org.apache.commons.numbers.gamma.InvGamma1pm1 Maven / Gradle / Ivy
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* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You 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,
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* See the License for the specific language governing permissions and
* limitations under the License.
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package org.apache.commons.numbers.gamma;
/**
* Function \( \frac{1}{\Gamma(1 + x)} - 1 \).
*
* Class is immutable.
*/
final class InvGamma1pm1 {
/*
* Constants copied from DGAM1 in the NSWC library.
*/
/** The constant {@code A0} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_A0 = .611609510448141581788E-08;
/** The constant {@code A1} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_A1 = .624730830116465516210E-08;
/** The constant {@code B1} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_B1 = .203610414066806987300E+00;
/** The constant {@code B2} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_B2 = .266205348428949217746E-01;
/** The constant {@code B3} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_B3 = .493944979382446875238E-03;
/** The constant {@code B4} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_B4 = -.851419432440314906588E-05;
/** The constant {@code B5} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_B5 = -.643045481779353022248E-05;
/** The constant {@code B6} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_B6 = .992641840672773722196E-06;
/** The constant {@code B7} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_B7 = -.607761895722825260739E-07;
/** The constant {@code B8} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_B8 = .195755836614639731882E-09;
/** The constant {@code P0} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_P0 = .6116095104481415817861E-08;
/** The constant {@code P1} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_P1 = .6871674113067198736152E-08;
/** The constant {@code P2} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_P2 = .6820161668496170657918E-09;
/** The constant {@code P3} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_P3 = .4686843322948848031080E-10;
/** The constant {@code P4} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_P4 = .1572833027710446286995E-11;
/** The constant {@code P5} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_P5 = -.1249441572276366213222E-12;
/** The constant {@code P6} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_P6 = .4343529937408594255178E-14;
/** The constant {@code Q1} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_Q1 = .3056961078365221025009E+00;
/** The constant {@code Q2} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_Q2 = .5464213086042296536016E-01;
/** The constant {@code Q3} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_Q3 = .4956830093825887312020E-02;
/** The constant {@code Q4} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_Q4 = .2692369466186361192876E-03;
/** The constant {@code C} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C = -.422784335098467139393487909917598E+00;
/** The constant {@code C0} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C0 = .577215664901532860606512090082402E+00;
/** The constant {@code C1} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C1 = -.655878071520253881077019515145390E+00;
/** The constant {@code C2} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C2 = -.420026350340952355290039348754298E-01;
/** The constant {@code C3} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C3 = .166538611382291489501700795102105E+00;
/** The constant {@code C4} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C4 = -.421977345555443367482083012891874E-01;
/** The constant {@code C5} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C5 = -.962197152787697356211492167234820E-02;
/** The constant {@code C6} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C6 = .721894324666309954239501034044657E-02;
/** The constant {@code C7} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C7 = -.116516759185906511211397108401839E-02;
/** The constant {@code C8} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C8 = -.215241674114950972815729963053648E-03;
/** The constant {@code C9} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C9 = .128050282388116186153198626328164E-03;
/** The constant {@code C10} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C10 = -.201348547807882386556893914210218E-04;
/** The constant {@code C11} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C11 = -.125049348214267065734535947383309E-05;
/** The constant {@code C12} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C12 = .113302723198169588237412962033074E-05;
/** The constant {@code C13} defined in {@code DGAM1}. */
private static final double INV_GAMMA1P_M1_C13 = -.205633841697760710345015413002057E-06;
/** Private constructor. */
private InvGamma1pm1() {
// intentionally empty.
}
/**
* Computes the function \( \frac{1}{\Gamma(1 + x)} - 1 \) for {@code -0.5 <= x <= 1.5}.
*
* This implementation is based on the double precision implementation in
* the NSWC Library of Mathematics Subroutines, {@code DGAM1}.
*
* @param x Argument.
* @return \( \frac{1}{\Gamma(1 + x)} - 1 \)
* @throws IllegalArgumentException if {@code x < -0.5} or {@code x > 1.5}
*/
public static double value(final double x) {
if (x < -0.5 || x > 1.5) {
throw new GammaException(GammaException.OUT_OF_RANGE, x, -0.5, 1.5);
}
final double t = x <= 0.5 ? x : (x - 0.5) - 0.5;
if (t < 0) {
final double a = INV_GAMMA1P_M1_A0 + t * INV_GAMMA1P_M1_A1;
double b = INV_GAMMA1P_M1_B8;
b = INV_GAMMA1P_M1_B7 + t * b;
b = INV_GAMMA1P_M1_B6 + t * b;
b = INV_GAMMA1P_M1_B5 + t * b;
b = INV_GAMMA1P_M1_B4 + t * b;
b = INV_GAMMA1P_M1_B3 + t * b;
b = INV_GAMMA1P_M1_B2 + t * b;
b = INV_GAMMA1P_M1_B1 + t * b;
b = 1.0 + t * b;
double c = INV_GAMMA1P_M1_C13 + t * (a / b);
c = INV_GAMMA1P_M1_C12 + t * c;
c = INV_GAMMA1P_M1_C11 + t * c;
c = INV_GAMMA1P_M1_C10 + t * c;
c = INV_GAMMA1P_M1_C9 + t * c;
c = INV_GAMMA1P_M1_C8 + t * c;
c = INV_GAMMA1P_M1_C7 + t * c;
c = INV_GAMMA1P_M1_C6 + t * c;
c = INV_GAMMA1P_M1_C5 + t * c;
c = INV_GAMMA1P_M1_C4 + t * c;
c = INV_GAMMA1P_M1_C3 + t * c;
c = INV_GAMMA1P_M1_C2 + t * c;
c = INV_GAMMA1P_M1_C1 + t * c;
c = INV_GAMMA1P_M1_C + t * c;
if (x > 0.5) {
return t * c / x;
} else {
return x * ((c + 0.5) + 0.5);
}
} else {
double p = INV_GAMMA1P_M1_P6;
p = INV_GAMMA1P_M1_P5 + t * p;
p = INV_GAMMA1P_M1_P4 + t * p;
p = INV_GAMMA1P_M1_P3 + t * p;
p = INV_GAMMA1P_M1_P2 + t * p;
p = INV_GAMMA1P_M1_P1 + t * p;
p = INV_GAMMA1P_M1_P0 + t * p;
double q = INV_GAMMA1P_M1_Q4;
q = INV_GAMMA1P_M1_Q3 + t * q;
q = INV_GAMMA1P_M1_Q2 + t * q;
q = INV_GAMMA1P_M1_Q1 + t * q;
q = 1.0 + t * q;
double c = INV_GAMMA1P_M1_C13 + (p / q) * t;
c = INV_GAMMA1P_M1_C12 + t * c;
c = INV_GAMMA1P_M1_C11 + t * c;
c = INV_GAMMA1P_M1_C10 + t * c;
c = INV_GAMMA1P_M1_C9 + t * c;
c = INV_GAMMA1P_M1_C8 + t * c;
c = INV_GAMMA1P_M1_C7 + t * c;
c = INV_GAMMA1P_M1_C6 + t * c;
c = INV_GAMMA1P_M1_C5 + t * c;
c = INV_GAMMA1P_M1_C4 + t * c;
c = INV_GAMMA1P_M1_C3 + t * c;
c = INV_GAMMA1P_M1_C2 + t * c;
c = INV_GAMMA1P_M1_C1 + t * c;
c = INV_GAMMA1P_M1_C0 + t * c;
if (x > 0.5) {
return (t / x) * ((c - 0.5) - 0.5);
} else {
return x * c;
}
}
}
}