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* @license Apache-2.0
*
* Copyright (c) 2025 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/k_sin.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 float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
// VARIABLES //
var S1 = -1.6666667e-01; // 0xBFC55555
var S2 = 8.3333333e-03; // 0x3F811111
var S3 = -1.9841270e-04; // 0xBF2A01A0
var S4 = 2.7557314e-06; // 0x3EC71DE3
var S5 = -2.5050760e-08; // 0xBE5AE5E6
var S6 = 1.5896910e-10; // 0x3DE5D93A
// MAIN //
/**
* Computes the sine on \\( \approx \[-\pi/4, \pi/4] \\) (except on \\(-0\\)), where \\( \pi/4 \approx 0.7854 \\) in single precision.
*
* ## Method
*
* - Since \\( \sin(-x) = -\sin(x) \\), we need only to consider positive \\(x\\).
*
* - Callers must return \\( \sin(-0) = -0 \\) without calling here since our odd polynomial is not evaluated in a way that preserves \\(-0\\). Callers may do the optimization \\( \sin(x) \approx x \\) for tiny \\(x\\).
*
* - \\( \sin(x) \\) is approximated by a polynomial of degree \\(13\\) on \\( \left\[0,\tfrac{pi}{4}\right] \\)
*
* ```tex
* \sin(x) \approx x + S_1 \cdot x^3 + \ldots + S_6 \cdot x^{13}
* ```
*
* where
*
* ```tex
* \left| \frac{\sin(x)}{x} \left( 1 + S_1 \cdot x + S_2 \cdot x + S_3 \cdot x + S_4 \cdot x + S_5 \cdot x + S_6 \cdot x \right) \right| \le 2^{-58}
* ```
*
* - We have
*
* ```tex
* \sin(x+y) = \sin(x) + \sin'(x') \cdot y \approx \sin(x) + (1-x*x/2) \cdot y
* ```
*
* For better accuracy, let
*
* ```tex
* r = x^3 * \left( S_2 + x^2 \cdot \left( S_3 + x^2 * \left( S_4 + x^2 \cdot ( S_5+x^2 \cdot S_6 ) \right) \right) \right)
* ```
*
* then
*
* ```tex
* \sin(x) = x + \left( S_1 \cdot x + ( x \cdot (r-y/2) + y ) \right)
* ```
*
* @param {number} x - input value (in radians, assumed to be bounded by `~pi/4` in magnitude)
* @param {number} y - tail of `x`
* @returns {number} sine
*
* @example
* var v = kernelSinf( 0.0, 0.0 );
* // returns ~0.0
*
* @example
* var v = kernelSinf( 3.14159/6.0, 0.0 );
* // returns ~0.5
*
* @example
* var v = kernelSinf( 0.619, 9.279e-10 );
* // returns ~0.58
*
* @example
* var v = kernelSinf( NaN, 0.0 );
* // returns NaN
*
* @example
* var v = kernelSinf( 3.0, NaN );
* // returns NaN
*
* @example
* var v = kernelSinf( NaN, NaN );
* // returns NaN
*/
function kernelSinf( x, y ) {
var r;
var v;
var w;
var z;
z = float64ToFloat32(x * x);
w = float64ToFloat32(z * z);
r = float64ToFloat32(S2 + float64ToFloat32(z * float64ToFloat32(S3 + float64ToFloat32(z*S4))));
r = float64ToFloat32(r + float64ToFloat32(z * w * float64ToFloat32(S5 + float64ToFloat32(z*S6))));
v = float64ToFloat32(z * x);
if ( y === 0.0 ) {
return float64ToFloat32(x + float64ToFloat32(v * float64ToFloat32(S1 + float64ToFloat32(z*r))));
}
var temp1 = float64ToFloat32(0.5*y);
var temp2 = float64ToFloat32(v*r);
var temp3 = float64ToFloat32(z*(temp1 - temp2));
var temp4 = float64ToFloat32(v*S1);
var temp5 = float64ToFloat32((temp3 - y) - temp4);
return float64ToFloat32(x - temp5);
}
// EXPORTS //
module.exports = kernelSinf;
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