binomcoefln.js (2193B)
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 // MODULES // 22 23 var isInteger = require( './../../../../base/assert/is-integer' ); 24 var isnan = require( './../../../../base/assert/is-nan' ); 25 var betaln = require( './../../../../base/special/betaln' ); 26 var abs = require( './../../../../base/special/abs' ); 27 var ln = require( './../../../../base/special/ln' ); 28 var NINF = require( '@stdlib/constants/float64/ninf' ); 29 30 31 // MAIN // 32 33 /** 34 * Computes the natural logarithm of the binomial coefficient of two integers. 35 * 36 * @param {integer} n - input value 37 * @param {integer} k - second input value 38 * @returns {number} function value 39 * 40 * @example 41 * var v = binomcoefln( 8, 2 ); 42 * // returns ~3.332 43 * 44 * @example 45 * var v = binomcoefln( 0, 0 ); 46 * // returns 0.0 47 * 48 * @example 49 * var v = binomcoefln( -4, 2 ); 50 * // returns ~2.303 51 * 52 * @example 53 * var v = binomcoefln( 88, 3 ); 54 * // returns ~11.606 55 * 56 * @example 57 * var v = binomcoefln( NaN, 3 ); 58 * // returns NaN 59 * 60 * @example 61 * var v = binomcoefln( 5, NaN ); 62 * // returns NaN 63 * 64 * @example 65 * var v = binomcoefln( NaN, NaN ); 66 * // returns NaN 67 */ 68 function binomcoefln( n, k ) { 69 if ( isnan( n ) || isnan( k ) ) { 70 return NaN; 71 } 72 if ( !isInteger( n ) || !isInteger( k ) ) { 73 return NaN; 74 } 75 if ( n < 0.0 ) { 76 return binomcoefln( -n + k - 1.0, k ); 77 } 78 if ( k < 0 ) { 79 return NINF; 80 } 81 if ( k === 0 ) { 82 return 0.0; 83 } 84 if ( k === 1 ) { 85 return ln( abs( n ) ); 86 } 87 if ( n < k ) { 88 return NINF; 89 } 90 if ( n - k < 2 ) { 91 return binomcoefln( n, n - k ); 92 } 93 // Case: n - k >= 2 94 return -ln( n + 1 ) - betaln( n - k + 1, k + 1 ); 95 } 96 97 98 // EXPORTS // 99 100 module.exports = binomcoefln;