gamma1pm1.js (2515B)
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 http://www.boost.org/doc/libs/1_64_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript. 22 * 23 * ```text 24 * (C) Copyright John Maddock 2006-7, 2013-14. 25 * (C) Copyright Paul A. Bristow 2007, 2013-14. 26 * (C) Copyright Nikhar Agrawal 2013-14. 27 * (C) Copyright Christopher Kormanyos 2013-14. 28 * 29 * Use, modification and distribution are subject to the 30 * Boost Software License, Version 1.0. (See accompanying file 31 * LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt) 32 * ``` 33 */ 34 35 'use strict'; 36 37 // MODULES // 38 39 var gamma = require( './../../../../base/special/gamma' ); 40 var expm1 = require( './../../../../base/special/expm1' ); 41 var log1p = require( './../../../../base/special/log1p' ); 42 var isnan = require( './../../../../base/assert/is-nan' ); 43 var lgammaSmallImp = require( './lgamma_small_imp.js' ); 44 45 46 // MAIN // 47 48 /** 49 * Computes `gamma(x+1) - 1`. 50 * 51 * @param {number} x - input value 52 * @returns {number} function value 53 * 54 * @example 55 * var v = gammap1m1( 0.2 ); 56 * // returns ~-0.082 57 * 58 * @example 59 * var v = gammap1m1( -9.2 ); 60 * // returns ~-1.0 61 * 62 * @example 63 * var v = gammap1m1( 0.0 ); 64 * // returns 0.0 65 * 66 * @example 67 * var v = gammap1m1( -3.0 ); 68 * // returns NaN 69 * 70 * @example 71 * var v = gammap1m1( NaN ); 72 * // returns NaN 73 */ 74 function gammap1m1( x ) { 75 if ( isnan( x ) ) { 76 return NaN; 77 } 78 if ( x < 0.0 ) { 79 if ( x < -0.5 ) { 80 // Best method is simply to subtract 1 from gamma: 81 return gamma( 1.0+x ) - 1.0; 82 } 83 // Use expm1 on the logarithm of gamma: 84 return expm1( -log1p( x ) + lgammaSmallImp( x+2.0, x+1.0, x ) ); 85 } 86 if ( x < 2.0 ) { 87 // Use expm1 on the logarithm of gamma: 88 return expm1( lgammaSmallImp( x+1.0, x, x-1.0 ) ); 89 } 90 // Best method is simply to subtract 1 from gamma: 91 return gamma( 1.0+x ) - 1.0; 92 } 93 94 95 // EXPORTS // 96 97 module.exports = gammap1m1;