sqrt1pm1.js (2182B)
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 original C++ code and copyright notice are from the [Boost library]{@link https://github.com/boostorg/math/blob/fa1896fbc4c6fadc167307342ceb20bf2b6c0688/include/boost/math/special_functions/sqrt1pm1.hpp}. This implementation follows the original, but has been modified for JavaScript. 22 * 23 * ```text 24 * (C) Copyright John Maddock 2006. 25 * 26 * Use, modification and distribution are subject to the 27 * Boost Software License, Version 1.0. (See accompanying file 28 * LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt) 29 * ``` 30 */ 31 32 'use strict'; 33 34 // MODULES // 35 36 var isnan = require( './../../../../base/assert/is-nan' ); 37 var expm1 = require( './../../../../base/special/expm1' ); 38 var log1p = require( './../../../../base/special/log1p' ); 39 var sqrt = require( './../../../../base/special/sqrt' ); 40 var abs = require( './../../../../base/special/abs' ); 41 42 43 // MAIN // 44 45 /** 46 * Computes the value of `sqrt(1+x)-1`. 47 * 48 * @param {number} x - input value 49 * @returns {number} square root of `1+x` minus one 50 * 51 * @example 52 * var v = sqrt1pm1( 3.0 ); 53 * // returns 1.0 54 * 55 * @example 56 * var v = sqrt1pm1( 0.5 ); 57 * // returns ~0.225 58 * 59 * @example 60 * var v = sqrt1pm1( 0.02 ); 61 * // returns ~0.01 62 * 63 * @example 64 * var v = sqrt1pm1( -0.5 ); 65 * // returns ~-0.293 66 * 67 * @example 68 * var v = sqrt1pm1( -1.1 ); 69 * // returns NaN 70 * 71 * @example 72 * var v = sqrt1pm1( NaN ); 73 * // returns NaN 74 */ 75 function sqrt1pm1( x ) { 76 if ( isnan( x ) ) { 77 return NaN; 78 } 79 if ( abs( x ) > 0.75 ) { 80 return sqrt( 1.0+x ) - 1.0; 81 } 82 return expm1( log1p( x ) / 2.0 ); 83 } 84 85 86 // EXPORTS // 87 88 module.exports = sqrt1pm1;