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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 setLowWord = require( '@stdlib/number/float64/base/set-low-word' );
var polyvalW = require( './polyval_w.js' );
// VARIABLES //
// 1/LN2
var INV_LN2 = 1.44269504088896338700e+00; // 0x3FF71547, 0x652B82FE
// High (24 bits): 1/LN2
var INV_LN2_HI = 1.44269502162933349609e+00; // 0x3FF71547, 0x60000000
// Low: 1/LN2
var INV_LN2_LO = 1.92596299112661746887e-08; // 0x3E54AE0B, 0xF85DDF44
// MAIN //
/**
* Computes \\(\operatorname{log}(x)\\) assuming \\(|1-x|\\) is small and using the approximation \\(x - x^2/2 + x^3/3 - x^4/4\\).
*
* @private
* @param {Array} out - output array
* @param {number} ax - absolute value of `x`
* @returns {Array} output array containing a tuple comprised of high and low parts
*
* @example
* var t = logx( [ 0.0, 0.0 ], 9.0 ); // => [ t1, t2 ]
* // returns [ -1265.7236328125, -0.0008163940840404393 ]
*/
function logx( out, ax ) {
var t2;
var t1;
var t;
var w;
var u;
var v;
t = ax - 1.0; // `t` has `20` trailing zeros
w = t * t * polyvalW( t );
u = INV_LN2_HI * t; // `INV_LN2_HI` has `21` significant bits
v = ( t*INV_LN2_LO ) - ( w*INV_LN2 );
t1 = u + v;
t1 = setLowWord( t1, 0 );
t2 = v - (t1 - u);
out[ 0 ] = t1;
out[ 1 ] = t2;
return out;
}
// EXPORTS //
module.exports = logx;
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