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‎lib/node_modules/@stdlib/math/base/special/gamma-lanczos-sumf/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2025 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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# Gamma Lanczos Sum
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> Calculate the Lanczos sum for the approximation of the [gamma function][gamma-function].
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<section class="intro">
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The [Lanczos approximation][lanczos-approximation] for the [gamma function][gamma-function] can be written in partial fraction form as follows:
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<!-- <equation class="equation" label="eq:lanczos_approximation" align="center" raw="\Gamma ( n ) = \frac{(n+g-0.5)^{n-0.5}}{e^{n+g-0.5}} L_g(n)" alt="Lanczos approximation for gamma function."> -->
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```math
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\Gamma ( n ) = \frac{(n+g-0.5)^{n-0.5}}{e^{n+g-0.5}} L_g(n)
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```
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<!-- <div class="equation" align="center" data-raw-text="\Gamma ( n ) = \frac{(n+g-0.5)^{n-0.5}}{e^{n+g-0.5}} L_g(n)" data-equation="eq:lanczos_approximation">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/gamma-lanczos-sum/docs/img/equation_lanczos_approximation.svg" alt="Lanczos approximation for gamma function.">
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<br>
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</div> -->
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<!-- </equation> -->
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where `g` is an [arbitrary constant][@stdlib/constants/float32/gamma-lanczos-g] and `L_g(n)` is the Lanczos sum.
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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 gammaLanczosSumf = require( '@stdlib/math/base/special/gamma-lanczos-sumf' );
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```
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#### gammaLanczosSumf( x )
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Calculates the Lanczos sum for the approximation of the [gamma function][gamma-function] for single-precision floating-point number.
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```javascript
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var v = gammaLanczosSumf( 4.0 );
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// returns ~950.366
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v = gammaLanczosSumf( -1.5 );
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// returns ~1373366.245
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v = gammaLanczosSumf( -0.5 );
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// returns ~-699841.735
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v = gammaLanczosSumf( 0.5 );
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// returns ~96074.186
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v = gammaLanczosSumf( 0.0 );
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// returns Infinity
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v = gammaLanczosSumf( 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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<!-- 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 gammaLanczosSumf = require( '@stdlib/math/base/special/gamma-lanczos-sumf' );
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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): %d', x[ i ], gammaLanczosSumf( 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/gamma_lanczos_sumf.h"
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```
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#### stdlib_base_gamma_lanczos_sumf( x )
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Calculates the Lanczos sum for the approximation of the [gamma function][gamma-function] for single-precision floating-point number.
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```c
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float out = stdlib_base_gamma_lanczos_sumf( 4.0f );
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// returns ~950.366f
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out = stdlib_base_gamma_lanczos_sumf( -1.5f );
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// returns ~1373366.245f
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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_gamma_lanczos_sumf( 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/gamma_lanczos_sumf.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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const float x[] = { 4.0f, -1.5f, -0.5f, 0.5f };
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float y;
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int i;
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for ( i = 0; i < 4; i++ ) {
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y = stdlib_base_gamma_lanczos_sumf( x[ i ] );
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printf( "gamma_lanczos_sumf(%f) = %f\n", x[ i ], y );
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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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* * *
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## See Also
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- <span class="package-name">[`@stdlib/math/base/special/gamma-lanczos-sum`][@stdlib/math/base/special/gamma-lanczos-sum]</span><span class="delimiter">: </span><span class="description">gamma function.</span>
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- <span class="package-name">[`@stdlib/math/base/special/gamma`][@stdlib/math/base/special/gamma]</span><span class="delimiter">: </span><span class="description">gamma function.</span>
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- <span class="package-name">[`@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled`][@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled]</span><span class="delimiter">: </span><span class="description">calculate a scaled Lanczos sum for the approximation of the gamma function.</span>
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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/constants/float64/gamma-lanczos-g]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/constants/float64/gamma-lanczos-g
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[gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
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[lanczos-approximation]: https://en.wikipedia.org/wiki/Lanczos_approximation
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<!-- <related-links> -->
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[@stdlib/math/base/special/gamma-lanczos-sum]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/gamma-lanczos-sum
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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/gamma-lanczos-sum-expg-scaled]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/gamma-lanczos-sum-expg-scaled
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/math/base/special/gamma-lanczos-sumf/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) 2025 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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
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var pkg = require( './../package.json' ).name;
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var gammaLanczosSumf = 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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discreteUniform( 100, -50.0, 50.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = gammaLanczosSumf( x[ i % x.length ] );
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if ( isnanf( 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 ( isnanf( 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/gamma-lanczos-sumf/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) 2025 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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
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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 gammaLanczosSumf = tryRequire( resolve( __dirname, './../lib/native.js' ) );
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var opts = {
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'skip': ( gammaLanczosSumf 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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discreteUniform( 100, -50.0, 50.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = gammaLanczosSumf( x[ i % x.length ] );
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if ( isnanf( 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 ( isnanf( 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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