Add support for computing the derivative of cardinal sine (cosc)

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

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2018 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.
+
+-->
+
+# cosc
+
+> Compute the derivative of the [cardinal sine][sinc] of a number.
+
+<section class="intro">
+
+The derivative of the normalized [cardinal sine][sinc] function is defined as
+
+` { cosc(x) = (cos( PI*x ) - sin( PI*x )/(PI*x)) / x } if x != 0, and 0 if x == 0 `
+
+
+<!-- </equation> -->
+
+for any real number `x`.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var cosc = require( '@stdlib/math/base/special/cosc' );
+```
+
+#### cosc( x )
+
+Computes the derivative of the normalized [cardinal sine][sinc] of a `number`.
+
+```javascript
+var v = cosc( 0.5 );
+
+// Return ~-1.273
+
+var x = cosc( -1.2 );
+
+// Return ~0.544
+
+var y = cosc( 0.0 );
+
+// Return 0
+
+var z = cosc( NaN );
+
+// Return NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var linspace = require( '@stdlib/math/utils/linspace' );
+var cosc = require( '@stdlib/math/base/special/cosc' );
+
+var x = linspace( -5.0, 5.0, 100 );
+var i;
+
+for ( i = 0; i < x.length; i++ ) {
+    console.log( cosc( x[ i ] ) );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<section class="links">
+
+[sinc]: https://en.wikipedia.org/wiki/Sinc_function
+
+</section>
+
+<!-- /.links -->

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

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 cosc = 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() * 2.0 ) - 2.0;
+		y = cosc( 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();
+});

lib/node_modules/@stdlib/math/base/special/cosc/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 derivative of the normalized cardinal sine of a number.
+*
+* @param x - input value
+* @returns derivative of cardinal sine
+*
+* @example
+* var v = cosc( 0.5 );
+* // returns ~-1.273
+*
+* @example
+* var v = cosc( -1.2 );
+* // returns ~0.544
+*
+* @example
+* var v = cosc( 0.0 );
+* // returns 0.0
+*
+* @example
+* var v = cosc( NaN );
+* // returns NaN
+*/
+declare function cosc( x: number ): number;
+
+
+// EXPORTS //
+
+export = cosc;

lib/node_modules/@stdlib/math/base/special/cosc/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 cosc = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+	cosc( 8 ); // $ExpectType number
+}
+
+// The function does not compile if provided a value other than a number...
+{
+	cosc( true ); // $ExpectError
+	cosc( false ); // $ExpectError
+	cosc( null ); // $ExpectError
+	cosc( undefined ); // $ExpectError
+	cosc( '5' ); // $ExpectError
+	cosc( [] ); // $ExpectError
+	cosc( {} ); // $ExpectError
+	cosc( ( x: number ): number => x ); // $ExpectError
+}
+
+// The function does not compile if provided insufficient arguments...
+{
+	cosc(); // $ExpectError
+}

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

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 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 linspace = require( '@stdlib/math/utils/linspace' );
+var cosc = require( './../lib' );
+
+var x = linspace( -5.0, 5.0, 100 );
+var i;
+
+for ( i = 0; i < x.length; i++ ) {
+	console.log( 'cosc( %d ) = %d', x[ i ], cosc( x[ i ] ) );
+}

lib/node_modules/@stdlib/math/base/special/cosc/lib/cosc.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 sinpi = require('@stdlib/math/base/special/sinpi');
+var cospi = require('@stdlib/math/base/special/cospi');
+var isnan = require('@stdlib/math/base/assert/is-nan');
+var isInfinite = require('@stdlib/math/base/assert/is-infinite');
+var PI = require('@stdlib/constants/math/float64-pi');
+
+
+// MAIN //
+
+/**
+ * Computes the derivative of the normalized cardinal sine of a number.
+ *
+ * ## Method
+ *
+ * For \\( x \neq 0 \\), the derivative of \operatorname{sinc}(x) is calculated as
+ *
+ * ```tex
+ * \operatorname{cosc}(x) = \frac{\operatorname{cos}(\pi x)}{x} - \frac{\operatorname{sin}(\pi x)}{\pi x^2}
+ * ```
+ *
+ *
+ * ## Special Cases
+ *
+ * ```tex
+ * \begin{align*}
+ * \operatorname{cosc}(0) &= 0 & \\
+ * \operatorname{cosc}(\infty) &= 0 & \\
+ * \operatorname{cosc}(-\infty) &= 0 & \\
+ * \operatorname{cosc}(\mathrm{NaN}) &= \mathrm{NaN}
+ * \end{align*}
+ * ```
+ *
+ *
+ * @param {number} x - input value
+ * @returns {number} derivative of normalized sinc(x)
+ *
+ * @example
+ * var v = cosc( 0.5 )
+ * // return ~-1.273
+ *
+ * @example
+ * var v = cosc( -1.2 )
+ * // return ~0.544
+ *
+ * @example
+ * var v = cosc( 0.0 )
+ * // return 0
+ *
+ * @example
+ * var v = cosc( NaN )
+ * // return NaN
+ */
+function cosc(x) {
+	if (isnan(x)) {
+		return NaN;
+	}
+	if (isInfinite(x)) {
+		return 0.0;
+	}
+	if (x === 0.0) {
+		return 0.0;
+	}
+	return ( cospi(x) - ( sinpi(x) / ( PI * x ))) / x;
+}
+
+
+// EXPORTS //
+
+module.exports = cosc;