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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/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 gammaLanczosSum = require( './../../../../../base/special/gamma-lanczos-sum' );
var isNegativeZero = require( './../../../../../base/assert/is-negative-zero' );
var isInteger = require( './../../../../../base/assert/is-integer' );
var isnan = require( './../../../../../base/assert/is-nan' );
var signum = require( './../../../../../base/special/signum' );
var floor = require( './../../../../../base/special/floor' );
var abs = require( './../../../../../base/special/abs' );
var exp = require( './../../../../../base/special/exp' );
var pow = require( './../../../../../base/special/pow' );
var ln = require( './../../../../../base/special/ln' );
var SQRT_EPSILON = require( '@stdlib/constants/float64/sqrt-eps' );
var LANCZOS_G = require( '@stdlib/constants/float64/gamma-lanczos-g' );
var EULERGAMMA = require( '@stdlib/constants/float64/eulergamma' );
var MAX_VALUE = require( '@stdlib/constants/float64/max' );
var MAX_LN = require( '@stdlib/constants/float64/max-ln' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var PI = require( '@stdlib/constants/float64/pi' );
var sinpx = require( './sinpx.js' );
var FACTORIALS = require( './factorials.json' );
// VARIABLES //
var MAX_FACTORIAL = 170;
var HALF = 0.5;
// MAIN //
/**
* Evaluates the gamma function.
*
* @param {number} x - input value
* @returns {number} function value
*
* @example
* var v = gamma( 4.0 );
* // returns 6.0
*
* @example
* var v = gamma( -1.5 );
* // returns ~2.363
*
* @example
* var v = gamma( -0.5 );
* // returns ~-3.545
*
* @example
* var v = gamma( 0.5 );
* // returns ~1.772
*
* @example
* var v = gamma( 0.0 );
* // returns Infinity
*
* @example
* var v = gamma( -0.0 );
* // returns -Infinity
*
* @example
* var v = gamma( NaN );
* // returns NaN
*/
function gamma( x ) {
var result;
var lzgh;
var zgh;
var hp;
if ( x === NINF || isnan( x ) ) {
return NaN;
}
if ( x === 0.0 ) {
if ( isNegativeZero( x ) ) {
return NINF;
}
return PINF;
}
result = 1.0;
if ( x < 0.0 ) {
if ( isInteger( x ) ) {
return NaN;
}
if ( x <= -20.0 ) {
result = gamma( -x ) * sinpx( x );
if ( abs(result) < 1.0 && MAX_VALUE * abs(result) < PI ) {
return ( signum( result ) === 1 ) ? NINF : PINF;
}
result = -PI / result;
return result;
}
// Shift x to > 1:
while ( x < 0.0 ) {
result /= x;
x += 1.0;
}
}
if ( floor( x ) === x && x < MAX_FACTORIAL ) {
result *= FACTORIALS[ floor( x ) - 1 ];
}
else if ( x < SQRT_EPSILON ) {
if ( x < 1.0 / MAX_VALUE ) {
result = PINF;
}
result *= ( 1.0 / x ) - EULERGAMMA;
}
else {
result *= gammaLanczosSum( x );
zgh = ( x + LANCZOS_G - HALF );
lzgh = ln( zgh );
if ( x * lzgh > MAX_LN ) {
// We're going to overflow unless this is done with care:
if ( lzgh * x / 2.0 > MAX_LN ) {
return ( signum( result ) === 1 ) ? PINF : NINF;
}
hp = pow( zgh, ( x / 2.0 ) - 0.25 );
result *= hp / exp( zgh );
if ( MAX_VALUE / hp < result ) {
return ( signum( result ) === 1 ) ? PINF : NINF;
}
result *= hp;
} else {
result *= pow( zgh, x - HALF ) / exp( zgh );
}
}
return result;
}
// EXPORTS //
module.exports = gamma;
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