@stdlib/math-base-special-gammainc/lib/full_igamma_prefix.js

Incomplete gamma function.

/**
* @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_37_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript.
*
* ```text
* (C) Copyright John Maddock 2006.
* (C) Copyright Paul A. Bristow 2007.
*
* 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 exp = require( '@stdlib/math-base-special-exp' );
var pow = require( '@stdlib/math-base-special-pow' );
var ln = require( '@stdlib/math-base-special-ln' );
var MAX_LN = require( '@stdlib/constants-float64-max-ln' );
var MIN_LN = require( '@stdlib/constants-float64-min-ln' );


// MAIN //

/**
* Calculates the power term prefix `(z^a)(e^-z)` used in the non-normalized incomplete gammas.
*
* @private
* @param {number} a - function parameter
* @param {number} z - function parameter
* @returns {number} power term prefix
*/
function fullIGammaPrefix( a, z ) {
	var prefix;
	var alz;

	alz = a * ln( z );
	if ( z >= 1.0 ) {
		if ( ( alz < MAX_LN ) && ( -z > MIN_LN ) ) {
			prefix = pow( z, a ) * exp( -z );
		}
		else if ( a >= 1.0 ) {
			prefix = pow( z / exp(z/a), a );
		}
		else {
			prefix = exp( alz - z );
		}
	}
	else {
		/* eslint-disable no-lonely-if */
		if ( alz > MIN_LN ) {
			prefix = pow( z, a ) * exp( -z );
		}
		else if ( z/a < MAX_LN ) {
			prefix = pow( z / exp(z/a), a );
		} else {
			prefix = exp( alz - z );
		}
	}
	return prefix;
}


// EXPORTS //

module.exports = fullIGammaPrefix;