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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, copyright, license, and constants are from [Cephes]{@link http://www.netlib.org/cephes}. The implementation follows the original, but has been modified for JavaScript.
*
* ```text
* Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
*
* 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.
*
* Stephen L. Moshier
* moshier@na-net.ornl.gov
* ```
*/
'use strict';
// MODULES //
var SQRT_TWO_PI = require( '@stdlib/constants/float64/sqrt-two-pi' );
var pow = require( '@stdlib/math/base/special/pow' );
var exp = require( '@stdlib/math/base/special/exp' );
var polyval = require( './polyval_s.js' );
// VARIABLES //
var MAX_STIRLING = 143.01608;
// MAIN //
/**
* Evaluates the gamma function using Stirling's formula. The polynomial is valid for \\(33 \leq x \leq 172\\).
*
* @private
* @param {number} x - input value
* @returns {number} function value
*/
function gamma( x ) {
var w;
var y;
var v;
w = 1.0 / x;
w = 1.0 + ( w * polyval( w ) );
y = exp( x );
// Check `x` to avoid `pow()` overflow...
if ( x > MAX_STIRLING ) {
v = pow( x, ( 0.5*x ) - 0.25 );
y = v * (v/y);
} else {
y = pow( x, x-0.5 ) / y;
}
return SQRT_TWO_PI * y * w;
}
// EXPORTS //
module.exports = gamma;
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