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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.
*
*
* ## Notice
*
* The following copyright and license were part of the original implementation available as part of FreeBSD [k_sin.c]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/k_sin.c} and [k_cos.c]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/k_cos.c}. The implementation follows the original sine and cosine kernels, but has been modified for JavaScript and combined into a single function.
*
* ```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';
// VARIABLES //
var S1 = -1.66666666666666324348e-01; // 0xBFC55555, 0x55555549
var S2 = 8.33333333332248946124e-03; // 0x3F811111, 0x1110F8A6
var S3 = -1.98412698298579493134e-04; // 0xBF2A01A0, 0x19C161D5
var S4 = 2.75573137070700676789e-06; // 0x3EC71DE3, 0x57B1FE7D
var S5 = -2.50507602534068634195e-08; // 0xBE5AE5E6, 0x8A2B9CEB
var S6 = 1.58969099521155010221e-10; // 0x3DE5D93A, 0x5ACFD57C
var C1 = 4.16666666666666019037e-02; // 0x3FA55555, 0x5555554C
var C2 = -1.38888888888741095749e-03; // 0xBF56C16C, 0x16C15177
var C3 = 2.48015872894767294178e-05; // 0x3EFA01A0, 0x19CB1590
var C4 = -2.75573143513906633035e-07; // 0xBE927E4F, 0x809C52AD
var C5 = 2.08757232129817482790e-09; // 0x3E21EE9E, 0xBDB4B1C4
var C6 = -1.13596475577881948265e-11; // 0xBDA8FAE9, 0xBE8838D4
// MAIN //
/**
* Computes the sine and cosine on \\( \approx \[-\pi/4, \pi/4\] \\) (except for \\(-0\\)), where \\( \pi/4 \approx 0.7854 \\).
*
* @private
* @param {number} x - input value (in radians, assumed to be bounded by `~π/4` in magnitude)
* @param {number} y - tail of `x`
* @param {Collection} out - output array
* @param {integer} stride - output array stride
* @param {NonNegativeInteger} offset - output array index offset
* @returns {Collection} sine and cosine
*/
function kernelSincos( x, y, out, stride, offset ) {
var hz;
var r;
var v;
var w;
var z;
z = x * x;
w = z * z;
r = S2 + (z * (S3 + (z*S4))) + (z * w * (S5 + (z*S6)));
v = z * x;
if ( y === 0.0 ) {
out[ offset ] = x + (v * (S1 + (z*r)));
} else {
out[ offset ] = x - (((z*((0.5*y) - (v*r))) - y) - (v*S1));
}
r = z * (C1 + (z * (C2 + (z*C3))));
r += w * w * (C4 + (z * (C5 + (z*C6))));
hz = 0.5 * z;
w = 1.0 - hz;
out[ offset + stride ] = w + ( ((1.0-w) - hz) + ((z*r) - (x*y)) );
return out;
}
// EXPORTS //
module.exports = kernelSincos;
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