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/**
* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*
* ## Notice
*
* 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/factorials.hpp}. The implementation has been modified for JavaScript.
*
* ```text
* (C) Copyright John Maddock 2006, 2010.
*
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
* ```
*/
'use strict';
// MODULES //
var isInteger = require( './../../../../base/assert/is-integer' );
var isnan = require( './../../../../base/assert/is-nan' );
var gammaDeltaRatio = require( './../../../../base/special/gamma-delta-ratio' );
var fallingFactorial = require( './../../../../base/special/falling-factorial' );
// MAIN //
/**
* Computes the rising factorial of `x` and `n`.
*
* ## Notes
*
* - The rising factorial is defined as
*
* ```tex
* \operatorname{risingFactorial}(x, n) = x (x-1) (x-2) (x-3) \ldots (x-n+1)
* ```
*
* or equivalently
*
* ```tex
* \operatorname{risingFactorial}(x, n) = \frac{ \Gamma(x + n) }{ \Gamma(x) };
* ```
*
* @param {number} x - first function parameter
* @param {integer} n - second function parameter
* @returns {number} function value
*
* @example
* var v = risingFactorial( 0.9, 5 );
* // returns ~94.766
*
* @example
* var v = risingFactorial( -9.0, 3 );
* // returns -504.0
*
* @example
* var v = risingFactorial( 0.0, 2 );
* // returns 0.0
*
* @example
* var v = risingFactorial( 3.0, -2 );
* // returns 0.5
*/
function risingFactorial( x, n ) {
var result;
var inv;
if ( isnan( x ) || !isInteger( n ) ) {
return NaN;
}
if ( x < 0.0 ) {
// For `x < 0`, we really have a falling factorial, modulo a possible change of sign. Note that the falling factorial isn't defined for negative `n`, so we'll get rid of that case first:
if ( n < 0.0 ) {
x += n;
n = -n;
inv = true;
}
result = ( (n&1) ? -1.0 : 1.0 ) * fallingFactorial( -x, n );
if ( inv ) {
result = 1.0 / result;
}
return result;
}
if ( n === 0 ) {
return 1.0;
}
if ( x === 0.0 ) {
if ( n < 0 ) {
return -gammaDeltaRatio( x+1.0, -n );
}
return 0.0;
}
if ( x < 1.0 && x+n < 0.0 ) {
result = gammaDeltaRatio( 1.0-x, -n );
return ( n&1 ) ? -result : result;
}
// We don't optimize this for small `n`, because `gammaDeltaRatio` is already optimized for that use case:
return 1.0 / gammaDeltaRatio( x, n );
}
// EXPORTS //
module.exports = risingFactorial;
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