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<pre class="metadata">
title: Float16Array
status: proposal
stage: 3
copyright: false
contributors: Kevin Gibbons
</pre>

<div id="metadata-block">
  <h1>Contributing to this Proposal</h1>
  <p>You can discuss this proposal <a href="https://github.com/tc39/proposal-float16array">on GitHub</a>.</p>
</div>

<emu-clause id="sec-proposal-intro">
  <h1>Introduction</h1>
  <p>This proposal adds a new kind of TypedArray. TypedArrays are specified in a slightly different way from the rest of the standard library, so the specification for this proposal consists of a surprisingly small change.</p>
</emu-clause>

<emu-clause id="sec-constructor-properties-of-the-global-object">
  <h1>Constructor Properties of the Global Object</h1>
  <p>The following subclause is inserted.</p>

  <emu-clause id="sec-float16array">
    <h1><ins>Float16Array ( . . . )</ins></h1>
    <p>See <emu-xref href="#sec-typedarray-constructors"></emu-xref>.</p>
  </emu-clause>
</emu-clause>

<emu-clause id="sec-function-properties-of-the-math-object">
  <h1>Function Properties of the Math Object</h1>

  <emu-clause id="sec-math.f16round">
    <h1><ins>Math.f16round ( _x_ )</ins></h1>
    <p>This function performs the following steps when called:</p>
    <emu-alg>
      1. Let _n_ be ? ToNumber(_x_).
      1. If _n_ is *NaN*, return *NaN*.
      1. If _n_ is one of *+0*<sub>𝔽</sub>, *-0*<sub>𝔽</sub>, *+∞*<sub>𝔽</sub>, or *-∞*<sub>𝔽</sub>, return _n_.
      1. Let _n16_ be the result of converting _n_ to IEEE 754-2019 binary16 format using roundTiesToEven mode.
      1. Let _n64_ be the result of converting _n16_ to IEEE 754-2019 binary64 format.
      1. Return the ECMAScript Number value corresponding to _n64_.
    </emu-alg>

    <emu-note>
      <p>This operation is not the same as casting to binary32 and then to binary16 because of the possibility of double-rounding: consider the number _k_ = *1.00048828125000022204*<sub>𝔽</sub>, for example, for which which Math.f16round(_k_) is *1.0009765625*<sub>𝔽</sub>, but Math.f16round(Math.fround(_k_)) is *1*<sub>𝔽</sub>.</p>
      <p>Not all platforms provide native support for casting from binary64 to binary16. There are various libraries which can provide this, including the MIT-licensed <a href="https://half.sourceforge.net/">half</a> library. Alternatively, it is possible to first cast from binary64 to binary32 under roundTiesToEven and then check whether the result could lead to incorrect double-rounding. The cases which could can be handled explicitly by adjusting the mantissa of the binary32 value so that it is the value which would be produced by performing the initial cast under roundTiesToOdd. Casting the adjusted value to binary16 under roundTiesToEven then produces the correct value.</p>
    </emu-note>
  </emu-clause>
</emu-clause>

<emu-clause id="sec-typedarray-objects">
  <h1>TypedArray Objects</h1>
  <p>The table below is modified by the addition of a row for float16.</p>
  <emu-table id="table-the-typedarray-constructors" caption="The TypedArray Constructors">
    <table>
      <tr>
        <th>
          Constructor Name and Intrinsic
        </th>
        <th>
          Element Type
        </th>
        <th>
          Element Size
        </th>
        <th>
          Conversion Operation
        </th>
        <th>
          Description
        </th>
      </tr>
      <tr>
        <td>
          Int8Array<br>
          <dfn>%Int8Array%</dfn>
        </td>
        <td>
          ~Int8~
        </td>
        <td>
          1
        </td>
        <td>
          ToInt8
        </td>
        <td>
          8-bit two's complement signed integer
        </td>
      </tr>
      <tr>
        <td>
          Uint8Array<br>
          <dfn>%Uint8Array%</dfn>
        </td>
        <td>
          ~Uint8~
        </td>
        <td>
          1
        </td>
        <td>
          ToUint8
        </td>
        <td>
          8-bit unsigned integer
        </td>
      </tr>
      <tr>
        <td>
          Uint8ClampedArray<br>
          <dfn>%Uint8ClampedArray%</dfn>
        </td>
        <td>
          ~Uint8C~
        </td>
        <td>
          1
        </td>
        <td>
          ToUint8Clamp
        </td>
        <td>
          8-bit unsigned integer (clamped conversion)
        </td>
      </tr>
      <tr>
        <td>
          Int16Array<br>
          <dfn>%Int16Array%</dfn>
        </td>
        <td>
          ~Int16~
        </td>
        <td>
          2
        </td>
        <td>
          ToInt16
        </td>
        <td>
          16-bit two's complement signed integer
        </td>
      </tr>
      <tr>
        <td>
          Uint16Array<br>
          <dfn>%Uint16Array%</dfn>
        </td>
        <td>
          ~Uint16~
        </td>
        <td>
          2
        </td>
        <td>
          ToUint16
        </td>
        <td>
          16-bit unsigned integer
        </td>
      </tr>
      <tr>
        <td>
          Int32Array<br>
          <dfn>%Int32Array%</dfn>
        </td>
        <td>
          ~Int32~
        </td>
        <td>
          4
        </td>
        <td>
          ToInt32
        </td>
        <td>
          32-bit two's complement signed integer
        </td>
      </tr>
      <tr>
        <td>
          Uint32Array<br>
          <dfn>%Uint32Array%</dfn>
        </td>
        <td>
          ~Uint32~
        </td>
        <td>
          4
        </td>
        <td>
          ToUint32
        </td>
        <td>
          32-bit unsigned integer
        </td>
      </tr>
      <tr>
        <td>
          BigInt64Array<br>
          <dfn>%BigInt64Array%</dfn>
        </td>
        <td>
          ~BigInt64~
        </td>
        <td>
          8
        </td>
        <td>
          ToBigInt64
        </td>
        <td>
          64-bit two's complement signed integer
        </td>
      </tr>
      <tr>
        <td>
          BigUint64Array<br>
          <dfn>%BigUint64Array%</dfn>
        </td>
        <td>
          ~BigUint64~
        </td>
        <td>
          8
        </td>
        <td>
          ToBigUint64
        </td>
        <td>
          64-bit unsigned integer
        </td>
      </tr>
      <tr>
        <td>
          <ins>Float16Array<br>
            <dfn>%Float16Array%</dfn></ins>
        </td>
        <td>
          <ins>~Float16~</ins>
        </td>
        <td>
          <ins>2</ins>
        </td>
        <td>
        </td>
        <td>
          <ins>16-bit IEEE floating point</ins>
        </td>
      </tr>
      <tr>
        <td>
          Float32Array<br>
          <dfn>%Float32Array%</dfn>
        </td>
        <td>
          ~Float32~
        </td>
        <td>
          4
        </td>
        <td>
        </td>
        <td>
          32-bit IEEE floating point
        </td>
      </tr>
      <tr>
        <td>
          Float64Array<br>
          <dfn>%Float64Array%</dfn>
        </td>
        <td>
          ~Float64~
        </td>
        <td>
          8
        </td>
        <td>
        </td>
        <td>
          64-bit IEEE floating point
        </td>
      </tr>
    </table>
  </emu-table>
</emu-clause>

<emu-clause id="sec-rawbytestonumeric" type="abstract operation" oldids="sec-rawbytestonumber">
  <h1>
    RawBytesToNumeric (
      _type_: a TypedArray element type,
      _rawBytes_: a List of byte values,
      _isLittleEndian_: a Boolean,
    ): a Number or a BigInt
  </h1>
  <dl class="header">
  </dl>
  <p>The algorithm below is modified by the addition of a case for ~Float16~.</p>
  <emu-alg>
    1. Let _elementSize_ be the Element Size value specified in <emu-xref href="#table-the-typedarray-constructors"></emu-xref> for Element Type _type_.
    1. If _isLittleEndian_ is *false*, reverse the order of the elements of _rawBytes_.
    1. <ins>If _type_ is ~Float16~, then</ins>
      1. <ins>Let _value_ be the byte elements of _rawBytes_ concatenated and interpreted as a little-endian bit string encoding of an IEEE 754-2019 binary16 value.</ins>
      1. <ins>If _value_ is an IEEE 754-2019 binary16 NaN value, return the *NaN* Number value.</ins>
      1. <ins>Return the Number value that corresponds to _value_.</ins>
    1. If _type_ is ~Float32~, then
      1. Let _value_ be the byte elements of _rawBytes_ concatenated and interpreted as a little-endian bit string encoding of an IEEE 754-2019 binary32 value.
      1. If _value_ is an IEEE 754-2019 binary32 NaN value, return the *NaN* Number value.
      1. Return the Number value that corresponds to _value_.
    1. If _type_ is ~Float64~, then
      1. Let _value_ be the byte elements of _rawBytes_ concatenated and interpreted as a little-endian bit string encoding of an IEEE 754-2019 binary64 value.
      1. If _value_ is an IEEE 754-2019 binary64 NaN value, return the *NaN* Number value.
      1. Return the Number value that corresponds to _value_.
    1. If IsUnsignedElementType(_type_) is *true*, then
      1. Let _intValue_ be the byte elements of _rawBytes_ concatenated and interpreted as a bit string encoding of an unsigned little-endian binary number.
    1. Else,
      1. Let _intValue_ be the byte elements of _rawBytes_ concatenated and interpreted as a bit string encoding of a binary little-endian two's complement number of bit length _elementSize_ × 8.
    1. If IsBigIntElementType(_type_) is *true*, return the BigInt value that corresponds to _intValue_.
    1. Otherwise, return the Number value that corresponds to _intValue_.
  </emu-alg>
</emu-clause>

<emu-clause id="sec-numerictorawbytes" type="abstract operation" oldids="sec-numbertorawbytes">
  <h1>
    NumericToRawBytes (
      _type_: a TypedArray element type,
      _value_: a Number or a BigInt,
      _isLittleEndian_: a Boolean,
    ): a List of byte values
  </h1>
  <dl class="header">
  </dl>
  <p>The algorithm below is modified by the addition of a case for ~Float16~.</p>
  <emu-alg>
    1. <ins>If _type_ is ~Float16~, then</ins>
      1. <ins>Let _rawBytes_ be a List whose elements are the 2 bytes that are the result of converting _value_ to IEEE 754-2019 binary16 format using roundTiesToEven mode. The bytes are arranged in little endian order. If _value_ is *NaN*, _rawBytes_ may be set to any implementation chosen IEEE 754-2019 binary16 format Not-a-Number encoding. An implementation must always choose the same encoding for each implementation distinguishable *NaN* value.</ins>
    1. Else if _type_ is ~Float32~, then
      1. Let _rawBytes_ be a List whose elements are the 4 bytes that are the result of converting _value_ to IEEE 754-2019 binary32 format using roundTiesToEven mode. The bytes are arranged in little endian order. If _value_ is *NaN*, _rawBytes_ may be set to any implementation chosen IEEE 754-2019 binary32 format Not-a-Number encoding. An implementation must always choose the same encoding for each implementation distinguishable *NaN* value.
    1. Else if _type_ is ~Float64~, then
      1. Let _rawBytes_ be a List whose elements are the 8 bytes that are the IEEE 754-2019 binary64 format encoding of _value_. The bytes are arranged in little endian order. If _value_ is *NaN*, _rawBytes_ may be set to any implementation chosen IEEE 754-2019 binary64 format Not-a-Number encoding. An implementation must always choose the same encoding for each implementation distinguishable *NaN* value.
    1. Else,
      1. Let _n_ be the Element Size value specified in <emu-xref href="#table-the-typedarray-constructors"></emu-xref> for Element Type _type_.
      1. Let _convOp_ be the abstract operation named in the Conversion Operation column in <emu-xref href="#table-the-typedarray-constructors"></emu-xref> for Element Type _type_.
      1. Let _intValue_ be ℝ(_convOp_(_value_)).
      1. If _intValue_ ≥ 0, then
        1. Let _rawBytes_ be a List whose elements are the _n_-byte binary encoding of _intValue_. The bytes are ordered in little endian order.
      1. Else,
        1. Let _rawBytes_ be a List whose elements are the _n_-byte binary two's complement encoding of _intValue_. The bytes are ordered in little endian order.
    1. If _isLittleEndian_ is *false*, reverse the order of the elements of _rawBytes_.
    1. Return _rawBytes_.
  </emu-alg>
</emu-clause>

<emu-clause id="sec-properties-of-the-dataview-prototype-object">
  <h1>Properties of the DataView Prototype Object</h1>
  <p>The following two subclauses are inserted.</p>

  <emu-clause id="sec-dataview.prototype.getfloat16">
    <h1><ins>DataView.prototype.getFloat16 ( _byteOffset_ [ , _littleEndian_ ] )</ins></h1>
    <p>This method performs the following steps when called:</p>
    <emu-alg>
      1. Let _v_ be the *this* value.
      1. If _littleEndian_ is not present, set _littleEndian_ to *false*.
      1. Return ? GetViewValue(_v_, _byteOffset_, _littleEndian_, ~Float16~).
    </emu-alg>
  </emu-clause>

  <emu-clause id="sec-dataview.prototype.setfloat16">
    <h1><ins>DataView.prototype.setFloat16 ( _byteOffset_, _value_ [ , _littleEndian_ ] )</ins></h1>
    <p>This method performs the following steps when called:</p>
    <emu-alg>
      1. Let _v_ be the *this* value.
      1. If _littleEndian_ is not present, set _littleEndian_ to *false*.
      1. Return ? SetViewValue(_v_, _byteOffset_, _littleEndian_, ~Float16~, _value_).
    </emu-alg>
  </emu-clause>
</emu-clause>