feat: add math/base/special/binomcoeff

lib/node_modules/@stdlib/math/base/special/binomcoeff/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.
+
+-->
+
+# Binomial Coefficient
+
+> Compute the [binomial coefficient][binomial-coefficient] as a single-precision floating-point number.
+
+<section class="intro">
+
+The [binomial coefficient][binomial-coefficient] of two nonnegative integers `n` and `k` is defined as
+
+<!-- <equation class="equation" label="eq:binomial_coefficient" align="center" raw="\binom {n}{k} = \frac{n!}{k!\,(n-k)!} \quad \text{for }\ 0\leq k\leq n" alt="Factorial formula for the Binomial coefficient."> -->
+
+```math
+\binom {n}{k} = \frac{n!}{k!\,(n-k)!} \quad \text{for }\ 0\leq k\leq n
+```
+
+<!-- </equation> -->
+
+The [binomial coefficient][binomial-coefficient] can be generalized to negative integers `n` as follows:
+
+<!-- <equation class="equation" label="eq:binomial_coefficient_negative_integers" align="center" raw="\binom {-n}{k} = (-1)^{k} \binom{n + k - 1}{k} = (-1)^{k} \left(\!\!{\binom {n}{k}}\!\!\right)" alt="Generalization of the binomial coefficient to negative n."> -->
+
+```math
+\binom {-n}{k} = (-1)^{k} \binom{n + k - 1}{k} = (-1)^{k} \left(\!\!{\binom {n}{k}}\!\!\right)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var binomcoeff = require( '@stdlib/math/base/special/binomcoeff' );
+```
+
+#### binomcoeff( n, k )
+
+Evaluates the [binomial coefficient][binomial-coefficient] of two integers `n` and `k` as a single-precision floating-point number.
+
+```javascript
+var v = binomcoeff( 8, 2 );
+// returns 28
+
+v = binomcoeff( 0, 0 );
+// returns 1
+
+v = binomcoeff( -4, 2 );
+// returns 10
+
+v = binomcoeff( 5, 3 );
+// returns 10
+
+v = binomcoeff( NaN, 3 );
+// returns NaN
+
+v = binomcoeff( 5, NaN );
+// returns NaN
+
+v = binomcoeff( NaN, NaN );
+// returns NaN
+```
+
+For negative `k`, the function returns `0`.
+
+```javascript
+var v = binomcoeff( 2, -1 );
+// returns 0
+
+v = binomcoeff( -3, -1 );
+// returns 0
+```
+
+The function returns `NaN` for non-integer `n` or `k`.
+
+```javascript
+var v = binomcoeff( 2, 1.5 );
+// returns NaN
+
+v = binomcoeff( 5.5, 2 );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var binomcoeff = require( '@stdlib/math/base/special/binomcoeff' );
+
+var opts = {
+    'dtype': 'int32'
+};
+var n = discreteUniform( 100, -10, 30, opts );
+var k = discreteUniform( 100, 0, 20, opts );
+
+logEachMap( 'binomcoeff(%d,%d) = %0.4f', n, k, binomcoeff );
+```
+
+</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/binomcoeff.h"
+```
+
+#### stdlib_base_binomcoeff( n, k )
+
+Evaluates the [binomial coefficient][binomial-coefficient] of two integers `n` and `k` as a single-precision floating-point number.
+
+```c
+float v = stdlib_base_binomcoeff( 8, 2 );
+// returns 28.0f
+```
+
+The function accepts the following arguments:
+
+-   **n**: `[in] int32_t` input value.
+-   **k**: `[in] int32_t` input value.
+
+```c
+float stdlib_base_binomcoeff( const int32_t n, const int32_t k );
+```
+
+</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/binomcoeff.h"
+#include <stdio.h>
+#include <stdint.h>
+
+int main( void ) {
+    const int32_t a[] = { 24, 32, 48, 116, 33 };
+    const int32_t b[] = { 12, 6, 15, 52, 22 };
+
+    float out;
+    int i;
+    for ( i = 0; i < 5; i++ ) {
+        out = stdlib_base_binomcoeff( a[ i ], b[ i ] );
+        printf( "binomcoeff(%d, %d) = %f\n", a[ i ], b[ i ], out );
+    }
+}
+```
+
+</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">
+
+[binomial-coefficient]: https://en.wikipedia.org/wiki/Binomial_coefficient
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/math/base/special/binomcoeff/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 binomcoeff = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var opts;
+	var x;
+	var y;
+	var z;
+	var i;
+
+	opts = {
+		'dtype': 'int32'
+	};
+	x = discreteUniform( 100, 20, 70, opts );
+	y = discreteUniform( 100, 0, 20, opts );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		z = binomcoeff( x[ i%x.length ], y[ i%y.length ] );
+		if ( isnanf( z ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnanf( z ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

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

@@ -0,0 +1,67 @@
+/**
+* @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 binomcoeff = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+	'skip': ( binomcoeff instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, function benchmark( b ) {
+	var options;
+	var x;
+	var y;
+	var z;
+	var i;
+
+	options = {
+		'dtype': 'int32'
+	};
+	x = discreteUniform( 100, 20, 70, options );
+	y = discreteUniform( 100, 0, 20, options );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		z = binomcoeff( x[ i%x.length ], y[ i%y.length ] );
+		if ( isnanf( z ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnanf( z ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});