feat: add math/base/special/ahavercosf

PR-URL: #3072
Closes: #649

Co-authored-by: Philipp Burckhardt <[email protected]>
Reviewed-by: Philipp Burckhardt <[email protected]>
Signed-off-by: Philipp Burckhardt <[email protected]>

lib/node_modules/@stdlib/math/base/special/ahavercosf/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2024 The Stdlib Authors.
+
+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.
+
+-->
+
+# ahavercosf
+
+> Compute the [inverse half-value versed cosine][archavercosine] of a single-precision floating point number.
+
+<section class="intro">
+
+The [inverse half-value versed cosine][archavercosine] is defined as
+
+<!-- <equation class="equation" label="eq:archavercosine" align="center" raw="\operatorname{ahavercos}(\theta) = 2 \cdot \arccos(\sqrt{\theta})" alt="Inverse half-value versed cosine."> -->
+
+```math
+\mathop{\mathrm{ahavercos}}(\theta) = 2 \cdot \arccos(\sqrt{\theta})
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\operatorname{ahavercos}(\theta) = 2 \cdot \arccos(\sqrt{\theta})" data-equation="eq:archavercosine">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/ahavercos/docs/img/equation_archavercosine.svg" alt="Inverse half-value versed cosine.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var ahavercosf = require( '@stdlib/math/base/special/ahavercosf' );
+```
+
+#### ahavercosf( x )
+
+Computes the [inverse half-value versed cosine][archavercosine] of a single-precision floating point number (in radians).
+
+```javascript
+var v = ahavercosf( 0.0 );
+// returns ~3.1416
+
+v = ahavercosf( 1.0 );
+// returns 0.0
+
+v = ahavercosf( 0.5 );
+// returns ~1.5708
+```
+
+If `x < 0`, `x > 1`, or `x` is `NaN`, the function returns `NaN`.
+
+```javascript
+var v = ahavercosf( 1.5 );
+// returns NaN
+
+v = ahavercosf( -3.14 );
+// returns NaN
+
+v = ahavercosf( NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var linspace = require( '@stdlib/array/base/linspace' );
+var ahavercosf = require( '@stdlib/math/base/special/ahavercosf' );
+
+var x = linspace( 0.0, 1.0, 100 );
+
+var i;
+for ( i = 0; i < x.length; i++ ) {
+    console.log( ahavercosf( x[ i ] ) );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/math/base/special/ahavercosf.h"
+```
+
+#### stdlib_base_ahavercosf( x )
+
+Computes the [inverse half-value versed cosine][archavercosine] of a single-precision floating-point number (in radians).
+
+```c
+float out = stdlib_base_ahavercosf( 0.0f );
+// returns ~3.1416f
+```
+
+If `x < 0`, `x > 1`, or `x` is `NaN`, the function returns `NaN`.
+
+```c
+float out = stdlib_base_ahavercosf( -3.14f );
+// returns NaN
+```
+
+The function accepts the following arguments:
+
+-   **x**: `[in] float` input value.
+
+```c
+float stdlib_base_ahavercosf( const float x );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/math/base/special/ahavercosf.h"
+#include <stdio.h>
+
+int main( void ) {
+    const float x[] = { -2.0f, -1.6f, -1.2f, -0.8f, -0.4f, 0.4f, 0.8f, 1.2f, 1.6f, 2.0f };
+    
+    float v;
+    int i;
+    for ( i = 0; i < 10; i++ ) {
+        v = stdlib_base_ahavercosf( x[ i ] );
+        printf( "ahavercosf(%f) = %f\n", x[ i ], v );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[archavercosine]: https://en.wikipedia.org/wiki/Versine
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

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

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 The Stdlib Authors.
+*
+* 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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/base/randu' );
+var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
+var pkg = require( './../package.json' ).name;
+var ahavercosf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		x = randu();
+		y = ahavercosf( x );
+		if ( isnanf( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnanf( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/math/base/special/ahavercosf/benchmark/benchmark.native.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* 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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var resolve = require( 'path' ).resolve;
+var bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/base/randu' );
+var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var ahavercosf = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+	'skip': ( ahavercosf instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		x = randu();
+		y = ahavercosf( x );
+		if ( isnanf( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnanf( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});