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feat: add math/base/special/bernoullif
PR-URL: #3037 Ref: #649 Signed-off-by: Gururaj Gurram <[email protected]> Signed-off-by: Gunj Joshi <[email protected]> Signed-off-by: Philipp Burckhardt <[email protected]> Co-authored-by: Athan Reines <[email protected]> Co-authored-by: stdlib-bot <[email protected]> Co-authored-by: Gunj Joshi <[email protected]> Co-authored-by: Karan Anand <[email protected]> Co-authored-by: Philipp Burckhardt <[email protected]> Reviewed-by: Karan Anand <[email protected]> Reviewed-by: Gunj Joshi <[email protected]> Reviewed-by: Philipp Burckhardt <[email protected]> Reviewed-by: Athan Reines <[email protected]>
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‎lib/node_modules/@stdlib/math/base/special/bernoullif/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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# bernoullif
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> Compute the nth [Bernoulli number][bernoulli-number] as a single-precision floating-point number.
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<section class="intro">
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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 bernoullif = require( '@stdlib/math/base/special/bernoullif' );
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```
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#### bernoullif( n )
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Computes the nth [Bernoulli number][bernoulli-number] as a single-precision floating-point number.
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```javascript
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var v = bernoullif( 0 );
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// returns 1.0
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v = bernoullif( 1 );
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// returns 0.5
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v = bernoullif( 2 );
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// returns ~0.167
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v = bernoullif( 3 );
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// returns 0.0
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v = bernoullif( 4 );
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// returns ~-0.033
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v = bernoullif( 5 );
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// returns 0.0
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v = bernoullif( 20 );
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// returns ~-529.124
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```
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For even integers `n >= 66`, the function alternates between returning positive and negative infinity, as larger [Bernoulli numbers][bernoulli-number] cannot be safely represented in [single-precision floating-point format][ieee754]
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```javascript
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var v = bernoullif( 66 );
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// returns Infinity
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v = bernoullif( 68 );
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// returns -Infinity
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v = bernoullif( 70 );
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// returns Infinity
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```
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If not provided a nonnegative integer value, the function returns `NaN`.
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```javascript
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var v = bernoullif( 3.14 );
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// returns NaN
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v = bernoullif( -1 );
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// returns NaN
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```
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If provided `NaN`, the function returns `NaN`.
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```javascript
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var v = bernoullif( 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="notes">
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</section>
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<!-- /.notes -->
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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 logEachMap = require( '@stdlib/console/log-each-map' );
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var bernoullif = require( '@stdlib/math/base/special/bernoullif' );
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var x = discreteUniform( 100, 0, 70, {
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'dtype': 'int32'
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});
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logEachMap( 'bernoullif(%d) = %0.4f', x, bernoullif );
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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/bernoullif.h"
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```
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#### stdlib_base_bernoullif( n )
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Computes the nth [Bernoulli number][bernoulli-number] as a single-precision floating-point number.
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```c
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float out = stdlib_base_bernoullif( 0 );
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// returns 1.0f
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out = stdlib_base_bernoullif( 1 );
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// returns 0.5f
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```
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The function accepts the following arguments:
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- **n**: `[in] int32_t` input value.
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```c
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float stdlib_base_bernoullif( const int32_t n );
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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/bernoullif.h"
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#include <stdio.h>
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#include <stdint.h>
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int main( void ) {
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int32_t i;
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float v;
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for ( i = 0; i < 70; i++ ) {
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v = stdlib_base_bernoullif( i );
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printf( "bernoullif(%d) = %f\n", i, v );
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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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[bernoulli-number]: https://en.wikipedia.org/wiki/Bernoulli_number
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[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/math/base/special/bernoullif/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 bernoullif = 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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x = discreteUniform( 100, 0, 100 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = bernoullif( 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/bernoullif/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 bernoullif = tryRequire( resolve( __dirname, './../lib/native.js' ) );
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var opts = {
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'skip': ( bernoullif 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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x = discreteUniform( 100, 0, 100 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = bernoullif( 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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