mult2.js (1762B)
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 'use strict'; 20 21 // VARIABLES // 22 23 var MAX_ITER = 149; // 127+22 (subnormals) => BIAS+NUM_SIGNFICAND_BITS-1 24 var MAX_BITS = 24; // only 23 bits for fraction 25 26 27 // MAIN // 28 29 /** 30 * Converts a fraction to a literal bit representation using the multiply-by-2 algorithm. 31 * 32 * @private 33 * @param {number} x - number less than 1 34 * @returns {BinaryString} bit representation 35 * 36 * @example 37 * var v = mult2( 0.234375 ); 38 * // returns '001111' 39 * 40 * @example 41 * var v = mult2( 0.0 ); 42 * // returns '' 43 */ 44 function mult2( x ) { 45 var str; 46 var y; 47 var i; 48 var j; 49 50 str = ''; 51 if ( x === 0.0 ) { 52 return str; 53 } 54 j = MAX_ITER; 55 56 // Each time we multiply by 2 and find a ones digit, add a '1'; otherwise, add a '0'.. 57 for ( i = 0; i < MAX_ITER; i++ ) { 58 y = x * 2.0; 59 if ( y >= 1.0 ) { 60 x = y - 1.0; 61 str += '1'; 62 if ( j === MAX_ITER ) { 63 j = i; // first '1' 64 } 65 } else { 66 x = y; 67 str += '0'; 68 } 69 // Stop when we have no more decimals to process or in the event we found a fraction which cannot be represented in a finite number of bits... 70 if ( y === 1.0 || i-j > MAX_BITS ) { 71 break; 72 } 73 } 74 75 return str; 76 } 77 78 79 // EXPORTS // 80 81 module.exports = mult2;