feat: 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) 2024 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 cardinal sine][cosc] of a number.
+
+<section class="intro">
+
+The normalized [derivative of cardinal sine][cosc] function is defined as
+
+<!-- <equation class="equation" label="eq:cosc_function" align="center" raw="\operatorname{cosc}(x) := \begin{cases} \frac{{\operatorname{cos}(\pi x)}-\frac{\operatorname{sin}(\pi x)}{\pi x}}{x} & \textrm{if}\ x \neq 0 \\ 0 & \textrm{if}\ x = 0 \end{cases}" alt="Cosc function"> -->
+
+```math
+\mathop{\mathrm{cosc}}(x) := \begin{cases} \frac {{\operatorname{cos}(\pi x)}-\frac{\operatorname{sin}(\pi x)}{\pi x}}{x} & \textrm{if}\ x \neq 0 \\ 0 & \textrm{if}\ x = 0 \end{cases}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\operatorname{cosc}(x) := \begin{cases} \frac {{\operatorname{cos}(\pi x)}-\frac{\operatorname{sin}(\pi x)}{\pi x}}{x} &amp; \textrm{if}\ x \neq 0 \\ 0 &amp; \textrm{if}\ x = 0 \end{cases}" data-equation="eq:cosc_function">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/cosc/docs/img/equation_cosc_function.svg" alt="Cosc function">
+    <br>
+</div> -->
+
+<!-- </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 normalized [derivative of cardinal sine][cosc] of a `number`.
+
+```javascript
+var v = cosc( 0.5 );
+// returns ~-1.273
+
+v = cosc( -1.2 );
+// returns ~0.544
+
+v = cosc( 0.0 );
+// returns 0.0
+
+v = cosc( NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var linspace = require( '@stdlib/array/base/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 -->
+
+<!-- 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/cosc.h"
+```
+
+#### stdlib_base_cosc( x )
+
+Computes the normalized [derivative of cardinal sine][cosc] of a `number`.
+
+```c
+double y = stdlib_base_cosc( 0.5 );
+// returns ~-1.273
+```
+
+The function accepts the following arguments:
+
+-   **x**: `[in] double` input value.
+
+```c
+double stdlib_base_cosc( const double x );
+```
+
+</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/cosc.h"
+#include <stdio.h>
+
+int main( void ) {
+    const double x[] = { 0.0, 0.523, 0.785, 1.047, 3.14 };
+
+    double y;
+    int i;
+    for ( i = 0; i < 5; i++ ) {
+        y = stdlib_base_cosc( x[ i ] );
+        printf( "cosc(%lf) = %lf\n", x[ i ], y );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+* * *
+
+## See Also
+
+-   <span class="package-name">[`@stdlib/math/base/special/cos`][@stdlib/math/base/special/cos]</span><span class="delimiter">: </span><span class="description">compute the cos of a number.</span>
+
+</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">
+
+[cosc]: https://en.wikipedia.org/wiki/cosc_function
+
+<!-- <related-links> -->
+
+[@stdlib/math/base/special/cos]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cos
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

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

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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/benchmark/benchmark.native.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 randu = require( '@stdlib/random/base/randu' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var cosc = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+	'skip': ( cosc instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, 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();
+});