logx.js (2453B)
1 /** 2 * @license Apache-2.0 3 * 4 * Copyright (c) 2018 The Stdlib Authors. 5 * 6 * Licensed under the Apache License, Version 2.0 (the "License"); 7 * you may not use this file except in compliance with the License. 8 * You may obtain a copy of the License at 9 * 10 * http://www.apache.org/licenses/LICENSE-2.0 11 * 12 * Unless required by applicable law or agreed to in writing, software 13 * distributed under the License is distributed on an "AS IS" BASIS, 14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 15 * See the License for the specific language governing permissions and 16 * limitations under the License. 17 * 18 * 19 * ## Notice 20 * 21 * 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. 22 * 23 * ```text 24 * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. 25 * 26 * Developed at SunPro, a Sun Microsystems, Inc. business. 27 * Permission to use, copy, modify, and distribute this 28 * software is freely granted, provided that this notice 29 * is preserved. 30 * ``` 31 */ 32 33 'use strict'; 34 35 // MODULES // 36 37 var setLowWord = require( '@stdlib/number/float64/base/set-low-word' ); 38 var polyvalW = require( './polyval_w.js' ); 39 40 41 // VARIABLES // 42 43 // 1/LN2 44 var INV_LN2 = 1.44269504088896338700e+00; // 0x3FF71547, 0x652B82FE 45 46 // High (24 bits): 1/LN2 47 var INV_LN2_HI = 1.44269502162933349609e+00; // 0x3FF71547, 0x60000000 48 49 // Low: 1/LN2 50 var INV_LN2_LO = 1.92596299112661746887e-08; // 0x3E54AE0B, 0xF85DDF44 51 52 53 // MAIN // 54 55 /** 56 * Computes \\(\operatorname{log}(x)\\) assuming \\(|1-x|\\) is small and using the approximation \\(x - x^2/2 + x^3/3 - x^4/4\\). 57 * 58 * @private 59 * @param {Array} out - output array 60 * @param {number} ax - absolute value of `x` 61 * @returns {Array} output array containing a tuple comprised of high and low parts 62 * 63 * @example 64 * var t = logx( [ 0.0, 0.0 ], 9.0 ); // => [ t1, t2 ] 65 * // returns [ -1265.7236328125, -0.0008163940840404393 ] 66 */ 67 function logx( out, ax ) { 68 var t2; 69 var t1; 70 var t; 71 var w; 72 var u; 73 var v; 74 75 t = ax - 1.0; // `t` has `20` trailing zeros 76 w = t * t * polyvalW( t ); 77 u = INV_LN2_HI * t; // `INV_LN2_HI` has `21` significant bits 78 v = ( t*INV_LN2_LO ) - ( w*INV_LN2 ); 79 t1 = u + v; 80 t1 = setLowWord( t1, 0 ); 81 t2 = v - (t1 - u); 82 83 out[ 0 ] = t1; 84 out[ 1 ] = t2; 85 return out; 86 } 87 88 89 // EXPORTS // 90 91 module.exports = logx;