@stdlib/math-base-special-rempio2/lib/rempio2_medium.js

Compute `x - nπ/2 = r`.

/**
* @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]{@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 round = require( '@stdlib/math-base-special-round' );
var getHighWord = require( '@stdlib/number-float64-base-get-high-word' );


// VARIABLES //

// 53 bits of 2/π:
var INVPIO2 = 6.36619772367581382433e-01; // 0x3FE45F30, 0x6DC9C883

// First 33 bits of π/2:
var PIO2_1 = 1.57079632673412561417e+00;  // 0x3FF921FB, 0x54400000

// PIO2_1T = π/2 - PIO2_1:
var PIO2_1T = 6.07710050650619224932e-11; // 0x3DD0B461, 0x1A626331

// Another 33 bits of π/2:
var PIO2_2 = 6.07710050630396597660e-11;  // 0x3DD0B461, 0x1A600000

// PIO2_2T = π/2 - ( PIO2_1 + PIO2_2 ):
var PIO2_2T = 2.02226624879595063154e-21; // 0x3BA3198A, 0x2E037073

// Another 33 bits of π/2:
var PIO2_3 = 2.02226624871116645580e-21;  // 0x3BA3198A, 0x2E000000

// PIO2_3T = π/2 - ( PIO2_1 + PIO2_2 + PIO2_3 ):
var PIO2_3T = 8.47842766036889956997e-32; // 0x397B839A, 0x252049C1

// Exponent mask (2047 => 0x7ff):
var EXPONENT_MASK = 0x7ff|0; // asm type annotation


// MAIN //

/**
* Computes `x - nπ/2 = r` for medium-sized inputs.
*
* @private
* @param {number} x - input value
* @param {uint32} ix - high word of `x`
* @param {(Array|TypedArray|Object)} y - remainder elements
* @returns {integer} factor of `π/2`
*/
function rempio2Medium( x, ix, y ) {
	var high;
	var n;
	var t;
	var r;
	var w;
	var i;
	var j;

	n = round( x * INVPIO2 );
	r = x - ( n * PIO2_1 );
	w = n * PIO2_1T;

	// First rounding (good to 85 bits)...
	j = (ix >> 20)|0; // asm type annotation
	y[ 0 ] = r - w;
	high = getHighWord( y[0] );
	i = j - ( (high >> 20) & EXPONENT_MASK );

	// Check if a second iteration is needed (good to 118 bits)...
	if ( i > 16 ) {
		t = r;
		w = n * PIO2_2;
		r = t - w;
		w = (n * PIO2_2T) - ((t-r) - w);
		y[ 0 ] = r - w;
		high = getHighWord( y[0] );
		i = j - ( (high >> 20) & EXPONENT_MASK );

		// Check if a third iteration is needed (151 bits accumulated)...
		if ( i > 49 ) {
			t = r;
			w = n * PIO2_3;
			r = t - w;
			w = (n * PIO2_3T) - ((t-r) - w);
			y[ 0 ] = r - w;
		}
	}
	y[ 1 ] = (r - y[0]) - w;
	return n;
}


// EXPORTS //

module.exports = rempio2Medium;