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/**
* @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/s_pow.c}. The implementation follows the original, but has been modified for JavaScript.
*
* ```text
* Copyright (C) 2004 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 getHighWord = require( '@stdlib/number/float64/base/get-high-word' );
var setHighWord = require( '@stdlib/number/float64/base/set-high-word' );
var setLowWord = require( '@stdlib/number/float64/base/set-low-word' );
var uint32ToInt32 = require( '@stdlib/number/uint32/base/to-int32' );
var ldexp = require( './../../../../base/special/ldexp' );
var LN2 = require( '@stdlib/constants/float64/ln-two' );
var BIAS = require( '@stdlib/constants/float64/exponent-bias' );
var polyvalP = require( './polyval_p.js' );
// VARIABLES //
// 0x7fffffff = 2147483647 => 0 11111111111 11111111111111111111
var ABS_MASK = 0x7fffffff|0; // asm type annotation
// 0x000fffff = 1048575 => 0 00000000000 11111111111111111111
var HIGH_SIGNIFICAND_MASK = 0x000fffff|0; // asm type annotation
// 0x00100000 = 1048576 => 0 00000000001 00000000000000000000 => biased exponent: 1 = -1022+1023 => 2^-1022
var HIGH_MIN_NORMAL_EXP = 0x00100000|0; // asm type annotation
// 0x3fe00000 = 1071644672 => 0 01111111110 00000000000000000000 => biased exponent: 1022 = -1+1023 => 2^-1
var HIGH_BIASED_EXP_NEG_1 = 0x3fe00000|0; // asm type annotation
// TODO: consider making into an external constant
var HIGH_NUM_SIGNIFICAND_BITS = 20|0; // asm type annotation
// High: LN2
var LN2_HI = 6.93147182464599609375e-01; // 0x3FE62E43, 0x00000000
// Low: LN2
var LN2_LO = -1.90465429995776804525e-09; // 0xBE205C61, 0x0CA86C39
// MAIN //
/**
* Computes \\(2^{\mathrm{hp} + \mathrm{lp}\\).
*
* @private
* @param {number} j - high word of `hp + lp`
* @param {number} hp - first power summand
* @param {number} lp - second power summand
* @returns {number} function value
*
* @example
* var z = pow2( 1065961648, -0.3398475646972656, -0.000002438187359100815 );
* // returns ~0.79
*/
function pow2( j, hp, lp ) {
var tmp;
var t1;
var t;
var r;
var u;
var v;
var w;
var z;
var n;
var i;
var k;
i = (j & ABS_MASK)|0; // asm type annotation
k = ((i>>HIGH_NUM_SIGNIFICAND_BITS) - BIAS)|0; // asm type annotation
n = 0;
// `|z| > 0.5`, set `n = z+0.5`
if ( i > HIGH_BIASED_EXP_NEG_1 ) {
n = (j + (HIGH_MIN_NORMAL_EXP>>(k+1)))>>>0; // asm type annotation
k = (((n & ABS_MASK)>>HIGH_NUM_SIGNIFICAND_BITS) - BIAS)|0; // new k for n
tmp = ((n & ~(HIGH_SIGNIFICAND_MASK >> k)))>>>0; // asm type annotation
t = setHighWord( 0.0, tmp );
n = (((n & HIGH_SIGNIFICAND_MASK)|HIGH_MIN_NORMAL_EXP) >> (HIGH_NUM_SIGNIFICAND_BITS-k))>>>0; // eslint-disable-line max-len
if ( j < 0 ) {
n = -n;
}
hp -= t;
}
t = lp + hp;
t = setLowWord( t, 0 );
u = t * LN2_HI;
v = ( (lp - (t-hp))*LN2 ) + ( t*LN2_LO );
z = u + v;
w = v - (z - u);
t = z * z;
t1 = z - ( t*polyvalP( t ) );
r = ( (z*t1) / (t1-2.0) ) - ( w + (z*w) );
z = 1.0 - (r - z);
j = getHighWord( z );
j = uint32ToInt32( j );
j += (n << HIGH_NUM_SIGNIFICAND_BITS)>>>0; // asm type annotation
// Check for subnormal output...
if ( (j>>HIGH_NUM_SIGNIFICAND_BITS) <= 0 ) {
z = ldexp( z, n );
} else {
z = setHighWord( z, j );
}
return z;
}
// EXPORTS //
module.exports = pow2;
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