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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/e_log.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 getHighWord = require( '@stdlib/number/float64/base/get-high-word' );
var setHighWord = require( '@stdlib/number/float64/base/set-high-word' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var BIAS = require( '@stdlib/constants/float64/exponent-bias' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var polyvalP = require( './polyval_p.js' );
var polyvalQ = require( './polyval_q.js' );
// VARIABLES //
var LN2_HI = 6.93147180369123816490e-01; // 3FE62E42 FEE00000
var LN2_LO = 1.90821492927058770002e-10; // 3DEA39EF 35793C76
var TWO54 = 1.80143985094819840000e+16; // 0x43500000, 0x00000000
var ONE_THIRD = 0.33333333333333333;
// 0x000fffff = 1048575 => 0 00000000000 11111111111111111111
var HIGH_SIGNIFICAND_MASK = 0x000fffff|0; // asm type annotation
// 0x7ff00000 = 2146435072 => 0 11111111111 00000000000000000000 => biased exponent: 2047 = 1023+1023 => 2^1023
var HIGH_MAX_NORMAL_EXP = 0x7ff00000|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
// 0x3ff00000 = 1072693248 => 0 01111111111 00000000000000000000 => biased exponent: 1023 = 0+1023 => 2^0 = 1
var HIGH_BIASED_EXP_0 = 0x3ff00000|0; // asm type annotation
// MAIN //
/**
* Evaluates the natural logarithm of a double-precision floating-point number.
*
* @param {NonNegativeNumber} x - input value
* @returns {number} function value
*
* @example
* var v = ln( 4.0 );
* // returns ~1.386
*
* @example
* var v = ln( 0.0 );
* // returns -Infinity
*
* @example
* var v = ln( Infinity );
* // returns Infinity
*
* @example
* var v = ln( NaN );
* // returns NaN
*
* @example
* var v = ln( -4.0 );
* // returns NaN
*/
function ln( x ) {
var hfsq;
var hx;
var t2;
var t1;
var k;
var R;
var f;
var i;
var j;
var s;
var w;
var z;
if ( x === 0.0 ) {
return NINF;
}
if ( isnan( x ) || x < 0.0 ) {
return NaN;
}
hx = getHighWord( x );
k = 0|0; // asm type annotation
if ( hx < HIGH_MIN_NORMAL_EXP ) {
// Case: 0 < x < 2**-1022
k -= 54|0; // asm type annotation
// Subnormal number, scale up `x`:
x *= TWO54;
hx = getHighWord( x );
}
if ( hx >= HIGH_MAX_NORMAL_EXP ) {
return x + x;
}
k += ( ( hx>>20 ) - BIAS )|0; // asm type annotation
hx &= HIGH_SIGNIFICAND_MASK;
i = ( (hx+0x95f64) & 0x100000 )|0; // asm type annotation
// Normalize `x` or `x/2`...
x = setHighWord( x, hx|(i^HIGH_BIASED_EXP_0) );
k += ( i>>20 )|0; // asm type annotation
f = x - 1.0;
if ( (HIGH_SIGNIFICAND_MASK&(2+hx)) < 3 ) {
// Case: -2**-20 <= f < 2**-20
if ( f === 0.0 ) {
if ( k === 0 ) {
return 0.0;
}
return (k * LN2_HI) + (k * LN2_LO);
}
R = f * f * ( 0.5 - (ONE_THIRD*f) );
if ( k === 0 ) {
return f - R;
}
return (k * LN2_HI) - ( (R-(k*LN2_LO)) - f );
}
s = f / (2.0 + f);
z = s * s;
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;
if ( k === 0 ) {
return f - ( hfsq - (s * (hfsq+R)) );
}
return (k * LN2_HI) - ( hfsq - ((s*(hfsq+R))+(k*LN2_LO)) - f );
}
if ( k === 0 ) {
return f - (s*(f-R));
}
return (k * LN2_HI) - ( ( (s*(f-R)) - (k*LN2_LO) ) - f );
}
// EXPORTS //
module.exports = ln;
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