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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_85_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript.
*
* ```text
* Copyright John Maddock 2006-7, 2013-14.
* Copyright Paul A. Bristow 2007, 2013-14.
* Copyright Nikhar Agrawal 2013-14.
* Copyright Christopher Kormanyos 2013-14.
*
* 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 abs = require( '@stdlib/math/base/special/abs' );
var floor = require( '@stdlib/math/base/special/floor' );
var gamma = require( '@stdlib/math/base/special/gamma' );
var factorial = require( '@stdlib/math/base/special/factorial' );
var FLOAT64_MAX_NTH_FACTORIAL = require( '@stdlib/constants/float64/max-nth-factorial' );
var gammaDeltaRatioLanczos = require( './gamma_delta_ratio_lanczos.js' );
// MAIN //
/**
* Computes the ratio of two gamma functions.
*
* ## Notes
*
* - Specifically, the function evaluates
*
* ```tex
* \frac{ \Gamma( z ) }{ \Gamma( z + \delta ) }
* ```
*
* @param {number} z - first gamma parameter
* @param {number} delta - difference
* @returns {number} gamma ratio
*
* @example
* var y = gammaDeltaRatio( 2.0, 3.0 );
* // returns ~0.042
*
* @example
* var y = gammaDeltaRatio( 4.0, 0.5 );
* // returns ~0.516
*
* @example
* var y = gammaDeltaRatio( 100.0, 0.0 );
* // returns 1.0
*/
function gammaDeltaRatio( z, delta ) {
var result;
var idelta;
var iz;
if ( z <= 0.0 || z + delta <= 0.0 ) {
// This isn't very sophisticated, or accurate, but it does work:
return gamma( z ) / gamma( z + delta );
}
idelta = floor( delta );
if ( idelta === delta ) {
iz = floor( z );
if ( iz === z ) {
// As both `z` and `delta` are integers, see if we can use a table lookup:
if ( z <= FLOAT64_MAX_NTH_FACTORIAL && ( z + delta <= FLOAT64_MAX_NTH_FACTORIAL ) ) {
return factorial( iz - 1.0 ) / factorial( idelta + iz - 1.0 );
}
}
if ( abs(delta) < 20.0 ) {
// As `delta` is a small integer, we can use a finite product:
if ( delta === 0.0 ) {
return 1.0;
}
if ( delta < 0.0 ) {
z -= 1.0;
result = z;
delta += 1.0;
while ( delta !== 0.0 ) {
z -= 1.0;
result *= z;
delta += 1.0;
}
return result;
}
result = 1.0 / z;
delta -= 1.0;
while ( delta !== 0.0 ) {
z += 1.0;
result /= z;
delta -= 1.0;
}
return result;
}
}
return gammaDeltaRatioLanczos( z, delta );
}
// EXPORTS //
module.exports = gammaDeltaRatio;
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