@stdlib/math-base-special-gammaincinv/lib/chepolsum.js

Inverse 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.
*/

'use strict';

// VARIABLES //

// Chebyshev polynomial coefficients...
var A = [
	1.996379051590076518221,
	-0.17971032528832887213e-2,
	0.131292857963846713e-4,
	-0.2340875228178749e-6,
	0.72291210671127e-8,
	-0.3280997607821e-9,
	0.198750709010e-10,
	-0.15092141830e-11,
	0.1375340084e-12,
	-0.145728923e-13,
	0.17532367e-14,
	-0.2351465e-15,
	0.346551e-16,
	-0.55471e-17,
	0.9548e-18,
	-0.1748e-18,
	0.332e-19,
	-0.58e-20
];


// MAIN //

/**
* Computes the sum of a Chebyshev polynomial.
*
* @private
* @param {PositiveInteger} n - degree of polynomial
* @param {number} t - input value
* @returns {number} Chebyshev sum
*/
function chepolsum( n, t ) {
	var tt;
	var u0;
	var u1;
	var u2;
	var k;

	u0 = 0.0;
	u1 = 0.0;
	tt = t + t;
	k = n;
	do {
		u2 = u1;
		u1 = u0;
		u0 = ( tt*u1 ) - u2 + A[ k ];
		k -= 1;
	} while ( k >= 0 );
	return ( u0-u2 ) / 2.0;
}


// EXPORTS //

module.exports = chepolsum;