssembly. It enables a WebAssembly instance to import JavaScript objects and functions from an import object, but otherwise provides no access to the embedding environment. Thus a WebAssembly instance is bounds to the same constraints as JavaScript.

    +
    +
    +

    Conformance

    +

    Document conventions

    +

    Conformance requirements are expressed + with a combination of descriptive assertions + and RFC 2119 terminology. + The key words “MUST”, “MUST NOT”, “REQUIRED”, “SHALL”, “SHALL NOT”, “SHOULD”, “SHOULD NOT”, “RECOMMENDED”, “MAY”, and “OPTIONAL” + in the normative parts of this document + are to be interpreted as described in RFC 2119. + However, for readability, + these words do not appear in all uppercase letters in this specification.

    +

    All of the text of this specification is normative + except sections explicitly marked as non-normative, examples, and notes. [RFC2119]

    +

    Examples in this specification are introduced with the words “for example” + or are set apart from the normative text + with class="example", + like this:

    +
    + +

    This is an example of an informative example.

    +
    +

    Informative notes begin with the word “Note” + and are set apart from the normative text + with class="note", + like this:

    +

    Note, this is an informative note.

    +

    Conformant Algorithms

    +

    Requirements phrased in the imperative as part of algorithms + (such as "strip any leading space characters" + or "return false and abort these steps") + are to be interpreted with the meaning of the key word + ("must", "should", "may", etc) + used in introducing the algorithm.

    +

    Conformance requirements phrased as algorithms or specific steps + can be implemented in any manner, + so long as the end result is equivalent. + In particular, the algorithms defined in this specification + are intended to be easy to understand + and are not intended to be performant. + Implementers are encouraged to optimize.

    +
    + +

    Index

    +

    Terms defined by this specification

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Terms defined by reference

    +
      +
    • + [ECMASCRIPT] defines the following terms: +
        +
      • @@iterator +
      • ArrayBuffer +
      • CreateMethodProperty +
      • RangeError +
      • TypeError +
      • agent +
      • agent cluster +
      • bigint +
      • built-in function objects +
      • call +
      • createarrayfromlist +
      • createbuiltinfunction +
      • createdataproperty +
      • current realm +
      • data block +
      • detacharraybuffer +
      • get +
      • getmethod +
      • iscallable +
      • iterabletolist +
      • nativeerror object structure +
      • numbertorawbytes +
      • objectcreate +
      • setintegritylevel +
      • surrounding agent +
      • the number value +
      • tobigint64 +
      • toint32 +
      • tonumber +
      • tostring +
      • type +
      +
    • + [ENCODING] defines the following terms: +
        +
      • utf-8 decode without bom or fail +
      +
    • + [HTML] defines the following terms: +
        +
      • clean up after running a callback +
      • clean up after running script +
      • in parallel +
      • incumbent settings object +
      • prepare to run a callback +
      • prepare to run script +
      • queue a task +
      • settings object +
      • task source +
      +
    • + [INFRA] defines the following terms: +
        +
      • append +
      • exist +
      • is empty +
      • iterate +
      • list +
      • ordered map +
      • set +
      • size +
      +
    • + [WEBASSEMBLY] defines the following terms: +
        +
      • address +
      • const +
      • current frame +
      • custom section +
      • customsec +
      • error +
      • extern address +
      • external value +
      • externref +
      • f32 +
      • f32.const +
      • f64 +
      • f64.const +
      • func +
      • func_alloc +
      • func_invoke +
      • func_type +
      • funcref +
      • function address +
      • global +
      • global address +
      • global instance +
      • global_alloc +
      • global_read +
      • global_type +
      • global_write +
      • host function +
      • i32 +
      • i32.const +
      • i64 +
      • i64.const +
      • import +
      • imports +
      • instance_export +
      • mem +
      • mem_alloc +
      • mem_grow +
      • mem_size +
      • memaddrs +
      • memory address +
      • memory instance +
      • memory.grow +
      • module (for frame) +
      • module grammar +
      • module_decode +
      • module_exports +
      • module_imports +
      • module_instantiate +
      • module_validate +
      • ref.extern +
      • ref.func +
      • ref.null +
      • reftype +
      • sequence +
      • signed_32 +
      • signed_64 +
      • store +
      • store_init +
      • table +
      • table address +
      • table instance +
      • table type +
      • table_alloc +
      • table_grow +
      • table_read +
      • table_size +
      • table_type +
      • table_write +
      • v128 +
      • v128.const +
      • valid +
      • var +
      • webassembly module validation +
      • webassembly value +
      +
    • + [WEBIDL] defines the following terms: +
        +
      • BufferSource +
      • DOMString +
      • EnforceRange +
      • Exposed +
      • LegacyNamespace +
      • Promise +
      • USVString +
      • a new promise +
      • any +
      • associated realm +
      • boolean +
      • create a namespace object +
      • get a copy of the buffer source +
      • implements +
      • namespace object +
      • new +
      • object +
      • reject +
      • resolve +
      • sequence +
      • throw +
      • undefined +
      • unsigned long +
      • upon fulfillment +
      • upon rejection +
      +
    +

    References

    +

    Normative References

    +
    +
    [ECMASCRIPT] +
    ECMAScript Language Specification. URL: https://tc39.es/ecma262/multipage/ +
    [ENCODING] +
    Anne van Kesteren. Encoding Standard. Living Standard. URL: https://encoding.spec.whatwg.org/ +
    [HTML] +
    Anne van Kesteren; et al. HTML Standard. Living Standard. URL: https://html.spec.whatwg.org/multipage/ +
    [INFRA] +
    Anne van Kesteren; Domenic Denicola. Infra Standard. Living Standard. URL: https://infra.spec.whatwg.org/ +
    [RFC2119] +
    S. Bradner. Key words for use in RFCs to Indicate Requirement Levels. March 1997. Best Current Practice. URL: https://datatracker.ietf.org/doc/html/rfc2119 +
    [WEBASSEMBLY] +
    WebAssembly Core Specification. Draft. URL: https://webassembly.github.io/spec/core/ +
    [WEBIDL] +
    Edgar Chen; Timothy Gu. Web IDL Standard. Living Standard. URL: https://webidl.spec.whatwg.org/ +
    +

    IDL Index

    +
    dictionary WebAssemblyInstantiatedSource {
+    required Module module;
+    required Instance instance;
+};
+
+[Exposed=(Window,Worker,Worklet)]
+namespace WebAssembly {
+    boolean validate(BufferSource bytes);
+    Promise<Module> compile(BufferSource bytes);
+
+    Promise<WebAssemblyInstantiatedSource> instantiate(
+        BufferSource bytes, optional object importObject);
+
+    Promise<Instance> instantiate(
+        Module moduleObject, optional object importObject);
+};
+
+enum ImportExportKind {
+  "function",
+  "table",
+  "memory",
+  "global"
+};
+
+dictionary ModuleExportDescriptor {
+  required USVString name;
+  required ImportExportKind kind;
+  // Note: Other fields such as signature may be added in the future.
+};
+
+dictionary ModuleImportDescriptor {
+  required USVString module;
+  required USVString name;
+  required ImportExportKind kind;
+};
+
+[LegacyNamespace=WebAssembly, Exposed=(Window,Worker,Worklet)]
+interface Module {
+  constructor(BufferSource bytes);
+  static sequence<ModuleExportDescriptor> exports(Module moduleObject);
+  static sequence<ModuleImportDescriptor> imports(Module moduleObject);
+  static sequence<ArrayBuffer> customSections(Module moduleObject, DOMString sectionName);
+};
+
+[LegacyNamespace=WebAssembly, Exposed=(Window,Worker,Worklet)]
+interface Instance {
+  constructor(Module module, optional object importObject);
+  readonly attribute object exports;
+};
+
+dictionary MemoryDescriptor {
+  required [EnforceRange] unsigned long initial;
+  [EnforceRange] unsigned long maximum;
+};
+
+[LegacyNamespace=WebAssembly, Exposed=(Window,Worker,Worklet)]
+interface Memory {
+  constructor(MemoryDescriptor descriptor);
+  unsigned long grow([EnforceRange] unsigned long delta);
+  readonly attribute ArrayBuffer buffer;
+};
+
+enum TableKind {
+  "externref",
+  "anyfunc",
+  // Note: More values may be added in future iterations,
+  // e.g., typed function references, typed GC references
+};
+
+dictionary TableDescriptor {
+  required TableKind element;
+  required [EnforceRange] unsigned long initial;
+  [EnforceRange] unsigned long maximum;
+};
+
+[LegacyNamespace=WebAssembly, Exposed=(Window,Worker,Worklet)]
+interface Table {
+  constructor(TableDescriptor descriptor, optional any value);
+  unsigned long grow([EnforceRange] unsigned long delta, optional any value);
+  any get([EnforceRange] unsigned long index);
+  undefined set([EnforceRange] unsigned long index, optional any value);
+  readonly attribute unsigned long length;
+};
+
+enum ValueType {
+  "i32",
+  "i64",
+  "f32",
+  "f64",
+  "v128",
+  "externref",
+  "anyfunc",
+};
+
+dictionary GlobalDescriptor {
+  required ValueType value;
+  boolean mutable = false;
+};
+
+[LegacyNamespace=WebAssembly, Exposed=(Window,Worker,Worklet)]
+interface Global {
+  constructor(GlobalDescriptor descriptor, optional any v);
+  any valueOf();
+  attribute any value;
+};
+
+
    +

    Issues Index

    +
    +
    + A failed allocation of a large table or memory may either result in + + In a future revision, we may reconsider more reliable and recoverable errors for allocations of large amounts of memory. +

    See Issue 879 for further discussion.

    + ↵ +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/web-api/index.html b/web-api/index.html new file mode 100644 index 00000000..c183660c --- /dev/null +++ b/web-api/index.html @@ -0,0 +1,1146 @@ + + + + + WebAssembly Web API + + + + + + + + + + + + + + +
    +

    +

    WebAssembly Web API

    +

    Editor’s Draft,

    +
    + More details about this document +
    +
    +
    This version: +
    https://webassembly.github.io/spec/web-api/ +
    Latest published version: +
    https://www.w3.org/TR/wasm-web-api-2/ +
    Editor: +
    Ms2ger (Igalia) +
    Issue Tracking: +
    GitHub Issues +
    +
    +
    +
    +

    Copyright © 2022 W3C® (MIT, ERCIM, Keio, Beihang). W3C liability, trademark and permissive document license rules apply.

    +
    +
    +
    +

    Abstract

    +

    This document describes the integration of WebAssembly with the broader web platform.

    + This is part of a collection of related documents: +the Core WebAssembly Specification, +the WebAssembly JS Interface, +and the WebAssembly Web API. +
    +

    Status of this document

    +
    +

    This is a public copy of the editors’ draft. + It is provided for discussion only and may change at any moment. + Its publication here does not imply endorsement of its contents by W3C. + Don’t cite this document other than as work in progress.

    +

    GitHub Issues are preferred for discussion of this specification. + All issues and comments are archived.

    +

    This document was produced by the WebAssembly Working Group.

    +

    This document was produced by a group operating under + the W3C Patent Policy. + W3C maintains a public list of any patent disclosures made in connection with the deliverables of the group; + that page also includes instructions for disclosing a patent. + An individual who has actual knowledge of a patent which the individual believes contains Essential Claim(s) must disclose the information in accordance with section 6 of the W3C Patent Policy.

    +

    This document is governed by the 2 November 2021 W3C Process Document.

    +

    +
    +
    + +
    +

    This document builds off of the WebAssembly specification [WEBASSEMBLY] and the WebAssembly JavaScript embedding [WASMJS].

    +

    1. Streaming Module Compilation and Instantiation

    +
    [Exposed=(Window,Worker)]
+partial namespace WebAssembly {
+  Promise<Module> compileStreaming(Promise<Response> source);
+  Promise<WebAssemblyInstantiatedSource> instantiateStreaming(
+      Promise<Response> source, optional object importObject);
+};
+
    +
    The compileStreaming(source) method, when invoked, returns the result of compiling a potential WebAssembly response with source.
    +
    + The instantiateStreaming(source, importObject) method, when invoked, performs the following steps: +
      +
    1. +

      Let promiseOfModule be the result of compiling a potential WebAssembly response with source.

      +
    2. +

      Return the result of instantiating the promise of a module promiseOfModule with imports importObject.

      +
    +
    +
    + To compile a potential WebAssembly response with a promise of a Response source, perform the following steps: +

    Note: This algorithm accepts a Response object, or a + promise for one, and compiles and instantiates the resulting bytes of the response. This compilation + can be performed in the background and in a streaming manner. If the Response is not CORS-same-origin, does not represent an ok status, or does not match the `application/wasm` MIME type, the returned promise will be rejected with a TypeError; if + compilation or instantiation fails, the returned promise will be rejected with a CompileError or other relevant error type, depending on the cause of failure.

    +
      +
    1. +

      Let returnValue be a new promise

      +
    2. +

      Upon fulfillment of source with value unwrappedSource:

      +
        +
      1. +

        Let response be unwrappedSource’s response.

        +
      2. +

        Let mimeType be the result of extracting a MIME type from response’s header list.

        +
      3. +

        If mimeType is not `application/wasm`, reject returnValue with a TypeError and abort these substeps.

        +

        Note: extra parameters are not allowed, including the empty `application/wasm;`.

        +
      4. +

        If response is not CORS-same-origin, reject returnValue with a TypeError and abort these substeps.

        +
      5. +

        If response’s status is not an ok status, reject returnValue with a TypeError and abort these substeps.

        +
      6. +

        consume response’s body as an ArrayBuffer, and let bodyPromise be the result.

        +

        Note: Although it is specified here that the response is consumed entirely before compilation proceeds, that is purely for ease of specification; implementations are likely to instead perform processing in a streaming fashion. The difference is unobservable, and thus the simpler model is specified.

        +
      7. +

        Upon fulfillment of bodyPromise with value bodyArrayBuffer:

        +
          +
        1. +

          Let stableBytes be a copy of the bytes held by the buffer bodyArrayBuffer.

          +
        2. +

          Asynchronously compile the WebAssembly module stableBytes using the networking task source and resolve returnValue with the result.

          +
        +
      8. +

        Upon rejection of bodyPromise with reason reason:

        +
          +
        1. +

          Reject returnValue with reason.

          +
        +
      +
    3. +

      Upon rejection of source with reason reason:

      +
        +
      1. +

        Reject returnValue with reason.

        +
      +
    4. +

      Return returnValue.

      +
    +
    +

    2. Serialization

    +

    Web user agents must augment the Module interface with the [Serializable] extended attribute.

    +

    The serialization steps, given value, serialized, and forStorage, are:

    +
      +
    1. +

      If forStorage is true, throw a "DataCloneError" DOMException

      +
    2. +

      Set serialized.[[Bytes]] to the sub-serialization of value.[[Bytes]].

      +
    3. +

      Set serialized.[[AgentCluster]] to the current Realm's corresponding agent cluster.

      +
    +

    The deserialization steps, given serialized and value, are:

    +
      +
    1. +

      Let bytes be the sub-deserialization of serialized.[[Bytes]].

      +
    2. +

      Set value.[[Bytes]] to bytes.

      +
    3. +

      If targetRealm’s corresponding agent cluster is not serialized.[[AgentCluster]], then throw a "DataCloneError" DOMException.

      +
    4. +

      Compile a WebAssembly module from bytes and set value.[[Module]] to the result.

      +
    +

    Engines should attempt to share/reuse internal compiled code when performing +a structured serialization, although in corner cases like CPU upgrade or browser +update, this might not be possible and full recompilation may be necessary.

    +

    Note: The semantics of a structured serialization is as-if the binary source, from which the Module was compiled, is serialized, then deserialized, and recompiled into the target realm. +Given the above engine optimizations, structured serialization provides developers +explicit control over both compiled-code caching and cross-window/worker code +sharing.

    +

    3. Developer-Facing Display Conventions

    +

    This section is non-normative.

    +

    Browsers, JavaScript engines, and offline tools have common ways of referring to +JavaScript artifacts and language constructs. For example, locations in +JavaScript source code are printed in stack traces or error messages, and are +represented naturally as decimal-format lines and columns in text files. Names +of functions and variables are taken directly from the sources. Therefore (for +example) even though the exact format of implementation-dependent stack trace +strings does not always match, the locations are easily understandable and the +same across browsers.

    +

    To achieve the same goal of a common representations for WebAssembly constructs, the +following conventions are adopted.

    +

    A WebAssembly location is a reference to a particular instruction in the binary, and may be +displayed by a browser or engine in similar contexts as JavaScript source locations. +It has the following format:

    +

    ${url}:wasm-function[${funcIndex}]:${pcOffset}

    +

    Where

    +
      +
    • +

      ${url} is the URL associated with the module, if applicable (see notes).

      +
    • +

      ${funcIndex} is the function index relative to the module.

      +
    • +

      ${pcOffset} is the offset in the module binary of the first byte of the instruction, printed in hexadecimal with lower-case digits, with a leading 0x prefix.

      +
    +

    Notes:

    +
      +
    • +

      The URL field may be interpreted differently depending on the +context. When the response-based +instantiation API is used in a +browser, the associated URL should be used; or when the ArrayBuffer-based instantiation API is used, the browser should represent +the location of the API call. This kind of instantiation is analogous to +executing JavaScript using eval; therefore if the browser has an existing +method to represent the location of the eval call it can use a similar +one for WebAssembly.instantiate. For example if the browser uses foo.js line 10 > eval or eval at bar (foo.js:10:3) for eval, it could +use foo.js line 10 > WebAssembly.instantiate or WebAssembly.instantiate at bar (foo.js:10:3), respectively. +Offline tools may use a filename instead.

      +
    • +

      Using hexadecimal for module offsets matches common conventions in native tools +such as objdump (where addresses are printed in hex) and makes them visually +distinct from JavaScript line numbers. Other numbers are represented in decimal.

      +
    +

    While the "name" property of an Exported Function instance +is specified by the JS API, synthesized function names are also +displayed in other contexts like call stacks in debuggers and string representations +of stack traces. +If a WebAssembly module contains a name section, +these names should be used to synthesize a function name as follows:

    +
      +
    • +

      If a function name subsection is present, the displayed name should be ${module_name}.${function_name} or ${function_name}, depending on whether the module name is present.

      +
    • +

      Otherwise, the output can be context-dependent:

      +
        +
      • +

        If the function name is shown alongside its location in a stack trace, then just the module name (if present) or an empty string can be used (because the function index is already in the location).

        +
      • +

        Otherwise, ${module_name}.wasm-function[${funcIndex}] or wasm-function[${funcIndex}] should be used to convey the function index.

        +
      +
    +

    Note that this document does not specify the full format of strings such as +stack frame representations; this allows engines to continue using their +existing formats for JavaScript (which existing code may already be depending +on) while still printing WebAssembly frames in a format consistent with +JavaScript.

    +

    4. Media-type Registration

    +

    This section will be submitted to the Internet Engineering Steering Group (IESG) for +review, approval, and registration with IANA.

    +

    application/wasm

    +
    +
    Type Name: +
    application +
    Subtype Name: +
    wasm +
    Required Parameters: +
    None +
    Optional Parameters: +
    None +
    Encoding Considerations: +
    binary +
    Security Considerations: +
    +

    WebAssembly is a standard, a safe, portable, low-level code format. The + security considerations associated with executing WebAssembly code are + described in https://www.w3.org/TR/wasm-core/#security-considerations.

    +

    The WebAssembly format includes no integrity or privacy protection. If + such protection is needed it must be provided externally, e.g., through + the use of HTTPS.

    +
    Interoperability Considerations: +
    See WebAssembly Core Conformance
    https://www.w3.org/TR/wasm-core/#conformance +
    Published specification: +
    https://www.w3.org/TR/wasm-core-1/ + https://www.w3.org/TR/wasm-js-api-1/ + https://www.w3.org/TR/wasm-web-api-1/ +
    Application Usage: +
    The application/wasm media type is intended for use as the type used to + describe WebAssembly files when sent over HTTP to be executed by browsers, + which is a common scenario. Additionally, the type is used by several + WebAssembly runtimes that take advantage of the safety and portability + while targeting efficient execution and compact representation. +
    Fragment Identifier Considerations: +
    None +
    Restrictions on usage: +
    None +
    Provisional Registrations: +
    N/A +
    Additional information: +
    +
    +
    Deprecated alias names for this type: +
    None +
    Magic number(s): +
    0x00 0x61 0x73 0x6D +
    File extension(s): +
    .wasm +
    Macintosh file type code(s): +
    None +
    Object Identifier(s) or OID(s): +
    None +
    +
    Intended usage: +
    Common +
    Other Information & Comments: +
    Common +
    Contact Person: +
    +
    +
    Contact Name: +
    Eric Prud’hommeaux +
    Contact Email Address: +
    eric@w3.org +
    Author/Change Controller: +
    W3C +
    +
    +
    +
    +

    Conformance

    +

    Document conventions

    +

    Conformance requirements are expressed + with a combination of descriptive assertions + and RFC 2119 terminology. + The key words “MUST”, “MUST NOT”, “REQUIRED”, “SHALL”, “SHALL NOT”, “SHOULD”, “SHOULD NOT”, “RECOMMENDED”, “MAY”, and “OPTIONAL” + in the normative parts of this document + are to be interpreted as described in RFC 2119. + However, for readability, + these words do not appear in all uppercase letters in this specification.

    +

    All of the text of this specification is normative + except sections explicitly marked as non-normative, examples, and notes. [RFC2119]

    +

    Examples in this specification are introduced with the words “for example” + or are set apart from the normative text + with class="example", + like this:

    +
    + +

    This is an example of an informative example.

    +
    +

    Informative notes begin with the word “Note” + and are set apart from the normative text + with class="note", + like this:

    +

    Note, this is an informative note.

    +

    Conformant Algorithms

    +

    Requirements phrased in the imperative as part of algorithms + (such as "strip any leading space characters" + or "return false and abort these steps") + are to be interpreted with the meaning of the key word + ("must", "should", "may", etc) + used in introducing the algorithm.

    +

    Conformance requirements phrased as algorithms or specific steps + can be implemented in any manner, + so long as the end result is equivalent. + In particular, the algorithms defined in this specification + are intended to be easy to understand + and are not intended to be performant. + Implementers are encouraged to optimize.

    +
    + +

    Index

    +

    Terms defined by this specification

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Terms defined by reference

    +
      +
    • + [ECMA-262] defines the following terms: +
        +
      • ArrayBuffer +
      • TypeError +
      • agent cluster +
      • current realm +
      +
    • + [FETCH] defines the following terms: +
        +
      • Response +
      • consume body +
      • extracting a mime type +
      • header list +
      • ok status +
      • response +
      • status +
      +
    • + [HTML] defines the following terms: +
        +
      • Serializable +
      • cors-same-origin +
      • deserialization steps +
      • networking task source +
      • serialization steps +
      • sub-deserialization +
      • sub-serialization +
      +
    • + [WASMJS] defines the following terms: +
        +
      • CompileError +
      • Module +
      • WebAssembly +
      • WebAssemblyInstantiatedSource +
      • asynchronously compile a webassembly module +
      • compile a webassembly module +
      • exported function +
      • instantiate +
      • instantiate a promise of a module +
      +
    • + [WEBASSEMBLY] defines the following terms: +
        +
      • function index +
      • name section +
      +
    • + [WEBIDL] defines the following terms: +
        +
      • DOMException +
      • DataCloneError +
      • Exposed +
      • Promise +
      • a new promise +
      • get a copy of the buffer source +
      • object +
      • reject +
      • resolve +
      • upon fulfillment +
      • upon rejection +
      +
    +

    References

    +

    Normative References

    +
    +
    [ECMA-262] +
    ECMAScript® Language Specification. Current Editor's Draft. URL: https://tc39.github.io/ecma262 +
    [FETCH] +
    Anne van Kesteren. Fetch Standard. Living Standard. URL: https://fetch.spec.whatwg.org/ +
    [HTML] +
    Anne van Kesteren; et al. HTML Standard. Living Standard. URL: https://html.spec.whatwg.org/multipage/ +
    [RFC2119] +
    S. Bradner. Key words for use in RFCs to Indicate Requirement Levels. March 1997. Best Current Practice. URL: https://datatracker.ietf.org/doc/html/rfc2119 +
    [WASMJS] +
    WebAssembly JS Integration Specification. Draft. URL: https://webassembly.github.io/spec/js-api/ +
    [WEBASSEMBLY] +
    WebAssembly Core Specification. Draft. URL: https://webassembly.github.io/spec/core/ +
    [WEBIDL] +
    Edgar Chen; Timothy Gu. Web IDL Standard. Living Standard. URL: https://webidl.spec.whatwg.org/ +
    +

    IDL Index

    +
    [Exposed=(Window,Worker)]
+partial namespace WebAssembly {
+  Promise<Module> compileStreaming(Promise<Response> source);
+  Promise<WebAssemblyInstantiatedSource> instantiateStreaming(
+      Promise<Response> source, optional object importObject);
+};
+
+
    + + + + + \ No newline at end of file From bb6fbcf37e3348d01e3b98070c8b5b2b5553a79d Mon Sep 17 00:00:00 2001 From: wingo Date: Wed, 22 Jun 2022 08:50:33 +0000 Subject: [PATCH 02/14] deploy: f9024a25e6a44aa5967c0eb6878b4bedeefc49c9 --- core/.buildinfo | 2 +- core/_download/WebAssembly.pdf | Bin 1510762 -> 1510954 bytes core/_static/documentation_options.js | 2 +- core/appendix/algorithm.html | 2 +- core/appendix/changes.html | 2 +- core/appendix/custom.html | 2 +- core/appendix/embedding.html | 2 +- core/appendix/implementation.html | 2 +- core/appendix/index-instructions.html | 2 +- core/appendix/index-rules.html | 2 +- core/appendix/index-types.html | 2 +- core/appendix/index.html | 2 +- core/appendix/properties.html | 2 +- core/bikeshed/index.html | 24 ++++++++++++------------ core/binary/conventions.html | 2 +- core/binary/index.html | 2 +- core/binary/instructions.html | 2 +- core/binary/modules.html | 2 +- core/binary/types.html | 2 +- core/binary/values.html | 2 +- core/exec/conventions.html | 2 +- core/exec/index.html | 2 +- core/exec/instructions.html | 2 +- core/exec/modules.html | 2 +- core/exec/numerics.html | 2 +- core/exec/runtime.html | 2 +- core/genindex.html | 2 +- core/index.html | 4 ++-- core/intro/index.html | 2 +- core/intro/introduction.html | 4 ++-- core/intro/overview.html | 2 +- core/search.html | 2 +- core/searchindex.js | 2 +- core/syntax/conventions.html | 2 +- core/syntax/index.html | 2 +- core/syntax/instructions.html | 2 +- core/syntax/modules.html | 2 +- core/syntax/types.html | 2 +- core/syntax/values.html | 2 +- core/text/conventions.html | 2 +- core/text/index.html | 2 +- core/text/instructions.html | 2 +- core/text/lexical.html | 2 +- core/text/modules.html | 2 +- core/text/types.html | 2 +- core/text/values.html | 2 +- core/valid/conventions.html | 2 +- core/valid/index.html | 2 +- core/valid/instructions.html | 2 +- core/valid/modules.html | 2 +- core/valid/types.html | 2 +- js-api/index.html | 8 ++++---- web-api/index.html | 8 ++++---- 53 files changed, 71 insertions(+), 71 deletions(-) diff --git a/core/.buildinfo b/core/.buildinfo index 1fca0ce5..e3d3ba39 100644 --- a/core/.buildinfo +++ b/core/.buildinfo @@ -1,4 +1,4 @@ # Sphinx build info version 1 # This file hashes the configuration used when building these files. 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zSW*zy{6rHma>?q@%b1K%IBtwxR#0AJA`RfPjyTT8aSFI_(mv{fR!GFT>mfhABL4o4_3U<9-JD&{|o#VCF_OxA28w_BlW(0}VqskfWBt%X~8T zWMoiqwL(yn5WFV3RqLaGWW2TqTXf4Y>ZNBjDt?LP69`Uf3%YamnI~3Q1-*WQ`5N1C zI+&-fn5vqw);2nQj4~aXX`0i62v-ubv=TjsRx^rw-4!b6vqp%nj>R6x-XY`oY%Nv@FYXF$;im;$`IQvP7*bQ9kyQYp(o0zseZ$6azd+qJI z_rV@gCZz$=5*_k1-xn!k`Xfw|ox&Z%%7wF)*4e zHRgvjs(smMel@$V3~2H5KnH&%GUz9=A&KI@*uh1VH*+T~I%tNu)I7sr2Z>pL>BT

    WebAssembly Core Specification

    -

    Editor’s Draft,

    +

    Editor’s Draft,

    More details about this document
    @@ -648,7 +648,7 @@

    Table of Contents

    - WebAssembly 2.0 + stringref (Draft 2022-04-27) + WebAssembly 2.0 + stringref (Draft 2022-06-22) @@ -657,8 +657,8 @@

    Table of Contents

    @@ -667,7 +667,7 @@

    Table of Contents

    WebAssembly Specification

    -
    Release 2.0 + stringref (Draft 2022-04-27)
    +
    Release 2.0 + stringref (Draft 2022-06-22)
    Editor: Andreas Rossberg
    @@ -688,7 +688,7 @@

    1) is a safe, portable, low-level code format designed for efficient execution and compact representation. Its main goal is to enable high performance applications on the Web, but it does not make any Web-specific assumptions or provide Web-specific features, so it can be employed in other environments as well.

    WebAssembly is an open standard developed by a W3C Community Group.

    -

    This document describes version 2.0 + stringref (Draft 2022-04-27) of the core WebAssembly standard. +

    This document describes version 2.0 + stringref (Draft 2022-06-22) of the core WebAssembly standard. It is intended that it will be superseded by new incremental releases with additional features in the future.

    @@ -17057,11 +17057,11 @@

    Execution

    - +

    Conformance

    @@ -17088,7 +17088,7 @@

    , like this:

    -

    Note, this is an informative note.

    +

    Note, this is an informative note.

    Conformant Algorithms

    Requirements phrased in the imperative as part of algorithms (such as "strip any leading space characters" diff --git a/core/binary/conventions.html b/core/binary/conventions.html index 079d7a59..0b880edc 100644 --- a/core/binary/conventions.html +++ b/core/binary/conventions.html @@ -6,7 +6,7 @@ - Conventions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Conventions — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/binary/index.html b/core/binary/index.html index 3d8ffb86..2b4ce2d6 100644 --- a/core/binary/index.html +++ b/core/binary/index.html @@ -6,7 +6,7 @@ - Binary Format — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Binary Format — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/binary/instructions.html b/core/binary/instructions.html index 66833c26..cf8ce3a0 100644 --- a/core/binary/instructions.html +++ b/core/binary/instructions.html @@ -6,7 +6,7 @@ - Instructions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Instructions — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/binary/modules.html b/core/binary/modules.html index 439735c5..2fd1c7ae 100644 --- a/core/binary/modules.html +++ b/core/binary/modules.html @@ -6,7 +6,7 @@ - Modules — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Modules — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/binary/types.html b/core/binary/types.html index 31573886..8e1dc74f 100644 --- a/core/binary/types.html +++ b/core/binary/types.html @@ -6,7 +6,7 @@ - Types — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Types — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/binary/values.html b/core/binary/values.html index 7efd7ff7..f18f9acf 100644 --- a/core/binary/values.html +++ b/core/binary/values.html @@ -6,7 +6,7 @@ - Values — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Values — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/exec/conventions.html b/core/exec/conventions.html index 2004b56b..7a419715 100644 --- a/core/exec/conventions.html +++ b/core/exec/conventions.html @@ -6,7 +6,7 @@ - Conventions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Conventions — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/exec/index.html b/core/exec/index.html index 14a4537b..b177ede2 100644 --- a/core/exec/index.html +++ b/core/exec/index.html @@ -6,7 +6,7 @@ - Execution — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Execution — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/exec/instructions.html b/core/exec/instructions.html index add88423..7080cbe3 100644 --- a/core/exec/instructions.html +++ b/core/exec/instructions.html @@ -6,7 +6,7 @@ - Instructions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Instructions — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/exec/modules.html b/core/exec/modules.html index 103c3cfb..42c0f86e 100644 --- a/core/exec/modules.html +++ b/core/exec/modules.html @@ -6,7 +6,7 @@ - Modules — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Modules — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/exec/numerics.html b/core/exec/numerics.html index b1f6963e..206d5138 100644 --- a/core/exec/numerics.html +++ b/core/exec/numerics.html @@ -6,7 +6,7 @@ - Numerics — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Numerics — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/exec/runtime.html b/core/exec/runtime.html index 4eb896a6..92d7073c 100644 --- a/core/exec/runtime.html +++ b/core/exec/runtime.html @@ -6,7 +6,7 @@ - Runtime Structure — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Runtime Structure — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/genindex.html b/core/genindex.html index 0adb322f..75259dc2 100644 --- a/core/genindex.html +++ b/core/genindex.html @@ -5,7 +5,7 @@ - Index — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Index — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/index.html b/core/index.html index 586df31b..b6b2c960 100644 --- a/core/index.html +++ b/core/index.html @@ -6,7 +6,7 @@ - WebAssembly Specification — WebAssembly 2.0 + stringref (Draft 2022-04-27) + WebAssembly Specification — WebAssembly 2.0 + stringref (Draft 2022-06-22) @@ -78,7 +78,7 @@

    Quick search

    WebAssembly Specification

    -
    Release 2.0 + stringref (Draft 2022-04-27)
    +
    Release 2.0 + stringref (Draft 2022-06-22)
    Editor: Andreas Rossberg
    diff --git a/core/intro/index.html b/core/intro/index.html index 998f8048..6478aee8 100644 --- a/core/intro/index.html +++ b/core/intro/index.html @@ -6,7 +6,7 @@ - Introduction — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Introduction — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/intro/introduction.html b/core/intro/introduction.html index 614de8bf..cd20eb5e 100644 --- a/core/intro/introduction.html +++ b/core/intro/introduction.html @@ -6,7 +6,7 @@ - Introduction — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Introduction — WebAssembly 2.0 + stringref (Draft 2022-06-22) @@ -86,7 +86,7 @@

    IntroductionW3C Community Group.

    -

    This document describes version 2.0 + stringref (Draft 2022-04-27) of the core WebAssembly standard. +

    This document describes version 2.0 + stringref (Draft 2022-06-22) of the core WebAssembly standard. It is intended that it will be superseded by new incremental releases with additional features in the future.

    Design Goals

    diff --git a/core/intro/overview.html b/core/intro/overview.html index 778a2b7f..96360977 100644 --- a/core/intro/overview.html +++ b/core/intro/overview.html @@ -6,7 +6,7 @@ - Overview — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Overview — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/search.html b/core/search.html index 4591a88e..64532a7c 100644 --- a/core/search.html +++ b/core/search.html @@ -5,7 +5,7 @@ - Search — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Search — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/searchindex.js b/core/searchindex.js index ed31bc93..a9b20297 100644 --- a/core/searchindex.js +++ b/core/searchindex.js @@ -1 +1 @@ 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,43],_3:13,_4:[13,34],_5:13,_6:13,_7:13,_8:[13,20,34],_9:13,_:[1,6,12,13,15,19,21,28,34,36,38],_e:20,_f32:[28,34],_f32x4:[1,6,12,28,34],_f64:[28,34],_f64x2:[1,6,12,28,34],_f:[1,18,21,28],_high:[6,12,34],_i16x8:[1,6,12,28,34],_i32:[28,34],_i32x4:[1,6,12,28,34],_i64:[28,34],_i8x16:[1,6,12,28,34],_i:[1,3,9,19,26,28,34,36,41,42],_if:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_indirect:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_lane:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_low:[1,6,12,28,34],_m:[18,20,21],_n:[2,13,18,21,31,34,38,39],_null:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_pairwis:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_s:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_sat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],_splat:[1,6,12,28,34],_t:[18,20,21],_tabl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_true:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],_x:18,_y:18,_zero:[1,6,12,28,34],a0:[6,12],a1:[6,12],a2:[6,12],a3:[6,12],a4:[6,12],a5:[6,12],a6:[6,12],a7:[6,12],a8:[6,12],a9:[6,12],a_1:[10,26,32],a_2:26,a_i:[10,26,32],a_n:[10,26,32],aa:[6,12],ab:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],abbrevi:[21,24,33,38],abil:1,abl:[9,13],abort:[16,18,25,28],about:[3,9,16,21,24,39],abov:[0,4,9,18,31,35],abrupt:21,absent:[9,39,41],absolut:34,ac:[6,12],accept:30,access:[0,1,3,9,18,24,25,26,28,29,34,39,42],accord:[3,18,28,35,39],accordingli:[39,41],accumul:[0,21,41],acm:[9,16,39],acronym:24,across:24,activ:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],actual:[0,2,10,12,13,18,19,25,32,42],ad:[1,6,9,12,13,19,20,28],add:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],addit:[0,1,3,4,9,10,12,13,15,21,24,25,28,29,30,32,34,36,39],addition:[0,28],addr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],address:[3,9,17,19,25,28],adher:[9,18],admin:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],administr:[5,17,18],adopt:[3,10,16,26,32,39],advantag:24,ae:[6,12],af:[6,12],affect:[2,18,19,28,35],aforement:24,after:[0,2,13,16,18,28,29,34],afterward:[0,16],again:20,against:[0,18,19,28,43],ahead:[24,35],akin:41,algorithm:[5,22,39,41],align:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],alik:24,all:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],alloc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocdata:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocelem:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocfunc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocglob:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allochostfunc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocmem:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocmodul:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],alloct:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocx:19,allow:[0,1,4,9,10,12,14,15,18,20,21,24,25,28,29,32,34,35,36,38,39,41,43],alon:[9,16,24,39],along:0,alreadi:[4,18,38],also:[1,3,9,10,12,14,16,18,19,20,21,24,25,26,28,29,30,31,32,34,36,38,39,41],alter:25,altern:[10,20,28],alwai:[9,20,21,25,28,35,38,39,43],ambient:24,ambigu:21,amen:[16,39],among:[20,31],an:[0,1,2,3,4,9,10,12,13,15,16,18,19,20,21,24,25,26,28,29,30,31,32,34,36,38,39,41,42,43],analog:34,andnot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],andrea:[9,16,22,39],ani:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],annot:[12,18,28,34,39,41],anonym:[25,36,37],anoth:[28,36,41],anyth:41,anywher:[21,34,37],aot:24,api:[19,24,25],appear:[2,10,18,26,32,34,36,42],append:[19,26,39],appendix:[0,1,2,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],appli:[9,16,18,20,21,32,36,39,43],applic:[4,10,16,20,24,32],approach:[16,39],appropri:[9,16,19,28],ar:[0,1,2,3,4,9,10,12,13,14,15,16,18,19,20,21,24,25,26,28,29,30,31,32,34,35,36,38,39,41,42,43],arbitrari:[1,20,31,32,38],arbitrarili:[21,41],architectur:24,argument:[3,9,12,18,19,20,21,25,28,34],arithmet:[20,31],ariti:[0,18,21],around:[25,34],arrai:[2,3,9,10,12,13,14,15,16,18,19,20,21,25,26,28,29,30,31,32,34,35,36,37,38,39,41,42],articl:[9,16,39],ascii:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ascrib:18,aspect:[0,4,24],assembl:25,assert:[3,16,18,19],assign:[2,21,32,35],associ:[0,2,9,18,19,21,28,30,32],assum:[3,4,9,16,19,20,21,26,32,35,39,41],assumpt:[9,24,39],ast:[6,7,8,10,12,13,14,15,16,19,20,21,26,28,29,30,31,32,34,35,36,37,38,39,43],ast_i:19,atom:[19,26],attach:2,attack:24,attribut:[10,20,32,36],augment:[10,26,32,36],authorit:24,automat:[3,9,25,29,36],aux:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],auxiliari:[0,3,11,15,18,19,20,21,27,29,30,31,34,36,41],avail:[18,24,25,28,29,39],averylonginstructionnameforvectext:34,avgr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],avoid:[1,12,16,21,32],awai:28,axiom:39,b0:[6,12],b1:[6,12],b2:[6,12],b3:[6,12],b4:[6,12],b5:[6,12],b6:[6,12],b7:[6,12],b8:[6,12],b9:[6,12],b:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],b_1:[9,10,15,26],b_2:[9,15,26],b_3:15,b_4:15,b_:12,b_i:10,b_n:10,ba:[6,12],back:[0,18,25,28,41],backslash0asm:13,backslash:38,backward:[13,18,28,34,36],base:[18,20,25,28,29,31,34],basic:[10,21,25,28],bastien:[9,16,39],bb:[6,12],bc:[6,12],bd:[6,12],becaus:[18,19,20,21,24,41],becom:29,been:[0,1,16,19,21,24,29],befor:[4,13,19,24,29,32,36],beforehand:19,begin:[2,3,4,9,10,12,13,14,15,16,18,19,20,21,24,26,28,29,30,31,32,34,35,36,37,38,39,41,42],behav:[9,21,28],behavior:[9,16,18,21,24,28],being:[13,24,28,41],below:[9,19,42],ben:[9,16,39],benjamin:[16,39],besid:[20,21],between:[3,20,25,31,32],beyond:[24,25],bf:[6,12],big:39,bigoplu:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bigwedg:18,biject:20,binari:[0,1,2,3,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bind:[10,32,34,36],binop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],bit:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bitfield:13,bitmask:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],bitselect:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bitwidth:28,bitwis:[20,28],block:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42],blockchar:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],blockcom:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],blockinstr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],blocktyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],bodi:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],book:[16,21,39],bool:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bot:[9,18,41],both:[9,14,15,16,20,26,28,29,34,36,38,39,41,43],bottom:41,bound:[10,13,15,25,26,28,31,32,34,36,43],boundari:1,br:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],br_if:0,br_tabl:0,bracket:[12,28,30,34,35,38],branch:[0,18,21,25,28,34],breach:24,brief:[16,39],bring:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],broadli:24,browser:24,bt:[6,12,18,34],bubbl:21,bytes_:[12,20],c0:[6,12,15],c1:[6,12],c2:[6,12,18],c3:[6,12],c4:[6,12],c5:6,c6:6,c7:6,c8:6,c9:6,c:[3,7,9,15,28,34,35,38,39,42,43],c_0:20,c_1:[18,20],c_2:18,c_3:18,c_:20,c_i:20,c_k:20,ca:6,cach:24,calcul:19,call:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],calle:28,can:[0,1,2,3,9,10,12,13,14,16,18,19,20,21,24,25,26,28,29,30,31,32,34,35,36,38,39,41,42],candid:20,candidatepair:20,cannot:[0,12,19,24,25,28,29,35,37],canon:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],cap:[20,24],capabl:24,carri:[3,21],carriag:35,categori:[8,21,25,28,35],caught:25,caus:28,cb:6,cc:6,ccc:9,cd:6,cdot2:31,cdot64:18,cdot:[3,9,15,16,18,19,20,31,38,41],ce:6,ceil:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],certain:[9,16,20,21,25],certifi:9,cf:6,chang:[0,5,9,13,22,39],channel:24,chapter:35,charact:[4,15,24,31,32,33,38],check:[0,1,13,18,19,25,28,30,34,39,41,42,43],choic:[18,21,36,41],chosen:[20,41],clamp:20,classif:3,classifi:[9,19,30,39,41,42,43],claus:[20,36],clear:[21,30,31],clll:36,cllll:36,close:[10,28,32,42],closest:20,closur:[19,21],clutter:[16,32],clz:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],code:[0,1,2,3,4,5,6,7,8,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],codesec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],codifi:9,coexist:14,coincid:[9,16,18],collect:[21,29,39],collid:12,com:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],combin:[1,20,36,37,41],combinatori:[10,26,32],come:28,comma:38,comment:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,36,37,38,39,40,41,42,43],common:[4,21,24,26],commun:24,compact:24,comparison:28,compat:[13,34,36],compil:[1,2,4,13,24,25,29],complement:[15,20,24,25,28,31],complementari:25,complet:[0,3,10,25,29,32,39],complex:[26,31],compon:[9,13,16,21,26,29,32,39,42],compos:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],composit:[26,36],compound:[9,41],compress:[10,12,13],comput:[4,9,16,18,20,21,24,25,28,30,32],concat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],concaten:[3,9,13,18,19,26,42],concept:23,conceptu:25,concern:[24,28],concis:[16,26,39],conclus:39,concret:[4,26,32,39],condit:[5,9,10,15,18,19,20,25,26,28,32,34,36,39],confer:[9,16,39],config:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],configur:[5,7,16],conform:4,conjunct:20,connect:3,conrad:9,consecut:[0,4,21,36],consequ:[0,9,10,28,29,35,36,41,42],consid:[20,21,24,32,34,35],consider:23,consist:[0,2,9,12,13,16,18,19,20,21,25,28,29,34,35,36],constant:[0,1,2,3,4,5,6,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],constitut:18,constrain:[30,41],constraint:[0,4,9,15,21,39,41],construct:[16,21,25,26,28,29,31,32,36,39,42],constructor:[8,14],consum:[18,24,28,39,41],cont:13,contain:[0,9,10,13,15,16,18,19,21,24,25,28,29,32,34,35,36,38,39,41,42],contemporari:24,content:[2,13,18,19,21,26,29,39,42],context:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,31,33,34,35,36,37,38,40,41,42,43],contigu:25,continu:[18,21,26,28],contract:24,contrast:[21,41],contribut:2,control:[0,1,2,3,4,5,6,7,8,10,11,13,14,15,16,17,19,20,21,22,23,24,25,26,27,29,30,31,32,33,35,36,37,38,39,40,42,43],conveni:[16,20,21,28,32],convent:[0,1,2,3,4,5,6,7,8,9,11,12,13,14,15,17,18,19,20,22,23,24,25,27,33,34,35,36,37,40,41,42,43],convers:[17,18,21,25,28],convert:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],convert_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],convert_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],copi:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],copysign:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],core:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],corollari:9,correct:9,correctli:38,correspond:[3,12,13,14,18,19,20,21,26,29,30,31,32,34,35,38,39,41],corrupt:24,could:25,count:[1,11,18,20,21],cours:24,courtesi:21,cover:9,cpp:9,crash:9,creat:[3,21,25],crucial:16,ctrl:0,ctrl_frame:0,ctrl_stack:0,ctxt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ctz:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],cup:20,current:[0,2,9,10,13,16,18,21,25,28,29,36,39,41],custom:[0,1,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],customsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],cvtop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],d0:[6,12],d1:[6,12],d2:[6,12],d3:6,d4:6,d5:6,d6:6,d7:6,d7ff:[31,35],d800:[15,38],d8:6,d9:6,d:[13,18,20,36,38],d_0:20,d_1:[18,20],d_2:[18,20],d_:20,da:[6,18,36],dan:[9,16,39],data:[1,2,3,4,5,6,7,8,10,11,12,14,15,16,17,20,22,23,24,25,26,27,28,30,31,32,33,34,35,37,38,39,40,43],dataaddr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],datacountsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],dataidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],datainst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],datamod:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],datasec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],datastr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],db:6,dc:6,dd:6,de:6,deal:[10,26],debug:[13,24],debugg:2,decim:38,declar:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],decod:[0,10,13,24,25],decompos:21,decreas:20,dedic:2,deduct:39,def:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],defer:[4,13],defin:[1,2,3,9,10,13,15,16,18,19,20,21,24,25,26,29,30,31,32,34,35,36,38,39,41,42,43],definit:[2,3,9,13,16,18,19,20,21,24,25,26,29,31,35,36,39,41,42],degre:41,delimit:[34,35],delta:28,demot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],denot:[10,13,14,18,20,21,26,28,29,30,31,32,38,39],dens:10,depend:[2,4,13,18,19,20,23,28,29,31,38,39,42],deploy:29,depth:[4,28],derek:[9,16,39],deriv:[3,9,10,16,39],desc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],describ:[0,9,13,16,21,24,26,28,29,31,39,41],descript:[3,7,13,16,29,32,36,39,42],descriptor:[29,34,36],design:[4,9,16,23,39],desktop:24,destin:28,detail:25,detect:0,determin:[0,16,19,20,28,30,31,34,42],determinist:[16,18,20,21],develop:24,devic:[19,24,42],df:6,diagnost:3,differ:[0,3,9,10,12,18,19,20,21,24,25,26,28,29,31,41,42],digit:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],dim:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],dimens:[4,41],dimension:2,dinstr:19,direct:[20,28],directli:[0,1,3,9,15,18,24,25,32,34,36],disallow:35,disambigu:35,discrep:24,disjoint:[9,42],disjunct:20,distinct:[25,31,32],distinguish:[10,13,21,28,29,31,32,34,41],distribut:25,div:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],diverg:[9,18],divid:[3,18,19,20,21,25,28,35,41],dividend:20,divis:[19,20],dmode:19,document:[24,37],documentari:36,doe:[0,3,9,13,18,19,20,24,28,35,38,39,42],dot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],doubl:[30,35],draft:[22,24],drawn:32,drop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],due:[3,18,19,31],dummi:19,dup:0,duplic:[0,28,32,36],dure:[4,9,18,21,29,30,43],dynam:[9,19,21,25,28],e000:[15,31,35,38],e0:[6,15],e1:6,e2:6,e3:6,e4:6,e5:6,e6:6,e7:6,e8:6,e9:6,e:[0,2,9,10,13,18,19,20,21,24,28,31,36,38],e_i:[13,42],ea:[6,18],each:[0,2,3,9,10,12,13,16,18,19,20,21,24,25,26,28,29,32,36,38,39,41,42,43],earlier:[18,36],eas:43,easi:[0,24],easili:[19,42],eb:6,ec:6,ed:6,editor:22,ee:6,ef:6,effect:[0,16,18,21,28,34,35,41,42],effector:35,effici:[24,41],einit:19,einstr:19,either:[0,9,10,12,15,16,18,19,20,21,24,25,26,28,29,30,31,32,35,36,38,41,43],el:[13,36],elem:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,43],elemaddr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],element:[0,1,3,4,7,10,11,14,17,18,20,25,26,27,28,30,33,38,39,40,41],elemexpr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elemidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],eleminst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elemkind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elemlist:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elemmod:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],elemsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elimin:21,ellips:26,els:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],elsewher:39,emb:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],embed:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],embedd:[3,4,9,18,19,21,24,25,29,30],embodi:39,emploi:[24,26],empti:[0,3,9,10,12,13,16,18,19,20,21,26,29,32,34,36,39,42,43],emptyset:[9,13],emul:25,enabl:[4,13,21,24],encapsul:9,enclos:[28,32,35,38],encod:[2,10,12,13,14,15,21,24,25,31,32,38,39],encompass:24,end:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],end_typ:0,endian:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],enforc:[15,28,34,36,39,41],enough:28,enrich:1,ensur:[0,9,18,19,21,25,36],enter:[0,16,28],entir:[16,21,29,36,41,42],entiti:[21,25,29,30],entri:[1,3,13,18,19,21,28,30,32,34,39],enumer:0,environ:[3,4,24,25,29],eof:35,epsilon:[3,8,9,10,12,13,14,16,18,19,20,21,26,32,34,36,37,38,42,43],eq:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],equal:[3,9,10,19,20,21,24,26,41,43],equat:20,equiv:[32,34,36,37],equival:[13,16,29,39],eqz:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],err:18,error:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],error_if:0,escap:38,especi:24,establish:24,et:[13,14,19,36,37,42],ev:3,evalu:[9,16,18,19],even:[0,3,20,21,29],event:4,ever:13,everi:[3,4,9,13,16,18,29,31,39],ex:[3,13,19,36],exact:[20,28],exactli:[10,20,21],exampl:[0,3,9,10,15,16,18,20,21,25,28,29,32,34,35,39,41],exce:[15,21],exceed:[4,18],except:[9,10,12,13,16,20,26,32,35,38,41,42],exclud:20,exclus:[20,35],exec:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],execut:[5,6,9,16,18,19,21,22,24,25,28,30,41],exist:[0,3,9,18,19,20,21,24,34,36,39],exit:[0,16],expand:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],expans:[10,20,26,32,36,38],expect:[0,3,4,9,13,18,19,28,41],experi:2,explan:[16,39],explanatori:0,explicit:[9,12,13,21,26,34,36,38],explicitli:[3,9,16,18,39],expon:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],exportdesc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],exportinst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],exportsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],expr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],express:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23,24,25,26,27,29,30,31,32,33,35,36,37,38,39,40,42,43],extadd:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],extend16:34,extend32:34,extend8:34,extend:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],extend_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],extend_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],extens:[0,5,10,12,13,18,20,28,32,39],extern:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,20,22,23,24,25,26,27,28,29,31,32,33,34,35,36,37,38,39,40,41,42],externaddr:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],externref:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],externtyp:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],externv:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],extmul:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],extra:9,extract:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],f0:[6,15],f1:6,f2:6,f32:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f32x4:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f3:6,f4:6,f5:6,f64:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f64x2:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f6:6,f7:6,f8:6,f9:6,f:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f_:19,fa:6,fab:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fact:[0,18,34,35],fadd:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fail:[18,19],failur:[3,18,19],fall:[18,25,35],fals:0,farther:28,fashion:[21,29,30],fast:24,fb:6,fbia:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fbit:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fc:[6,12],fceil:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fcopysign:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fd:[6,12],fdiv:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fe:[6,15],featur:[4,24],feed:35,feq:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],few:[10,16,32],ff:[6,15,31],ffloor:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fge:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fgt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],field:[13,19,26,36,39,42],file:[10,32,36],fill:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],filter:[21,29,30],finit:9,first:[0,4,19,20,26,28,29,30,36,41],fit:19,fix:[4,26,31],flag:[0,14,20],flat:[0,26],flavor:28,fle:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],floor:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],flow:[25,28],flt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fmax:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fmin:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fmul:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fn:36,fne:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fnearest:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fneg:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fold:[4,33],foldedinstr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],follow:[0,1,2,3,4,9,10,12,13,14,15,16,18,19,20,21,24,25,26,28,29,30,32,34,35,36,38,39,43],font:[10,26,32],foral:[9,20],foreach:0,forev:9,form:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],formal:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,40,41,42,43],format:[0,1,2,3,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,36,37,38,39,40,41,42,43],formed:[25,36,42],former:[0,10,32],formul:39,forth:10,forward:[13,28,29],found:[16,39],four:[21,25,28],fpmax:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fpmin:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],frac:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fraction:38,frame:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],free:[19,29,39],freed:28,frelop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fresh:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],from:[0,3,4,9,10,13,16,19,20,21,24,25,26,28,29,30,31,32,34,35,36,37,39,41,42],front:39,fshape:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fsign:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fsqrt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fsub:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ft:[3,13,18,36,42],ftestop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ftrunc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],full:25,fulli:[4,24,41],func:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],funcaddr:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcbind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcinst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcnamesec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcnamesubsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcref:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],functyp:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],funop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],further:[13,15,16,25,28,41],furthermor:[9,13,16,18,36,38,42],futur:[4,9,12,13,14,18,20,21,24,28,29,30,41,42],g:[0,2,9,19,24,31],gap:12,garbag:21,ge:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],gener:[0,1,9,10,13,16,18,20,26,32,39],geq:[10,12,15,20,26,31,32,38,43],get:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],gi:3,ginit:19,github:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],give:[16,39],given:[2,4,9,10,16,18,19,20,21,24,25,26,28,29,30,32,34,36,38,39,41,43],gl:36,glob:[13,18],global:[0,1,2,4,5,6,7,8,10,11,12,15,16,17,20,22,23,24,25,26,27,28,31,32,33,34,35,38,39,40],globaladdr:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globalbind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globalidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globalinst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globalsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globaltyp:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],go:29,goal:23,gohman:[9,16,39],grammar:[3,11,13,27,28,31,33,34,35,36,38],grave:38,greater:20,group:[2,24,28,34],grow:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],growmem:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],grown:25,growtabl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],gt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],guarante:[3,16,24,25],h:38,ha:[0,1,2,3,9,10,13,16,18,19,20,21,24,25,26,29,31,32,39,41],haa:[9,16,39],had:10,half:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],hand:[3,21],handl:[0,20,21,25,34],happen:19,hardwar:[18,24,28],hat:38,have:[1,4,10,12,13,18,20,21,24,26,28,29,31,32,34,37,39,41,43],head:34,heap:37,heaptyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],height:[0,21,25,28],help:20,henc:[3,20,21,24,38,39],here:[0,3,10,13,18,19,21,35,39,41,43],heterogen:28,hexadecim:[10,31,38],hexdigit:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hexfloat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hexfrac:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hexnum:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hf:18,hfill:19,hh:38,high:[18,24,28],hint:[2,18,28],histori:[5,22],hold:[9,18,20,21,30,39],hole:21,holman:[9,16,39],hookrightarrow:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hop:21,horizont:35,host:[3,21,24,25,29],hostcod:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hostfunc:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],how:[19,24,25,28,29,34,41],howev:[0,2,4,10,13,15,18,19,21,24,25,28,29,31,32,34,36,39,42,43],hspace:34,http:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i128:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i16:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i16x8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i2:20,i32:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i32x4:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i64:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i64x2:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i8x16:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],i:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i_1:18,i_2:18,iab:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iadd:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iaddsat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iaddsat_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iaddsat_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iand:[0,1,2,3,4,5,6,7,8,9,10,11,12,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1,32,33,34,35,36,37,38,39,40,41,42,43],opposit:20,optim:[18,28],option:[1,10,13,25,26,28,30,32,34,36,37,38,39],order:[0,2,3,9,10,12,13,15,16,19,20,21,25,28,29,30,31,32,36,42],organ:[13,25,29],origin:[0,1,9,16,18,20,21],other:[0,3,4,9,10,12,13,15,16,18,19,20,21,24,25,28,29,31,32,34,35,38,39,41,42],otherwis:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],out:[0,4,13,20,21,28,29,30,32,39],outcom:[9,18,21,42],outer:21,outermost:28,output:[20,28,30,41],outsid:[9,10,21,25,28,38,39],outward:28,over:[0,3,4,13,20,21,26,28,29,30,31,32,36,39,42],overflow:38,overlap:[28,35,36],overload:29,overview:[1,22,23],own:[9,19,21,24,25,29,30],p:[20,38],p_1:20,p_2:20,pack:[20,25,28,30,41],page:[3,9,18,19,21,28,29,30,36],pair:[2,3,10,13,18,20,25,29,36],parallel:[1,13,24],paralleliz:24,param:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],paramet:[1,3,4,14,18,19,25,29,30,32,36,37,39,42],parameter:13,parametr:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23,24,25,26,27,29,30,31,32,33,35,36,37,38,39,40,42,43],parenthes:[10,26,31,32,34,35],pars:[3,10,32,34],part:[2,3,16,18,21,24,25,26,28,39,41],parti:13,partial:[18,20],particular:[16,20,24,25,29],particularli:42,pass:[0,3,13,19,21,24,30,42],passiv:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],path:26,pattern:[12,15,30],payload:[20,31,38],per:[1,2,3,16,18,32,41],perform:[0,1,16,18,19,21,24,25,28,41,42],permit:20,phantom:[12,34],phase:23,phrase:[10,34,39],physic:4,pick:[10,20,41],piec:39,pierc:[16,39],place:[13,14,16,19,21,24,28,32,36,39],placehold:20,placement:13,plain:[12,20,32,34,43],plaininstr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],platform:24,pldi:[9,16,39],pm:[20,31,38],pmax:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],pmin:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],point:[1,3,11,17,18,21,24,26,27,28,30,33,41],pointer:25,pointwis:[19,20],polici:24,polymorph:[0,41],pop:[0,16,18,19,25,28,41],pop_ctrl:0,pop_val:0,popcnt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],portabl:24,posit:[8,12,14,15,18,20,31,34,39],possibl:[3,9,10,12,13,14,18,19,20,21,24,26,28,29,30,31,32,35,36,41],post:[5,9,18],potenti:24,power:[20,28],practic:[18,19,21,25],pre:[5,9,18,19,42],preambl:13,preced:[14,20,29,36],preceq:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],precis:[9,16,18,21,24,30],predic:20,prefix:[12,28,41],premis:39,prepend:[0,9,39,41],prescrib:[13,28,41],presenc:[0,13,16,18],present:[0,12,13,14,19,21,29,41],preserv:[9,21,29,30],press:[16,39],presum:38,prevent:[24,28,38],previou:[9,28],previous:36,primari:2,primarili:[19,39],primit:[20,31],printabl:[2,38],privileg:24,proce:[21,39],proceed:[9,16,39],process:[25,30,31,43],produc:[13,16,18,19,20,21,25,28,29,36,39,41],product:[10,15,26,32,35,36,38],program:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],progress:9,project:1,promot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],proof:[9,16,39],prop:9,propag:21,proper:0,properti:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],propos:1,proposit:39,prose:[17,40],prove:9,provid:[1,2,3,10,19,21,24,25,26,28,29,32,38,39,41,43],pseudo:[0,28,34,35],pth:26,pure:0,purg:0,purpos:[0,2,19,21,37],push:[0,16,18,19,21,25,28,41],push_ctrl:0,push_val:0,put:24,q15mulr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],q:[20,38],q_1:20,q_2:20,qquad:[3,9,10,13,14,15,18,19,20,21,31,32,34,35,36,37,38,39,41,42,43],quad:[9,13,16,18,19,21,29,32,34,36,42,43],qualif:20,quiet:[20,31],quot:32,quotat:38,r:[3,9,18,19,20,21,26,38],r_1:26,r_2:26,rang:[1,3,4,12,13,20,21,24,26,28,29,30,31,38,43],rather:21,ration:20,raw:[25,29,31,36,38],rcl:21,rcll:19,re:19,reach:[3,9,18,21],reachabl:0,read:[9,13,16,20,28,39],readabl:32,reader:[16,39],readili:[16,39],real:[20,25],reason:[4,24],recent:[16,41],recogn:35,recommend:[10,20,32],record:[0,13,16,21,26,32,39],rectifi:20,recurs:[19,25,26,32,34,39,41,42],reduc:[16,18,21],reduct:[16,18,21],ref:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],refer:[3,8,9,11,16,17,21,25,27,29,33,36,39,40,42],referenc:[18,19,21,25,28,29,36,37],refin:[0,3],reftyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],regard:[20,34],regardless:[18,28,30],region:28,regist:25,regular:[3,9,34,36],regularli:18,reinterpret:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],reject:4,rel:[9,18,19,20,21,28,34,39,41],relat:[1,9,19,20,28],releas:[5,22,24],relev:[10,21,24,26,32,35,36,39],relop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],rem:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],remain:9,remaind:[0,20],remov:[0,9,16,18,21],render:[2,16,32,39],reorder:1,repeat:[18,34],repeatedli:36,replac:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],report:[4,19,25],repres:[0,2,12,13,16,20,21,25,28,31,34,35,38,39],represent:[0,1,10,15,16,17,21,24,25,26,30,31,38],repurpos:9,requir:[0,3,4,9,10,13,16,18,19,20,21,25,26,28,29,38,39,41,42],reserv:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],resiz:[0,30],resolv:[20,21,29,32,36],resourc:[4,18,24],respect:[0,1,3,9,10,12,13,14,16,18,20,21,24,25,26,28,29,30,31,32,34,36,38,39,41,43],respons:[3,24],rest:[19,35],restart:[21,28],restrict:[4,10,15,21,28,29,32,35,36,42,43],result:[0,1,2,3,4,5,6,7,8,10,11,12,13,15,16,17,18,19,20,22,23,24,25,26,27,28,29,31,32,33,34,35,36,37,38,39,40,41,42,43],resulttyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],resum:28,retriev:28,reus:[21,24,36],revers:0,rewrit:32,right:[0,9,16,18,20,35],rightarrow:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],rlll:19,rllll:19,role:36,root:20,rossberg:[9,16,22,39],rotat:20,rotl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],rotr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],round:[24,36,38],rt:[14,42],rule:[9,10,13,16,18,19,21,22,26,32,34,35,38,39,41,42,43],run:[9,21,24],rundata:19,runelem:19,runtim:[0,1,2,4,5,6,8,10,11,12,13,14,15,16,17,18,20,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s16:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s32:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s64:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s_0:19,s_1:[9,19],s_2:[9,19],s_3:19,s_4:19,s_5:19,s_:19,s_i:[19,26],s_n:19,safe:[24,25],safeti:9,sai:39,said:39,same:[4,9,10,13,14,18,20,21,26,28,29,31,32,34,36,39,41,42,43],san:26,sandbox:24,sat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],sat_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],sat_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],satisfi:[3,9,18],satur:[12,20,28],scalar:[31,32,35,38],schuff:[9,16,39],scope:[9,10,21,23,25,36,39],second:[0,28,36],secondari:[2,19],section:[0,1,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],secur:23,see:36,seen:24,seg:13,segment:[1,4,7,13,18,21,25,27,28,33,39,40,41],select:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],self:[0,24],semant:[0,2,3,9,13,16,18,19,21,22,23,24,39],semicolon:[35,38],sens:3,separ:[0,9,10,12,13,16,20,21,24,25,26,28,32,35,38],seq:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],sequenc:[2,3,5,7,9,10,12,13,15,16,18,19,20,21,25,26,28,29,30,31,32,34,35,36,38,39,40,42],serif:26,serv:[25,29,36],set:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],sever:[12,20,24,28,41],shape:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],share:21,shift:[20,28,34,39,41],shl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],shortcut:28,shorten:26,shorthand:[10,19,20,26,28,32],should:2,show:0,shown:0,shr:[0,1,2,3,4,5,6,7,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0,t2:0,t:[0,3,6,12,13,14,15,20,21,28,30,32,34,36,37,38,39],t_0:41,t_1:[6,9,19,32,36,37,39,42],t_2:[6,9,19,36,37,39,42],t_3:41,t_i:[9,13,19,32,41],t_j:41,t_n:32,ta:[18,36],tab:[13,18],tabl:[0,2,4,5,6,7,8,10,11,15,16,17,20,22,23,24,25,26,27,31,32,33,35,38,39,40],tableaddr:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tablebind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tableidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tableinst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tablesec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tabletyp:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],tableus:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tabul:35,take:[0,1,2,4,9,19,20,21,24,25,28,32],taken:21,target:[16,20,21,25,28],task:24,technic:20,techniqu:21,tee:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],term:[10,16,18,21,26,32,36],termin:[4,9,10,12,15,16,18,21,26,28,29,32,35],ternari:[1,28],test:[1,20,28],testop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],text:[0,1,2,3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,35,36,37,38,39,40,41,42,43],textual:[24,32,38],th:[18,26],than:[1,3,13,18,19,20,21,24,25,28,31,38,41,42,43],thei:[2,4,9,10,12,13,14,18,20,21,24,25,28,29,30,31,32,34,35,36,37,38,39,41,42],them:[0,3,9,16,20,21,25,28,29,31,34,36,39],themselv:[9,15,21,28,35,42],theorem:5,therebi:[16,25,36],therefor:[0,18,21,41],thereof:30,thi:[0,2,3,4,9,10,13,15,16,18,19,20,21,24,25,26,28,29,30,31,32,34,35,38,39,41,42,43],third:[13,28],thisisenough:34,thisshouldbeenough:[12,34],thorough:[16,39],those:[9,10,26,28,32,42],thread:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],three:[16,18,21,25,28],through:[0,3,13,18,21,25,28,29],thu:[10,14,20,25,29,32],ti:[3,20],tild:38,time:[1,4,9,10,18,19,21,24,26,28,29,32],titzer:[9,16,39],togeth:28,token:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,36,37,38,39,40,41,42,43],tool:36,top:[0,10,18,19],toplevel:36,total:15,touch:16,toward:[20,25],track:0,tracker:22,trail:[15,20],transfer:41,translat:24,transmit:24,transpar:30,trap:[0,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],treat:[3,12,26,28],tree:1,tripl:3,trunc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],trunc_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],trunc_sat_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],trunc_sat_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],trunc_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],truncat:[12,20],tt:[3,9,13,36,42],tupl:16,turn:[2,4,13],two:[0,2,10,13,15,16,18,20,24,25,26,28,29,31,35,39,41,43],ty:36,type:[0,2,4,5,6,10,11,12,15,16,17,20,21,22,23,24,25,26,27,28,31,32,33,34,35,38,39,40],typebind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],typedef:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],typeidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],typesec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],typeus:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],typewrit:[10,32],typic:[3,4,16,24,25,28],u16:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u1:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u32:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u64:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ultim:21,unalign:[18,25],unambigu:[14,32],unari:[1,20,28],unchang:9,uncondit:[0,28,41],uncondition:39,unconstrain:41,undefin:[9,20],under:[0,9,18,21,25,30,39,41,42],underflow:0,underli:[18,20,31],underscor:38,understand:[16,39],unicod:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],unifi:21,uniniti:29,uninterpret:[13,15,21,29,31,38],union:30,uniqu:[2,21,29],unit:[28,29,30],univers:[24,43],unknown:[0,13],unless:[9,16,18],unlik:[12,15,25,28,29],unnam:[32,34],unnecessari:[16,32],unop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],unpack:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],unravel:19,unreach:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],unsaf:24,unsign:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],unspecif:3,unspecifi:20,until:[4,13,18],untyp:25,unus:15,unwind:28,up:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],updat:[3,19,26,34,36],upon:29,upper:20,us:[0,1,2,3,4,10,12,13,15,16,18,20,21,24,25,26,28,29,30,31,32,33,34,35,38,39],usabl:25,user:2,usual:[4,10,20,25,28,32],utf8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],utf:[2,15,24,31,32,38],v128:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],v:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],val:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],val_i:19,val_stack:0,val_typ:0,valid:[1,2,3,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,41,42,43],valtyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42],valu:[0,2,4,5,6,7,8,10,11,12,13,16,17,18,20,22,23,24,25,26,27,28,29,32,33,34,35,36,39,40,41,43],vari:[4,12,31],variabl:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23,24,25,26,27,29,30,31,32,33,35,36,37,38,39,40,42,43],variant:[12,15],varieti:24,variou:[0,16,30],vbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vcvtop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vdash:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vechaslongerinstructionnam:12,vechasreallylonginstructionnam:34,vector:[2,8,9,11,13,15,17,19,21,25,27,29,33,40,42],vectyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vee:[9,13,15,18,20,34,36,38],veebar:20,verbatim:34,veri:[13,16],verifi:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],version:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vextmul:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vfbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vfrelop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vfunop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],via:[18,19],vibinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],view:25,viminmaxop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],violat:18,virelop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],virtual:[24,25],visatbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vishiftop:[0,1,2,3,4,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Algorithm","Change History","Custom Sections","Embedding","Implementation Limitations","Appendix","Index of Instructions","Index of Semantic Rules","Index of Types","Soundness","Conventions","Binary Format","Instructions","Modules","Types","Values","Conventions","Execution","Instructions","Modules","Numerics","Runtime Structure","WebAssembly Specification","Introduction","Introduction","Overview","Conventions","Structure","Instructions","Modules","Types","Values","Conventions","Text Format","Instructions","Lexical 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,43],_3:13,_4:[13,34],_5:13,_6:13,_7:13,_8:[13,20,34],_9:13,_:[1,6,12,13,15,19,21,28,34,36,38],_e:20,_f32:[28,34],_f32x4:[1,6,12,28,34],_f64:[28,34],_f64x2:[1,6,12,28,34],_f:[1,18,21,28],_high:[6,12,34],_i16x8:[1,6,12,28,34],_i32:[28,34],_i32x4:[1,6,12,28,34],_i64:[28,34],_i8x16:[1,6,12,28,34],_i:[1,3,9,19,26,28,34,36,41,42],_if:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_indirect:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_lane:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_low:[1,6,12,28,34],_m:[18,20,21],_n:[2,13,18,21,31,34,38,39],_null:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_pairwis:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_s:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_sat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],_splat:[1,6,12,28,34],_t:[18,20,21],_tabl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],_true:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],_x:18,_y:18,_zero:[1,6,12,28,34],a0:[6,12],a1:[6,12],a2:[6,12],a3:[6,12],a4:[6,12],a5:[6,12],a6:[6,12],a7:[6,12],a8:[6,12],a9:[6,12],a_1:[10,26,32],a_2:26,a_i:[10,26,32],a_n:[10,26,32],aa:[6,12],ab:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],abbrevi:[21,24,33,38],abil:1,abl:[9,13],abort:[16,18,25,28],about:[3,9,16,21,24,39],abov:[0,4,9,18,31,35],abrupt:21,absent:[9,39,41],absolut:34,ac:[6,12],accept:30,access:[0,1,3,9,18,24,25,26,28,29,34,39,42],accord:[3,18,28,35,39],accordingli:[39,41],accumul:[0,21,41],acm:[9,16,39],acronym:24,across:24,activ:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],actual:[0,2,10,12,13,18,19,25,32,42],ad:[1,6,9,12,13,19,20,28],add:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],addit:[0,1,3,4,9,10,12,13,15,21,24,25,28,29,30,32,34,36,39],addition:[0,28],addr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],address:[3,9,17,19,25,28],adher:[9,18],admin:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],administr:[5,17,18],adopt:[3,10,16,26,32,39],advantag:24,ae:[6,12],af:[6,12],affect:[2,18,19,28,35],aforement:24,after:[0,2,13,16,18,28,29,34],afterward:[0,16],again:20,against:[0,18,19,28,43],ahead:[24,35],akin:41,algorithm:[5,22,39,41],align:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],alik:24,all:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],alloc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocdata:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocelem:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocfunc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocglob:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allochostfunc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocmem:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocmodul:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],alloct:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],allocx:19,allow:[0,1,4,9,10,12,14,15,18,20,21,24,25,28,29,32,34,35,36,38,39,41,43],alon:[9,16,24,39],along:0,alreadi:[4,18,38],also:[1,3,9,10,12,14,16,18,19,20,21,24,25,26,28,29,30,31,32,34,36,38,39,41],alter:25,altern:[10,20,28],alwai:[9,20,21,25,28,35,38,39,43],ambient:24,ambigu:21,amen:[16,39],among:[20,31],an:[0,1,2,3,4,9,10,12,13,15,16,18,19,20,21,24,25,26,28,29,30,31,32,34,36,38,39,41,42,43],analog:34,andnot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],andrea:[9,16,22,39],ani:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],annot:[12,18,28,34,39,41],anonym:[25,36,37],anoth:[28,36,41],anyth:41,anywher:[21,34,37],aot:24,api:[19,24,25],appear:[2,10,18,26,32,34,36,42],append:[19,26,39],appendix:[0,1,2,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],appli:[9,16,18,20,21,32,36,39,43],applic:[4,10,16,20,24,32],approach:[16,39],appropri:[9,16,19,28],ar:[0,1,2,3,4,9,10,12,13,14,15,16,18,19,20,21,24,25,26,28,29,30,31,32,34,35,36,38,39,41,42,43],arbitrari:[1,20,31,32,38],arbitrarili:[21,41],architectur:24,argument:[3,9,12,18,19,20,21,25,28,34],arithmet:[20,31],ariti:[0,18,21],around:[25,34],arrai:[2,3,9,10,12,13,14,15,16,18,19,20,21,25,26,28,29,30,31,32,34,35,36,37,38,39,41,42],articl:[9,16,39],ascii:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ascrib:18,aspect:[0,4,24],assembl:25,assert:[3,16,18,19],assign:[2,21,32,35],associ:[0,2,9,18,19,21,28,30,32],assum:[3,4,9,16,19,20,21,26,32,35,39,41],assumpt:[9,24,39],ast:[6,7,8,10,12,13,14,15,16,19,20,21,26,28,29,30,31,32,34,35,36,37,38,39,43],ast_i:19,atom:[19,26],attach:2,attack:24,attribut:[10,20,32,36],augment:[10,26,32,36],authorit:24,automat:[3,9,25,29,36],aux:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],auxiliari:[0,3,11,15,18,19,20,21,27,29,30,31,34,36,41],avail:[18,24,25,28,29,39],averylonginstructionnameforvectext:34,avgr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],avoid:[1,12,16,21,32],awai:28,axiom:39,b0:[6,12],b1:[6,12],b2:[6,12],b3:[6,12],b4:[6,12],b5:[6,12],b6:[6,12],b7:[6,12],b8:[6,12],b9:[6,12],b:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],b_1:[9,10,15,26],b_2:[9,15,26],b_3:15,b_4:15,b_:12,b_i:10,b_n:10,ba:[6,12],back:[0,18,25,28,41],backslash0asm:13,backslash:38,backward:[13,18,28,34,36],base:[18,20,25,28,29,31,34],basic:[10,21,25,28],bastien:[9,16,39],bb:[6,12],bc:[6,12],bd:[6,12],becaus:[18,19,20,21,24,41],becom:29,been:[0,1,16,19,21,24,29],befor:[4,13,19,24,29,32,36],beforehand:19,begin:[2,3,4,9,10,12,13,14,15,16,18,19,20,21,24,26,28,29,30,31,32,34,35,36,37,38,39,41,42],behav:[9,21,28],behavior:[9,16,18,21,24,28],being:[13,24,28,41],below:[9,19,42],ben:[9,16,39],benjamin:[16,39],besid:[20,21],between:[3,20,25,31,32],beyond:[24,25],bf:[6,12],big:39,bigoplu:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bigwedg:18,biject:20,binari:[0,1,2,3,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bind:[10,32,34,36],binop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],bit:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bitfield:13,bitmask:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],bitselect:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bitwidth:28,bitwis:[20,28],block:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42],blockchar:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],blockcom:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],blockinstr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],blocktyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],bodi:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],book:[16,21,39],bool:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],bot:[9,18,41],both:[9,14,15,16,20,26,28,29,34,36,38,39,41,43],bottom:41,bound:[10,13,15,25,26,28,31,32,34,36,43],boundari:1,br:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],br_if:0,br_tabl:0,bracket:[12,28,30,34,35,38],branch:[0,18,21,25,28,34],breach:24,brief:[16,39],bring:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],broadli:24,browser:24,bt:[6,12,18,34],bubbl:21,bytes_:[12,20],c0:[6,12,15],c1:[6,12],c2:[6,12,18],c3:[6,12],c4:[6,12],c5:6,c6:6,c7:6,c8:6,c9:6,c:[3,7,9,15,28,34,35,38,39,42,43],c_0:20,c_1:[18,20],c_2:18,c_3:18,c_:20,c_i:20,c_k:20,ca:6,cach:24,calcul:19,call:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],calle:28,can:[0,1,2,3,9,10,12,13,14,16,18,19,20,21,24,25,26,28,29,30,31,32,34,35,36,38,39,41,42],candid:20,candidatepair:20,cannot:[0,12,19,24,25,28,29,35,37],canon:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],cap:[20,24],capabl:24,carri:[3,21],carriag:35,categori:[8,21,25,28,35],caught:25,caus:28,cb:6,cc:6,ccc:9,cd:6,cdot2:31,cdot64:18,cdot:[3,9,15,16,18,19,20,31,38,41],ce:6,ceil:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],certain:[9,16,20,21,25],certifi:9,cf:6,chang:[0,5,9,13,22,39],channel:24,chapter:35,charact:[4,15,24,31,32,33,38],check:[0,1,13,18,19,25,28,30,34,39,41,42,43],choic:[18,21,36,41],chosen:[20,41],clamp:20,classif:3,classifi:[9,19,30,39,41,42,43],claus:[20,36],clear:[21,30,31],clll:36,cllll:36,close:[10,28,32,42],closest:20,closur:[19,21],clutter:[16,32],clz:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],code:[0,1,2,3,4,5,6,7,8,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],codesec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],codifi:9,coexist:14,coincid:[9,16,18],collect:[21,29,39],collid:12,com:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],combin:[1,20,36,37,41],combinatori:[10,26,32],come:28,comma:38,comment:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,36,37,38,39,40,41,42,43],common:[4,21,24,26],commun:24,compact:24,comparison:28,compat:[13,34,36],compil:[1,2,4,13,24,25,29],complement:[15,20,24,25,28,31],complementari:25,complet:[0,3,10,25,29,32,39],complex:[26,31],compon:[9,13,16,21,26,29,32,39,42],compos:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],composit:[26,36],compound:[9,41],compress:[10,12,13],comput:[4,9,16,18,20,21,24,25,28,30,32],concat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],concaten:[3,9,13,18,19,26,42],concept:23,conceptu:25,concern:[24,28],concis:[16,26,39],conclus:39,concret:[4,26,32,39],condit:[5,9,10,15,18,19,20,25,26,28,32,34,36,39],confer:[9,16,39],config:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],configur:[5,7,16],conform:4,conjunct:20,connect:3,conrad:9,consecut:[0,4,21,36],consequ:[0,9,10,28,29,35,36,41,42],consid:[20,21,24,32,34,35],consider:23,consist:[0,2,9,12,13,16,18,19,20,21,25,28,29,34,35,36],constant:[0,1,2,3,4,5,6,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],constitut:18,constrain:[30,41],constraint:[0,4,9,15,21,39,41],construct:[16,21,25,26,28,29,31,32,36,39,42],constructor:[8,14],consum:[18,24,28,39,41],cont:13,contain:[0,9,10,13,15,16,18,19,21,24,25,28,29,32,34,35,36,38,39,41,42],contemporari:24,content:[2,13,18,19,21,26,29,39,42],context:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,31,33,34,35,36,37,38,40,41,42,43],contigu:25,continu:[18,21,26,28],contract:24,contrast:[21,41],contribut:2,control:[0,1,2,3,4,5,6,7,8,10,11,13,14,15,16,17,19,20,21,22,23,24,25,26,27,29,30,31,32,33,35,36,37,38,39,40,42,43],conveni:[16,20,21,28,32],convent:[0,1,2,3,4,5,6,7,8,9,11,12,13,14,15,17,18,19,20,22,23,24,25,27,33,34,35,36,37,40,41,42,43],convers:[17,18,21,25,28],convert:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],convert_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],convert_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],copi:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],copysign:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],core:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],corollari:9,correct:9,correctli:38,correspond:[3,12,13,14,18,19,20,21,26,29,30,31,32,34,35,38,39,41],corrupt:24,could:25,count:[1,11,18,20,21],cours:24,courtesi:21,cover:9,cpp:9,crash:9,creat:[3,21,25],crucial:16,ctrl:0,ctrl_frame:0,ctrl_stack:0,ctxt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ctz:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],cup:20,current:[0,2,9,10,13,16,18,21,25,28,29,36,39,41],custom:[0,1,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],customsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],cvtop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],d0:[6,12],d1:[6,12],d2:[6,12],d3:6,d4:6,d5:6,d6:6,d7:6,d7ff:[31,35],d800:[15,38],d8:6,d9:6,d:[13,18,20,36,38],d_0:20,d_1:[18,20],d_2:[18,20],d_:20,da:[6,18,36],dan:[9,16,39],data:[1,2,3,4,5,6,7,8,10,11,12,14,15,16,17,20,22,23,24,25,26,27,28,30,31,32,33,34,35,37,38,39,40,43],dataaddr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],datacountsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],dataidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],datainst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],datamod:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],datasec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],datastr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],db:6,dc:6,dd:6,de:6,deal:[10,26],debug:[13,24],debugg:2,decim:38,declar:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],decod:[0,10,13,24,25],decompos:21,decreas:20,dedic:2,deduct:39,def:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],defer:[4,13],defin:[1,2,3,9,10,13,15,16,18,19,20,21,24,25,26,29,30,31,32,34,35,36,38,39,41,42,43],definit:[2,3,9,13,16,18,19,20,21,24,25,26,29,31,35,36,39,41,42],degre:41,delimit:[34,35],delta:28,demot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],denot:[10,13,14,18,20,21,26,28,29,30,31,32,38,39],dens:10,depend:[2,4,13,18,19,20,23,28,29,31,38,39,42],deploy:29,depth:[4,28],derek:[9,16,39],deriv:[3,9,10,16,39],desc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],describ:[0,9,13,16,21,24,26,28,29,31,39,41],descript:[3,7,13,16,29,32,36,39,42],descriptor:[29,34,36],design:[4,9,16,23,39],desktop:24,destin:28,detail:25,detect:0,determin:[0,16,19,20,28,30,31,34,42],determinist:[16,18,20,21],develop:24,devic:[19,24,42],df:6,diagnost:3,differ:[0,3,9,10,12,18,19,20,21,24,25,26,28,29,31,41,42],digit:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],dim:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],dimens:[4,41],dimension:2,dinstr:19,direct:[20,28],directli:[0,1,3,9,15,18,24,25,32,34,36],disallow:35,disambigu:35,discrep:24,disjoint:[9,42],disjunct:20,distinct:[25,31,32],distinguish:[10,13,21,28,29,31,32,34,41],distribut:25,div:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],diverg:[9,18],divid:[3,18,19,20,21,25,28,35,41],dividend:20,divis:[19,20],dmode:19,document:[24,37],documentari:36,doe:[0,3,9,13,18,19,20,24,28,35,38,39,42],dot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],doubl:[30,35],draft:[22,24],drawn:32,drop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],due:[3,18,19,31],dummi:19,dup:0,duplic:[0,28,32,36],dure:[4,9,18,21,29,30,43],dynam:[9,19,21,25,28],e000:[15,31,35,38],e0:[6,15],e1:6,e2:6,e3:6,e4:6,e5:6,e6:6,e7:6,e8:6,e9:6,e:[0,2,9,10,13,18,19,20,21,24,28,31,36,38],e_i:[13,42],ea:[6,18],each:[0,2,3,9,10,12,13,16,18,19,20,21,24,25,26,28,29,32,36,38,39,41,42,43],earlier:[18,36],eas:43,easi:[0,24],easili:[19,42],eb:6,ec:6,ed:6,editor:22,ee:6,ef:6,effect:[0,16,18,21,28,34,35,41,42],effector:35,effici:[24,41],einit:19,einstr:19,either:[0,9,10,12,15,16,18,19,20,21,24,25,26,28,29,30,31,32,35,36,38,41,43],el:[13,36],elem:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,43],elemaddr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],element:[0,1,3,4,7,10,11,14,17,18,20,25,26,27,28,30,33,38,39,40,41],elemexpr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elemidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],eleminst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elemkind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elemlist:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elemmod:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],elemsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],elimin:21,ellips:26,els:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],elsewher:39,emb:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],embed:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],embedd:[3,4,9,18,19,21,24,25,29,30],embodi:39,emploi:[24,26],empti:[0,3,9,10,12,13,16,18,19,20,21,26,29,32,34,36,39,42,43],emptyset:[9,13],emul:25,enabl:[4,13,21,24],encapsul:9,enclos:[28,32,35,38],encod:[2,10,12,13,14,15,21,24,25,31,32,38,39],encompass:24,end:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],end_typ:0,endian:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],enforc:[15,28,34,36,39,41],enough:28,enrich:1,ensur:[0,9,18,19,21,25,36],enter:[0,16,28],entir:[16,21,29,36,41,42],entiti:[21,25,29,30],entri:[1,3,13,18,19,21,28,30,32,34,39],enumer:0,environ:[3,4,24,25,29],eof:35,epsilon:[3,8,9,10,12,13,14,16,18,19,20,21,26,32,34,36,37,38,42,43],eq:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],equal:[3,9,10,19,20,21,24,26,41,43],equat:20,equiv:[32,34,36,37],equival:[13,16,29,39],eqz:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],err:18,error:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],error_if:0,escap:38,especi:24,establish:24,et:[13,14,19,36,37,42],ev:3,evalu:[9,16,18,19],even:[0,3,20,21,29],event:4,ever:13,everi:[3,4,9,13,16,18,29,31,39],ex:[3,13,19,36],exact:[20,28],exactli:[10,20,21],exampl:[0,3,9,10,15,16,18,20,21,25,28,29,32,34,35,39,41],exce:[15,21],exceed:[4,18],except:[9,10,12,13,16,20,26,32,35,38,41,42],exclud:20,exclus:[20,35],exec:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],execut:[5,6,9,16,18,19,21,22,24,25,28,30,41],exist:[0,3,9,18,19,20,21,24,34,36,39],exit:[0,16],expand:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],expans:[10,20,26,32,36,38],expect:[0,3,4,9,13,18,19,28,41],experi:2,explan:[16,39],explanatori:0,explicit:[9,12,13,21,26,34,36,38],explicitli:[3,9,16,18,39],expon:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],exportdesc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],exportinst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],exportsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],expr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],express:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23,24,25,26,27,29,30,31,32,33,35,36,37,38,39,40,42,43],extadd:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],extend16:34,extend32:34,extend8:34,extend:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],extend_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],extend_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],extens:[0,5,10,12,13,18,20,28,32,39],extern:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,20,22,23,24,25,26,27,28,29,31,32,33,34,35,36,37,38,39,40,41,42],externaddr:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],externref:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],externtyp:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],externv:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],extmul:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],extra:9,extract:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],f0:[6,15],f1:6,f2:6,f32:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f32x4:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f3:6,f4:6,f5:6,f64:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f64x2:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f6:6,f7:6,f8:6,f9:6,f:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],f_:19,fa:6,fab:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fact:[0,18,34,35],fadd:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fail:[18,19],failur:[3,18,19],fall:[18,25,35],fals:0,farther:28,fashion:[21,29,30],fast:24,fb:6,fbia:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fbit:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fc:[6,12],fceil:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fcopysign:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fd:[6,12],fdiv:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fe:[6,15],featur:[4,24],feed:35,feq:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],few:[10,16,32],ff:[6,15,31],ffloor:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fge:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fgt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],field:[13,19,26,36,39,42],file:[10,32,36],fill:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],filter:[21,29,30],finit:9,first:[0,4,19,20,26,28,29,30,36,41],fit:19,fix:[4,26,31],flag:[0,14,20],flat:[0,26],flavor:28,fle:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],floor:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],flow:[25,28],flt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fmax:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fmin:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fmul:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fn:36,fne:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fnearest:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fneg:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fold:[4,33],foldedinstr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],follow:[0,1,2,3,4,9,10,12,13,14,15,16,18,19,20,21,24,25,26,28,29,30,32,34,35,36,38,39,43],font:[10,26,32],foral:[9,20],foreach:0,forev:9,form:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],formal:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,40,41,42,43],format:[0,1,2,3,5,6,7,8,9,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,36,37,38,39,40,41,42,43],formed:[25,36,42],former:[0,10,32],formul:39,forth:10,forward:[13,28,29],found:[16,39],four:[21,25,28],fpmax:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fpmin:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],frac:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fraction:38,frame:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],free:[19,29,39],freed:28,frelop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fresh:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],from:[0,3,4,9,10,13,16,19,20,21,24,25,26,28,29,30,31,32,34,35,36,37,39,41,42],front:39,fshape:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fsign:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fsqrt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],fsub:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ft:[3,13,18,36,42],ftestop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ftrunc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],full:25,fulli:[4,24,41],func:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],funcaddr:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcbind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcinst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcnamesec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcnamesubsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcref:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],funcsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],functyp:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],funop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],further:[13,15,16,25,28,41],furthermor:[9,13,16,18,36,38,42],futur:[4,9,12,13,14,18,20,21,24,28,29,30,41,42],g:[0,2,9,19,24,31],gap:12,garbag:21,ge:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],gener:[0,1,9,10,13,16,18,20,26,32,39],geq:[10,12,15,20,26,31,32,38,43],get:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],gi:3,ginit:19,github:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],give:[16,39],given:[2,4,9,10,16,18,19,20,21,24,25,26,28,29,30,32,34,36,38,39,41,43],gl:36,glob:[13,18],global:[0,1,2,4,5,6,7,8,10,11,12,15,16,17,20,22,23,24,25,26,27,28,31,32,33,34,35,38,39,40],globaladdr:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globalbind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globalidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globalinst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globalsec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],globaltyp:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],go:29,goal:23,gohman:[9,16,39],grammar:[3,11,13,27,28,31,33,34,35,36,38],grave:38,greater:20,group:[2,24,28,34],grow:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],growmem:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],grown:25,growtabl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],gt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],guarante:[3,16,24,25],h:38,ha:[0,1,2,3,9,10,13,16,18,19,20,21,24,25,26,29,31,32,39,41],haa:[9,16,39],had:10,half:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],hand:[3,21],handl:[0,20,21,25,34],happen:19,hardwar:[18,24,28],hat:38,have:[1,4,10,12,13,18,20,21,24,26,28,29,31,32,34,37,39,41,43],head:34,heap:37,heaptyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],height:[0,21,25,28],help:20,henc:[3,20,21,24,38,39],here:[0,3,10,13,18,19,21,35,39,41,43],heterogen:28,hexadecim:[10,31,38],hexdigit:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hexfloat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hexfrac:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hexnum:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hf:18,hfill:19,hh:38,high:[18,24,28],hint:[2,18,28],histori:[5,22],hold:[9,18,20,21,30,39],hole:21,holman:[9,16,39],hookrightarrow:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hop:21,horizont:35,host:[3,21,24,25,29],hostcod:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],hostfunc:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],how:[19,24,25,28,29,34,41],howev:[0,2,4,10,13,15,18,19,21,24,25,28,29,31,32,34,36,39,42,43],hspace:34,http:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i128:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i16:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i16x8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i2:20,i32:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i32x4:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i64:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i64x2:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i8x16:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],i:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],i_1:18,i_2:18,iab:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iadd:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iaddsat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iaddsat_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iaddsat_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],iand:[0,1,2,3,4,5,6,7,8,9,10,11,12,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1,32,33,34,35,36,37,38,39,40,41,42,43],opposit:20,optim:[18,28],option:[1,10,13,25,26,28,30,32,34,36,37,38,39],order:[0,2,3,9,10,12,13,15,16,19,20,21,25,28,29,30,31,32,36,42],organ:[13,25,29],origin:[0,1,9,16,18,20,21],other:[0,3,4,9,10,12,13,15,16,18,19,20,21,24,25,28,29,31,32,34,35,38,39,41,42],otherwis:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],out:[0,4,13,20,21,28,29,30,32,39],outcom:[9,18,21,42],outer:21,outermost:28,output:[20,28,30,41],outsid:[9,10,21,25,28,38,39],outward:28,over:[0,3,4,13,20,21,26,28,29,30,31,32,36,39,42],overflow:38,overlap:[28,35,36],overload:29,overview:[1,22,23],own:[9,19,21,24,25,29,30],p:[20,38],p_1:20,p_2:20,pack:[20,25,28,30,41],page:[3,9,18,19,21,28,29,30,36],pair:[2,3,10,13,18,20,25,29,36],parallel:[1,13,24],paralleliz:24,param:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],paramet:[1,3,4,14,18,19,25,29,30,32,36,37,39,42],parameter:13,parametr:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23,24,25,26,27,29,30,31,32,33,35,36,37,38,39,40,42,43],parenthes:[10,26,31,32,34,35],pars:[3,10,32,34],part:[2,3,16,18,21,24,25,26,28,39,41],parti:13,partial:[18,20],particular:[16,20,24,25,29],particularli:42,pass:[0,3,13,19,21,24,30,42],passiv:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,43],path:26,pattern:[12,15,30],payload:[20,31,38],per:[1,2,3,16,18,32,41],perform:[0,1,16,18,19,21,24,25,28,41,42],permit:20,phantom:[12,34],phase:23,phrase:[10,34,39],physic:4,pick:[10,20,41],piec:39,pierc:[16,39],place:[13,14,16,19,21,24,28,32,36,39],placehold:20,placement:13,plain:[12,20,32,34,43],plaininstr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],platform:24,pldi:[9,16,39],pm:[20,31,38],pmax:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],pmin:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],point:[1,3,11,17,18,21,24,26,27,28,30,33,41],pointer:25,pointwis:[19,20],polici:24,polymorph:[0,41],pop:[0,16,18,19,25,28,41],pop_ctrl:0,pop_val:0,popcnt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],portabl:24,posit:[8,12,14,15,18,20,31,34,39],possibl:[3,9,10,12,13,14,18,19,20,21,24,26,28,29,30,31,32,35,36,41],post:[5,9,18],potenti:24,power:[20,28],practic:[18,19,21,25],pre:[5,9,18,19,42],preambl:13,preced:[14,20,29,36],preceq:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],precis:[9,16,18,21,24,30],predic:20,prefix:[12,28,41],premis:39,prepend:[0,9,39,41],prescrib:[13,28,41],presenc:[0,13,16,18],present:[0,12,13,14,19,21,29,41],preserv:[9,21,29,30],press:[16,39],presum:38,prevent:[24,28,38],previou:[9,28],previous:36,primari:2,primarili:[19,39],primit:[20,31],printabl:[2,38],privileg:24,proce:[21,39],proceed:[9,16,39],process:[25,30,31,43],produc:[13,16,18,19,20,21,25,28,29,36,39,41],product:[10,15,26,32,35,36,38],program:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],progress:9,project:1,promot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],proof:[9,16,39],prop:9,propag:21,proper:0,properti:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],propos:1,proposit:39,prose:[17,40],prove:9,provid:[1,2,3,10,19,21,24,25,26,28,29,32,38,39,41,43],pseudo:[0,28,34,35],pth:26,pure:0,purg:0,purpos:[0,2,19,21,37],push:[0,16,18,19,21,25,28,41],push_ctrl:0,push_val:0,put:24,q15mulr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],q:[20,38],q_1:20,q_2:20,qquad:[3,9,10,13,14,15,18,19,20,21,31,32,34,35,36,37,38,39,41,42,43],quad:[9,13,16,18,19,21,29,32,34,36,42,43],qualif:20,quiet:[20,31],quot:32,quotat:38,r:[3,9,18,19,20,21,26,38],r_1:26,r_2:26,rang:[1,3,4,12,13,20,21,24,26,28,29,30,31,38,43],rather:21,ration:20,raw:[25,29,31,36,38],rcl:21,rcll:19,re:19,reach:[3,9,18,21],reachabl:0,read:[9,13,16,20,28,39],readabl:32,reader:[16,39],readili:[16,39],real:[20,25],reason:[4,24],recent:[16,41],recogn:35,recommend:[10,20,32],record:[0,13,16,21,26,32,39],rectifi:20,recurs:[19,25,26,32,34,39,41,42],reduc:[16,18,21],reduct:[16,18,21],ref:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],refer:[3,8,9,11,16,17,21,25,27,29,33,36,39,40,42],referenc:[18,19,21,25,28,29,36,37],refin:[0,3],reftyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],regard:[20,34],regardless:[18,28,30],region:28,regist:25,regular:[3,9,34,36],regularli:18,reinterpret:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],reject:4,rel:[9,18,19,20,21,28,34,39,41],relat:[1,9,19,20,28],releas:[5,22,24],relev:[10,21,24,26,32,35,36,39],relop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],rem:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],remain:9,remaind:[0,20],remov:[0,9,16,18,21],render:[2,16,32,39],reorder:1,repeat:[18,34],repeatedli:36,replac:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],report:[4,19,25],repres:[0,2,12,13,16,20,21,25,28,31,34,35,38,39],represent:[0,1,10,15,16,17,21,24,25,26,30,31,38],repurpos:9,requir:[0,3,4,9,10,13,16,18,19,20,21,25,26,28,29,38,39,41,42],reserv:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],resiz:[0,30],resolv:[20,21,29,32,36],resourc:[4,18,24],respect:[0,1,3,9,10,12,13,14,16,18,20,21,24,25,26,28,29,30,31,32,34,36,38,39,41,43],respons:[3,24],rest:[19,35],restart:[21,28],restrict:[4,10,15,21,28,29,32,35,36,42,43],result:[0,1,2,3,4,5,6,7,8,10,11,12,13,15,16,17,18,19,20,22,23,24,25,26,27,28,29,31,32,33,34,35,36,37,38,39,40,41,42,43],resulttyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],resum:28,retriev:28,reus:[21,24,36],revers:0,rewrit:32,right:[0,9,16,18,20,35],rightarrow:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],rlll:19,rllll:19,role:36,root:20,rossberg:[9,16,22,39],rotat:20,rotl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],rotr:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],round:[24,36,38],rt:[14,42],rule:[9,10,13,16,18,19,21,22,26,32,34,35,38,39,41,42,43],run:[9,21,24],rundata:19,runelem:19,runtim:[0,1,2,4,5,6,8,10,11,12,13,14,15,16,17,18,20,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s16:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s32:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s64:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],s_0:19,s_1:[9,19],s_2:[9,19],s_3:19,s_4:19,s_5:19,s_:19,s_i:[19,26],s_n:19,safe:[24,25],safeti:9,sai:39,said:39,same:[4,9,10,13,14,18,20,21,26,28,29,31,32,34,36,39,41,42,43],san:26,sandbox:24,sat:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],sat_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],sat_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],satisfi:[3,9,18],satur:[12,20,28],scalar:[31,32,35,38],schuff:[9,16,39],scope:[9,10,21,23,25,36,39],second:[0,28,36],secondari:[2,19],section:[0,1,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],secur:23,see:36,seen:24,seg:13,segment:[1,4,7,13,18,21,25,27,28,33,39,40,41],select:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],self:[0,24],semant:[0,2,3,9,13,16,18,19,21,22,23,24,39],semicolon:[35,38],sens:3,separ:[0,9,10,12,13,16,20,21,24,25,26,28,32,35,38],seq:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],sequenc:[2,3,5,7,9,10,12,13,15,16,18,19,20,21,25,26,28,29,30,31,32,34,35,36,38,39,40,42],serif:26,serv:[25,29,36],set:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],sever:[12,20,24,28,41],shape:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],share:21,shift:[20,28,34,39,41],shl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],shortcut:28,shorten:26,shorthand:[10,19,20,26,28,32],should:2,show:0,shown:0,shr:[0,1,2,3,4,5,6,7,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0,t2:0,t:[0,3,6,12,13,14,15,20,21,28,30,32,34,36,37,38,39],t_0:41,t_1:[6,9,19,32,36,37,39,42],t_2:[6,9,19,36,37,39,42],t_3:41,t_i:[9,13,19,32,41],t_j:41,t_n:32,ta:[18,36],tab:[13,18],tabl:[0,2,4,5,6,7,8,10,11,15,16,17,20,22,23,24,25,26,27,31,32,33,35,38,39,40],tableaddr:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tablebind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tableidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tableinst:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tablesec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tabletyp:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],tableus:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],tabul:35,take:[0,1,2,4,9,19,20,21,24,25,28,32],taken:21,target:[16,20,21,25,28],task:24,technic:20,techniqu:21,tee:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],term:[10,16,18,21,26,32,36],termin:[4,9,10,12,15,16,18,21,26,28,29,32,35],ternari:[1,28],test:[1,20,28],testop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],text:[0,1,2,3,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,35,36,37,38,39,40,41,42,43],textual:[24,32,38],th:[18,26],than:[1,3,13,18,19,20,21,24,25,28,31,38,41,42,43],thei:[2,4,9,10,12,13,14,18,20,21,24,25,28,29,30,31,32,34,35,36,37,38,39,41,42],them:[0,3,9,16,20,21,25,28,29,31,34,36,39],themselv:[9,15,21,28,35,42],theorem:5,therebi:[16,25,36],therefor:[0,18,21,41],thereof:30,thi:[0,2,3,4,9,10,13,15,16,18,19,20,21,24,25,26,28,29,30,31,32,34,35,38,39,41,42,43],third:[13,28],thisisenough:34,thisshouldbeenough:[12,34],thorough:[16,39],those:[9,10,26,28,32,42],thread:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],three:[16,18,21,25,28],through:[0,3,13,18,21,25,28,29],thu:[10,14,20,25,29,32],ti:[3,20],tild:38,time:[1,4,9,10,18,19,21,24,26,28,29,32],titzer:[9,16,39],togeth:28,token:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,36,37,38,39,40,41,42,43],tool:36,top:[0,10,18,19],toplevel:36,total:15,touch:16,toward:[20,25],track:0,tracker:22,trail:[15,20],transfer:41,translat:24,transmit:24,transpar:30,trap:[0,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],treat:[3,12,26,28],tree:1,tripl:3,trunc:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],trunc_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],trunc_sat_:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],trunc_sat_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],trunc_u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],truncat:[12,20],tt:[3,9,13,36,42],tupl:16,turn:[2,4,13],two:[0,2,10,13,15,16,18,20,24,25,26,28,29,31,35,39,41,43],ty:36,type:[0,2,4,5,6,10,11,12,15,16,17,20,21,22,23,24,25,26,27,28,31,32,33,34,35,38,39,40],typebind:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],typedef:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],typeidx:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42],typesec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],typeus:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],typewrit:[10,32],typic:[3,4,16,24,25,28],u16:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u1:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u32:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u64:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],u:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],ultim:21,unalign:[18,25],unambigu:[14,32],unari:[1,20,28],unchang:9,uncondit:[0,28,41],uncondition:39,unconstrain:41,undefin:[9,20],under:[0,9,18,21,25,30,39,41,42],underflow:0,underli:[18,20,31],underscor:38,understand:[16,39],unicod:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],unifi:21,uniniti:29,uninterpret:[13,15,21,29,31,38],union:30,uniqu:[2,21,29],unit:[28,29,30],univers:[24,43],unknown:[0,13],unless:[9,16,18],unlik:[12,15,25,28,29],unnam:[32,34],unnecessari:[16,32],unop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],unpack:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],unravel:19,unreach:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],unsaf:24,unsign:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],unspecif:3,unspecifi:20,until:[4,13,18],untyp:25,unus:15,unwind:28,up:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],updat:[3,19,26,34,36],upon:29,upper:20,us:[0,1,2,3,4,10,12,13,15,16,18,20,21,24,25,26,28,29,30,31,32,33,34,35,38,39],usabl:25,user:2,usual:[4,10,20,25,28,32],utf8:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],utf:[2,15,24,31,32,38],v128:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],v:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],val:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],val_i:19,val_stack:0,val_typ:0,valid:[1,2,3,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,41,42,43],valtyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42],valu:[0,2,4,5,6,7,8,10,11,12,13,16,17,18,20,22,23,24,25,26,27,28,29,32,33,34,35,36,39,40,41,43],vari:[4,12,31],variabl:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23,24,25,26,27,29,30,31,32,33,35,36,37,38,39,40,42,43],variant:[12,15],varieti:24,variou:[0,16,30],vbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vcvtop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vdash:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vec:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vechaslongerinstructionnam:12,vechasreallylonginstructionnam:34,vector:[2,8,9,11,13,15,17,19,21,25,27,29,33,40,42],vectyp:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vee:[9,13,15,18,20,34,36,38],veebar:20,verbatim:34,veri:[13,16],verifi:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],version:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vextmul:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vfbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vfrelop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vfunop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],via:[18,19],vibinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],view:25,viminmaxop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],violat:18,virelop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],virtual:[24,25],visatbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vishiftop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],visual:34,vitestop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],viunop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vm:24,vrelop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vternop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],vtestop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vulner:24,vunop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vvbinop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vvternop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vvtestop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],vvunop:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43],w3c:24,w:18,wa:28,wagner:[9,16,39],wai:[3,9,21,24,25],wasm:[10,24],wat:32,watt:9,we:[29,39,41],web:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],webassembl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],wedg:[3,9,15,18,19,20,35,36,38],well:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],were:0,wf:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],what:[1,39],when:[0,1,2,3,9,10,13,16,18,20,21,26,29,32,36,38,39,41,42,43],where:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],wherea:12,whether:[0,9,13,14,21,28,29,31],which:[0,2,3,4,9,10,12,13,15,16,18,19,20,21,24,25,28,29,30,31,32,34,35,36,38,39,41,42,43],white:[32,33,34,38],whitespac:35,whose:[0,2,9,10,13,18,19,20,31,32,36,39,43],wide:[16,25,39],width:[18,20,21,25,28,30,31,41],wise:[16,18,20,26,28,41],within:[1,9,15,20,21,25,28,29,30,38,43],without:[4,12,13,18,41],word:[9,39],would:[0,13,18,21,41],wrap:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],write:32,written:[9,10,20,26,28,30,32,34,36,38,39],ww:28,x:[1,6,8,10,12,13,19,20,26,28,29,32,34,35,36,39],x_1:[16,21],x_2:[16,21],x_3:[16,21],x_4:16,x_5:16,x_6:16,x_i:18,xor:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43],xref:[0,1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40],y:[6,12,13,29,34,36],yield:[3,18,28],z:[12,18,31,34,35,38],z_1:18,z_k:18,zakai:[9,16,39],zero:[10,12,15,18,19,20,28,29,31]},titles:["Validation Algorithm","Change History","Custom Sections","Embedding","Implementation Limitations","Appendix","Index of Instructions","Index of Semantic Rules","Index of Types","Soundness","Conventions","Binary Format","Instructions","Modules","Types","Values","Conventions","Execution","Instructions","Modules","Numerics","Runtime Structure","WebAssembly Specification","Introduction","Introduction","Overview","Conventions","Structure","Instructions","Modules","Types","Values","Conventions","Text Format","Instructions","Lexical Format","Modules","Types","Values","Conventions","Validation","Instructions","Modules","Types"],titleterms:{"0":1,"16":41,"2":1,"boolean":20,"byte":[3,15,31],"char":3,"const":[18,19,41],"export":[9,13,21,29,36,42],"float":[1,15,20,31,38],"function":[2,3,9,13,14,18,19,21,29,30,36,37,42,43],"import":[13,29,36,42,43],"int":[1,3],"null":[18,19,41],"return":[18,41],"static":7,_0:9,_1:[18,41,42],_2:[18,41,42],_:[18,20,41],_alloc:3,_decod:3,_export:3,_grow:3,_i16x8:18,_if:[18,41],_import:3,_indirect:[18,41],_init:3,_instanti:3,_invok:3,_lane:[18,41],_n:[9,20,41],_null:[18,41],_pairwis:[18,41],_pars:3,_read:3,_s:[18,20,41],_sat:20,_size:3,_splat:[18,41],_t_1:18,_tabl:[18,41],_true:18,_type:3,_u:20,_valid:3,_write:3,_zero:[18,41],abbrevi:[32,34,36,37],activ:[21,42],address:[18,21],administr:[9,21],algorithm:0,all:18,alloc:19,ani:18,appendix:[3,5],ast:[3,9,18,41,42],auxiliari:[10,26],b:[9,42],binari:[4,11],binop:[18,41],bitmask:[18,41],block:[18,21,41,43],blocktyp:[18,41],bodi:42,br:[18,41],bulk:1,c:[18,19,20,41],call:[18,41],chang:1,charact:35,code:[9,13],comment:35,concept:25,condit:3,configur:[9,21],consider:24,constant:[7,41],construct:7,context:[21,32,39],control:[9,12,18,28,34,41],convent:[10,16,21,26,28,29,30,31,32,38,39],convers:[1,20],convert:20,convert_:20,convert_u:20,copi:[18,41],count:13,custom:[2,13],cvtop:[18,41],data:[0,9,13,18,19,21,29,36,41,42],datainst:9,datamod:42,declar:42,demot:20,depend:24,desc:42,design:24,dot:[18,41],drop:[18,41],e:42,elem:[9,18,41,42],element:[9,13,19,21,29,36,42],eleminst:9,elemmod:42,els:[18,41],emb:3,embed:3,empti:41,end:[9,18,41],enter:18,epsilon:41,error:3,evalu:21,exec:[3,9,19,20],execut:[4,7,17],exit:18,exportdesc:42,exportinst:9,expr:42,express:[12,18,28,34,41],extadd:[18,41],extend:20,extend_:20,extend_u:20,extens:[1,7,9],extern:[9,19,21,30,43],externaddr:9,externtyp:[3,43],externv:[3,9,19],extmul:[18,41],extract:[18,41],f:9,fa:9,fab:20,fadd:20,fceil:20,fcopysign:20,fdiv:20,feq:20,ffloor:20,fge:20,fgt:20,fill:[18,41],fle:20,flt:20,fmax:20,fmin:20,fmul:20,fne:20,fnearest:20,fneg:20,fold:34,formal:[16,39],format:[4,11,33,35],fpmax:20,fpmin:20,frame:[9,21],from:18,fsqrt:20,fsub:20,ftrunc:20,func:[3,9,18,19,41,42,43],funcaddr:[3,9],funcinst:9,functyp:[3,9,43],get:[18,41],global:[3,9,13,14,18,19,21,29,30,36,37,41,42,43],globaladdr:3,globalinst:9,globaltyp:[3,42,43],goal:24,grammar:[10,26,32],grow:[18,19,41],half:[18,41],hf:9,histori:1,host:[9,18,19],hostcod:9,hostfunc:3,i32x4:18,i8x16:[18,41],i:[3,20],i_1:20,i_2:20,i_3:20,iab:20,iadd:20,iaddsat:20,iaddsat_:20,iaddsat_u:20,iand:20,iandnot:20,iavgr:20,iavgr_u:20,ibitselect:20,iclz:20,ictz:20,identifi:38,idiv:20,idiv_:20,idiv_u:20,ieq:20,ieqz:20,iextend:20,iextendn_:20,ig:20,ige_:20,ige_u:20,igt:20,igt_:20,igt_u:20,il:20,ile_:20,ile_u:20,ilt:20,ilt_:20,ilt_u:20,imax:20,imax_:20,imax_u:20,imin:20,imin_:20,imin_u:20,implement:4,importdesc:42,imul:20,index:[6,7,8],indic:[13,29,36],ine:20,ineg:20,init:[18,41,42],inot:20,instanc:[3,9,21],instanti:19,instr:[9,18,19,41],instruct:[1,6,9,12,18,19,21,28,34,41,42],integ:[15,20,31,38],interpret:20,introduct:[23,24],invoc:[18,19],invok:9,ior:20,ipopcnt:20,iq15mulrsat:20,iq15mulrsat_:20,irem:20,irem_:20,irem_u:20,irotl:20,irotr:20,ishap:41,ishl:20,ishr:20,ishr_:20,ishr_u:20,isub:20,isubsat:20,isubsat_:20,isubsat_u:20,ixor:20,l:[18,41],l_n:[18,41],label:[9,18,21,34],laneidx:41,lexic:35,limit:[4,9,14,30,37,43],load:[18,41],local:[2,9,18,41,42],loop:[18,41],m:[18,20,41,43],map:2,match:7,mathit:[3,9,18,41,42,43],mathrm:[3,20],mathsf:[9,18,19,20,41,42,43],max:43,mem:[3,19,42,43],memaddr:3,memarg:[18,41],meminst:9,memori:[1,3,9,12,13,14,18,19,21,28,29,30,34,36,37,41,42,43],memtyp:[3,42,43],min:43,mode:42,modul:[2,3,9,13,19,21,29,36,42,43],moduleinst:[3,9],multipl:1,mut:[9,42,43],n:[3,18,20,41,43],name:[2,3,9,15,31,38,42],nan:20,narrow:[18,20,41],narrow_:20,narrow_u:20,non:[1,41],nop:[18,41],notat:[10,16,26,39],number:[14,30,37],numer:[12,18,19,20,28,34,41],offset:42,op:20,opcod:0,oper:20,overview:25,parametr:[12,18,28,34,41],passiv:42,phase:25,point:[15,20,31,38],post:3,pre:3,promot:20,propag:20,prose:[16,39],ref:[3,9,18,19,41],refer:[1,12,14,18,19,28,30,34,37,41],reftyp:43,reinterpret:20,releas:1,relop:[18,41],replac:[18,41],represent:20,result:[9,14,21,30],rightarrow:43,round:20,rule:7,runtim:[3,7,9,19,21],s:[9,20],scope:24,section:[2,13],secur:24,segment:[19,29,36,42],select:[18,41],semant:[7,25],sequenc:[0,41],set:[18,41],shape:[18,41],shuffl:[18,41],sign:[1,20],size:[18,41],sound:9,space:35,specif:22,splat:[18,41],stack:21,start:[13,29,36,42],storag:20,store:[3,7,9,18,21,41],string:38,structur:[0,4,21,27],subsect:2,subtyp:43,swizzl:[18,41],sx:[18,41],syntact:4,syntax:[3,9,18,19,41,42,43],t:[9,18,19,41,42],t_1:[18,20,41,43],t_2:[18,20,41,43],tabl:[1,3,9,12,13,14,18,19,21,28,29,30,34,36,37,41,42,43],tableaddr:3,tableinst:9,tabletyp:[3,42,43],tee:[18,41],testop:[18,41],text:[4,33],theorem:9,thread:9,token:35,trap:[1,9],trunc:20,trunc_:20,trunc_sat_:20,trunc_sat_u:20,trunc_u:20,type:[1,3,7,8,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\ No newline at end of file diff --git a/core/syntax/conventions.html b/core/syntax/conventions.html index 87e171b0..3477f839 100644 --- a/core/syntax/conventions.html +++ b/core/syntax/conventions.html @@ -6,7 +6,7 @@ - Conventions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Conventions — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/syntax/index.html b/core/syntax/index.html index 1ea446c5..e686359c 100644 --- a/core/syntax/index.html +++ b/core/syntax/index.html @@ -6,7 +6,7 @@ - Structure — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Structure — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/syntax/instructions.html b/core/syntax/instructions.html index 227af43b..183dd285 100644 --- a/core/syntax/instructions.html +++ b/core/syntax/instructions.html @@ -6,7 +6,7 @@ - Instructions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Instructions — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/syntax/modules.html b/core/syntax/modules.html index 9b41c91f..fb5dc5ff 100644 --- a/core/syntax/modules.html +++ b/core/syntax/modules.html @@ -6,7 +6,7 @@ - Modules — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Modules — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/syntax/types.html b/core/syntax/types.html index 76ece205..24d3c25a 100644 --- a/core/syntax/types.html +++ b/core/syntax/types.html @@ -6,7 +6,7 @@ - Types — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Types — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/syntax/values.html b/core/syntax/values.html index ab13c1fc..6075634a 100644 --- a/core/syntax/values.html +++ b/core/syntax/values.html @@ -6,7 +6,7 @@ - Values — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Values — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/text/conventions.html b/core/text/conventions.html index 2896d4b5..1deaf0ba 100644 --- a/core/text/conventions.html +++ b/core/text/conventions.html @@ -6,7 +6,7 @@ - Conventions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Conventions — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/text/index.html b/core/text/index.html index 269f9248..0f9e2628 100644 --- a/core/text/index.html +++ b/core/text/index.html @@ -6,7 +6,7 @@ - Text Format — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Text Format — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/text/instructions.html b/core/text/instructions.html index 4589d9c7..b1fc319b 100644 --- a/core/text/instructions.html +++ b/core/text/instructions.html @@ -6,7 +6,7 @@ - Instructions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Instructions — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/text/lexical.html b/core/text/lexical.html index bbd962da..e8583051 100644 --- a/core/text/lexical.html +++ b/core/text/lexical.html @@ -6,7 +6,7 @@ - Lexical Format — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Lexical Format — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/text/modules.html b/core/text/modules.html index 838660a9..0278b692 100644 --- a/core/text/modules.html +++ b/core/text/modules.html @@ -6,7 +6,7 @@ - Modules — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Modules — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/text/types.html b/core/text/types.html index 45e17456..6bdea72b 100644 --- a/core/text/types.html +++ b/core/text/types.html @@ -6,7 +6,7 @@ - Types — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Types — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/text/values.html b/core/text/values.html index be60f715..84a2f14f 100644 --- a/core/text/values.html +++ b/core/text/values.html @@ -6,7 +6,7 @@ - Values — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Values — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/valid/conventions.html b/core/valid/conventions.html index f2b18f4f..778af2ee 100644 --- a/core/valid/conventions.html +++ b/core/valid/conventions.html @@ -6,7 +6,7 @@ - Conventions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Conventions — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/valid/index.html b/core/valid/index.html index cf58ab56..c4f8e0b8 100644 --- a/core/valid/index.html +++ b/core/valid/index.html @@ -6,7 +6,7 @@ - Validation — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Validation — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/valid/instructions.html b/core/valid/instructions.html index 388e27c0..f07cbc34 100644 --- a/core/valid/instructions.html +++ b/core/valid/instructions.html @@ -6,7 +6,7 @@ - Instructions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Instructions — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/valid/modules.html b/core/valid/modules.html index bd150cca..3639ffee 100644 --- a/core/valid/modules.html +++ b/core/valid/modules.html @@ -6,7 +6,7 @@ - Modules — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Modules — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/valid/types.html b/core/valid/types.html index 380c829f..24cda8dc 100644 --- a/core/valid/types.html +++ b/core/valid/types.html @@ -6,7 +6,7 @@ - Types — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Types — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/js-api/index.html b/js-api/index.html index 0dfdf601..334f604f 100644 --- a/js-api/index.html +++ b/js-api/index.html @@ -4,9 +4,9 @@ WebAssembly JavaScript Interface - + - +

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C_>qbL diff --git a/core/_static/documentation_options.js b/core/_static/documentation_options.js index 5dae6739..3b0773cf 100644 --- a/core/_static/documentation_options.js +++ b/core/_static/documentation_options.js @@ -1,6 +1,6 @@ var DOCUMENTATION_OPTIONS = { URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), - VERSION: '2.0 + stringref (Draft 2022-04-27)', + VERSION: '2.0 + stringref (Draft 2022-06-22)', LANGUAGE: 'None', COLLAPSE_INDEX: false, BUILDER: 'html', diff --git a/core/appendix/algorithm.html b/core/appendix/algorithm.html index 5b94883e..1fb1fe74 100644 --- a/core/appendix/algorithm.html +++ b/core/appendix/algorithm.html @@ -6,7 +6,7 @@ - Validation Algorithm — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Validation Algorithm — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/appendix/changes.html b/core/appendix/changes.html index 325dbe16..1bdc061b 100644 --- a/core/appendix/changes.html +++ b/core/appendix/changes.html @@ -6,7 +6,7 @@ - Change History — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Change History — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/appendix/custom.html b/core/appendix/custom.html index 4b9855d6..434de2fd 100644 --- a/core/appendix/custom.html +++ b/core/appendix/custom.html @@ -6,7 +6,7 @@ - Custom Sections — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Custom Sections — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/appendix/embedding.html b/core/appendix/embedding.html index 145be23a..953a0523 100644 --- a/core/appendix/embedding.html +++ b/core/appendix/embedding.html @@ -6,7 +6,7 @@ - Embedding — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Embedding — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/appendix/implementation.html b/core/appendix/implementation.html index 7abf7cbe..9c4cf7c2 100644 --- a/core/appendix/implementation.html +++ b/core/appendix/implementation.html @@ -6,7 +6,7 @@ - Implementation Limitations — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Implementation Limitations — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/appendix/index-instructions.html b/core/appendix/index-instructions.html index 8eaa5ffb..d110b6ad 100644 --- a/core/appendix/index-instructions.html +++ b/core/appendix/index-instructions.html @@ -6,7 +6,7 @@ - Index of Instructions — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Index of Instructions — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/appendix/index-rules.html b/core/appendix/index-rules.html index 2a244376..27614046 100644 --- a/core/appendix/index-rules.html +++ b/core/appendix/index-rules.html @@ -6,7 +6,7 @@ - Index of Semantic Rules — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Index of Semantic Rules — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/appendix/index-types.html b/core/appendix/index-types.html index c67f84ac..60aec66f 100644 --- a/core/appendix/index-types.html +++ b/core/appendix/index-types.html @@ -6,7 +6,7 @@ - Index of Types — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Index of Types — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/appendix/index.html b/core/appendix/index.html index b4c366f3..8c411b7d 100644 --- a/core/appendix/index.html +++ b/core/appendix/index.html @@ -6,7 +6,7 @@ - Appendix — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Appendix — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/appendix/properties.html b/core/appendix/properties.html index 2544f7b2..837ad3e3 100644 --- a/core/appendix/properties.html +++ b/core/appendix/properties.html @@ -6,7 +6,7 @@ - Soundness — WebAssembly 2.0 + stringref (Draft 2022-04-27) + Soundness — WebAssembly 2.0 + stringref (Draft 2022-06-22) diff --git a/core/bikeshed/index.html b/core/bikeshed/index.html index e04eefb1..82ebc670 100644 --- a/core/bikeshed/index.html +++ b/core/bikeshed/index.html @@ -4,9 +4,9 @@ WebAssembly Core Specification - + - + @@ -187,7 +187,7 @@

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