feat: add math/base/special/bernoullif

lib/node_modules/@stdlib/math/base/special/bernoullif/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.
+
+-->
+
+# bernoullif
+
+> Compute the nth [Bernoulli number][bernoulli-number] as a single-precision floating-point number.
+
+<section class="intro">
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var bernoullif = require( '@stdlib/math/base/special/bernoullif' );
+```
+
+#### bernoullif( n )
+
+Computes the nth [Bernoulli number][bernoulli-number] as a single-precision floating-point number.
+
+```javascript
+var v = bernoullif( 0 );
+// returns 1.0
+
+v = bernoullif( 1 );
+// returns 0.5
+
+v = bernoullif( 2 );
+// returns ~0.167
+
+v = bernoullif( 3 );
+// returns 0.0
+
+v = bernoullif( 4 );
+// returns ~-0.033
+
+v = bernoullif( 5 );
+// returns 0.0
+
+v = bernoullif( 20 );
+// returns ~-529.124
+```
+
+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]
+
+```javascript
+var v = bernoullif( 66 );
+// returns Infinity
+
+v = bernoullif( 68 );
+// returns -Infinity
+
+v = bernoullif( 70 );
+// returns Infinity
+```
+
+If not provided a nonnegative integer value, the function returns `NaN`.
+
+```javascript
+var v = bernoullif( 3.14 );
+// returns NaN
+
+v = bernoullif( -1 );
+// returns NaN
+```
+
+If provided `NaN`, the function returns `NaN`.
+
+```javascript
+var v = bernoullif( NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var bernoullif = require( '@stdlib/math/base/special/bernoullif' );
+
+var x = discreteUniform( 100, 0, 70, {
+    'dtype': 'int32'
+});
+
+logEachMap( 'bernoullif(%d) = %0.4f', x, bernoullif );
+```
+
+</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/bernoullif.h"
+```
+
+#### stdlib_base_bernoullif( n )
+
+Computes the nth [Bernoulli number][bernoulli-number] as a single-precision floating-point number.
+
+```c
+float out = stdlib_base_bernoullif( 0 );
+// returns 1.0f
+
+out = stdlib_base_bernoullif( 1 );
+// returns 0.5f
+```
+
+The function accepts the following arguments:
+
+-   **n**: `[in] int32_t` input value.
+
+```c
+float stdlib_base_bernoullif( const int32_t n );
+```
+
+</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/bernoullif.h"
+#include <stdio.h>
+#include <stdint.h>
+
+int main( void ) {
+    int32_t i;
+    float v;
+
+    for ( i = 0; i < 70; i++ ) {
+        v = stdlib_base_bernoullif( i );
+        printf( "bernoullif(%d) = %f\n", i, v );
+    }
+}
+```
+
+</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">
+
+[bernoulli-number]: https://en.wikipedia.org/wiki/Bernoulli_number
+
+[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/math/base/special/bernoullif/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 bernoullif = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	x = discreteUniform( 100, 0, 100 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = bernoullif( 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/bernoullif/benchmark/benchmark.native.js

@@ -0,0 +1,61 @@
+/**
+* @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 bernoullif = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+	'skip': ( bernoullif instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	x = discreteUniform( 100, 0, 100 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = bernoullif( 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();
+});