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feat(math): add math/base/special/gammasgnf
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‎lib/node_modules/@stdlib/math/base/special/gammasgnf/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2022 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# gammasgnf
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> Sign of the [gamma function][@stdlib/math/base/special/gamma] for a single precision-floating point number.
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<section class="intro">
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The sign of the [gamma-function][@stdlib/math/base/special/gamma] is defined as
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<!-- <equation class="equation" label="eq:gamma_sign_function" align="center" raw="\operatorname{gammasgnf} ( x ) = \begin{cases} 1 & \textrm{if}\ \Gamma > 1 \\ -1 & \textrm{if}\ \Gamma < 1 \\ 0 & \textrm{otherwise}\ \end{cases}" alt="Sign of the gamma function"> -->
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```math
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\mathop{\mathrm{gammasgnf}} ( x ) = \begin{cases} 1 & \textrm{if}\ \Gamma > 1 \\ -1 & \textrm{if}\ \Gamma < 1 \\ 0 & \textrm{otherwise}\ \end{cases}
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```
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<!-- <div class="equation" align="center" data-raw-text="\operatorname{gammasgnf} ( x ) = \begin{cases} 1 &amp; \textrm{if}\ \Gamma &gt; 1 \\ -1 &amp; \textrm{if}\ \Gamma &lt; 1 \\ 0 &amp; \textrm{otherwise}\ \end{cases}" data-equation="eq:gamma_sign_function">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@50b141156b147529227e2eb4247eda81c781dec9/lib/node_modules/@stdlib/math/base/special/gammasgnf/docs/img/equation_gamma_sign_function.svg" alt="Sign of the gamma function">
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<br>
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</div> -->
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<!-- </equation> -->
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The [gamma function][@stdlib/math/base/special/gamma] can be computed as the product of `gammasgnf(x)` and `exp(gammaln(x))`.
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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 gammasgnf = require( '@stdlib/math/base/special/gammasgnf' );
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```
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#### gammasgnf( x )
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Returns the sign of the [gamma function][@stdlib/math/base/special/gamma].
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```javascript
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var v = gammasgnf( 1.0 );
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// returns 1.0
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v = gammasgnf( -2.5 );
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// returns -1.0
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v = gammasgnf( 0.0 );
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// returns 0.0
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v = gammasgnf( 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="notes">
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## Notes
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- The [gamma function][@stdlib/math/base/special/gamma] is not defined for negative integer values (i.e., `gamma(x) === NaN` when `x` is a negative integer). The [natural logarithm of the gamma function][@stdlib/math/base/special/gammaln] is defined for negative integer values (i.e., `gammaln(x) === Infinity` when `x` is a negative integer). Accordingly, in order for the equality `gamma(x) === gammasgnf(x) * exp(gammaln(x))` to hold (i.e., return `NaN`), `gammasgnf` needs to either return `NaN` or `0`. By convention, this function returns `0`.
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</section>
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<!-- /. notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var linspace = require( '@stdlib/array/base/linspace' );
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var gammasgnf = require( '@stdlib/math/base/special/gammasgnf' );
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var x = linspace( -10.0, 10.0, 100 );
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var i;
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for ( i = 0; i < x.length; i++ ) {
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console.log( 'x: %d, f(x): %f', x[ i ], gammasgnf( x[ i ] ) );
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}
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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#include "stdlib/math/base/special/gammasgnf.h"
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```
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#### stdlib_base_gammasgnf( x )
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Returns the sign of the [gamma-function][@stdlib/math/base/special/gamma].
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```c
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float out = stdlib_base_gammasgnf( 1.0 );
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// returns 1.0
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out = stdlib_base_gammasgnf( -2.5 );
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// returns -1.0
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```
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The function accepts the following arguments:
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- **x**: `[in] float` input value.
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```c
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float stdlib_base_gammasgnf( const float x );
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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#include "stdlib/math/base/special/gammasgnf.h"
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#include <stdlib.h>
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#include <stdio.h>
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int main( void ) {
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float x;
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float v;
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int i;
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for ( i = 0; i < 100; i++ ) {
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x = ( (float)rand() / (float)RAND_MAX ) * 100.0f;
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v = stdlib_base_gammasgnf( x );
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printf( "gammasgnf%f = %f\n", x, v );
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}
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}
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[@stdlib/math/base/special/gamma]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/gamma
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[@stdlib/math/base/special/gammaln]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/gammaln
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<!-- <related-links> -->
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

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

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2022 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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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/random/base/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 gammasgnf = 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()*171.0 ) - 0.0;
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y = gammasgnf( 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/gammasgnf/benchmark/benchmark.native.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var resolve = require( 'path' ).resolve;
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var bench = require( '@stdlib/bench' );
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var randu = require( '@stdlib/random/base/randu' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var tryRequire = require( '@stdlib/utils/try-require' );
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var pkg = require( './../package.json' ).name;
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// VARIABLES //
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var gammasgnf = tryRequire( resolve( __dirname, './../lib/native.js' ) );
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var opts = {
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'skip': ( gammasgnf instanceof Error )
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};
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// MAIN //
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bench( pkg+'::native', opts, 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() * 171.0 ) - 0.0;
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y = gammasgnf( 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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});

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