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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/k_log.h}. 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 getHighWord = require( '@stdlib/number/float64/base/get-high-word' );
var polyvalP = require( './polyval_p.js' );
var polyvalQ = require( './polyval_q.js' );
// VARIABLES //
// 0x000fffff = 1048575 => 0 00000000000 11111111111111111111
var HIGH_SIGNIFICAND_MASK = 0x000fffff|0; // asm type annotation
// 1/3
var ONE_THIRD = 0.33333333333333333;
// MAIN //
/**
* Return `log(x) - (x-1)` for `x` in `~[sqrt(2)/2, sqrt(2)]`.
*
* @private
* @param {number} x - input value
* @returns {number} function value
*/
function klog( x ) {
var hfsq;
var t1;
var t2;
var hx;
var f;
var s;
var z;
var R;
var w;
var i;
var j;
hx = getHighWord( x );
f = x - 1.0;
if ( ( HIGH_SIGNIFICAND_MASK & (2+hx) ) < 3 ) {
// Case: -2**-20 <= f < 2**-20
if ( f === 0.0 ) {
return 0.0;
}
return f * f * ( (ONE_THIRD*f) - 0.5 );
}
s = f / ( 2.0 + f );
z = s * s;
hx &= HIGH_SIGNIFICAND_MASK;
i = (hx - 0x6147a)|0; // asm type annotation
w = z * z;
j = (0x6b851 - hx)|0; // asm type annotation
t1 = w * polyvalP( w );
t2 = z * polyvalQ( w );
i |= j;
R = t2 + t1;
if ( i > 0 ) {
hfsq = 0.5 * f * f;
return ( s * (hfsq+R) ) - hfsq;
}
return s * (R-f);
}
// EXPORTS //
module.exports = klog;
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