@stdlib/math-base-special-gamma1pm1/lib/main.js

Compute gamma(x+1) - 1.

/**
* @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
* (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 = gammap1m1( 0.2 );
* // returns ~-0.082
*
* @example
* var v = gammap1m1( -9.2 );
* // returns ~-1.0
*
* @example
* var v = gammap1m1( 0.0 );
* // returns 0.0
*
* @example
* var v = gammap1m1( -3.0 );
* // returns NaN
*
* @example
* var v = gammap1m1( NaN );
* // returns NaN
*/
function gammap1m1( 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 = gammap1m1;