Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | /**
* @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/12.2.0/lib/msun/src/e_log2.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 setLowWord = require( '@stdlib/number/float64/base/set-low-word' );
var toWords = require( '@stdlib/number/float64/base/to-words' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var ABS_MASK = require( '@stdlib/constants/float64/high-word-abs-mask' );
var HIGH_SIGNIFICAND_MASK = require( '@stdlib/constants/float64/high-word-significand-mask' );
var BIAS = require( '@stdlib/constants/float64/exponent-bias' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var kernelLog1p = require( '@stdlib/math/base/special/kernel-log1p' );
// VARIABLES //
var TWO54 = 1.80143985094819840000e+16; // 0x43500000, 0x00000000
var IVLN2HI = 1.44269504072144627571e+00; // 0x3ff71547, 0x65200000
var IVLN2LO = 1.67517131648865118353e-10; // 0x3de705fc, 0x2eefa200
// 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
// High/low words workspace:
var WORDS = [ 0|0, 0|0 ];
// MAIN //
/**
* Evaluates the binary logarithm (base two).
*
* @param {NonNegativeNumber} x - input value
* @returns {number} function value
*
* @example
* var v = log2( 4.0 );
* // returns 2.0
*
* @example
* var v = log2( 8.0 );
* // returns 3.0
*
* @example
* var v = log2( 0.0 );
* // returns -Infinity
*
* @example
* var v = log2( Infinity );
* // returns Infinity
*
* @example
* var v = log2( NaN );
* // returns NaN
*
* @example
* var v = log2( -4.0 );
* // returns NaN
*/
function log2( x ) {
var valHi;
var valLo;
var hfsq;
var hx;
var lx;
var hi;
var lo;
var f;
var R;
var w;
var y;
var i;
var k;
if ( isnan( x ) || x < 0.0 ) {
return NaN;
}
toWords.assign( x, WORDS, 1, 0 );
hx = WORDS[ 0 ] | 0; // asm type annotation
lx = WORDS[ 1 ];
k = 0|0; // asm type annotation
if ( hx < HIGH_MIN_NORMAL_EXP ) {
// Case: x < 2**-1022
if ( ( (hx&ABS_MASK) | lx ) === 0 ) {
return NINF;
}
k -= 54|0; // asm type annotation
// Subnormal number, scale up x:
x *= TWO54;
hx = getHighWord( x ) | 0; // asm type annotation
}
if ( hx >= HIGH_MAX_NORMAL_EXP ) {
return x + x;
}
// Case: log(1) = +0
if ( hx === HIGH_BIASED_EXP_0 && lx === 0 ) {
return 0.0;
}
k += ( (hx>>20) - BIAS )|0; // asm type annotation
hx &= HIGH_SIGNIFICAND_MASK;
i = ( ( hx+0x95f64 ) & HIGH_MIN_NORMAL_EXP )|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
y = k;
f = x - 1.0;
hfsq = 0.5 * f * f;
R = kernelLog1p( f );
/*
* Notes:
*
* - `f-hfsq` must (for args near `1`) be evaluated in extra precision to avoid a large cancellation when `x` is near `sqrt(2)` or `1/sqrt(2)`.This is fairly efficient since `f-hfsq` only depends on `f`, so can be evaluated in parallel with `R`. Not combining `hfsq` with `R` also keeps `R` small (though not as small as a true `lo` term would be), so that extra precision is not needed for terms involving `R`.
* - When implemented in C, compiler bugs involving extra precision used to break Dekker's theorem for spitting `f-hfsq` as `hi+lo`. These problems are now automatically avoided as a side effect of the optimization of combining the Dekker splitting step with the clear-low-bits step.
* - `y` must (for args near `sqrt(2)` and `1/sqrt(2)`) be added in extra precision to avoid a very large cancellation when `x` is very near these values. Unlike the above cancellations, this problem is specific to base `2`. It is strange that adding `+-1` is so much harder than adding `+-ln2` or `+-log10_2`.
* - This implementation uses Dekker's theorem to normalize `y+val_hi`, so, when implemented in C, compiler bugs may reappear in some configurations.
* - The multi-precision calculations for the multiplications are routine.
*/
hi = f - hfsq;
hi = setLowWord( hi, 0 );
lo = ( f - hi ) - hfsq + R;
valHi = hi * IVLN2HI;
valLo = ( ( lo + hi ) * IVLN2LO ) + ( lo * IVLN2HI );
w = y + valHi;
valLo += ( y - w ) + valHi;
valHi = w;
return valLo + valHi;
}
// EXPORTS //
module.exports = log2;
|