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License.\nYou may obtain a copy of the License at\n\n   http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n\n-->\n\n\n<details>\n  <summary>\n    About stdlib...\n  </summary>\n  <p>We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.</p>\n  <p>The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.</p>\n  <p>When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.</p>\n  <p>To join us in bringing numerical computing to the web, get started by checking us out on <a href=\"https://github.com/stdlib-js/stdlib\">GitHub</a>, and please consider <a href=\"https://opencollective.com/stdlib\">financially supporting stdlib</a>. We greatly appreciate your continued support!</p>\n</details>\n\n# Binomial Coefficient\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->\n\n> Compute the [binomial coefficient][binomial-coefficient].\n\n<section class=\"intro\">\n\nThe [binomial coefficient][binomial-coefficient] of two nonnegative integers `n` and `k` is defined as\n\n<!-- <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.\"> -->\n\n<div class=\"equation\" align=\"center\" data-raw-text=\"\\binom {n}{k} = \\frac{n!}{k!\\,(n-k)!} \\quad \\text{for }\\ 0\\leq k\\leq n\" data-equation=\"eq:binomial_coefficient\">\n    <img src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/binomcoef/docs/img/equation_binomial_coefficient.svg\" alt=\"Factorial formula for the Binomial coefficient.\">\n    <br>\n</div> -->\n\n<!-- </equation> -->\n\nThe [binomial coefficient][binomial-coefficient] can be generalized to negative integers `n` as follows:\n\n<!-- <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.\"> -->\n\n<!-- <div class=\"equation\" align=\"center\" data-raw-text=\"\\binom {-n}{k} = (-1)^{k} \\binom{n + k - 1}{k} = (-1)^{k} \\left(\\!\\!{\\binom {n}{k}}\\!\\!\\right)\" data-equation=\"eq:binomial_coefficient_negative_integers\">\n    <img src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/math/base/special/binomcoef/docs/img/equation_binomial_coefficient_negative_integers.svg\" alt=\"Generalization of the binomial coefficient to negative n.\">\n    <br>\n</div>\n\n<!-- </equation> -->\n\n</section>\n\n<!-- /.intro -->\n\n<section class=\"installation\">\n\n## Installation\n\n```bash\nnpm install @stdlib/math-base-special-binomcoef\n```\n\n</section>\n\n<section class=\"usage\">\n\n## Usage\n\n```javascript\nvar binomcoef = require( '@stdlib/math-base-special-binomcoef' );\n```\n\n#### binomcoef( n, k )\n\nEvaluates the [binomial coefficient][binomial-coefficient] of two integers `n` and `k`.\n\n```javascript\nvar v = binomcoef( 8, 2 );\n// returns 28\n\nv = binomcoef( 0, 0 );\n// returns 1\n\nv = binomcoef( -4, 2 );\n// returns 10\n\nv = binomcoef( 5, 3 );\n// returns 10\n\nv = binomcoef( NaN, 3 );\n// returns NaN\n\nv = binomcoef( 5, NaN );\n// returns NaN\n\nv = binomcoef( NaN, NaN );\n// returns NaN\n```\n\nFor negative `k`, the function returns `0`.\n\n```javascript\nvar v = binomcoef( 2, -1 );\n// returns 0\n\nv = binomcoef( -3, -1 );\n// returns 0\n```\n\nThe function returns `NaN` for non-integer `n` or `k`.\n\n```javascript\nvar v = binomcoef( 2, 1.5 );\n// returns NaN\n\nv = binomcoef( 5.5, 2 );\n// returns NaN\n```\n\n</section>\n\n<!-- /.usage -->\n\n<section class=\"examples\">\n\n## Examples\n\n<!-- eslint no-undef: \"error\" -->\n\n```javascript\nvar discreteUniform = require( '@stdlib/random-array-discrete-uniform' );\nvar logEachMap = require( '@stdlib/console-log-each-map' );\nvar binomcoef = require( '@stdlib/math-base-special-binomcoef' );\n\nvar opts = {\n    'dtype': 'float64'\n};\nvar n = discreteUniform( 100, -10, 30, opts );\nvar k = discreteUniform( 100, 0, 20, opts );\n\nlogEachMap( '%d choose %d = %d', n, k, binomcoef );\n```\n\n</section>\n\n<!-- /.examples -->\n\n<!-- C interface documentation. -->\n\n* * *\n\n<section class=\"c\">\n\n## C APIs\n\n<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->\n\n<section class=\"intro\">\n\n</section>\n\n<!-- /.intro -->\n\n<!-- C usage documentation. -->\n\n<section class=\"usage\">\n\n### Usage\n\n```c\n#include \"stdlib/math/base/special/binomcoef.h\"\n```\n\n#### stdlib_base_binomcoef( n, k )\n\nEvaluates the [binomial coefficient][binomial-coefficient] of two integers `n` and `k`.\n\n```c\ndouble v = stdlib_base_binomcoef( 8.0, 2.0 );\n// returns 28.0\n```\n\nThe function accepts the following arguments:\n\n-   **n**: `[in] double` input value.\n-   **k**: `[in] double` input value.\n\n```c\ndouble stdlib_base_binomcoef( const double n, const double k );\n```\n\n</section>\n\n<!-- /.usage -->\n\n<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n<section class=\"notes\">\n\n</section>\n\n<!-- /.notes -->\n\n<!-- C API usage examples. -->\n\n<section class=\"examples\">\n\n### Examples\n\n```c\n#include \"stdlib/math/base/special/binomcoef.h\"\n#include <stdio.h>\n\nint main( void ) {\n    const double a[] = { 24.0, 32.0, 48.0, 116.0, 33.0 };\n    const double b[] = { 12.0, 6.0, 15.0, 52.0, 22.0 };\n\n    double out;\n    int i;\n    for ( i = 0; i < 5; i++ ) {\n        out = stdlib_base_binomcoef( a[ i ], b[ i ] );\n        printf( \"binomcoef(%lf, %lf) = %lf\\n\", a[ i ], b[ i ], out );\n    }\n}\n```\n\n</section>\n\n<!-- /.examples -->\n\n</section>\n\n<!-- /.c -->\n\n<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->\n\n<section class=\"related\">\n\n</section>\n\n<!-- /.related -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n\n<section class=\"main-repo\" >\n\n* * *\n\n## Notice\n\nThis package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.\n\nFor more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].\n\n#### Community\n\n[![Chat][chat-image]][chat-url]\n\n---\n\n## License\n\nSee [LICENSE][stdlib-license].\n\n\n## Copyright\n\nCopyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].\n\n</section>\n\n<!-- /.stdlib -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n<section class=\"links\">\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-binomcoef.svg\n[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-binomcoef\n\n[test-image]: https://github.com/stdlib-js/math-base-special-binomcoef/actions/workflows/test.yml/badge.svg?branch=v0.3.1\n[test-url]: https://github.com/stdlib-js/math-base-special-binomcoef/actions/workflows/test.yml?query=branch:v0.3.1\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-binomcoef/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-binomcoef?branch=main\n\n<!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/math-base-special-binomcoef.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/math-base-special-binomcoef/main\n\n-->\n\n[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg\n[chat-url]: https://stdlib.zulipchat.com\n\n[stdlib]: https://github.com/stdlib-js/stdlib\n\n[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors\n\n[umd]: https://github.com/umdjs/umd\n[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules\n\n[deno-url]: https://github.com/stdlib-js/math-base-special-binomcoef/tree/deno\n[deno-readme]: https://github.com/stdlib-js/math-base-special-binomcoef/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/math-base-special-binomcoef/tree/umd\n[umd-readme]: https://github.com/stdlib-js/math-base-special-binomcoef/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/math-base-special-binomcoef/tree/esm\n[esm-readme]: https://github.com/stdlib-js/math-base-special-binomcoef/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/math-base-special-binomcoef/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-binomcoef/main/LICENSE\n\n[binomial-coefficient]: https://en.wikipedia.org/wiki/Binomial_coefficient\n\n</section>\n\n<!-- /.links -->\n","readmeFilename":"README.md"}