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‎lib/node_modules/@stdlib/math/base/special/binomcoeff/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2018 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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# Binomial Coefficient
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> Compute the [binomial coefficient][binomial-coefficient].
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<section class="intro">
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The [binomial coefficient][binomial-coefficient] of two nonnegative integers `n` and `k` is defined as
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<!-- <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."> -->
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```math
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\binom {n}{k} = \frac{n!}{k!\,(n-k)!} \quad \text{for }\ 0\leq k\leq n
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```
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<!-- <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">
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<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.">
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<br>
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</div> -->
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<!-- </equation> -->
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The [binomial coefficient][binomial-coefficient] can be generalized to negative integers `n` as follows:
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<!-- <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."> -->
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```math
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\binom {-n}{k} = (-1)^{k} \binom{n + k - 1}{k} = (-1)^{k} \left(\!\!{\binom {n}{k}}\!\!\right)
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```
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<!-- <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">
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<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.">
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<br>
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</div> -->
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<!-- </equation> -->
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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 binomcoef = require( '@stdlib/math/base/special/binomcoef' );
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```
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#### binomcoef( n, k )
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Evaluates the [binomial coefficient][binomial-coefficient] of two integers `n` and `k`.
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```javascript
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var v = binomcoef( 8, 2 );
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// returns 28
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v = binomcoef( 0, 0 );
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// returns 1
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v = binomcoef( -4, 2 );
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// returns 10
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v = binomcoef( 5, 3 );
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// returns 10
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v = binomcoef( NaN, 3 );
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// returns NaN
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v = binomcoef( 5, NaN );
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// returns NaN
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v = binomcoef( NaN, NaN );
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// returns NaN
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```
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For negative `k`, the function returns `0`.
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```javascript
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var v = binomcoef( 2, -1 );
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// returns 0
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v = binomcoef( -3, -1 );
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// returns 0
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```
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The function returns `NaN` for non-integer `n` or `k`.
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```javascript
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var v = binomcoef( 2, 1.5 );
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// returns NaN
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v = binomcoef( 5.5, 2 );
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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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var logEachMap = require( '@stdlib/console/log-each-map' );
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var binomcoef = require( '@stdlib/math/base/special/binomcoef' );
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var opts = {
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'dtype': 'float64'
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};
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var n = discreteUniform( 100, -10, 30, opts );
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var k = discreteUniform( 100, 0, 20, opts );
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logEachMap( '%d choose %d = %d', n, k, binomcoef );
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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/binomcoef.h"
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```
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#### stdlib_base_binomcoef( n, k )
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Evaluates the [binomial coefficient][binomial-coefficient] of two integers `n` and `k`.
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```c
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double v = stdlib_base_binomcoef( 8, 2 );
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// returns 28.0
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```
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The function accepts the following arguments:
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- **n**: `[in] int64_t` input value.
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- **k**: `[in] int64_t` input value.
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```c
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double stdlib_base_binomcoef( const int64_t n, const int64_t k );
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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/binomcoef.h"
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#include <stdio.h>
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#include <stdint.h>
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#include <inttypes.h>
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int main( void ) {
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const int64_t a[] = { 24, 32, 48, 116, 33 };
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const int64_t b[] = { 12, 6, 15, 52, 22 };
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double out;
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int i;
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for ( i = 0; i < 5; i++ ) {
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out = stdlib_base_binomcoef( a[ i ], b[ i ] );
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printf( "binomcoef(%" PRId64 ", %" PRId64 ") = %lf\n", a[ i ], b[ i ], out );
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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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[binomial-coefficient]: https://en.wikipedia.org/wiki/Binomial_coefficient
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/math/base/special/binomcoeff/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) 2018 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 isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pkg = require( './../package.json' ).name;
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var binomcoef = 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 z;
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var i;
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x = discreteUniform( 100, 20, 70 );
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y = discreteUniform( 100, 0, 20 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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z = binomcoef( x[ i%x.length ], y[ i%y.length ] );
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if ( isnan( z ) ) {
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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( z ) ) {
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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/binomcoeff/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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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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 binomcoef = tryRequire( resolve( __dirname, './../lib/native.js' ) );
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var opts = {
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'skip': ( binomcoef 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 z;
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var i;
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x = discreteUniform( 100, 20, 70 );
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y = discreteUniform( 100, 0, 20 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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z = binomcoef( x[ i%x.length ], y[ i%y.length ] );
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if ( isnan( z ) ) {
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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( z ) ) {
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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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