stirling_approximation.js (2170B)
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, copyright, license, and constants are from [Cephes]{@link http://www.netlib.org/cephes}. The implementation follows the original, but has been modified for JavaScript. 22 * 23 * ```text 24 * Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier 25 * 26 * Some software in this archive may be from the book _Methods and Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster International, 1989) or from the Cephes Mathematical Library, a commercial product. In either event, it is copyrighted by the author. What you see here may be used freely but it comes with no support or guarantee. 27 * 28 * Stephen L. Moshier 29 * moshier@na-net.ornl.gov 30 * ``` 31 */ 32 33 'use strict'; 34 35 // MODULES // 36 37 var SQRT_TWO_PI = require( '@stdlib/constants/float64/sqrt-two-pi' ); 38 var pow = require( './../../../../base/special/pow' ); 39 var exp = require( './../../../../base/special/exp' ); 40 var polyval = require( './polyval_s.js' ); 41 42 43 // VARIABLES // 44 45 var MAX_STIRLING = 143.01608; 46 47 48 // MAIN // 49 50 /** 51 * Evaluates the gamma function using Stirling's formula. The polynomial is valid for \\(33 \leq x \leq 172\\). 52 * 53 * @private 54 * @param {number} x - input value 55 * @returns {number} function value 56 */ 57 function gamma( x ) { 58 var w; 59 var y; 60 var v; 61 62 w = 1.0 / x; 63 w = 1.0 + ( w * polyval( w ) ); 64 y = exp( x ); 65 66 // Check `x` to avoid `pow()` overflow... 67 if ( x > MAX_STIRLING ) { 68 v = pow( x, ( 0.5*x ) - 0.25 ); 69 y = v * (v/y); 70 } else { 71 y = pow( x, x-0.5 ) / y; 72 } 73 return SQRT_TWO_PI * y * w; 74 } 75 76 77 // EXPORTS // 78 79 module.exports = gamma;