Add support for computing the reciprocal square root

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2019 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.
+
+-->
+
+# Reciprocal Square Root
+
+> Compute the reciprocal of the principal [square root][square-root].
+
+<section class="intro">
+
+Reciprocal of the principal [square root][square-root] is defined as
+
+<!-- <equation class="equation" label="eq:reciprocal_square_root" align="center" raw="\operatorname{rsqrt}(x)=\frac{1}{\sqrt{x}}" alt="Reciprocal square root"> -->
+
+<div class="equation" align="center" data-raw-text="\operatorname{rsqrt}(x)=\frac{1}{\sqrt{x}}" data-equation="eq:reciprocal_square_root">
+    <img src="" alt="Reciprocal square root">
+    <br>
+</div>
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var rsqrt = require( '@stdlib/math/base/special/rsqrt' );
+```
+
+#### rsqrt( x )
+
+Computes the reciprocal (inverse) square root.
+
+```javascript
+var v = rsqrt( 1.0 );
+// returns 1.0
+
+v = rsqrt( 4.0 );
+// returns 0.5
+
+v = rsqrt( 100.0 );
+// returns 0.1
+
+v = rsqrt( 0.0 );
+// returns Infinity
+
+v = rsqrt( NaN );
+// returns NaN
+
+v = rsqrt( Infinity );
+// returns 0.0
+```
+
+For negative numbers, the reciprocal square root is **not** defined.
+
+```javascript
+var v = rsqrt( -4.0 );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var round = require( '@stdlib/math/base/special/round' );
+var rsqrt = require( '@stdlib/math/base/special/rsqrt' );
+
+var x;
+var i;
+
+for ( i = 0; i < 100; i++ ) {
+    x = round( randu() * 100.0 );
+    console.log( 'rsqrt(%d) = %d', x, rsqrt( x ) );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<section class="links">
+
+[square-root]: https://en.wikipedia.org/wiki/Square_root
+
+</section>
+
+<!-- /.links -->

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

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2019 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 randu = require( '@stdlib/random/base/randu' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var rsqrt = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		x = ( randu()*100000.0 ) - 0.0;
+		y = rsqrt( x );
+		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();
+});
+
+bench( pkg+'::built-in', function benchmark( b ) {
+	var x;
+	var y;
+	var i;
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		x = ( randu()*100000.0 ) - 0.0;
+		y = 1.0 / Math.sqrt( x ); // eslint-disable-line stdlib/no-builtin-math
+		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/rsqrt/docs/repl.txt

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+
+{{alias}}( x )
+    Computes the reciprocal square root.
+
+    For `x < 0`, the reciprocal square root is not defined.
+
+    Parameters
+    ----------
+    x: number
+        Input value.
+
+    Returns
+    -------
+    y: number
+        Reciprocal square root.
+
+    Examples
+    --------
+    > var y = {{alias}}( 4.0 )
+    0.5
+    > y = {{alias}}( 100.0 )
+    0.1
+    > y = {{alias}}( 0.0 )
+    0.0
+    > y = {{alias}}( Infinity )
+    0.0
+    > y = {{alias}}( -4.0 )
+    NaN
+    > y = {{alias}}( NaN )
+    NaN
+
+    See Also
+    --------
+

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

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2019 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: 2.0
+
+/**
+* Computes the reciprocal square root.
+*
+* ## Notes
+*
+* -   For `x < 0`, the reciprocal square root is not defined.
+*
+* @param x - input value
+* @returns reciprocal square root of `x`
+*
+* @example
+* var v = rsqrt( 4.0 );
+* // returns 0.5
+*
+* @example
+* var v = rsqrt( 100.0 );
+* // returns 0.1
+*
+* @example
+* var v = rsqrt( 0.0 );
+* // returns 0.0
+*
+* @example
+* var v = rsqrt( Infinity );
+* // returns 0.0
+*
+* @example
+* var v = rsqrt( -4.0 );
+* // returns NaN
+*
+* @example
+* var v = rsqrt( NaN );
+* // returns NaN
+*/
+declare function rsqrt( x: number ): number;
+
+
+// EXPORTS //
+
+export = rsqrt;

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

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2019 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 rsqrt = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+	rsqrt( 2 ); // $ExpectType number
+}
+
+// The function does not compile if provided a value other than a number...
+{
+	rsqrt( true ); // $ExpectError
+	rsqrt( false ); // $ExpectError
+	rsqrt( null ); // $ExpectError
+	rsqrt( undefined ); // $ExpectError
+	rsqrt( '5' ); // $ExpectError
+	rsqrt( [] ); // $ExpectError
+	rsqrt( {} ); // $ExpectError
+	rsqrt( ( x: number ): number => x ); // $ExpectError
+}
+
+// The function does not compile if provided insufficient arguments...
+{
+	rsqrt(); // $ExpectError
+}

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

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2019 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 randu = require( '@stdlib/random/base/randu' );
+var round = require( '@stdlib/math/base/special/round' );
+var rsqrt = require( './../lib' );
+
+var x;
+var i;
+
+for ( i = 0; i < 100; i++ ) {
+	x = round( randu() * 100.0 );
+	console.log( 'rsqrt(%d) = %d', x, rsqrt( x ) );
+}