@stdlib/math-base-special-cos/lib/main.js

Compute the cosine of a number.

/**
* @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.
*
*
* ## Notice
*
* The following copyright, license, and long comment were part of the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/s_cos.c}. The implementation follows the original, but has been modified for JavaScript.
*
* ```text
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ```
*/

'use strict';

// MODULES //

var getHighWord = require( '@stdlib/number-float64-base-get-high-word' );
var kernelCos = require( '@stdlib/math-base-special-kernel-cos' );
var kernelSin = require( '@stdlib/math-base-special-kernel-sin' );
var rempio2 = require( '@stdlib/math-base-special-rempio2' );
var ABS_MASK = require( '@stdlib/constants-float64-high-word-abs-mask' );
var EXPONENT_MASK = require( '@stdlib/constants-float64-high-word-exponent-mask' );


// VARIABLES //

// Scratch array for storing temporary values:
var buffer = [ 0.0, 0.0 ]; // WARNING: not thread safe

// High word of π/4: 0x3fe921fb => 00111111111010010010000111111011
var HIGH_WORD_PIO4 = 0x3fe921fb|0; // asm type annotation

// High word of 2^-27: 0x3e400000 => 00111110010000000000000000000000
var HIGH_WORD_TWO_NEG_27 = 0x3e400000|0; // asm type annotation


// MAIN //

/**
* Computes the cosine of a number.
*
* ## Method
*
* -   Let \\(S\\), \\(C\\), and \\(T\\) denote the \\(\sin\\), \\(\cos\\), and \\(\tan\\), respectively, on \\(\[-\pi/4, +\pi/4\]\\).
*
* -   Reduce the argument \\(x\\) to \\(y1+y2 = x-k\pi/2\\) in \\(\[-\pi/4, +\pi/4\]\\), and let \\(n = k \mod 4\\).
*
* -   We have
*
*     | n | sin(x) | cos(x) | tan(x) |
*     | - | ------ | ------ | ------ |
*     | 0 |   S    |   C    |    T   |
*     | 1 |   C    |  -S    |  -1/T  |
*     | 2 |  -S    |  -C    |    T   |
*     | 3 |  -C    |   S    |  -1/T  |
*
* @param {number} x - input value (in radians)
* @returns {number} cosine
*
* @example
* var v = cos( 0.0 );
* // returns 1.0
*
* @example
* var v = cos( 3.141592653589793/4.0 );
* // returns ~0.707
*
* @example
* var v = cos( -3.141592653589793/6.0 );
* // returns ~0.866
*
* @example
* var v = cos( NaN );
* // returns NaN
*/
function cos( x ) {
	var ix;
	var n;

	ix = getHighWord( x );
	ix &= ABS_MASK;

	// Case: |x| ~< pi/4
	if ( ix <= HIGH_WORD_PIO4 ) {
		// Case: x < 2**-27
		if ( ix < HIGH_WORD_TWO_NEG_27 ) {
			return 1.0;
		}
		return kernelCos( x, 0.0 );
	}
	// Case: cos(Inf or NaN) is NaN */
	if ( ix >= EXPONENT_MASK ) {
		return NaN;
	}
	// Case: Argument reduction needed...
	n = rempio2( x, buffer );
	switch ( n & 3 ) {
	case 0:
		return kernelCos( buffer[ 0 ], buffer[ 1 ] );
	case 1:
		return -kernelSin( buffer[ 0 ], buffer[ 1 ] );
	case 2:
		return -kernelCos( buffer[ 0 ], buffer[ 1 ] );
	default:
		return kernelSin( buffer[ 0 ], buffer[ 1 ] );
	}
}


// EXPORTS //

module.exports = cos;