feat: add support for computing the derivative of cardinal sine (cosc)

lib/node_modules/@stdlib/math/base/special/cosc/lib/main.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 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/float64/pi' );
+
+
+// MAIN //
+
+/**
+* Computes the normalized derivative of cardinal sine of a number.
+*
+* ## Method
+*
+* For \\( x \neq 0 \\), the normalized derivative of cardinal sine is calculated as
+*
+* ```tex
+* \operatorname{cosc}(x) = \frac{{\operatorname{cos}(\pi x)}-\frac{\operatorname{sin}(\pi x)}{\pi x}}{x}.
+* ```
+*
+* ## 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 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
+*/
+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;

lib/node_modules/@stdlib/math/base/special/cosc/lib/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 addon = require( './../src/addon.node' );
+
+
+// MAIN //
+
+/**
+* Computes the normalized derivative of cardinal sine of a number.
+*
+* @private
+* @param {number} x - input value
+* @returns {number} 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
+*/
+function cosc( x ) {
+	return addon( x );
+}
+
+
+// EXPORTS //
+
+module.exports = cosc;