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Add archavercosine
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‎lib/node_modules/@stdlib/math/base/special/ahavercos/README.md

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# Archavercosine
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> Compute the [inverse half-value versed cosine][archavercosine].
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<section class="intro">
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The [inverse half-value versed cosine][archavercosine] is defined as
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<!-- <equation class="equation" label="eq:archavercosine" align="center" raw="\operatorname{ahavercos}(\theta) = 2 \cdot \acos(\sqrt{\theta})" alt="Inverse half-value versed cosine."> -->
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<div class="equation" align="center" data-raw-text="\operatorname{ahavercos}(\theta) = 2 \cdot \acos(\sqrt{\theta})" data-equation="eq:archavercosine">
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<img src="" alt="Inverse half-value versed cosine.">
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<br>
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</div>
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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``` javascript
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var ahavercos = require( '@stdlib/math/base/special/ahavercos' );
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```
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#### ahavercos( x )
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Computes the [inverse half-value versed cosine][archavercosine].
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``` javascript
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var v = ahavercos( 0.0 );
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// returns ~3.1416
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v = ahavercos( 1.0 );
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// returns 0.0
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v = ahavercos( 0.5 );
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// returns ~1.5708
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```
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If `x < 0`, `x > 1`, or `x` is `NaN`, the function returns `NaN`.
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``` javascript
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var v = ahavercos( 1.5 );
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// returns NaN
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v = ahavercos( -3.14 );
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// returns NaN
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v = ahavercos( NaN );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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``` javascript
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var linspace = require( '@stdlib/math/utils/linspace' );
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var ahavercos = require( '@stdlib/math/base/special/ahavercos' );
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var x = linspace( 0.0, 1.0, 100 );
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var i;
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for ( i = 0; i < x.length; i++ ) {
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console.log( ahavercos( x[ i ] ) );
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}
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[archavercosine]: https://en.wikipedia.org/wiki/Versine
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/math/base/special/ahavercos/benchmark/benchmark.js

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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var randu = require( '@stdlib/math/base/random/randu' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pkg = require( './../package.json' ).name;
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var ahavercos = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var x;
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var y;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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x = randu();
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y = ahavercos( x );
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

‎lib/node_modules/@stdlib/math/base/special/ahavercos/benchmark/c/Makefile

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# VARIABLES #
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ifndef VERBOSE
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QUIET := @
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endif
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# Determine the OS:
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#
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# [1]: https://en.wikipedia.org/wiki/Uname#Examples
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# [2]: http://stackoverflow.com/a/27776822/2225624
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OS ?= $(shell uname)
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ifneq (, $(findstring MINGW,$(OS)))
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OS := WINNT
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else
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ifneq (, $(findstring MSYS,$(OS)))
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OS := WINNT
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else
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ifneq (, $(findstring CYGWIN,$(OS)))
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OS := WINNT
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endif
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endif
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endif
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# Define the program used for compiling C source files:
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ifdef C_COMPILER
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CC := $(C_COMPILER)
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else
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CC := gcc
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endif
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# Define the command-line options when compiling C files:
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CFLAGS ?= \
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-std=c99 \
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-O3 \
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-Wall \
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-pedantic
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# Determine whether to generate [position independent code][1]:
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#
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# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
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# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
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ifeq ($(OS), WINNT)
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fPIC ?=
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else
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fPIC ?= -fPIC
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endif
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# List of C targets:
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c_targets := benchmark.out
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# TARGETS #
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# Default target.
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#
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# This target is the default target.
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all: $(c_targets)
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.PHONY: all
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# Compile C source.
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#
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# This target compiles C source files.
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$(c_targets): %.out: %.c
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$(QUIET) $(CC) $(CFLAGS) $(fPIC) -o $@ $< -lm
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# Run a benchmark.
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#
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# This target runs a benchmark.
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run: $(c_targets)
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$(QUIET) ./$<
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.PHONY: run
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# Perform clean-up.
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#
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# This target removes generated files.
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clean:
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$(QUIET) -rm -f *.o *.out
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.PHONY: clean

‎lib/node_modules/@stdlib/math/base/special/ahavercos/benchmark/c/benchmark.c

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/**
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* Benchmark `ahavercos`.
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*/
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#include <stdlib.h>
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#include <stdio.h>
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#include <math.h>
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#include <sys/time.h>
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#define NAME "ahavercos"
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#define ITERATIONS 1000000
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#define REPEATS 3
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/**
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* Prints the TAP version.
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*/
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void print_version() {
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printf( "TAP version 13\n" );
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}
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/**
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* Prints the TAP summary.
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*
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* @param total total number of tests
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* @param passing total number of passing tests
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*/
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void print_summary( int total, int passing ) {
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printf( "#\n" );
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printf( "1..%d\n", total ); // TAP plan
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printf( "# total %d\n", total );
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printf( "# pass %d\n", passing );
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printf( "#\n" );
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printf( "# ok\n" );
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}
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/**
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* Prints benchmarks results.
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*
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* @param elapsed elapsed time in seconds
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*/
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void print_results( double elapsed ) {
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double rate = (double)ITERATIONS / elapsed;
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printf( " ---\n" );
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printf( " iterations: %d\n", ITERATIONS );
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printf( " elapsed: %0.9f\n", elapsed );
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printf( " rate: %0.9f\n", rate );
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printf( " ...\n" );
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}
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/**
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* Returns a clock time.
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*
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* @returns clock time
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*/
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double tic() {
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struct timeval now;
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gettimeofday( &now, NULL );
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return (double)now.tv_sec + (double)now.tv_usec/1.0e6;
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}
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/**
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* Generates a random double on the interval [0,1].
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*
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* @return random double
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*/
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double rand_double() {
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int r = rand();
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return (double)r / ( (double)RAND_MAX + 1.0 );
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}
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/**
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* Runs a benchmark.
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*
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* @return elapsed time in seconds
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*/
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double benchmark() {
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double elapsed;
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double x;
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double y;
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double t;
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int i;
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t = tic();
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for ( i = 0; i < ITERATIONS; i++ ) {
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x = rand_double();
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y = 2.0 * acos( sqrt( x ) );
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if ( y != y ) {
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printf( "should not return NaN\n" );
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break;
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}
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}
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elapsed = tic() - t;
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if ( y != y ) {
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printf( "should not return NaN\n" );
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}
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return elapsed;
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}
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/**
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* Main execution sequence.
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*/
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int main( void ) {
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double elapsed;
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int i;
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// Use the current time to seed the random number generator:
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srand( time( NULL ) );
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print_version();
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for ( i = 0; i < REPEATS; i++ ) {
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printf( "# c::%s\n", NAME );
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elapsed = benchmark();
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print_results( elapsed );
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printf( "ok %d benchmark finished\n", i+1 );
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}
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print_summary( REPEATS, REPEATS );
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}

‎lib/node_modules/@stdlib/math/base/special/ahavercos/docs/repl.txt

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{{alias}}( x )
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Computes the inverse half-value versed cosine.
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The inverse half-value versed cosine is defined as `2*acos(sqrt(x))`.
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If `x < 0`, `x > 1`, or `x` is `NaN`, the function returns `NaN`.
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Parameters
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----------
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x: number
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Input value.
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Returns
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-------
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y: number
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Inverse half-value versed cosine.
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Examples
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--------
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> var y = {{alias}}( 0.5 )
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~1.5708
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> y = {{alias}}( 0.0 )
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~3.1416
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See Also
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--------
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‎lib/node_modules/@stdlib/math/base/special/ahavercos/examples/index.js

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'use strict';
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var linspace = require( '@stdlib/math/utils/linspace' );
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var ahavercos = require( './../lib' );
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var x = linspace( 0.0, 1.0, 100 );
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var i;
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for ( i = 0; i < x.length; i++ ) {
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console.log( 'ahavercos(%d) = %d', x[ i ], ahavercos( x[ i ] ) );
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}

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