Java example source code file (GammaTest.java)
The GammaTest.java Java example source code/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* 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,
* 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.
*/
package org.apache.commons.math3.special;
import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
/**
*/
public class GammaTest {
private void testRegularizedGamma(double expected, double a, double x) {
double actualP = Gamma.regularizedGammaP(a, x);
double actualQ = Gamma.regularizedGammaQ(a, x);
TestUtils.assertEquals(expected, actualP, 10e-15);
TestUtils.assertEquals(actualP, 1.0 - actualQ, 10e-15);
}
private void testLogGamma(double expected, double x) {
double actual = Gamma.logGamma(x);
TestUtils.assertEquals(expected, actual, 10e-15);
}
@Test
public void testRegularizedGammaNanPositive() {
testRegularizedGamma(Double.NaN, Double.NaN, 1.0);
}
@Test
public void testRegularizedGammaPositiveNan() {
testRegularizedGamma(Double.NaN, 1.0, Double.NaN);
}
@Test
public void testRegularizedGammaNegativePositive() {
testRegularizedGamma(Double.NaN, -1.5, 1.0);
}
@Test
public void testRegularizedGammaPositiveNegative() {
testRegularizedGamma(Double.NaN, 1.0, -1.0);
}
@Test
public void testRegularizedGammaZeroPositive() {
testRegularizedGamma(Double.NaN, 0.0, 1.0);
}
@Test
public void testRegularizedGammaPositiveZero() {
testRegularizedGamma(0.0, 1.0, 0.0);
}
@Test
public void testRegularizedGammaPositivePositive() {
testRegularizedGamma(0.632120558828558, 1.0, 1.0);
}
@Test
public void testLogGammaNan() {
testLogGamma(Double.NaN, Double.NaN);
}
@Test
public void testLogGammaNegative() {
testLogGamma(Double.NaN, -1.0);
}
@Test
public void testLogGammaZero() {
testLogGamma(Double.NaN, 0.0);
}
@Test
public void testLogGammaPositive() {
testLogGamma(0.6931471805599457, 3.0);
}
@Test
public void testDigammaLargeArgs() {
double eps = 1e-8;
Assert.assertEquals(4.6001618527380874002, Gamma.digamma(100), eps);
Assert.assertEquals(3.9019896734278921970, Gamma.digamma(50), eps);
Assert.assertEquals(2.9705239922421490509, Gamma.digamma(20), eps);
Assert.assertEquals(2.9958363947076465821, Gamma.digamma(20.5), eps);
Assert.assertEquals(2.2622143570941481605, Gamma.digamma(10.1), eps);
Assert.assertEquals(2.1168588189004379233, Gamma.digamma(8.8), eps);
Assert.assertEquals(1.8727843350984671394, Gamma.digamma(7), eps);
Assert.assertEquals(0.42278433509846713939, Gamma.digamma(2), eps);
Assert.assertEquals(-100.56088545786867450, Gamma.digamma(0.01), eps);
Assert.assertEquals(-4.0390398965921882955, Gamma.digamma(-0.8), eps);
Assert.assertEquals(4.2003210041401844726, Gamma.digamma(-6.3), eps);
}
@Test
public void testDigammaSmallArgs() {
// values for negative powers of 10 from 1 to 30 as computed by webMathematica with 20 digits
// see functions.wolfram.com
double[] expected = {-10.423754940411076795, -100.56088545786867450, -1000.5755719318103005,
-10000.577051183514335, -100000.57719921568107, -1.0000005772140199687e6, -1.0000000577215500408e7,
-1.0000000057721564845e8, -1.0000000005772156633e9, -1.0000000000577215665e10, -1.0000000000057721566e11,
-1.0000000000005772157e12, -1.0000000000000577216e13, -1.0000000000000057722e14, -1.0000000000000005772e15, -1e+16,
-1e+17, -1e+18, -1e+19, -1e+20, -1e+21, -1e+22, -1e+23, -1e+24, -1e+25, -1e+26,
-1e+27, -1e+28, -1e+29, -1e+30};
for (double n = 1; n < 30; n++) {
checkRelativeError(String.format("Test %.0f: ", n), expected[(int) (n - 1)], Gamma.digamma(FastMath.pow(10.0, -n)), 1e-8);
}
}
@Test
public void testDigammaNonRealArgs() {
Assert.assertTrue(Double.isNaN(Gamma.digamma(Double.NaN)));
Assert.assertTrue(Double.isInfinite(Gamma.digamma(Double.POSITIVE_INFINITY)));
Assert.assertTrue(Double.isInfinite(Gamma.digamma(Double.NEGATIVE_INFINITY)));
}
@Test
public void testTrigamma() {
double eps = 1e-8;
// computed using webMathematica. For example, to compute trigamma($i) = Polygamma(1, $i), use
//
// http://functions.wolfram.com/webMathematica/Evaluated.jsp?name=PolyGamma2&plottype=0&vars={%221%22,%22$i%22}&digits=20
double[] data = {
1e-4, 1.0000000164469368793e8,
1e-3, 1.0000016425331958690e6,
1e-2, 10001.621213528313220,
1e-1, 101.43329915079275882,
1, 1.6449340668482264365,
2, 0.64493406684822643647,
3, 0.39493406684822643647,
4, 0.28382295573711532536,
5, 0.22132295573711532536,
10, 0.10516633568168574612,
20, 0.051270822935203119832,
50, 0.020201333226697125806,
100, 0.010050166663333571395
};
for (int i = data.length - 2; i >= 0; i -= 2) {
Assert.assertEquals(String.format("trigamma %.0f", data[i]), data[i + 1], Gamma.trigamma(data[i]), eps);
}
}
@Test
public void testTrigammaNonRealArgs() {
Assert.assertTrue(Double.isNaN(Gamma.trigamma(Double.NaN)));
Assert.assertTrue(Double.isInfinite(Gamma.trigamma(Double.POSITIVE_INFINITY)));
Assert.assertTrue(Double.isInfinite(Gamma.trigamma(Double.NEGATIVE_INFINITY)));
}
/**
* Reference data for the {@link Gamma#logGamma(double)} function. This data
* was generated with the following <a
* href="http://maxima.sourceforge.net/">Maxima</a> script.
*
* <pre>
* kill(all);
*
* fpprec : 64;
* gamln(x) := log(gamma(x));
* x : append(makelist(bfloat(i / 8), i, 1, 80),
* [0.8b0, 1b2, 1b3, 1b4, 1b5, 1b6, 1b7, 1b8, 1b9, 1b10]);
*
* for i : 1 while i <= length(x) do
* print("{", float(x[i]), ",", float(gamln(x[i])), "},");
* </pre>
*/
private static final double[][] LOG_GAMMA_REF = {
{ 0.125 , 2.019418357553796 },
{ 0.25 , 1.288022524698077 },
{ 0.375 , .8630739822706475 },
{ 0.5 , .5723649429247001 },
{ 0.625 , .3608294954889402 },
{ 0.75 , .2032809514312954 },
{ 0.875 , .08585870722533433 },
{ 0.890625 , .07353860936979656 },
{ 0.90625 , .06169536624059108 },
{ 0.921875 , .05031670080005688 },
{ 0.9375 , 0.0393909017345823 },
{ 0.953125 , .02890678734595923 },
{ 0.96875 , .01885367233441289 },
{ 0.984375 , .009221337197578781 },
{ 1.0 , 0.0 },
{ 1.015625 , - 0.00881970970573307 },
{ 1.03125 , - .01724677500176807 },
{ 1.046875 , - .02528981394675729 },
{ 1.0625 , - .03295710029357782 },
{ 1.078125 , - .04025658272400143 },
{ 1.09375 , - .04719590272716985 },
{ 1.109375 , - .05378241123619192 },
{ 1.125 , - .06002318412603958 },
{ 1.25 , - .09827183642181316 },
{ 1.375 , - .1177552707410788 },
{ 1.5 , - .1207822376352452 },
{ 1.625 , - .1091741337567954 },
{ 1.75 , - .08440112102048555 },
{ 1.875 , - 0.0476726853991883 },
{ 1.890625 , - .04229320615532515 },
{ 1.90625 , - .03674470657266143 },
{ 1.921875 , - .03102893865389552 },
{ 1.9375 , - .02514761940298887 },
{ 1.953125 , - .01910243184040138 },
{ 1.96875 , - .01289502598016741 },
{ 1.984375 , - .006527019770560387 },
{ 2.0 , 0.0 },
{ 2.015625 , .006684476830232185 },
{ 2.03125 , .01352488366498562 },
{ 2.046875 , .02051972208453692 },
{ 2.0625 , .02766752152285702 },
{ 2.078125 , 0.0349668385135861 },
{ 2.09375 , .04241625596251728 },
{ 2.109375 , .05001438244545164 },
{ 2.125 , .05775985153034387 },
{ 2.25 , .1248717148923966 },
{ 2.375 , .2006984603774558 },
{ 2.5 , .2846828704729192 },
{ 2.625 , .3763336820249054 },
{ 2.75 , .4752146669149371 },
{ 2.875 , .5809359740231859 },
{ 2.890625 , .5946142560817441 },
{ 2.90625 , .6083932548009232 },
{ 2.921875 , .6222723333588501 },
{ 2.9375 , .6362508628423761 },
{ 2.953125 , .6503282221022278 },
{ 2.96875 , .6645037976116387 },
{ 2.984375 , 0.678776983328359 },
{ 3.0 , .6931471805599453 },
{ 3.015625 , .7076137978322324 },
{ 3.03125 , .7221762507608962 },
{ 3.046875 , .7368339619260166 },
{ 3.0625 , 0.751586360749556 },
{ 3.078125 , .7664328833756681 },
{ 3.09375 , .7813729725537568 },
{ 3.109375 , .7964060775242092 },
{ 3.125 , 0.811531653906724 },
{ 3.25 , .9358019311087253 },
{ 3.375 , 1.06569589786406 },
{ 3.5 , 1.200973602347074 },
{ 3.625 , 1.341414578068493 },
{ 3.75 , 1.486815578593417 },
{ 3.875 , 1.6369886482725 },
{ 4.0 , 1.791759469228055 },
{ 4.125 , 1.950965937095089 },
{ 4.25 , 2.114456927450371 },
{ 4.375 , 2.282091222188554 },
{ 4.5 , 2.453736570842442 },
{ 4.625 , 2.62926886637513 },
{ 4.75 , 2.808571418575736 },
{ 4.875 , 2.99153431107781 },
{ 5.0 , 3.178053830347946 },
{ 5.125 , 3.368031956881733 },
{ 5.25 , 3.561375910386697 },
{ 5.375 , 3.757997741998131 },
{ 5.5 , 3.957813967618717 },
{ 5.625 , 4.160745237339519 },
{ 5.75 , 4.366716036622286 },
{ 5.875 , 4.57565441552762 },
{ 6.0 , 4.787491742782046 },
{ 6.125 , 5.002162481906205 },
{ 6.25 , 5.219603986990229 },
{ 6.375 , 5.439756316011858 },
{ 6.5 , 5.662562059857142 },
{ 6.625 , 5.887966185430003 },
{ 6.75 , 6.115915891431546 },
{ 6.875 , 6.346360475557843 },
{ 7.0 , 6.579251212010101 },
{ 7.125 , 6.814541238336996 },
{ 7.25 , 7.05218545073854 },
{ 7.375 , 7.292140407056348 },
{ 7.5 , 7.534364236758733 },
{ 7.625 , 7.778816557302289 },
{ 7.75 , 8.025458396315983 },
{ 7.875 , 8.274252119110479 },
{ 8.0 , 8.525161361065415 },
{ 8.125 , 8.77815096449171 },
{ 8.25 , 9.033186919605123 },
{ 8.375 , 9.290236309282232 },
{ 8.5 , 9.549267257300997 },
{ 8.625 , 9.810248879795765 },
{ 8.75 , 10.07315123968124 },
{ 8.875 , 10.33794530382217 },
{ 9.0 , 10.60460290274525 },
{ 9.125 , 10.87309669270751 },
{ 9.25 , 11.14340011995171 },
{ 9.375 , 11.41548738699336 },
{ 9.5 , 11.68933342079727 },
{ 9.625 , 11.96491384271319 },
{ 9.75 , 12.24220494005076 },
{ 9.875 , 12.52118363918365 },
{ 10.0 , 12.80182748008147 },
{ 0.8 , .1520596783998376 },
{ 100.0 , 359.1342053695754 },
{ 1000.0 , 5905.220423209181 },
{ 10000.0 , 82099.71749644238 },
{ 100000.0 , 1051287.708973657 },
{ 1000000.0 , 1.2815504569147612e+7 },
{ 10000000.0 , 1.511809493694739e+8 },
{ 1.e+8 , 1.7420680661038346e+9 },
{ 1.e+9 , 1.972326582750371e+10 },
{ 1.e+10 , 2.202585092888106e+11 },
};
@Test
public void testLogGamma() {
final int ulps = 3;
for (int i = 0; i < LOG_GAMMA_REF.length; i++) {
final double[] data = LOG_GAMMA_REF[i];
final double x = data[0];
final double expected = data[1];
final double actual = Gamma.logGamma(x);
final double tol;
if (expected == 0.0) {
tol = 1E-15;
} else {
tol = ulps * FastMath.ulp(expected);
}
Assert.assertEquals(Double.toString(x), expected, actual, tol);
}
}
@Test
public void testLogGammaPrecondition1() {
Assert.assertTrue(Double.isNaN(Gamma.logGamma(0.0)));
}
@Test
public void testLogGammaPrecondition2() {
Assert.assertTrue(Double.isNaN(Gamma.logGamma(-1.0)));
}
/**
* <p>
* Reference values for the {@link Gamma#invGamma1pm1(double)} method.
* These values were generated with the following <a
* href="http://maxima.sourceforge.net/">Maxima</a> script
* </p>
*
* <pre>
* kill(all);
*
* fpprec : 64;
* gam1(x) := 1 / gamma(1 + x) - 1;
* x : makelist(bfloat(i / 8), i, -4, 12);
*
* for i : 1 while i <= length(x) do print("{",
* float(x[i]),
* ",",
* float(gam1(x[i])),
* "},");
* </pre>
*/
private static final double[][] INV_GAMMA1P_M1_REF = {
{ -0.5 , -.4358104164522437 },
{ -0.375 , -.3029021533379859 },
{ -0.25 , -0.183951060901737 },
{ -0.125 , -.08227611018520711 },
{ 0.0 , 0.0 },
{ 0.125 , .06186116458306091 },
{ 0.25 , .1032626513208373 },
{ 0.375 , .1249687649039041 },
{ 0.5 , .1283791670955126 },
{ 0.625 , .1153565546592225 },
{ 0.75 , 0.0880652521310173 },
{ 0.875 , .04882730264547758 },
{ 1.0 , 0.0 },
{ 1.125 , -.05612340925950141 },
{ 1.25 , -.1173898789433302 },
{ 1.375 , -.1818408982517061 },
{ 1.5 , -0.247747221936325 },
};
@Test
public void testInvGamma1pm1() {
final int ulps = 3;
for (int i = 0; i < INV_GAMMA1P_M1_REF.length; i++) {
final double[] ref = INV_GAMMA1P_M1_REF[i];
final double x = ref[0];
final double expected = ref[1];
final double actual = Gamma.invGamma1pm1(x);
final double tol = ulps * FastMath.ulp(expected);
Assert.assertEquals(Double.toString(x), expected, actual, tol);
}
}
@Test(expected = NumberIsTooSmallException.class)
public void testInvGamma1pm1Precondition1() {
Gamma.invGamma1pm1(-0.51);
}
@Test(expected = NumberIsTooLargeException.class)
public void testInvGamma1pm1Precondition2() {
Gamma.invGamma1pm1(1.51);
}
private static final double[][] LOG_GAMMA1P_REF = {
{ - 0.5 , .5723649429247001 },
{ - 0.375 , .3608294954889402 },
{ - 0.25 , .2032809514312954 },
{ - 0.125 , .08585870722533433 },
{ 0.0 , 0.0 },
{ 0.125 , - .06002318412603958 },
{ 0.25 , - .09827183642181316 },
{ 0.375 , - .1177552707410788 },
{ 0.5 , - .1207822376352452 },
{ 0.625 , - .1091741337567954 },
{ 0.75 , - .08440112102048555 },
{ 0.875 , - 0.0476726853991883 },
{ 1.0 , 0.0 },
{ 1.125 , .05775985153034387 },
{ 1.25 , .1248717148923966 },
{ 1.375 , .2006984603774558 },
{ 1.5 , .2846828704729192 },
};
@Test
public void testLogGamma1p() {
final int ulps = 3;
for (int i = 0; i < LOG_GAMMA1P_REF.length; i++) {
final double[] ref = LOG_GAMMA1P_REF[i];
final double x = ref[0];
final double expected = ref[1];
final double actual = Gamma.logGamma1p(x);
final double tol = ulps * FastMath.ulp(expected);
Assert.assertEquals(Double.toString(x), expected, actual, tol);
}
}
@Test(expected = NumberIsTooSmallException.class)
public void testLogGamma1pPrecondition1() {
Gamma.logGamma1p(-0.51);
}
@Test(expected = NumberIsTooLargeException.class)
public void testLogGamma1pPrecondition2() {
Gamma.logGamma1p(1.51);
}
/**
* Reference data for the {@link Gamma#gamma(double)} function. This
* data was generated with the following <a
* href="http://maxima.sourceforge.net/">Maxima</a> script.
*
* <pre>
* kill(all);
*
* fpprec : 64;
*
* EPSILON : 10**(-fpprec + 1);
* isInteger(x) := abs(x - floor(x)) <= EPSILON * abs(x);
*
* x : makelist(bfloat(i / 8), i, -160, 160);
* x : append(x, makelist(bfloat(i / 2), i, 41, 200));
*
* for i : 1 while i <= length(x) do if not(isInteger(x[i])) then
* print("{", float(x[i]), ",", float(gamma(x[i])), "},");
* </pre>
*/
private static final double[][] GAMMA_REF = {
{ - 19.875 , 4.920331854832504e-18 },
{ - 19.75 , 3.879938752480031e-18 },
{ - 19.625 , 4.323498423815027e-18 },
{ - 19.5 , 5.811045977502237e-18 },
{ - 19.375 , 9.14330910942125e-18 },
{ - 19.25 , 1.735229114436739e-17 },
{ - 19.125 , 4.653521565668223e-17 },
{ - 18.875 , - 9.779159561479603e-17 },
{ - 18.75 , - 7.662879036148061e-17 },
{ - 18.625 , - 8.484865656736991e-17 },
{ - 18.5 , - 1.133153965612936e-16 },
{ - 18.375 , - 1.771516139950367e-16 },
{ - 18.25 , - 3.340316045290721e-16 },
{ - 18.125 , - 8.899859994340475e-16 },
{ - 17.875 , 1.845816367229275e-15 },
{ - 17.75 , 1.436789819277761e-15 },
{ - 17.625 , 1.580306228567265e-15 },
{ - 17.5 , 2.096334836383932e-15 },
{ - 17.375 , 3.255160907158799e-15 },
{ - 17.25 , 6.096076782655566e-15 },
{ - 17.125 , 1.613099623974211e-14 },
{ - 16.875 , - 3.29939675642233e-14 },
{ - 16.75 , - 2.550301929218027e-14 },
{ - 16.625 , - 2.785289727849803e-14 },
{ - 16.5 , - 3.66858596367188e-14 },
{ - 16.375 , - 5.655842076188414e-14 },
{ - 16.25 , - 1.051573245008085e-13 },
{ - 16.125 , - 2.762433106055837e-13 },
{ - 15.875 , 5.567732026462681e-13 },
{ - 15.75 , 4.271755731440195e-13 },
{ - 15.625 , 4.630544172550298e-13 },
{ - 15.5 , 6.053166840058604e-13 },
{ - 15.375 , 9.261441399758529e-13 },
{ - 15.25 , 1.708806523138138e-12 },
{ - 15.125 , 4.454423383515037e-12 },
{ - 14.875 , - 8.838774592009505e-12 },
{ - 14.75 , - 6.728015277018307e-12 },
{ - 14.625 , - 7.235225269609841e-12 },
{ - 14.5 , - 9.382408602090835e-12 },
{ - 14.375 , - 1.423946615212874e-11 },
{ - 14.25 , - 2.605929947785661e-11 },
{ - 14.125 , - 6.737315367566492e-11 },
{ - 13.875 , 1.314767720561414e-10 },
{ - 13.75 , 9.923822533602004e-11 },
{ - 13.625 , 1.058151695680439e-10 },
{ - 13.5 , 1.360449247303171e-10 },
{ - 13.375 , 2.046923259368506e-10 },
{ - 13.25 , 3.713450175594567e-10 },
{ - 13.125 , 9.516457956687671e-10 },
{ - 12.875 , - 1.8242402122789617e-9 },
{ - 12.75 , - 1.3645255983702756e-9 },
{ - 12.625 , - 1.4417316853645984e-9 },
{ - 12.5 , - 1.836606483859281e-9 },
{ - 12.375 , - 2.7377598594053765e-9 },
{ - 12.25 , - 4.9203214826628017e-9 },
{ - 12.125 , - 1.2490351068152569e-8 },
{ - 11.875 , 2.3487092733091633e-8 },
{ - 11.75 , 1.7397701379221012e-8 },
{ - 11.625 , 1.8201862527728055e-8 },
{ - 11.5 , 2.295758104824101e-8 },
{ - 11.375 , 3.3879778260141535e-8 },
{ - 11.25 , 6.027393816261931e-8 },
{ - 11.125 , 1.5144550670134987e-7 },
{ - 10.875 , - 2.7890922620546316e-7 },
{ - 10.75 , - 2.044229912058469e-7 },
{ - 10.625 , - 2.1159665188483867e-7 },
{ - 10.5 , - 2.640121820547716e-7 },
{ - 10.375 , - 3.8538247770911e-7 },
{ - 10.25 , - 6.780818043294673e-7 },
{ - 10.125 , - 1.6848312620525174e-6 },
{ - 9.875 , 3.0331378349844124e-6 },
{ - 9.75 , 2.1975471554628537e-6 },
{ - 9.625 , 2.2482144262764103e-6 },
{ - 9.5 , 2.772127911575102e-6 },
{ - 9.375 , 3.998343206232017e-6 },
{ - 9.25 , 6.95033849437704e-6 },
{ - 9.125 , 1.7058916528281737e-5 },
{ - 8.875 , - 2.9952236120471065e-5 },
{ - 8.75 , - 2.1426084765762826e-5 },
{ - 8.625 , - 2.163906385291045e-5 },
{ - 8.5 , - 2.633521515996347e-5 },
{ - 8.375 , - 3.748446755842515e-5 },
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{ - 8.125 , - 1.5566261332057085e-4 },
{ - 7.875 , 2.658260955691807e-4 },
{ - 7.75 , 1.874782417004247e-4 },
{ - 7.625 , 1.8663692573135265e-4 },
{ - 7.5 , 2.238493288596895e-4 },
{ - 7.375 , 3.1393241580181064e-4 },
{ - 7.25 , 5.303977063521479e-4 },
{ - 7.125 , .001264758733229638 },
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{ - 6.75 , - .001452956373178292 },
{ - 6.625 , - .001423106558701564 },
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{ 1.0 , 1.0 },
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{ 96.0 , 1.03299784882391e+148 },
{ 96.5 , 1.01081004380505e+149 },
{ 97.0 , 9.9167793487095e+149 },
{ 97.5 , 9.75431692271873e+150 },
{ 98.0 , 9.61927596824821e+151 },
{ 98.5 , 9.51045899965076e+152 },
{ 99.0 , 9.42689044888325e+153 },
{ 99.5 , 9.367802114656e+154 },
{ 100.0 , 9.33262154439441e+155 },
};
@Test
public void testGamma() {
for (int i = 0; i < GAMMA_REF.length; i++) {
final double[] ref = GAMMA_REF[i];
final double x = ref[0];
final double expected = ref[1];
final double actual = Gamma.gamma(x);
final double absX = FastMath.abs(x);
final int ulps;
if (absX <= 8.0) {
ulps = 3;
} else if (absX <= 20.0) {
ulps = 5;
} else if (absX <= 30.0) {
ulps = 50;
} else if (absX <= 50.0) {
ulps = 180;
} else {
ulps = 500;
}
final double tol = ulps * FastMath.ulp(expected);
Assert.assertEquals(Double.toString(x), expected, actual, tol);
}
}
@Test
public void testGammaNegativeInteger() {
for (int i = -100; i <= 0; i++) {
Assert.assertTrue(Integer.toString(i), Double.isNaN(Gamma.gamma(i)));
}
}
@Test
public void testGammaNegativeDouble() {
// check that the gamma function properly switches sign
// see: https://en.wikipedia.org/wiki/Gamma_function
double previousGamma = Gamma.gamma(-18.5);
for (double x = -19.5; x > -25; x -= 1.0) {
double gamma = Gamma.gamma(x);
Assert.assertEquals( (int) FastMath.signum(previousGamma),
- (int) FastMath.signum(gamma));
previousGamma = gamma;
}
}
private void checkRelativeError(String msg, double expected, double actual,
double tolerance) {
Assert.assertEquals(msg, expected, actual, FastMath.abs(tolerance * actual));
}
}
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