@stdlib/math-base-special-gamma-lanczos-sum/lib/rational_pq.js

Calculate the Lanczos sum for the approximation of the gamma function.

/**
* @license Apache-2.0
*
* Copyright (c) 2024 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.
*/

/* This is a generated file. Do not edit directly. */
'use strict';

// MAIN //

/**
* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)).
*
* ## Notes
*
* -   Coefficients should be sorted in ascending degree.
* -   The implementation uses [Horner's rule][horners-method] for efficient computation.
*
* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
*
* @private
* @param {number} x - value at which to evaluate the rational function
* @returns {number} evaluated rational function
*/
function evalrational( x ) {
	var ax;
	var s1;
	var s2;
	if ( x === 0.0 ) {
		return Infinity;
	}
	if ( x < 0.0 ) {
		ax = -x;
	} else {
		ax = x;
	}
	if ( ax <= 1.0 ) {
		s1 = 38474670393.31777 + (x * (36857665043.51951 + (x * (15889202453.72942 + (x * (4059208354.298835 + (x * (680547661.1834733 + (x * (78239755.00312005 + (x * (6246580.776401795 + (x * (341986.3488721347 + (x * (12287.194511824551 + (x * (261.61404416416684 + (x * 2.5066282746310007))))))))))))))))))); // eslint-disable-line max-len
		s2 = 0.0 + (x * (362880.0 + (x * (1026576.0 + (x * (1172700.0 + (x * (723680.0 + (x * (269325.0 + (x * (63273.0 + (x * (9450.0 + (x * (870.0 + (x * (45.0 + (x * 1.0))))))))))))))))))); // eslint-disable-line max-len
	} else {
		x = 1.0 / x;
		s1 = 2.5066282746310007 + (x * (261.61404416416684 + (x * (12287.194511824551 + (x * (341986.3488721347 + (x * (6246580.776401795 + (x * (78239755.00312005 + (x * (680547661.1834733 + (x * (4059208354.298835 + (x * (15889202453.72942 + (x * (36857665043.51951 + (x * 38474670393.31777))))))))))))))))))); // eslint-disable-line max-len
		s2 = 1.0 + (x * (45.0 + (x * (870.0 + (x * (9450.0 + (x * (63273.0 + (x * (269325.0 + (x * (723680.0 + (x * (1172700.0 + (x * (1026576.0 + (x * (362880.0 + (x * 0.0))))))))))))))))))); // eslint-disable-line max-len
	}
	return s1 / s2;
}


// EXPORTS //

module.exports = evalrational;