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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
* (C) Copyright John Maddock 2006-7, 2013-14.
* (C) Copyright Paul A. Bristow 2007, 2013-14.
* (C) Copyright Nikhar Agrawal 2013-14.
* (C) 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 gamma = require( '@stdlib/math/base/special/gamma' );
var expm1 = require( '@stdlib/math/base/special/expm1' );
var log1p = require( '@stdlib/math/base/special/log1p' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var lgammaSmallImp = require( './lgamma_small_imp.js' );
// MAIN //
/**
* Computes `gamma(x+1) - 1`.
*
* @param {number} x - input value
* @returns {number} function value
*
* @example
* var v = gamma1pm1( 0.2 );
* // returns ~-0.082
*
* @example
* var v = gamma1pm1( -9.2 );
* // returns ~-1.0
*
* @example
* var v = gamma1pm1( 0.0 );
* // returns 0.0
*
* @example
* var v = gamma1pm1( -3.0 );
* // returns NaN
*
* @example
* var v = gamma1pm1( NaN );
* // returns NaN
*/
function gamma1pm1( x ) {
if ( isnan( x ) ) {
return NaN;
}
if ( x < 0.0 ) {
if ( x < -0.5 ) {
// Best method is simply to subtract 1 from gamma:
return gamma( 1.0+x ) - 1.0;
}
// Use expm1 on the logarithm of gamma:
return expm1( -log1p( x ) + lgammaSmallImp( x+2.0, x+1.0, x ) );
}
if ( x < 2.0 ) {
// Use expm1 on the logarithm of gamma:
return expm1( lgammaSmallImp( x+1.0, x, x-1.0 ) );
}
// Best method is simply to subtract 1 from gamma:
return gamma( 1.0+x ) - 1.0;
}
// EXPORTS //
module.exports = gamma1pm1;
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