feat: add math/base/special/gelu

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 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.
+
+-->
+
+# gelu
+
+> Evaluate the [Gaussian error linear unit][gelu] (GELU).
+
+<section class="intro">
+
+The [Gaussian error linear unit][gelu] (GELU) activation function is defined as:
+
+```math
+\mathrm{gelu}(x) = x \cdot \Phi(x) = \frac{x}{2} \left[ 1 + \mathrm{erf}\left( \frac{x}{\sqrt{2}} \right) \right]
+```
+
+where $\Phi(x)$ is the cumulative distribution function of the standard normal distribution and $\mathrm{erf}(x)$ is the [error function][@stdlib/math/base/special/erf].
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var gelu = require( '@stdlib/math/base/special/gelu' );
+```
+
+#### gelu( x )
+
+Evaluates the Gaussian Error Linear Unit (GELU) activation function.
+
+```javascript
+var v = gelu( 0.0 );
+// returns 0.0
+
+v = gelu( 1.0 );
+// returns ~0.8413
+
+v = gelu( -Infinity );
+// returns 0.0
+
+v = gelu( Infinity );
+// returns Infinity
+
+v = gelu( NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var gelu = require( '@stdlib/math/base/special/gelu' );
+
+var opts = {
+    'dtype': 'float64'
+};
+var x = uniform( 100, -5.0, 5.0, opts );
+
+logEachMap( 'gelu(%0.4f) = %0.4f', x, gelu );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<section class="related">
+
+* * *
+
+## See Also
+
+-   <span class="package-name">[`@stdlib/math/base/special/erf`][@stdlib/math/base/special/erf]</span><span class="delimiter">: </span><span class="description">evaluate the error function.</span>
+-   <span class="package-name">[`@stdlib/math/base/special/erfc`][@stdlib/math/base/special/erfc]</span><span class="delimiter">: </span><span class="description">evaluate the complementary error function.</span>
+-   <span class="package-name">[`@stdlib/math/base/special/ramp`][@stdlib/math/base/special/ramp]</span><span class="delimiter">: </span><span class="description">evaluate the ramp function.</span>
+
+</section>
+
+<!-- /.related -->
+
+<section class="links">
+
+[gelu]: https://en.wikipedia.org/wiki/Gelu
+
+<!-- <related-links> -->
+
+[@stdlib/math/base/special/erf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/erf
+
+[@stdlib/math/base/special/erfc]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/erfc
+
+[@stdlib/math/base/special/ramp]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/ramp
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/math/base/special/gelu/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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 uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var gelu = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	x = uniform( 100, -10.0, 10.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = gelu( x[ i % x.length ] );
+		if ( isnan( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/math/base/special/gelu/docs/repl.txt

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+
+{{alias}}( x )
+    Evaluates the Gaussian Error Linear Unit (GELU) activation function.
+
+    Parameters
+    ----------
+    x: number
+        Input value.
+
+    Returns
+    -------
+    y: number
+        Function value.
+
+    Examples
+    --------
+    > var y = {{alias}}( 0.0 )
+    0.0
+    > y = {{alias}}( 1.0 )
+    ~0.8413
+    > y = {{alias}}( -Infinity )
+    0.0
+    > y = {{alias}}( Infinity )
+    Infinity
+    > y = {{alias}}( NaN )
+    NaN
+
+    See Also
+    --------
+

lib/node_modules/@stdlib/math/base/special/gelu/docs/types/index.d.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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.
+*/
+
+// TypeScript Version: 4.1
+
+/**
+* Evaluate the Gaussian Error Linear Unit (GELU) activation function.
+*
+* @param x - input value
+* @returns function value
+*
+* @example
+* var y = gelu( 0.0 );
+* // returns 0.0
+*
+* @example
+* var y = gelu( 1.0 );
+* // returns ~0.8413
+*
+* @example
+* var y = gelu( -Infinity );
+* // returns 0.0
+*
+* @example
+* var y = gelu( NaN );
+* // returns NaN
+*/
+declare function gelu( x: number ): number;
+
+
+// EXPORTS //
+
+export = gelu;

lib/node_modules/@stdlib/math/base/special/gelu/docs/types/test.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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.
+*/
+
+import gelu = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+	gelu( 8 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided a value other than a number...
+{
+	gelu( true ); // $ExpectError
+	gelu( false ); // $ExpectError
+	gelu( null ); // $ExpectError
+	gelu( undefined ); // $ExpectError
+	gelu( '5' ); // $ExpectError
+	gelu( [] ); // $ExpectError
+	gelu( {} ); // $ExpectError
+	gelu( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided insufficient arguments...
+{
+	gelu(); // $ExpectError
+}

lib/node_modules/@stdlib/math/base/special/gelu/examples/index.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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';
+
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var gelu = require( './../lib' );
+
+var opts = {
+	'dtype': 'float64'
+};
+var x = uniform( 100, -5.0, 5.0, opts );
+
+logEachMap( 'gelu(%0.4f) = %0.4f', x, gelu );

lib/node_modules/@stdlib/math/base/special/gelu/lib/index.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 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';
+
+/**
+* Evaluate the Gaussian Error Linear Unit (GELU) activation function.
+*
+* @module @stdlib/math/base/special/gelu
+*
+* @example
+* var gelu = require( '@stdlib/math/base/special/gelu' );
+*
+* var y = gelu( 0.0 );
+* // returns 0.0
+*
+* y = gelu( 1.0 );
+* // returns ~0.8413
+*
+* y = gelu( -Infinity );
+* // returns 0.0
+*
+* y = gelu( NaN );
+* // returns NaN
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;