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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 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';
// MODULES //
var toWordf = require( '@stdlib/number/float32/base/to-word' );
var rempio2f = require( '@stdlib/math/base/special/rempio2f' );
var f32 = require( '@stdlib/number/float64/base/to-float32' );
var FLOAT32_ABS_MASK = require( '@stdlib/constants/float32/abs-mask' );
var FLOAT32_EXPONENT_MASK = require( '@stdlib/constants/float32/exponent-mask' );
var FLOAT64_HALF_PI = require( '@stdlib/constants/float64/half-pi' );
var kernelSincosf = require( '@stdlib/math/base/special/kernel-sincosf' ).assign;
// VARIABLES //
// PI/4 = 0.7853981256484985 => 0 01111110 10010010000111111011010 => 0x3f490fda = 1061752768
var PIO4_WORD = 0x3f490fda|0; // asm type annotation
// 3*PI/4 = 2.356194257736206 => 0 10000000 00101101100101111100011 => 0x4016cbe3 = 1075235811
var THREE_PIO4_WORD = 0x4016cbe3|0; // asm type annotation
// 5*PI/4 = 3.9269907474517822 => 0 10000000 11110110101001111010001 => 0x407b53d1 = 1081824209
var FIVE_PIO4_WORD = 0x407b53d1|0; // asm type annotation
// 7*PI/4 = 5.497786998748779 => 0 10000001 01011111110110111011111 => 0x40afeddf = 1085271519
var SEVEN_PIO4_WORD = 0x40afeddf|0; // asm type annotation
// 9*PI/4 = 7.068583011627197 => 0 10000001 11000100011000111010101 => 0x40e231d5 = 1088565717
var NINE_PIO4_WORD = 0x40e231d5|0; // asm type annotation
// 2^-12 = 0.000244140625 => 0 01110011 00000000000000000000000 => 0x39800000 = 964689920
var SMALL_WORD = 0x39800000|0; // asm type annotation
// Small multiples of PI/2 in double-precision floating-point format:
var PIO2 = FLOAT64_HALF_PI; // 0x3FF921FB, 0x54442D18
var PI = 2.0 * FLOAT64_HALF_PI; // 0x400921FB, 0x54442D18
var THREE_PIO2 = 3.0 * FLOAT64_HALF_PI; // 0x4012D97C, 0x7F3321D2
var TWO_PI = 4.0 * FLOAT64_HALF_PI; // 0x401921FB, 0x54442D18
// Array for storing the remainder element:
var Y = [ 0.0 ];
// MAIN //
/**
* Simultaneously computes the sine and cosine of a single-precision floating-point number (in radians) and assigns the results to a provided output array.
*
* ## Method
*
* - Let \\(S\\), \\(C\\), and \\(T\\) denote the \\(\sin\\), \\(\cos\\) and \\(\tan\\), respectively, on \\(\[-\pi/4, +\pi/4\]\\).
*
* - Reduce the argument \\(x\\) to \\(y = 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 |
*
* @private
* @param {number} x - input value (in radians)
* @param {Collection} out - output array
* @param {integer} stride - output array stride
* @param {NonNegativeInteger} offset - output array index offset
* @returns {Collection} output array
*
* @example
* var v = sincosf( 0.0, [ 0.0, 0.0 ], 1, 0 );
* // returns [ ~0.0, ~1.0 ]
*
* @example
* var v = sincosf( 3.141592653589793/2.0, [ 0.0, 0.0 ], 1, 0 );
* // returns [ ~1.0, ~0.0 ]
*
* @example
* var v = sincosf( -3.141592653589793/6.0, [ 0.0, 0.0 ], 1, 0 );
* // returns [ ~-0.5, ~0.866 ]
*
* @example
* var v = sincosf( NaN, [ 0.0, 0.0 ], 1, 0 );
* // returns [ NaN, NaN ]
*/
function sincosf( x, out, stride, offset ) {
var tmp;
var hx;
var ix;
var n;
hx = toWordf( f32( x ) ) |0; // asm type annotation
ix = (hx & FLOAT32_ABS_MASK)|0; // asm type annotation
// Case: |x| ~<= π/4
if ( ix <= PIO4_WORD ) {
// Case: |x| < 2^-12
if ( ix < SMALL_WORD ) {
if ( (x|0) === 0 ) {
out[ offset ] = f32( x );
out[ offset+stride ] = f32( 1.0 );
return out;
}
}
return kernelSincosf( x, out, stride, offset );
}
// Case: |x| ~<= 5π/4
if ( ix <= FIVE_PIO4_WORD ) {
// Case: |x| ~<= 3π/4
if ( ix <= THREE_PIO4_WORD ) {
if ( hx > 0 ) {
kernelSincosf( x - PIO2, out, stride, offset );
tmp = f32( -out[ offset ] );
out[ offset ] = out[ offset+stride ];
out[ offset+stride ] = tmp;
} else {
kernelSincosf( x + PIO2, out, stride, offset );
tmp = f32( -out[ offset+stride ] );
out[ offset+stride ] = out[ offset ];
out[ offset ] = tmp;
}
} else {
if ( hx > 0 ) {
kernelSincosf( x - PI, out, stride, offset );
} else {
kernelSincosf( x + PI, out, stride, offset );
}
out[ offset ] = f32( -out[ offset ] );
out[ offset+stride ] = f32( -out[ offset+stride ] );
}
return out;
}
// Case: |x| ~<= 9π/4
if ( ix <= NINE_PIO4_WORD ) {
// Case: |x| ~<= 7π/4
if ( ix <= SEVEN_PIO4_WORD ) {
if ( hx > 0 ) {
kernelSincosf( x - THREE_PIO2, out, stride, offset );
tmp = f32( -out[ offset+stride ] );
out[ offset+stride ] = out[ offset ];
out[ offset ] = tmp;
} else {
kernelSincosf( x + THREE_PIO2, out, stride, offset );
tmp = f32( -out[ offset ] );
out[ offset ] = out[ offset+stride ];
out[ offset+stride ] = tmp;
}
} else if ( hx > 0 ) {
kernelSincosf( x - TWO_PI, out, stride, offset );
} else {
kernelSincosf( x + TWO_PI, out, stride, offset );
}
return out;
}
// Case: x is NaN or infinity
if ( ix >= FLOAT32_EXPONENT_MASK ) {
out[ offset ] = NaN;
out[ offset+stride ] = NaN;
return out;
}
// Argument reduction...
n = rempio2f( f32( x ), Y );
// Compute the sine and cosine together:
kernelSincosf( Y[ 0 ], out, stride, offset );
switch ( n & 3 ) {
case 0:
return out;
case 1:
tmp = out[ offset+stride ];
out[ offset+stride ] = f32( -out[ offset ] );
out[ offset ] = tmp;
return out;
case 2:
out[ offset ] = f32( -out[ offset ] );
out[ offset+stride ] = f32( -out[ offset+stride ] );
return out;
default:
tmp = f32( -out[ offset+stride ] );
out[ offset+stride ] = out[ offset ];
out[ offset ] = tmp;
return out;
}
}
// EXPORTS //
module.exports = sincosf;
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