feat: add math/base/special/gamma-lanczos-sumf

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+# Gamma Lanczos Sumf
+
+> Calculate the Lanczos sum for the approximation of the [gamma function][gamma-function].
+
+<section class="intro">
+
+The [Lanczos approximation][lanczos-approximation] for the [gamma function][gamma-function] can be written in partial fraction form as follows:
+
+<!-- <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."> -->
+
+```math
+\Gamma ( n ) = \frac{(n+g-0.5)^{n-0.5}}{e^{n+g-0.5}} L_g(n)
+```
+
+<!-- <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">
+    <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.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where `g` is an [arbitrary constant][@stdlib/constants/float32/gamma-lanczos-g] and `L_g(n)` is the Lanczos sum.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var gammaLanczosSumf = require( '@stdlib/math/base/special/gamma-lanczos-sumf' );
+```
+
+#### gammaLanczosSumf( x )
+
+Calculates the Lanczos sum for the approximation of the [gamma function][gamma-function] for single-precision floating-point number.
+
+```javascript
+var v = gammaLanczosSumf( 4.0 );
+// returns ~950.366
+
+v = gammaLanczosSumf( -1.5 );
+// returns ~1373366.245
+
+v = gammaLanczosSumf( -0.5 );
+// returns ~-699841.735
+
+v = gammaLanczosSumf( 0.5 );
+// returns ~96074.186
+
+v = gammaLanczosSumf( 0.0 );
+// returns Infinity
+
+v = gammaLanczosSumf( NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var linspace = require( '@stdlib/array/base/linspace' );
+var gammaLanczosSumf = require( '@stdlib/math/base/special/gamma-lanczos-sumf' );
+
+var x = linspace( -10.0, 10.0, 100 );
+
+var i;
+for ( i = 0; i < x.length; i++ ) {
+    console.log( 'x: %d, f(x): %d', x[ i ], gammaLanczosSumf( 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/gamma_lanczos_sumf.h"
+```
+
+#### stdlib_base_gamma_lanczos_sumf( x )
+
+Calculates the Lanczos sum for the approximation of the [gamma function][gamma-function] for single-precision floating-point number.
+
+```c
+float out = stdlib_base_gamma_lanczos_sumf( 4.0f );
+// returns ~950.366f
+
+out = stdlib_base_gamma_lanczos_sumf( -1.5f );
+// returns ~1373366.245f
+```
+
+The function accepts the following arguments:
+
+-   **x**: `[in] float` input value.
+
+```c
+float stdlib_base_gamma_lanczos_sumf( 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/gamma_lanczos_sumf.h"
+#include <stdlib.h>
+#include <stdio.h>
+
+int main( void ) {
+    const float x[] = { 4.0f, -1.5f, -0.5f, 0.5f };
+
+    float y;
+    int i;
+    for ( i = 0; i < 4; i++ ) {
+        y = stdlib_base_gamma_lanczos_sumf( x[ i ] );
+        printf( "gamma_lanczos_sumf(%f) = %f\n", x[ i ], y );
+    }
+}
+```
+
+</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">
+
+[@stdlib/constants/float32/gamma-lanczos-g]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/constants/float32/gamma-lanczos-g
+
+[gamma-function]: https://en.wikipedia.org/wiki/Gamma_function
+
+[lanczos-approximation]: https://en.wikipedia.org/wiki/Lanczos_approximation
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/math/base/special/gamma-lanczos-sumf/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
+var pkg = require( './../package.json' ).name;
+var gammaLanczosSumf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	discreteUniform( 100, -50.0, 50.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = gammaLanczosSumf( 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/gamma-lanczos-sumf/benchmark/benchmark.native.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 discreteUniform = require( '@stdlib/random/array/discrete-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 gammaLanczosSumf = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+	'skip': ( gammaLanczosSumf instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	discreteUniform( 100, -50.0, 50.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = gammaLanczosSumf( 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();
+});