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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
*
* Adapted from the original implementation available as part of [FreeBSD]{@link https://svnweb.freebsd.org/base/release/9.3.0/lib/msun/src/e_rem_pio2.c}.
*
* ```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.
*
* Optimized by Bruce D. Evans.
* ```
*/
'use strict';
// MODULES //
var ABS_MASK = require( '@stdlib/constants/float32/abs-mask' ); // 0x7fffffff
var EXPONENT_MASK = require( '@stdlib/constants/float32/exponent-mask' ); // 0x7f800000
var SIGNIFICAND_MASK = require( '@stdlib/constants/float32/significand-mask' ); // 0x007fffff
var getWord = require( '@stdlib/number/float32/base/to-word' ); // Single word for 32-bit float
var fromWord = require( '@stdlib/number/float32/base/from-word' );
var rempio2fKernel = require( './kernel_rempio2f.js' ); // Adjusted kernel for float
var rempio2fMedium = require( './rempio2f_medium.js' ); // Adjusted medium range function
// VARIABLES //
var ZERO = 0.0; // 0x00000000
var TWO8 = 256.0; // 0x43800000 (2^8 for 32-bit scaling)
// 24 bits of π/2 (single precision):
var PIO2_1 = 1.57079632679; // 0x3fc90fdb
// PIO2_1T = π/2 - PIO2_1 (less precision):
var PIO2_1T = 4.960468e-8; // 0x33a22169
var TWO_PIO2_1T = 2.0 * PIO2_1T;
var THREE_PIO2_1T = 3.0 * PIO2_1T;
var FOUR_PIO2_1T = 4.0 * PIO2_1T;
// High word significand for π and π/2: 0x490fdb => 0010010010000111111011011
var PI_HIGH_WORD_SIGNIFICAND = 0x490fdb|0;
// High word constants (32-bit float representation):
var PIO4_HIGH_WORD = 0x3f490fdb|0; // π/4: 0.785398163
var THREE_PIO4_HIGH_WORD = 0x4016cbe4|0; // 3π/4: 2.35619449
var FIVE_PIO4_HIGH_WORD = 0x405497ce|0; // 5π/4: 3.926990817
var THREE_PIO2_HIGH_WORD = 0x4096cbe4|0; // 3π/2: 4.71238898
var SEVEN_PIO4_HIGH_WORD = 0x40b78909|0; // 7π/4: 5.497787144
var TWO_PI_HIGH_WORD = 0x40c90fdb|0; // 2π: 6.283185307
var NINE_PIO4_HIGH_WORD = 0x40fb53d1|0; // 9π/4: 7.068583471
// Medium threshold: 2^8 * π/2 ≈ 402.123859659
var MEDIUM = 0x43c90fdb|0;
// Temporary arrays (smaller for single precision):
var TX = [ 0.0, 0.0 ];
var TY = [ 0.0 ];
// MAIN //
/**
* Computes `x - nπ/2 = r` for single-precision floating-point values.
*
* ## Notes
*
* - Returns `n` and stores the remainder `r` in `y[0]`.
*
* @param {number} x - input value (single precision)
* @param {(Array|TypedArray|Object)} y - remainder element
* @returns {integer} factor of `π/2`
*
* @example
* var y = [ 0.0 ];
* var n = rempio2f( 128.0, y );
* // returns ~81
*
* var y0 = y[ 0 ];
* // returns ~0.765
*
* @example
* var y = [ 0.0 ];
* var n = rempio2f( NaN, y );
* // returns 0
*
* var y0 = y[ 0 ];
* // returns NaN
*/
function rempio2f( x, y ) {
var e0;
var ix;
var nx;
var w;
var i;
var n;
var z;
w = getWord( x );
ix = (w & ABS_MASK)|0;
// Case: |x| ~<= π/4
if ( ix <= PIO4_HIGH_WORD ) {
y[ 0 ] = x;
return 0;
}
// Case: |x| ~<= 5π/4
if ( ix <= FIVE_PIO4_HIGH_WORD ) {
// Case: |x| ~= π/2 or π
if ( (ix & SIGNIFICAND_MASK) === PI_HIGH_WORD_SIGNIFICAND ) {
return rempio2fMedium( x, ix, y );
}
// Case: |x| ~<= 3π/4
if ( ix <= THREE_PIO4_HIGH_WORD ) {
if ( x > 0.0 ) {
z = x - PIO2_1;
y[ 0 ] = z - PIO2_1T;
return 1;
}
z = x + PIO2_1;
y[ 0 ] = z + PIO2_1T;
return -1;
}
if ( x > 0.0 ) {
z = x - ( 2.0 * PIO2_1 );
y[ 0 ] = z - TWO_PIO2_1T;
return 2;
}
z = x + ( 2.0 * PIO2_1 );
y[ 0 ] = z + TWO_PIO2_1T;
return -2;
}
// Case: |x| ~<= 9π/4
if ( ix <= NINE_PIO4_HIGH_WORD ) {
// Case: |x| ~<= 7π/4
if ( ix <= SEVEN_PIO4_HIGH_WORD ) {
if ( ix === THREE_PIO2_HIGH_WORD ) {
return rempio2fMedium( x, ix, y );
}
if ( x > 0.0 ) {
z = x - ( 3.0 * PIO2_1 );
y[ 0 ] = z - THREE_PIO2_1T;
return 3;
}
z = x + ( 3.0 * PIO2_1 );
y[ 0 ] = z + THREE_PIO2_1T;
return -3;
}
if ( ix === TWO_PI_HIGH_WORD ) {
return rempio2fMedium( x, ix, y );
}
if ( x > 0.0 ) {
z = x - ( 4.0 * PIO2_1 );
y[ 0 ] = z - FOUR_PIO2_1T;
return 4;
}
z = x + ( 4.0 * PIO2_1 );
y[ 0 ] = z + FOUR_PIO2_1T;
return -4;
}
// Case: |x| ~< 2^8 * π/2 (medium size)
if ( ix < MEDIUM ) {
return rempio2fMedium( x, ix, y );
}
// console.log("Inside kernel for x", x);
// Case: x is NaN or infinity
if ( ix >= EXPONENT_MASK ) {
y[ 0 ] = NaN;
return 0;
}
// Set z = scalbn(|x|, ilogb(x) - 7) for 8-bit chunks...
e0 = (ix >> 23) - 134; // ilogb(x) - 7 (127 bias + 7 for 24-bit significand shift)
z = fromWord( ix - ((e0 << 23)|0) );
for ( i = 0; i < 2; i++ ) {
TX[ i ] = z|0;
z = (z - TX[i]) * TWO8;
}
nx = 2;
while ( TX[ nx-1 ] === ZERO ) {
nx -= 1;
}
n = rempio2fKernel( TX, TY, e0, nx );
if ( x < 0.0 ) {
y[ 0 ] = -TY[ 0 ];
return -n;
}
y[ 0 ] = TY[ 0 ];
return n;
}
// EXPORTS //
module.exports = rempio2f;
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