feat: add math/base/special/avercosf

PR-URL: #2846
Ref: #649 

Reviewed-by: Philipp Burckhardt <[email protected]>

lib/node_modules/@stdlib/math/base/special/avercosf/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.
+
+-->
+
+# Arcvercosine
+
+> Compute the [inverse versed cosine][inverse-versed-cosine] of a single-precision floating-point number (in radians).
+
+<section class="intro">
+
+The [inverse versed cosine][inverse-versed-cosine] is defined as
+
+<!-- <equation class="equation" label="eq:arcvercosine" align="center" raw="\operatorname{avercos}(\theta) = \arccos(1+\theta)" alt="Inverse versed cosine."> -->
+
+```math
+\mathop{\mathrm{avercos}}(\theta) = \arccos(1+\theta)
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\operatorname{avercos}(\theta) = \arccos(1+\theta)" data-equation="eq:arcvercosine">
+ <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/avercos/docs/img/equation_arcvercosine.svg" alt="Inverse versed cosine.">
+ <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var avercosf = require( '@stdlib/math/base/special/avercosf' );
+```
+
+#### avercosf( x )
+
+Computes the [inverse versed cosine][inverse-versed-cosine] of a single-precision floating-point number (in radians).
+
+```javascript
+var v = avercosf( 0.0 );
+// returns 0.0
+
+v = avercosf( -3.141592653589793 / 2.0 );
+// returns ~2.1783
+
+v = avercosf( -3.141592653589793 / 6.0 );
+// returns ~1.0742
+```
+
+If `x < -2`, `x > 0`, or `x` is `NaN`, the function returns `NaN`.
+
+```javascript
+var v = avercosf( 1.0 );
+// returns NaN
+
+v = avercosf( -3.14 );
+// returns NaN
+
+v = avercosf( NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var linspace = require( '@stdlib/array/base/linspace' );
+var avercosf = require( '@stdlib/math/base/special/avercosf' );
+
+var x = linspace( -2.0, 0.0, 100 );
+
+var i;
+for ( i = 0; i < x.length; i++ ) {
+ console.log( avercosf( 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/avercosf.h"
+```
+
+#### stdlib_base_avercosf( x )
+
+Compute the [inverse versed cosine][inverse-versed-cosine] of a single-precision floating-point number (in radians).
+
+```c
+float out = stdlib_base_avercosf( -3.141592653589793f / 2.0f );
+// returns ~2.1783f
+```
+
+If `x < -2`, `x > 0`, or `x` is `NaN`, the function returns `NaN`.
+
+```c
+float out = stdlib_base_avercosf( -3.141592653589793f );
+// returns NaN
+```
+
+The function accepts the following arguments:
+
+- **x**: `[in] float` input value.
+
+```c
+float stdlib_base_avercosf( 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/avercosf.h"
+#include <stdio.h>
+
+int main( void ) {
+ const float x[] = { -2.5f, -2.0f, -1.5f, -1.0f, -0.5f, 0.5f, 1.0f, 1.5f, 2.0f, 2.5f };
+ 
+ float v;
+ int i;
+ for ( i = 0; i < 10; i++ ) {
+ v = stdlib_base_avercosf( x[ i ] );
+ printf( "avercosf(%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">
+
+[inverse-versed-cosine]: https://en.wikipedia.org/wiki/Versine
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/math/base/special/avercosf/benchmark/benchmark.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 bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/array/uniform' );
+var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
+var pkg = require( './../package.json' ).name;
+var avercosf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+ var x;
+ var y;
+ var i;
+
+ x = randu( 100, -2.0, 0.0 );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ y = avercosf( x[ i % x.length ] );
+ 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/avercosf/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/array/uniform' );
+var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var avercosf = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+ 'skip': ( avercosf instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, function benchmark( b ) {
+ var x;
+ var y;
+ var i;
+
+ x = randu( 100, -2.0, 0.0 );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ y = avercosf( x[ i % x.length ] );
+ 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();
+});