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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]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/k_rem_pio2.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 floorf = require( '@stdlib/math/base/special/floorf' );
var ldexpf = require( '@stdlib/math/base/special/ldexpf' );
var zeros = require( '@stdlib/array/base/zeros' );
// VARIABLES //
// Table of constants for 2/π (first few terms for single precision):
var IPIO2 = [
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C, 0xD8B3D3, 0x4A9D0D
];
// π/2 for single precision (24-bit precision):
var PIO2 = [
1.570796251, // 0x3fc90fda
4.960468e-8, // 0x33522168
2.5893025e-8, // 0x32d849ba
1.9539925e-11 // 0x2f2e71d2
];
var TWO24 = 1.6777216e7; // 0x4b800000
var TWON24 = 5.9604645e-8; // 0x33800000
// Temporary arrays (smaller for single precision):
var F = zeros( 10 );
var Q = zeros( 10 );
var FQ = zeros( 10 );
var IQ = zeros( 10 );
// FUNCTIONS //
/**
* Performs the computation for `kernelRempio2f()`.
*
* @private
* @param {Array<number>} x - input value array
* @param {(Array|TypedArray|Object)} y - output array for single remainder
* @param {integer} jz - number of terms of `ipio2[]` used
* @param {Array<number>} q - array with integral values, representing the 24-bit chunks of the product of `x` and `2/π`
* @param {integer} q0 - the corresponding exponent of `q[0]` (exponent for `q[i]` is `q0-24*i`)
* @param {integer} jk - `jk+1` is the initial number of terms of `IPIO2[]` needed
* @param {integer} jv - index for pointing to the suitable `ipio2[]`
* @param {integer} jx - `nx - 1`
* @param {Array<number>} f - `IPIO2[]` in floating point
* @returns {number} last three binary digits of `N`
*/
function compute( x, y, jz, q, q0, jk, jv, jx, f ) {
var fw;
var ih;
var jp;
var i;
var k;
var n;
var j;
var z;
// `jp+1` is the number of terms in `PIO2[]` needed:
jp = jk;
// Distill `q[]` into `IQ[]` in reverse order...
z = q[jz];
j = jz;
for ( i = 0; j > 0; i++ ) {
fw = (TWON24 * z)|0;
IQ[i] = (z - (TWO24 * fw))|0;
z = q[j - 1] + fw;
j -= 1;
}
// Compute `n`...
z = ldexpf( z, q0 );
z -= 8.0 * floorf( z * 0.125 ); // Trim off integer >= 8
n = z|0;
z -= n;
ih = (z >= 0.5) ? 2 : 0;
// Case: z > 0.5
if ( ih > 0 ) {
n += 1;
z = 1.0 - z; // No carry needed for single precision
}
// Check if re-computation is needed...
if ( z === 0.0 ) {
j = 0;
for ( i = jz - 1; i >= jk; i-- ) {
j |= IQ[i];
}
if ( j === 0 ) {
// Need re-computation...
for ( k = 1; IQ[jk - k] === 0; k++ ) {
// `k` is the number of terms needed...
}
for ( i = jz + 1; i <= jz + k; i++ ) {
f[jx + i] = IPIO2[jv + i];
fw = 0.0;
for ( j = 0; j <= jx; j++ ) {
fw += x[j] * f[jx + (i - j)];
}
q[i] = fw;
}
jz += k;
return compute( x, y, jz, q, q0, jk, jv, jx, f );
}
// Chop off zero terms...
jz -= 1;
q0 -= 24;
while ( IQ[jz] === 0 && jz >= 0 ) {
jz -= 1;
q0 -= 24;
}
} else {
// Break `z` into 24-bit chunks if necessary...
z = ldexpf( z, -q0 );
if ( z >= TWO24 ) {
fw = (TWON24 * z)|0;
IQ[jz] = (z - (TWO24 * fw))|0;
jz += 1;
q0 += 24;
IQ[jz] = fw;
} else {
IQ[jz] = z|0;
}
}
// Convert integer chunks to floating-point...
fw = ldexpf( 1.0, q0 );
for ( i = jz; i >= 0; i-- ) {
q[i] = fw * IQ[i];
fw *= TWON24;
}
// Compute `PIO2[0,...,jp] * q[jz,...,0]`...
for ( i = jz; i >= 0; i-- ) {
fw = 0.0;
for ( k = 0; k <= jp && k <= jz - i; k++ ) {
fw += PIO2[k] * q[i + k];
}
FQ[jz - i] = fw;
}
// Compress `FQ[]` into `y[]` (single value for single precision)...
fw = 0.0;
for ( i = jz; i >= 0; i-- ) {
fw += FQ[i];
}
y[0] = (ih === 0) ? fw : -fw;
return (n & 7);
}
/**
* Returns the last three binary digits of `N` with `y = x - Nπ/2` so that `|y| < π/2` using single precision.
*
* @private
* @param {Array<number>} x - input value array
* @param {(Array|TypedArray|Object)} y - remainder array (single value)
* @param {PositiveInteger} e0 - the exponent of `x[0]` (must be <= 127)
* @param {PositiveInteger} nx - dimension of `x[]`
* @returns {number} last three binary digits of `N`
*/
function kernelRempio2f( x, y, e0, nx ) {
var fw;
var jk;
var jv;
var jx;
var jz;
var q0;
var i;
var j;
var m;
// Initialize `jk` for single-precision:
jk = 3;
// Determine `jx`, `jv`, `q0`:
jx = nx - 1;
jv = ((e0 - 3) / 24)|0;
if ( jv < 0 ) {
jv = 0;
}
q0 = e0 - (24 * (jv + 1));
// Set up `F[0]` to `F[jx+jk]`:
j = jv - jx;
m = jx + jk;
for ( i = 0; i <= m; i++ ) {
F[i] = (j < 0) ? 0.0 : IPIO2[j];
j += 1;
}
// Compute `Q[0],Q[1],...,Q[jk]`:
for ( i = 0; i <= jk; i++ ) {
fw = 0.0;
for ( j = 0; j <= jx; j++ ) {
fw += x[j] * F[jx + (i - j)];
}
Q[i] = fw;
}
jz = jk;
return compute( x, y, jz, Q, q0, jk, jv, jx, F );
}
// EXPORTS //
module.exports = kernelRempio2f;
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