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Posted to commits@commons.apache.org by er...@apache.org on 2017/05/07 23:57:34 UTC
[1/2] commons-numbers git commit: NUMBERS-33: "Gamma" family of
functions (port from "Commons Math").
Repository: commons-numbers
Updated Branches:
refs/heads/task_NUMBERS-33__Gamma [created] 0c9f1cde2
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/GammaTest.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/GammaTest.java b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/GammaTest.java
new file mode 100644
index 0000000..ec7bcb9
--- /dev/null
+++ b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/GammaTest.java
@@ -0,0 +1,557 @@
+/*
+ * 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.numbers.gamma;
+
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * Tests for {@link Gamma}.
+ */
+public class GammaTest {
+ private static final Gamma FUNCTION = new Gamma();
+
+ /**
+ * Reference data for the {@link Gamma#value(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 },
+ { - 8.25 , - 6.429063107298763e-5 },
+ { - 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 },
+ { - 6.875 , - .002093380502607298 },
+ { - 6.75 , - .001452956373178292 },
+ { - 6.625 , - .001423106558701564 },
+ { - 6.5 , - .001678869966447671 },
+ { - 6.375 , - .002315251566538353 },
+ { - 6.25 , - .003845383371053072 },
+ { - 6.125 , - .009011405974261174 },
+ { - 5.875 , .01439199095542518 },
+ { - 5.75 , .009807455518953468 },
+ { - 5.625 , .009428080951397862 },
+ { - 5.5 , .01091265478190986 },
+ { - 5.375 , 0.014759728736682 },
+ { - 5.25 , 0.0240336460690817 },
+ { - 5.125 , .05519486159234969 },
+ { - 4.875 , - 0.0845529468631229 },
+ { - 4.75 , - .05639286923398244 },
+ { - 4.625 , - .05303295535161297 },
+ { - 4.5 , - .06001960130050425 },
+ { - 4.375 , - .07933354195966577 },
+ { - 4.25 , - .1261766418626789 },
+ { - 4.125 , - .2828736656607921 },
+ { - 3.875 , .4121956159577241 },
+ { - 3.75 , .2678661288614166 },
+ { - 3.625 , 0.24527741850121 },
+ { - 3.5 , .2700882058522691 },
+ { - 3.375 , .3470842460735378 },
+ { - 3.25 , .5362507279163854 },
+ { - 3.125 , 1.166853870850768 },
+ { - 2.875 , - 1.597258011836181 },
+ { - 2.75 , - 1.004497983230312 },
+ { - 2.625 , - .8891306420668862 },
+ { - 2.5 , - .9453087204829419 },
+ { - 2.375 , - 1.17140933049819 },
+ { - 2.25 , - 1.742814865728253 },
+ { - 2.125 , - 3.646418346408649 },
+ { - 1.875 , 4.59211678402902 },
+ { - 1.75 , 2.762369453883359 },
+ { - 1.625 , 2.333967935425576 },
+ { - 1.5 , 2.363271801207355 },
+ { - 1.375 , 2.782097159933201 },
+ { - 1.25 , 3.921333447888569 },
+ { - 1.125 , 7.748638986118379 },
+ { - 0.875 , - 8.610218970054413 },
+ { - 0.75 , - 4.834146544295877 },
+ { - 0.625 , - 3.792697895066561 },
+ { - 0.5 , - 3.544907701811032 },
+ { - 0.375 , - 3.825383594908152 },
+ { - 0.25 , - 4.901666809860711 },
+ { - 0.125 , - 8.717218859383175 },
+ { 0.125 , 7.533941598797612 },
+ { 0.25 , 3.625609908221908 },
+ { 0.375 , 2.370436184416601 },
+ { 0.5 , 1.772453850905516 },
+ { 0.625 , 1.434518848090557 },
+ { 0.75 , 1.225416702465178 },
+ { 0.875 , 1.089652357422897 },
+ { 1.0 , 1.0 },
+ { 1.125 , .9417426998497015 },
+ { 1.25 , 0.906402477055477 },
+ { 1.375 , .8889135691562253 },
+ { 1.5 , 0.886226925452758 },
+ { 1.625 , 0.896574280056598 },
+ { 1.75 , .9190625268488832 },
+ { 1.875 , .9534458127450348 },
+ { 2.0 , 1.0 },
+ { 2.125 , 1.059460537330914 },
+ { 2.25 , 1.133003096319346 },
+ { 2.375 , 1.22225615758981 },
+ { 2.5 , 1.329340388179137 },
+ { 2.625 , 1.456933205091972 },
+ { 2.75 , 1.608359421985546 },
+ { 2.875 , 1.78771089889694 },
+ { 3.0 , 2.0 },
+ { 3.125 , 2.251353641828193 },
+ { 3.25 , 2.549256966718529 },
+ { 3.375 , 2.902858374275799 },
+ { 3.5 , 3.323350970447843 },
+ { 3.625 , 3.824449663366426 },
+ { 3.75 , 4.422988410460251 },
+ { 3.875 , 5.139668834328703 },
+ { 4.0 , 6.0 },
+ { 4.125 , 7.035480130713102 },
+ { 4.25 , 8.28508514183522 },
+ { 4.375 , 9.797147013180819 },
+ { 4.5 , 11.63172839656745 },
+ { 4.625 , 13.86363002970329 },
+ { 4.75 , 16.58620653922594 },
+ { 4.875 , 19.91621673302373 },
+ { 5.0 , 24.0 },
+ { 5.125 , 29.02135553919155 },
+ { 5.25 , 35.21161185279968 },
+ { 5.375 , 42.86251818266609 },
+ { 5.5 , 52.34277778455352 },
+ { 5.625 , 64.11928888737773 },
+ { 5.75 , 78.78448106132322 },
+ { 5.875 , 97.09155657349066 },
+ { 6.0 , 120.0 },
+ { 6.125 , 148.7344471383567 },
+ { 6.25 , 184.8609622271983 },
+ { 6.375 , 230.3860352318302 },
+ { 6.5 , 287.8852778150443 },
+ { 6.625 , 360.6709999914997 },
+ { 6.75 , 453.0107661026085 },
+ { 6.875 , 570.4128948692577 },
+ { 7.0 , 720.0 },
+ { 7.125 , 910.9984887224346 },
+ { 7.25 , 1155.38101391999 },
+ { 7.375 , 1468.710974602918 },
+ { 7.5 , 1871.254305797788 },
+ { 7.625 , 2389.445374943686 },
+ { 7.75 , 3057.822671192607 },
+ { 7.875 , 3921.588652226146 },
+ { 8.0 , 5040.0 },
+ { 8.125 , 6490.864232147346 },
+ { 8.25 , 8376.512350919926 },
+ { 8.375 , 10831.74343769652 },
+ { 8.5 , 14034.40729348341 },
+ { 8.625 , 18219.5209839456 },
+ { 8.75 , 23698.12570174271 },
+ { 8.875 , 30882.5106362809 },
+ { 9.0 , 40320.0 },
+ { 9.125 , 52738.27188619719 },
+ { 9.25 , 69106.22689508938 },
+ { 9.375 , 90715.85129070834 },
+ { 9.5 , 119292.461994609 },
+ { 9.625 , 157143.3684865308 },
+ { 9.75 , 207358.5998902487 },
+ { 9.875 , 274082.281896993 },
+ { 10.0 , 362880.0 },
+ { 10.125 , 481236.7309615494 },
+ { 10.25 , 639232.5987795768 },
+ { 10.375 , 850461.1058503906 },
+ { 10.5 , 1133278.388948786 },
+ { 10.625 , 1512504.921682859 },
+ { 10.75 , 2021746.348929925 },
+ { 10.875 , 2706562.533732806 },
+ { 11.0 , 3628800.0 },
+ { 11.125 , 4872521.900985687 },
+ { 11.25 , 6552134.137490662 },
+ { 11.375 , 8823533.973197803 },
+ { 11.5 , 1.1899423083962249e+7 },
+ { 11.625 , 1.6070364792880382e+7 },
+ { 11.75 , 2.1733773250996688e+7 },
+ { 11.875 , 2.943386755434427e+7 },
+ { 12.0 , 3.99168e+7 },
+ { 12.125 , 5.420680614846578e+7 },
+ { 12.25 , 7.371150904676994e+7 },
+ { 12.375 , 1.0036769894512501e+8 },
+ { 12.5 , 1.3684336546556586e+8 },
+ { 12.625 , 1.8681799071723443e+8 },
+ { 12.75 , 2.5537183569921107e+8 },
+ { 12.875 , 3.4952717720783816e+8 },
+ { 13.0 , 4.790016e+8 },
+ { 13.125 , 6.572575245501475e+8 },
+ { 13.25 , 9.029659858229319e+8 },
+ { 13.375 , 1.2420502744459219e+9 },
+ { 13.5 , 1.7105420683195732e+9 },
+ { 13.625 , 2.3585771328050845e+9 },
+ { 13.75 , 3.2559909051649416e+9 },
+ { 13.875 , 4.500162406550916e+9 },
+ { 14.0 , 6.2270208e+9 },
+ { 14.125 , 8.626505009720685e+9 },
+ { 14.25 , 1.196429931215385e+10 },
+ { 14.375 , 1.66124224207142e+10 },
+ { 14.5 , 2.309231792231424e+10 },
+ { 14.625 , 3.213561343446927e+10 },
+ { 14.75 , 4.476987494601794e+10 },
+ { 14.875 , 6.243975339089396e+10 },
+ { 15.0 , 8.71782912e+10 },
+ { 15.125 , 1.218493832623047e+11 },
+ { 15.25 , 1.704912651981923e+11 },
+ { 15.375 , 2.388035722977667e+11 },
+ { 15.5 , 3.348386098735565e+11 },
+ { 15.625 , 4.699833464791132e+11 },
+ { 15.75 , 6.603556554537646e+11 },
+ { 15.875 , 9.287913316895475e+11 },
+ { 16.0 , 1.307674368e+12 },
+ { 16.125 , 1.842971921842358e+12 },
+ { 16.25 , 2.599991794272433e+12 },
+ { 16.375 , 3.671604924078163e+12 },
+ { 16.5 , 5.189998453040126e+12 },
+ { 16.625 , 7.343489788736144e+12 },
+ { 16.75 , 1.040060157339679e+13 },
+ { 16.875 , 1.474456239057157e+13 },
+ { 17.0 , 2.0922789888e+13 },
+ { 17.125 , 2.971792223970803e+13 },
+ { 17.25 , 4.224986665692704e+13 },
+ { 17.375 , 6.012253063177992e+13 },
+ { 17.5 , 8.563497447516206e+13 },
+ { 17.625 , 1.220855177377384e+14 },
+ { 17.75 , 1.742100763543963e+14 },
+ { 17.875 , 2.488144903408952e+14 },
+ { 18.0 , 3.55687428096e+14 },
+ { 18.125 , 5.08919418355e+14 },
+ { 18.25 , 7.288101998319914e+14 },
+ { 18.375 , 1.044628969727176e+15 },
+ { 18.5 , 1.498612053315336e+15 },
+ { 18.625 , 2.151757250127639e+15 },
+ { 18.75 , 3.092228855290534e+15 },
+ { 18.875 , 4.447559014843502e+15 },
+ { 19.0 , 6.402373705728e+15 },
+ { 19.125 , 9.224164457684374e+15 },
+ { 19.25 , 1.330078614693384e+16 },
+ { 19.375 , 1.919505731873686e+16 },
+ { 19.5 , 2.772432298633372e+16 },
+ { 19.625 , 4.007647878362728e+16 },
+ { 19.75 , 5.797929103669752e+16 },
+ { 19.875 , 8.39476764051711e+16 },
+ { 20.0 , 1.21645100408832e+17 },
+ { 20.5 , 5.406242982335075e+17 },
+ { 21.0 , 2.43290200817664e+18 },
+ { 21.5 , 1.10827981137869e+19 },
+ { 22.0 , 5.109094217170944e+19 },
+ { 22.5 , 2.382801594464184e+20 },
+ { 23.0 , 1.124000727777608e+21 },
+ { 23.5 , 5.361303587544415e+21 },
+ { 24.0 , 2.585201673888498e+22 },
+ { 24.5 , 1.259906343072938e+23 },
+ { 25.0 , 6.204484017332395e+23 },
+ { 25.5 , 3.086770540528697e+24 },
+ { 26.0 , 1.551121004333099e+25 },
+ { 26.5 , 7.871264878348176e+25 },
+ { 27.0 , 4.032914611266056e+26 },
+ { 27.5 , 2.085885192762267e+27 },
+ { 28.0 , 1.088886945041835e+28 },
+ { 28.5 , 5.736184280096234e+28 },
+ { 29.0 , 3.048883446117139e+29 },
+ { 29.5 , 1.634812519827427e+30 },
+ { 30.0 , 8.841761993739702e+30 },
+ { 30.5 , 4.822696933490909e+31 },
+ { 31.0 , 2.65252859812191e+32 },
+ { 31.5 , 1.470922564714727e+33 },
+ { 32.0 , 8.222838654177922e+33 },
+ { 32.5 , 4.633406078851391e+34 },
+ { 33.0 , 2.631308369336935e+35 },
+ { 33.5 , 1.505856975626702e+36 },
+ { 34.0 , 8.683317618811885e+36 },
+ { 34.5 , 5.044620868349451e+37 },
+ { 35.0 , 2.952327990396041e+38 },
+ { 35.5 , 1.740394199580561e+39 },
+ { 36.0 , 1.033314796638614e+40 },
+ { 36.5 , 6.178399408510991e+40 },
+ { 37.0 , 3.719933267899013e+41 },
+ { 37.5 , 2.255115784106512e+42 },
+ { 38.0 , 1.376375309122634e+43 },
+ { 38.5 , 8.456684190399419e+43 },
+ { 39.0 , 5.230226174666011e+44 },
+ { 39.5 , 3.255823413303776e+45 },
+ { 40.0 , 2.039788208119745e+46 },
+ { 40.5 , 1.286050248254992e+47 },
+ { 41.0 , 8.159152832478976e+47 },
+ { 41.5 , 5.208503505432716e+48 },
+ { 42.0 , 3.345252661316381e+49 },
+ { 42.5 , 2.161528954754577e+50 },
+ { 43.0 , 1.40500611775288e+51 },
+ { 43.5 , 9.186498057706953e+51 },
+ { 44.0 , 6.041526306337383e+52 },
+ { 44.5 , 3.996126655102524e+53 },
+ { 45.0 , 2.658271574788449e+54 },
+ { 45.5 , 1.778276361520623e+55 },
+ { 46.0 , 1.196222208654802e+56 },
+ { 46.5 , 8.091157444918836e+56 },
+ { 47.0 , 5.502622159812088e+57 },
+ { 47.5 , 3.762388211887259e+58 },
+ { 48.0 , 2.586232415111682e+59 },
+ { 48.5 , 1.787134400646448e+60 },
+ { 49.0 , 1.241391559253607e+61 },
+ { 49.5 , 8.667601843135273e+61 },
+ { 50.0 , 6.082818640342675e+62 },
+ { 50.5 , 4.290462912351959e+63 },
+ { 51.0 , 3.041409320171338e+64 },
+ { 51.5 , 2.16668377073774e+65 },
+ { 52.0 , 1.551118753287382e+66 },
+ { 52.5 , 1.115842141929936e+67 },
+ { 53.0 , 8.065817517094388e+67 },
+ { 53.5 , 5.858171245132164e+68 },
+ { 54.0 , 4.274883284060025e+69 },
+ { 54.5 , 3.134121616145708e+70 },
+ { 55.0 , 2.308436973392413e+71 },
+ { 55.5 , 1.70809628079941e+72 },
+ { 56.0 , 1.269640335365828e+73 },
+ { 56.5 , 9.479934358436728e+73 },
+ { 57.0 , 7.109985878048635e+74 },
+ { 57.5 , 5.356162912516752e+75 },
+ { 58.0 , 4.052691950487721e+76 },
+ { 58.5 , 3.079793674697132e+77 },
+ { 59.0 , 2.350561331282878e+78 },
+ { 59.5 , 1.801679299697822e+79 },
+ { 60.0 , 1.386831185456898e+80 },
+ { 60.5 , 1.071999183320204e+81 },
+ { 61.0 , 8.320987112741391e+81 },
+ { 61.5 , 6.485595059087236e+82 },
+ { 62.0 , 5.075802138772249e+83 },
+ { 62.5 , 3.98864096133865e+84 },
+ { 63.0 , 3.146997326038794e+85 },
+ { 63.5 , 2.492900600836656e+86 },
+ { 64.0 , 1.98260831540444e+87 },
+ { 64.5 , 1.582991881531277e+88 },
+ { 65.0 , 1.268869321858841e+89 },
+ { 65.5 , 1.021029763587673e+90 },
+ { 66.0 , 8.247650592082472e+90 },
+ { 66.5 , 6.687744951499262e+91 },
+ { 67.0 , 5.443449390774431e+92 },
+ { 67.5 , 4.447350392747009e+93 },
+ { 68.0 , 3.647111091818868e+94 },
+ { 68.5 , 3.001961515104231e+95 },
+ { 69.0 , 2.48003554243683e+96 },
+ { 69.5 , 2.056343637846398e+97 },
+ { 70.0 , 1.711224524281413e+98 },
+ { 70.5 , 1.429158828303247e+99 },
+ { 71.0 , 1.19785716699699e+100 },
+ { 71.5 , 1.00755697395379e+101 },
+ { 72.0 , 8.50478588567862e+101 },
+ { 72.5 , 7.20403236376959e+102 },
+ { 73.0 , 6.12344583768861e+103 },
+ { 73.5 , 5.22292346373295e+104 },
+ { 74.0 , 4.47011546151268e+105 },
+ { 74.5 , 3.83884874584372e+106 },
+ { 75.0 , 3.30788544151939e+107 },
+ { 75.5 , 2.85994231565357e+108 },
+ { 76.0 , 2.48091408113954e+109 },
+ { 76.5 , 2.15925644831845e+110 },
+ { 77.0 , 1.88549470166605e+111 },
+ { 77.5 , 1.65183118296361e+112 },
+ { 78.0 , 1.45183092028286e+113 },
+ { 78.5 , 1.2801691667968e+114 },
+ { 79.0 , 1.13242811782063e+115 },
+ { 79.5 , 1.00493279593549e+116 },
+ { 80.0 , 8.94618213078298e+116 },
+ { 80.5 , 7.98921572768712e+117 },
+ { 81.0 , 7.15694570462638e+118 },
+ { 81.5 , 6.43131866078814e+119 },
+ { 82.0 , 5.79712602074737e+120 },
+ { 82.5 , 5.24152470854233e+121 },
+ { 83.0 , 4.75364333701284e+122 },
+ { 83.5 , 4.32425788454742e+123 },
+ { 84.0 , 3.94552396972066e+124 },
+ { 84.5 , 3.6107553335971e+125 },
+ { 85.0 , 3.31424013456535e+126 },
+ { 85.5 , 3.05108825688955e+127 },
+ { 86.0 , 2.81710411438055e+128 },
+ { 86.5 , 2.60868045964056e+129 },
+ { 87.0 , 2.42270953836727e+130 },
+ { 87.5 , 2.25650859758909e+131 },
+ { 88.0 , 2.10775729837953e+132 },
+ { 88.5 , 1.97444502289045e+133 },
+ { 89.0 , 1.85482642257398e+134 },
+ { 89.5 , 1.74738384525805e+135 },
+ { 90.0 , 1.65079551609085e+136 },
+ { 90.5 , 1.56390854150595e+137 },
+ { 91.0 , 1.48571596448176e+138 },
+ { 91.5 , 1.41533723006289e+139 },
+ { 92.0 , 1.3520015276784e+140 },
+ { 92.5 , 1.29503356550754e+141 },
+ { 93.0 , 1.24384140546413e+142 },
+ { 93.5 , 1.19790604809448e+143 },
+ { 94.0 , 1.15677250708164e+144 },
+ { 94.5 , 1.12004215496834e+145 },
+ { 95.0 , 1.08736615665674e+146 },
+ { 95.5 , 1.05843983644508e+147 },
+ { 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 = FUNCTION.value(x);
+ final double absX = Math.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 * Math.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(FUNCTION.value(i)));
+ }
+ }
+
+ @Test
+ public void testGammaNegativeDouble() {
+ // check that the gamma function properly switches sign
+ // see: https://en.wikipedia.org/wiki/Gamma_function
+
+ double previousGamma = FUNCTION.value(-18.5);
+ for (double x = -19.5; x > -25; x -= 1.0) {
+ double gamma = FUNCTION.value(x);
+ Assert.assertEquals( (int) Math.signum(previousGamma),
+ - (int) Math.signum(gamma));
+
+ previousGamma = gamma;
+ }
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/InvGamma1pm1Test.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/InvGamma1pm1Test.java b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/InvGamma1pm1Test.java
new file mode 100644
index 0000000..6e3c97a
--- /dev/null
+++ b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/InvGamma1pm1Test.java
@@ -0,0 +1,91 @@
+/*
+ * 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.numbers.gamma;
+
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * Tests for {@link InvGamma1pm1}.
+ */
+public class InvGamma1pm1Test {
+ private static final InvGamma1pm1 FUNCTION = InvGamma1pm1.instance;
+
+ /**
+ * <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 = FUNCTION.value(x);
+ final double tol = ulps * Math.ulp(expected);
+ Assert.assertEquals(Double.toString(x), expected, actual, tol);
+ }
+ }
+
+ @Test(expected=GammaException.class)
+ public void testInvGamma1pm1Precondition1() {
+ FUNCTION.value(-0.51);
+ }
+
+ @Test(expected=GammaException.class)
+ public void testInvGamma1pm1Precondition2() {
+ FUNCTION.value(1.51);
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/LogGamma1pTest.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/LogGamma1pTest.java b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/LogGamma1pTest.java
new file mode 100644
index 0000000..ffdbe01
--- /dev/null
+++ b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/LogGamma1pTest.java
@@ -0,0 +1,70 @@
+/*
+ * 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.numbers.gamma;
+
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * Tests for {@link LogGamma1p}.
+ */
+public class LogGamma1pTest {
+ private static final LogGamma1p FUNCTION = LogGamma1p.instance;
+
+ 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 = FUNCTION.value(x);
+ final double tol = ulps * Math.ulp(expected);
+ Assert.assertEquals(Double.toString(x), expected, actual, tol);
+ }
+ }
+
+ @Test(expected=GammaException.class)
+ public void testLogGamma1pPrecondition1() {
+ FUNCTION.value(-0.51);
+ }
+
+ @Test(expected=GammaException.class)
+ public void testLogGamma1pPrecondition2() {
+ FUNCTION.value(1.51);
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/LogGammaTest.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/LogGammaTest.java b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/LogGammaTest.java
new file mode 100644
index 0000000..9568443
--- /dev/null
+++ b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/LogGammaTest.java
@@ -0,0 +1,232 @@
+/*
+ * 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.numbers.gamma;
+
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * Tests for {@link LogGamma}.
+ */
+public class LogGammaTest {
+ private static final LogGamma FUNCTION = LogGamma.instance;
+
+ @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);
+ }
+
+ /**
+ * 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 = FUNCTION.value(x);
+ final double tol;
+ if (expected == 0.0) {
+ tol = 1E-15;
+ } else {
+ tol = ulps * Math.ulp(expected);
+ }
+ Assert.assertEquals(Double.toString(x), expected, actual, tol);
+ }
+ }
+
+ @Test
+ public void testLogGammaPrecondition1() {
+ Assert.assertTrue(Double.isNaN(FUNCTION.value(0.0)));
+ }
+
+ @Test
+ public void testLogGammaPrecondition2() {
+ Assert.assertTrue(Double.isNaN(FUNCTION.value(-1.0)));
+ }
+
+ private void testLogGamma(double expected, double x) {
+ double actual = FUNCTION.value(x);
+ Assert.assertEquals(expected, actual, 10e-15);
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/RegularizedGammaTest.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/RegularizedGammaTest.java b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/RegularizedGammaTest.java
new file mode 100644
index 0000000..2d4510f
--- /dev/null
+++ b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/RegularizedGammaTest.java
@@ -0,0 +1,67 @@
+/*
+ * 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.numbers.gamma;
+
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * Tests for {@link RegularizedGamma}.
+ */
+public class RegularizedGammaTest {
+ @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);
+ }
+
+ private void testRegularizedGamma(double expected, double a, double x) {
+ double actualP = new RegularizedGamma.P().value(a, x);
+ double actualQ = new RegularizedGamma.Q().value(a, x);
+ Assert.assertEquals(expected, actualP, 10e-15);
+ Assert.assertEquals(actualP, 1 - actualQ, 10e-15);
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/TrigammaTest.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/TrigammaTest.java b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/TrigammaTest.java
new file mode 100644
index 0000000..50caf0b
--- /dev/null
+++ b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/TrigammaTest.java
@@ -0,0 +1,59 @@
+/*
+ * 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.numbers.gamma;
+
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * Tests for {@link Trigamma}.
+ */
+public class TrigammaTest {
+ @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], Trigamma.value(data[i]), eps);
+ }
+ }
+
+ @Test
+ public void testTrigammaNonRealArgs() {
+ Assert.assertTrue(Double.isNaN(Trigamma.value(Double.NaN)));
+ Assert.assertTrue(Double.isInfinite(Trigamma.value(Double.POSITIVE_INFINITY)));
+ Assert.assertTrue(Double.isInfinite(Trigamma.value(Double.NEGATIVE_INFINITY)));
+ }
+}
+
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/pom.xml
----------------------------------------------------------------------
diff --git a/pom.xml b/pom.xml
index a54a095..596828b 100644
--- a/pom.xml
+++ b/pom.xml
@@ -563,7 +563,7 @@
<module>commons-numbers-primes</module>
<module>commons-numbers-quaternion</module>
<module>commons-numbers-fraction</module>
- <!-- <module>commons-numbers-continuedfraction</module> -->
+ <module>commons-numbers-gamma</module>
</modules>
</project>
[2/2] commons-numbers git commit: NUMBERS-33: "Gamma" family of
functions (port from "Commons Math").
Posted by er...@apache.org.
NUMBERS-33: "Gamma" family of functions (port from "Commons Math").
Code in module "commons-numbers-gamma" is a refactoring of the utilities
contained in the "o.a.c.math4.special.Gamma" class.
Project: http://git-wip-us.apache.org/repos/asf/commons-numbers/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-numbers/commit/0c9f1cde
Tree: http://git-wip-us.apache.org/repos/asf/commons-numbers/tree/0c9f1cde
Diff: http://git-wip-us.apache.org/repos/asf/commons-numbers/diff/0c9f1cde
Branch: refs/heads/task_NUMBERS-33__Gamma
Commit: 0c9f1cde2f639d537306e8cbe6d8dd54d0374720
Parents: 3540a23
Author: Gilles Sadowski <gi...@harfang.homelinux.org>
Authored: Mon May 8 01:48:52 2017 +0200
Committer: Gilles Sadowski <gi...@harfang.homelinux.org>
Committed: Mon May 8 01:48:52 2017 +0200
----------------------------------------------------------------------
commons-numbers-gamma/LICENSE.txt | 201 +++++++
commons-numbers-gamma/NOTICE.txt | 6 +
commons-numbers-gamma/README.md | 98 ++++
commons-numbers-gamma/pom.xml | 69 +++
.../apache/commons/numbers/gamma/Digamma.java | 90 +++
.../org/apache/commons/numbers/gamma/Gamma.java | 107 ++++
.../commons/numbers/gamma/GammaException.java | 52 ++
.../commons/numbers/gamma/InvGamma1pm1.java | 187 +++++++
.../numbers/gamma/LanczosApproximation.java | 69 +++
.../apache/commons/numbers/gamma/LogGamma.java | 77 +++
.../commons/numbers/gamma/LogGamma1p.java | 47 ++
.../commons/numbers/gamma/RegularizedGamma.java | 214 +++++++
.../apache/commons/numbers/gamma/Trigamma.java | 66 +++
.../commons/numbers/gamma/package-info.java | 39 ++
commons-numbers-gamma/src/site/site.xml | 35 ++
commons-numbers-gamma/src/site/xdoc/index.xml | 40 ++
.../commons/numbers/gamma/DigammaTest.java | 72 +++
.../apache/commons/numbers/gamma/GammaTest.java | 557 +++++++++++++++++++
.../commons/numbers/gamma/InvGamma1pm1Test.java | 91 +++
.../commons/numbers/gamma/LogGamma1pTest.java | 70 +++
.../commons/numbers/gamma/LogGammaTest.java | 232 ++++++++
.../numbers/gamma/RegularizedGammaTest.java | 67 +++
.../commons/numbers/gamma/TrigammaTest.java | 59 ++
pom.xml | 2 +-
24 files changed, 2546 insertions(+), 1 deletion(-)
----------------------------------------------------------------------
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/LICENSE.txt
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/LICENSE.txt b/commons-numbers-gamma/LICENSE.txt
new file mode 100644
index 0000000..261eeb9
--- /dev/null
+++ b/commons-numbers-gamma/LICENSE.txt
@@ -0,0 +1,201 @@
+ Apache License
+ Version 2.0, January 2004
+ http://www.apache.org/licenses/
+
+ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+ 1. Definitions.
+
+ "License" shall mean the terms and conditions for use, reproduction,
+ and distribution as defined by Sections 1 through 9 of this document.
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+ "Licensor" shall mean the copyright owner or entity authorized by
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+ "Work" shall mean the work of authorship, whether in Source or
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+ (an example is provided in the Appendix below).
+
+ "Derivative Works" shall mean any work, whether in Source or Object
+ form, that is based on (or derived from) the Work and for which the
+ editorial revisions, annotations, elaborations, or other modifications
+ represent, as a whole, an original work of authorship. For the purposes
+ of this License, Derivative Works shall not include works that remain
+ separable from, or merely link (or bind by name) to the interfaces of,
+ the Work and Derivative Works thereof.
+
+ "Contribution" shall mean any work of authorship, including
+ the original version of the Work and any modifications or additions
+ to that Work or Derivative Works thereof, that is intentionally
+ submitted to Licensor for inclusion in the Work by the copyright owner
+ or by an individual or Legal Entity authorized to submit on behalf of
+ the copyright owner. For the purposes of this definition, "submitted"
+ means any form of electronic, verbal, or written communication sent
+ to the Licensor or its representatives, including but not limited to
+ communication on electronic mailing lists, source code control systems,
+ and issue tracking systems that are managed by, or on behalf of, the
+ Licensor for the purpose of discussing and improving the Work, but
+ excluding communication that is conspicuously marked or otherwise
+ designated in writing by the copyright owner as "Not a Contribution."
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+ "Contributor" shall mean Licensor and any individual or Legal Entity
+ on behalf of whom a Contribution has been received by Licensor and
+ subsequently incorporated within the Work.
+
+ 2. Grant of Copyright License. Subject to the terms and conditions of
+ this License, each Contributor hereby grants to You a perpetual,
+ worldwide, non-exclusive, no-charge, royalty-free, irrevocable
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+ Work and such Derivative Works in Source or Object form.
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+ 3. Grant of Patent License. Subject to the terms and conditions of
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+ (except as stated in this section) patent license to make, have made,
+ use, offer to sell, sell, import, and otherwise transfer the Work,
+ where such license applies only to those patent claims licensable
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+ Contribution(s) alone or by combination of their Contribution(s)
+ with the Work to which such Contribution(s) was submitted. If You
+ institute patent litigation against any entity (including a
+ cross-claim or counterclaim in a lawsuit) alleging that the Work
+ or a Contribution incorporated within the Work constitutes direct
+ or contributory patent infringement, then any patent licenses
+ granted to You under this License for that Work shall terminate
+ as of the date such litigation is filed.
+
+ 4. Redistribution. You may reproduce and distribute copies of the
+ Work or Derivative Works thereof in any medium, with or without
+ modifications, and in Source or Object form, provided that You
+ meet the following conditions:
+
+ (a) You must give any other recipients of the Work or
+ Derivative Works a copy of this License; and
+
+ (b) You must cause any modified files to carry prominent notices
+ stating that You changed the files; and
+
+ (c) You must retain, in the Source form of any Derivative Works
+ that You distribute, all copyright, patent, trademark, and
+ attribution notices from the Source form of the Work,
+ excluding those notices that do not pertain to any part of
+ the Derivative Works; and
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+ (d) If the Work includes a "NOTICE" text file as part of its
+ distribution, then any Derivative Works that You distribute must
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+ wherever such third-party notices normally appear. The contents
+ of the NOTICE file are for informational purposes only and
+ do not modify the License. You may add Your own attribution
+ notices within Derivative Works that You distribute, alongside
+ or as an addendum to the NOTICE text from the Work, provided
+ that such additional attribution notices cannot be construed
+ as modifying the License.
+
+ You may add Your own copyright statement to Your modifications and
+ may provide additional or different license terms and conditions
+ for use, reproduction, or distribution of Your modifications, or
+ for any such Derivative Works as a whole, provided Your use,
+ reproduction, and distribution of the Work otherwise complies with
+ the conditions stated in this License.
+
+ 5. Submission of Contributions. Unless You explicitly state otherwise,
+ any Contribution intentionally submitted for inclusion in the Work
+ by You to the Licensor shall be under the terms and conditions of
+ this License, without any additional terms or conditions.
+ Notwithstanding the above, nothing herein shall supersede or modify
+ the terms of any separate license agreement you may have executed
+ with Licensor regarding such Contributions.
+
+ 6. Trademarks. This License does not grant permission to use the trade
+ names, trademarks, service marks, or product names of the Licensor,
+ except as required for reasonable and customary use in describing the
+ origin of the Work and reproducing the content of the NOTICE file.
+
+ 7. Disclaimer of Warranty. Unless required by applicable law or
+ agreed to in writing, Licensor provides the Work (and each
+ Contributor provides its Contributions) on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+ implied, including, without limitation, any warranties or conditions
+ of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+ PARTICULAR PURPOSE. You are solely responsible for determining the
+ appropriateness of using or redistributing the Work and assume any
+ risks associated with Your exercise of permissions under this License.
+
+ 8. Limitation of Liability. In no event and under no legal theory,
+ whether in tort (including negligence), contract, or otherwise,
+ unless required by applicable law (such as deliberate and grossly
+ negligent acts) or agreed to in writing, shall any Contributor be
+ liable to You for damages, including any direct, indirect, special,
+ incidental, or consequential damages of any character arising as a
+ result of this License or out of the use or inability to use the
+ Work (including but not limited to damages for loss of goodwill,
+ work stoppage, computer failure or malfunction, or any and all
+ other commercial damages or losses), even if such Contributor
+ has been advised of the possibility of such damages.
+
+ 9. Accepting Warranty or Additional Liability. While redistributing
+ the Work or Derivative Works thereof, You may choose to offer,
+ and charge a fee for, acceptance of support, warranty, indemnity,
+ or other liability obligations and/or rights consistent with this
+ License. However, in accepting such obligations, You may act only
+ on Your own behalf and on Your sole responsibility, not on behalf
+ of any other Contributor, and only if You agree to indemnify,
+ defend, and hold each Contributor harmless for any liability
+ incurred by, or claims asserted against, such Contributor by reason
+ of your accepting any such warranty or additional liability.
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+ END OF TERMS AND CONDITIONS
+
+ APPENDIX: How to apply the Apache License to your work.
+
+ To apply the Apache License to your work, attach the following
+ boilerplate notice, with the fields enclosed by brackets "[]"
+ replaced with your own identifying information. (Don't include
+ the brackets!) The text should be enclosed in the appropriate
+ comment syntax for the file format. We also recommend that a
+ file or class name and description of purpose be included on the
+ same "printed page" as the copyright notice for easier
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+ Copyright [yyyy] [name of copyright owner]
+
+ 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
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+ 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.
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/NOTICE.txt
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/NOTICE.txt b/commons-numbers-gamma/NOTICE.txt
new file mode 100644
index 0000000..9091baa
--- /dev/null
+++ b/commons-numbers-gamma/NOTICE.txt
@@ -0,0 +1,6 @@
+Apache Commons Numbers
+Copyright 2001-2017 The Apache Software Foundation
+
+This product includes software developed at
+The Apache Software Foundation (http://www.apache.org/).
+
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/README.md
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/README.md b/commons-numbers-gamma/README.md
new file mode 100644
index 0000000..0701bed
--- /dev/null
+++ b/commons-numbers-gamma/README.md
@@ -0,0 +1,98 @@
+<!---
+ 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.
+-->
+<!---
+ +======================================================================+
+ |**** ****|
+ |**** THIS FILE IS GENERATED BY THE COMMONS BUILD PLUGIN ****|
+ |**** DO NOT EDIT DIRECTLY ****|
+ |**** ****|
+ +======================================================================+
+ | TEMPLATE FILE: readme-md-template.md |
+ | commons-build-plugin/trunk/src/main/resources/commons-xdoc-templates |
+ +======================================================================+
+ | |
+ | 1) Re-generate using: mvn commons:readme-md |
+ | |
+ | 2) Set the following properties in the component's pom: |
+ | - commons.componentid (required, alphabetic, lower case) |
+ | - commons.release.version (required) |
+ | |
+ | 3) Example Properties |
+ | |
+ | <properties> |
+ | <commons.componentid>math</commons.componentid> |
+ | <commons.release.version>1.2</commons.release.version> |
+ | </properties> |
+ | |
+ +======================================================================+
+--->
+Apache Commons Numbers Core
+===================
+
+Basic utilities.
+
+Documentation
+-------------
+
+More information can be found on the [homepage](https://commons.apache.org/proper/commons-numbers).
+The [JavaDoc](https://commons.apache.org/proper/commons-numbers/javadocs/api-release) can be browsed.
+Questions related to the usage of Apache Commons Numbers Core should be posted to the [user mailing list][ml].
+
+Where can I get the latest release?
+-----------------------------------
+You can download source and binaries from our [download page](https://commons.apache.org/proper/commons-numbers/download_numbers.cgi).
+
+Alternatively you can pull it from the central Maven repositories:
+
+```xml
+<dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-core</artifactId>
+ <version>1.0</version>
+</dependency>
+```
+
+Contributing
+------------
+
+We accept PRs via github. The [developer mailing list][ml] is the main channel of communication for contributors.
+There are some guidelines which will make applying PRs easier for us:
++ No tabs! Please use spaces for indentation.
++ Respect the code style.
++ Create minimal diffs - disable on save actions like reformat source code or organize imports. If you feel the source code should be reformatted create a separate PR for this change.
++ Provide JUnit tests for your changes and make sure your changes don't break any existing tests by running ```mvn clean test```.
+
+If you plan to contribute on a regular basis, please consider filing a [contributor license agreement](https://www.apache.org/licenses/#clas).
+You can learn more about contributing via GitHub in our [contribution guidelines](CONTRIBUTING.md).
+
+License
+-------
+Code is under the [Apache Licence v2](https://www.apache.org/licenses/LICENSE-2.0.txt).
+
+Donations
+---------
+You like Apache Commons Numbers Core? Then [donate back to the ASF](https://www.apache.org/foundation/contributing.html) to support the development.
+
+Additional Resources
+--------------------
+
++ [Apache Commons Homepage](https://commons.apache.org/)
++ [Apache Bugtracker (JIRA)](https://issues.apache.org/jira/)
++ [Apache Commons Twitter Account](https://twitter.com/ApacheCommons)
++ #apachecommons IRC channel on freenode.org
+
+[ml]:https://commons.apache.org/mail-lists.html
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/pom.xml
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/pom.xml b/commons-numbers-gamma/pom.xml
new file mode 100644
index 0000000..af530fe
--- /dev/null
+++ b/commons-numbers-gamma/pom.xml
@@ -0,0 +1,69 @@
+<?xml version="1.0"?>
+<!--
+ 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.
+-->
+<project xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd"
+ xmlns="http://maven.apache.org/POM/4.0.0"
+ xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
+ <modelVersion>4.0.0</modelVersion>
+
+ <parent>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-parent</artifactId>
+ <version>1.0-SNAPSHOT</version>
+ </parent>
+
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-gamma</artifactId>
+ <version>1.0-SNAPSHOT</version>
+ <name>Apache Commons Numbers Gamma</name>
+
+ <description>Gamma family of functions.</description>
+
+ <properties>
+ <!-- This value must reflect the current name of the base package. -->
+ <commons.osgi.symbolicName>org.apache.commons.numbers.gamma</commons.osgi.symbolicName>
+ <!-- OSGi -->
+ <commons.osgi.export>org.apache.commons.numbers.gamma</commons.osgi.export>
+ <!-- Workaround to avoid duplicating config files. -->
+ <numbers.parent.dir>${basedir}/..</numbers.parent.dir>
+ </properties>
+
+ <build>
+ <plugins>
+ <plugin>
+ <groupId>org.apache.maven.plugins</groupId>
+ <artifactId>maven-jar-plugin</artifactId>
+ <executions>
+ <execution>
+ <goals>
+ <goal>test-jar</goal>
+ </goals>
+ </execution>
+ </executions>
+ </plugin>
+ </plugins>
+ </build>
+
+ <dependencies>
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-fraction</artifactId>
+ <version>1.0-SNAPSHOT</version>
+ </dependency>
+ </dependencies>
+
+</project>
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Digamma.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Digamma.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Digamma.java
new file mode 100644
index 0000000..8b096d5
--- /dev/null
+++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Digamma.java
@@ -0,0 +1,90 @@
+/*
+ * 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.numbers.gamma;
+
+/**
+ * <a href="http://en.wikipedia.org/wiki/Digamma_function">Digamma function</a>.
+ *
+ * It is defined as the logarithmic derivative of the \( \Gamma \) function:
+ * \( \frac{d}{dx}(\ln \Gamma(x)) = \frac{\Gamma^\prime(x)}{\Gamma(x)} \).
+ */
+public class Digamma {
+ /** <a href="http://en.wikipedia.org/wiki/Euler-Mascheroni_constant">Euler-Mascheroni constant</a>. */
+ private static final double GAMMA = 0.577215664901532860606512090082;
+ /** C limit. */
+ private static final double C_LIMIT = 49;
+ /** S limit. */
+ private static final double S_LIMIT = 1e-5;
+ /** Fraction. */
+ private static final double F_1_12 = 1d / 12;
+ /** Fraction. */
+ private static final double F_1_120 = 1d / 120;
+ /** Fraction. */
+ private static final double F_1_252 = 1d / 252;
+
+ /** Class only contains a static method. */
+ private Digamma() {}
+
+ /**
+ * Computes the digamma function.
+ *
+ * This is an independently written implementation of the algorithm described in
+ * <a href="http://www.uv.es/~bernardo/1976AppStatist.pdf">Jose Bernardo,
+ * Algorithm AS 103: Psi (Digamma) Function, Applied Statistics, 1976</a>.
+ * A <a href="https://en.wikipedia.org/wiki/Digamma_function#Reflection_formula">
+ * reflection formula</a> is incorporated to improve performance on negative values.
+ *
+ * Some of the constants have been changed to increase accuracy at the moderate
+ * expense of run-time. The result should be accurate to within \( 10^{-8} \)
+ * relative tolerance for \( 0 < x < 10^{-5} \) and within \( 10^{-8} \) absolute
+ * tolerance otherwise.
+ *
+ * @param x Argument.
+ * @return digamma(x) to within \( 10^{-8} \) relative or absolute error whichever is larger.
+ */
+ public static double value(double x) {
+ if (Double.isNaN(x) || Double.isInfinite(x)) {
+ return x;
+ }
+
+ double digamma = 0;
+ if (x < 0) {
+ // Use reflection formula to fall back into positive values.
+ digamma -= Math.PI / Math.tan(Math.PI * x);
+ x = 1 - x;
+ }
+
+ if (x > 0 && x <= S_LIMIT) {
+ // Use method 5 from Bernardo AS103, accurate to O(x).
+ return digamma - GAMMA - 1 / x;
+ }
+
+ while (x < C_LIMIT) {
+ digamma -= 1 / x;
+ x += 1;
+ }
+
+ // Use method 4, accurate to O(1/x^8)
+ final double inv = 1 / (x * x);
+ // 1 1 1 1
+ // log(x) - --- - ------ + ------- - -------
+ // 2 x 12 x^2 120 x^4 252 x^6
+ digamma += Math.log(x) - 0.5 / x - inv * (F_1_12 + inv * (F_1_120 - F_1_252 * inv));
+
+ return digamma;
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Gamma.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Gamma.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Gamma.java
new file mode 100644
index 0000000..797c93a
--- /dev/null
+++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Gamma.java
@@ -0,0 +1,107 @@
+/*
+ * 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.numbers.gamma;
+
+
+/**
+ * <a href="http://mathworld.wolfram.com/GammaFunction.html">Gamma function</a>.
+ *
+ * Class is immutable.
+ */
+public class Gamma {
+ /** \( g = \frac{607}{128} \). */
+ private static final double LANCZOS_G = 607d / 128d;
+ /** Helper. */
+ private static final LanczosApproximation LANCZOS_APPROXIMATION = LanczosApproximation.instance;
+ /** Helper. */
+ private static final InvGamma1pm1 INV_GAMMA_1P_M1 = InvGamma1pm1.instance;
+ /** √(2π). */
+ private static final double SQRT_TWO_PI = 2.506628274631000502;
+
+ /**
+ * Computes the value of \( \Gamma(x) \).
+ *
+ * Based on the <em>NSWC Library of Mathematics Subroutines</em> double
+ * precision implementation, {@code DGAMMA}.
+ *
+ * @param x Argument.
+ * @return \( \Gamma(x) \)
+ */
+ public double value(final double x) {
+
+ if ((x == Math.rint(x)) && (x <= 0.0)) {
+ return Double.NaN;
+ }
+
+ final double ret;
+ final double absX = Math.abs(x);
+ if (absX <= 20) {
+ if (x >= 1) {
+ /*
+ * From the recurrence relation
+ * Gamma(x) = (x - 1) * ... * (x - n) * Gamma(x - n),
+ * then
+ * Gamma(t) = 1 / [1 + InvGamma1pm1.value(t - 1)],
+ * where t = x - n. This means that t must satisfy
+ * -0.5 <= t - 1 <= 1.5.
+ */
+ double prod = 1;
+ double t = x;
+ while (t > 2.5) {
+ t -= 1;
+ prod *= t;
+ }
+ ret = prod / (1 + INV_GAMMA_1P_M1.value(t - 1));
+ } else {
+ /*
+ * From the recurrence relation
+ * Gamma(x) = Gamma(x + n + 1) / [x * (x + 1) * ... * (x + n)]
+ * then
+ * Gamma(x + n + 1) = 1 / [1 + InvGamma1pm1.value(x + n)],
+ * which requires -0.5 <= x + n <= 1.5.
+ */
+ double prod = x;
+ double t = x;
+ while (t < -0.5) {
+ t += 1;
+ prod *= t;
+ }
+ ret = 1 / (prod * (1 + INV_GAMMA_1P_M1.value(t)));
+ }
+ } else {
+ final double y = absX + LANCZOS_G + 0.5;
+ final double gammaAbs = SQRT_TWO_PI / absX *
+ Math.pow(y, absX + 0.5) *
+ Math.exp(-y) * LANCZOS_APPROXIMATION.value(absX);
+ if (x > 0) {
+ ret = gammaAbs;
+ } else {
+ /*
+ * From the reflection formula
+ * Gamma(x) * Gamma(1 - x) * sin(pi * x) = pi,
+ * and the recurrence relation
+ * Gamma(1 - x) = -x * Gamma(-x),
+ * it is found
+ * Gamma(x) = -pi / [x * sin(pi * x) * Gamma(-x)].
+ */
+ ret = -Math.PI / (x * Math.sin(Math.PI * x) * gammaAbs);
+ }
+ }
+
+ return ret;
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/GammaException.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/GammaException.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/GammaException.java
new file mode 100644
index 0000000..7122f2e
--- /dev/null
+++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/GammaException.java
@@ -0,0 +1,52 @@
+/*
+ * 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.numbers.gamma;
+
+import java.text.MessageFormat;
+
+/**
+ * Package private exception class with constants for frequently used messages.
+ */
+class GammaException extends IllegalArgumentException {
+ /** Error message for "out of range" condition. */
+ static final String OUT_OF_RANGE = "Number {0} is out of range [{1}, {2}]";
+ /** Error message for convergence failure. */
+ static final String CONVERGENCE = "Failed to converge within {0} iterations";
+
+ /** Serializable version identifier. */
+ private static final long serialVersionUID = 20170505L;
+
+ /** Arguments for formatting the message. */
+ protected Object[] formatArguments;
+
+ /**
+ * Create an exception where the message is constructed by applying
+ * the {@code format()} method from {@code java.text.MessageFormat}.
+ *
+ * @param message the exception message with replaceable parameters
+ * @param formatArguments the arguments for formatting the message
+ */
+ GammaException(String message, Object... formatArguments) {
+ super(message);
+ this.formatArguments = formatArguments;
+ }
+
+ @Override
+ public String getMessage() {
+ return MessageFormat.format(super.getMessage(), formatArguments);
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/InvGamma1pm1.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/InvGamma1pm1.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/InvGamma1pm1.java
new file mode 100644
index 0000000..77203a0
--- /dev/null
+++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/InvGamma1pm1.java
@@ -0,0 +1,187 @@
+/*
+ * 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.numbers.gamma;
+
+/**
+ * Function \( \frac{1}{\Gamma(1 + x)} - 1 \).
+ *
+ * Class is immutable.
+ */
+class InvGamma1pm1 {
+ /** Singleton. */
+ static final InvGamma1pm1 instance = new 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;
+
+ /**
+ * Computes the function \( \frac{1}{\Gamma(1 + x)} - 1 \) for \( -0.5 \leq x \leq 1.5 \).
+ *
+ * This implementation is based on the double precision implementation in
+ * the <em>NSWC Library of Mathematics Subroutines</em>, {@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 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;
+ }
+ }
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LanczosApproximation.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LanczosApproximation.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LanczosApproximation.java
new file mode 100644
index 0000000..e21bc54
--- /dev/null
+++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LanczosApproximation.java
@@ -0,0 +1,69 @@
+/*
+ * 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.numbers.gamma;
+
+/**
+ * <a href="http://mathworld.wolfram.com/LanczosApproximation.html">
+ * Lanczos approximation</a> to the Gamma function.
+ *
+ * It is related to the Gamma function by the following equation
+ * \[
+ * \Gamma(x) = \sqrt{2\pi} \, \frac{(g + x + \frac{1}{2})^{x + \frac{1}{2}} \, e^{-(g + x + \frac{1}{2})} \, \mathrm{lanczos}(x)}
+ * {x}
+ * \]
+ * where \(g\) is the Lanczos constant.
+ *
+ * @see equations (1) through (5), and Paul Godfrey's
+ * <a href="http://my.fit.edu/~gabdo/gamma.txt">Note on the computation
+ * of the convergent Lanczos complex Gamma approximation</a>.
+ */
+class LanczosApproximation {
+ /** Singleton. */
+ static final LanczosApproximation instance = new LanczosApproximation();
+ /** Lanczos coefficients. */
+ private static final double[] LANCZOS = {
+ 0.99999999999999709182,
+ 57.156235665862923517,
+ -59.597960355475491248,
+ 14.136097974741747174,
+ -0.49191381609762019978,
+ .33994649984811888699e-4,
+ .46523628927048575665e-4,
+ -.98374475304879564677e-4,
+ .15808870322491248884e-3,
+ -.21026444172410488319e-3,
+ .21743961811521264320e-3,
+ -.16431810653676389022e-3,
+ .84418223983852743293e-4,
+ -.26190838401581408670e-4,
+ .36899182659531622704e-5,
+ };
+
+ /**
+ * Computes the Lanczos approximation.
+ *
+ * @param x Argument.
+ * @return the Lanczos approximation.
+ */
+ public double value(final double x) {
+ double sum = 0;
+ for (int i = LANCZOS.length - 1; i > 0; i--) {
+ sum += LANCZOS[i] / (x + i);
+ }
+ return sum + LANCZOS[0];
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LogGamma.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LogGamma.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LogGamma.java
new file mode 100644
index 0000000..57146a2
--- /dev/null
+++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LogGamma.java
@@ -0,0 +1,77 @@
+/*
+ * 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.numbers.gamma;
+
+/**
+ * Function \( \ln \Gamma(x) \).
+ *
+ * Class is immutable.
+ */
+public class LogGamma {
+ /** Singleton. */
+ static final LogGamma instance = new LogGamma();
+ /** \( g = \frac{607}{128} \). */
+ private static final double LANCZOS_G = 607d / 128d;
+ /** Performance. */
+ private static final double HALF_LOG_2_PI = 0.5 * Math.log(2.0 * Math.PI);
+ /** Helper. */
+ private static final LanczosApproximation LANCZOS_APPROXIMATION = LanczosApproximation.instance;
+ /** Helper. */
+ private static final LogGamma1p LOG_GAMMA_1P = LogGamma1p.instance;
+
+ /**
+ * Computes the function \( \ln \Gamma(x) \) for \( x > 0 \).
+ *
+ * For \( x \leq 8 \), the implementation is based on the double precision
+ * implementation in the <em>NSWC Library of Mathematics Subroutines</em>,
+ * {@code DGAMLN}. For \( x \geq 8 \), the implementation is based on
+ *
+ * <ul>
+ * <li><a href="http://mathworld.wolfram.com/GammaFunction.html">Gamma
+ * Function</a>, equation (28).</li>
+ * <li><a href="http://mathworld.wolfram.com/LanczosApproximation.html">
+ * Lanczos Approximation</a>, equations (1) through (5).</li>
+ * <li><a href="http://my.fit.edu/~gabdo/gamma.txt">Paul Godfrey, A note on
+ * the computation of the convergent Lanczos complex Gamma
+ * approximation</a></li>
+ * </ul>
+ *
+ * @param x Argument.
+ * @return \( \ln \Gamma(x) \), or {@code NaN} if {@code x <= 0}.
+ */
+ public double value(double x) {
+ if (Double.isNaN(x) || (x <= 0.0)) {
+ return Double.NaN;
+ } else if (x < 0.5) {
+ return LOG_GAMMA_1P.value(x) - Math.log(x);
+ } else if (x <= 2.5) {
+ return LOG_GAMMA_1P.value((x - 0.5) - 0.5);
+ } else if (x <= 8.0) {
+ final int n = (int) Math.floor(x - 1.5);
+ double prod = 1.0;
+ for (int i = 1; i <= n; i++) {
+ prod *= x - i;
+ }
+ return LOG_GAMMA_1P.value(x - (n + 1)) + Math.log(prod);
+ } else {
+ final double sum = LANCZOS_APPROXIMATION.value(x);
+ final double tmp = x + LANCZOS_G + .5;
+ return ((x + .5) * Math.log(tmp)) - tmp +
+ HALF_LOG_2_PI + Math.log(sum / x);
+ }
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LogGamma1p.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LogGamma1p.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LogGamma1p.java
new file mode 100644
index 0000000..2f26fcc
--- /dev/null
+++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/LogGamma1p.java
@@ -0,0 +1,47 @@
+/*
+ * 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.numbers.gamma;
+
+/**
+ * Function \( \ln \Gamma(1 + x) \).
+ *
+ * Class is immutable.
+ */
+class LogGamma1p {
+ /** Singleton. */
+ static final LogGamma1p instance = new LogGamma1p();
+ /** Helper. */
+ private static final InvGamma1pm1 invGamma1pm1 = InvGamma1pm1.instance;
+
+ /**
+ * Computes the function \( \ln \Gamma(1 + x) \) for \( -0.5 \leq x \leq 1.5 \).
+ *
+ * This implementation is based on the double precision implementation in
+ * the <em>NSWC Library of Mathematics Subroutines</em>, {@code DGMLN1}.
+ *
+ * @param x Argument.
+ * @return \( \ln \Gamma(1 + x) \)
+ * @throws IllegalArgumentException if {@code x < -0.5} or {@code x > 1.5}.
+ */
+ public double value(final double x) {
+ if (x < -0.5 || x > 1.5) {
+ throw new GammaException(GammaException.OUT_OF_RANGE, x, -0.5, 1.5);
+ }
+
+ return -Math.log1p(invGamma1pm1.value(x));
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/RegularizedGamma.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/RegularizedGamma.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/RegularizedGamma.java
new file mode 100644
index 0000000..7f39690
--- /dev/null
+++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/RegularizedGamma.java
@@ -0,0 +1,214 @@
+/*
+ * 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.numbers.gamma;
+
+import org.apache.commons.numbers.fraction.ContinuedFraction;
+
+/**
+ * <a href="http://mathworld.wolfram.com/RegularizedGammaFunction.html">
+ * Regularized Gamma functions</a>.
+ *
+ * Class is immutable.
+ */
+public abstract class RegularizedGamma {
+ /** Helper. */
+ private static final LogGamma LOG_GAMMA = LogGamma.instance;
+ /** Maximum allowed numerical error. */
+ private static final double DEFAULT_EPSILON = 10e-15; // XXX
+
+ /**
+ * @param a Parameter.
+ * @param x Argument.
+ * @param epsilon When the absolute value of the n-th element in the
+ * series is less than epsilon the approximation ceases to calculate
+ * further elements in the series.
+ * @param maxIterations Maximum number of iterations.
+ * @return the value of the function.
+ * @throws IllegalArgumentException if the algorithm fails to converge.
+ */
+ public abstract double value(double a,
+ double x,
+ double epsilon,
+ int maxIterations);
+
+ /**
+ * @param a Parameter.
+ * @param x Argument.
+ * @return the value of the function.
+ * @throws IllegalArgumentException if the algorithm fails to converge.
+ */
+ public abstract double value(double a,
+ double x);
+
+ /**
+ * \( P(a, x) \) <a href="http://mathworld.wolfram.com/RegularizedGammaFunction.html">
+ * regularized Gamma function</a>.
+ *
+ * Class is immutable.
+ */
+ public static class P {
+ /**
+ * Computes the regularized gamma function \( P(a, x) \).
+ *
+ * {@inheritDoc}
+ */
+ public double value(double a,
+ double x) {
+ return value(a, x, DEFAULT_EPSILON, Integer.MAX_VALUE);
+ }
+
+ /**
+ * Computes the regularized gamma function \( P(a, x) \).
+ *
+ * The implementation of this method is based on:
+ * <ul>
+ * <li>
+ * <a href="http://mathworld.wolfram.com/RegularizedGammaFunction.html">
+ * Regularized Gamma Function</a>, equation (1)
+ * </li>
+ * <li>
+ * <a href="http://mathworld.wolfram.com/IncompleteGammaFunction.html">
+ * Incomplete Gamma Function</a>, equation (4).
+ * </li>
+ * <li>
+ * <a href="http://mathworld.wolfram.com/ConfluentHypergeometricFunctionoftheFirstKind.html">
+ * Confluent Hypergeometric Function of the First Kind</a>, equation (1).
+ * </li>
+ * </ul>
+ *
+ * {@inheritDoc}
+ */
+ public double value(double a,
+ double x,
+ double epsilon,
+ int maxIterations) {
+ double ret;
+
+ if (Double.isNaN(a) ||
+ Double.isNaN(x) ||
+ a <= 0 ||
+ x < 0) {
+ ret = Double.NaN;
+ } else if (x == 0) {
+ ret = 0;
+ } else if (x >= a + 1) {
+ // Q should converge faster in this case.
+ final RegularizedGamma.Q q = new RegularizedGamma.Q();
+ ret = 1 - q.value(a, x, epsilon, maxIterations);
+ } else {
+ // Series.
+ double n = 0; // current element index
+ double an = 1 / a; // n-th element in the series
+ double sum = an; // partial sum
+ while (Math.abs(an / sum) > epsilon &&
+ n < maxIterations &&
+ sum < Double.POSITIVE_INFINITY) {
+ // compute next element in the series
+ n += 1;
+ an *= x / (a + n);
+
+ // update partial sum
+ sum += an;
+ }
+ if (n >= maxIterations) {
+ throw new GammaException(GammaException.CONVERGENCE, maxIterations);
+ } else if (Double.isInfinite(sum)) {
+ ret = 1;
+ } else {
+ ret = Math.exp(-x + (a * Math.log(x)) - LOG_GAMMA.value(a)) * sum;
+ }
+ }
+
+ return ret;
+ }
+ }
+
+ /**
+ * Creates the \( Q(a, x) \equiv 1 - P(a, x) \) \) <a href="http://mathworld.wolfram.com/RegularizedGammaFunction.html">
+ * regularized Gamma function</a>.
+ *
+ * Class is immutable.
+ */
+ public static class Q {
+ /**
+ * Computes the regularized gamma function \( Q(a, x) = 1 - P(a, x) \).
+ *
+ * {@inheritDoc}
+ */
+ public double value(double a,
+ double x) {
+ return value(a, x, DEFAULT_EPSILON, Integer.MAX_VALUE);
+ }
+
+ /**
+ * Computes the regularized gamma function \( Q(a, x) = 1 - P(a, x) \).
+ *
+ * The implementation of this method is based on:
+ * <ul>
+ * <li>
+ * <a href="http://mathworld.wolfram.com/RegularizedGammaFunction.html">
+ * Regularized Gamma Function</a>, equation (1).
+ * </li>
+ * <li>
+ * <a href="http://functions.wolfram.com/GammaBetaErf/GammaRegularized/10/0003/">
+ * Regularized incomplete gamma function: Continued fraction representations
+ * (formula 06.08.10.0003)</a>
+ * </li>
+ * </ul>
+ *
+ * {@inheritDoc}
+ */
+ public double value(final double a,
+ double x,
+ double epsilon,
+ int maxIterations) {
+ double ret;
+
+ if (Double.isNaN(a) ||
+ Double.isNaN(x) ||
+ a <= 0 ||
+ x < 0) {
+ ret = Double.NaN;
+ } else if (x == 0) {
+ ret = 1;
+ } else if (x < a + 1) {
+ // P should converge faster in this case.
+ final RegularizedGamma.P p = new RegularizedGamma.P();
+ ret = 1 - p.value(a, x, epsilon, maxIterations);
+ } else {
+ final ContinuedFraction cf = new ContinuedFraction() {
+ /** {@inheritDoc} */
+ @Override
+ protected double getA(int n, double x) {
+ return ((2 * n) + 1) - a + x;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ protected double getB(int n, double x) {
+ return n * (a - n);
+ }
+ };
+
+ ret = 1 / cf.evaluate(x, epsilon, maxIterations);
+ ret = Math.exp(-x + (a * Math.log(x)) - LOG_GAMMA.value(a)) * ret;
+ }
+
+ return ret;
+ }
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Trigamma.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Trigamma.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Trigamma.java
new file mode 100644
index 0000000..9e45601
--- /dev/null
+++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Trigamma.java
@@ -0,0 +1,66 @@
+/*
+ * 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.numbers.gamma;
+
+/**
+ * <a href="http://en.wikipedia.org/wiki/Trigamma_function">Trigamma function</a>.
+ *
+ * It is the derivative of the {@link Digamma digamma function}:
+ * \( \psi_1(x) = \frac{d^2}{dx^2} (\ln \Gamma(x)) \).
+ */
+public class Trigamma {
+ /** C limit. */
+ private static final double C_LIMIT = 49;
+ /** S limit. */
+ private static final double S_LIMIT = 1e-5;
+ /** Fraction. */
+ private static final double F_1_6 = 1d / 6;
+ /** Fraction. */
+ private static final double F_1_30 = 1d / 30;
+ /** Fraction. */
+ private static final double F_1_42 = 1d / 42;
+
+ /** Class only contains a static method. */
+ private Trigamma() {}
+
+ /**
+ * Computes the trigamma function.
+ *
+ * @param x Argument.
+ * @return trigamma(x) to within \( 10^{-8} \) relative or absolute error whichever is larger.
+ */
+ public static double value(double x) {
+ if (Double.isNaN(x) || Double.isInfinite(x)) {
+ return x;
+ }
+
+ if (x > 0 && x <= S_LIMIT) {
+ return 1 / (x * x);
+ }
+
+ if (x >= C_LIMIT) {
+ final double inv = 1 / (x * x);
+ // 1 1 1 1 1
+ // - + ---- + ---- - ----- + -----
+ // x 2 3 5 7
+ // 2 x 6 x 30 x 42 x
+ return 1 / x + inv / 2 + inv / x * (F_1_6 - inv * (F_1_30 + F_1_42 * inv));
+ }
+
+ return value(x + 1) + 1 / (x * x);
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/package-info.java
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/package-info.java b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/package-info.java
new file mode 100644
index 0000000..b44caa1
--- /dev/null
+++ b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/package-info.java
@@ -0,0 +1,39 @@
+/*
+ * 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.
+ */
+
+/**
+ * Γ (Gamma) family of functions.
+ *
+ * Implementation of {@link org.apache.commons.numbers.gamma.InvGamma1pm1 InvGamma1pm1}
+ * and {@link org.apache.commons.numbers.gamma.LogGamma1p LogGamma1p} is based on the
+ * algorithms described in
+ * <ul>
+ * <li>
+ * <a href="http://dx.doi.org/10.1145/22721.23109">Didonato and Morris (1986)</a>,
+ * <em>Computation of the Incomplete Gamma Function Ratios and their Inverse</em>,
+ * TOMS 12(4), 377-393,
+ * </li>
+ * <li>
+ * <a href="http://dx.doi.org/10.1145/131766.131776">Didonato and Morris (1992)</a>,
+ * <em>Algorithm 708: Significant Digit Computation of the Incomplete Beta Function
+ * Ratios</em>, TOMS 18(3), 360-373,
+ * </li>
+ * </ul>
+ * and implemented in the
+ * <a href="http://www.dtic.mil/docs/citations/ADA476840">NSWC Library of Mathematical Functions</a>.
+ */
+package org.apache.commons.numbers.gamma;
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/site/site.xml
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/site/site.xml b/commons-numbers-gamma/src/site/site.xml
new file mode 100644
index 0000000..ba0a795
--- /dev/null
+++ b/commons-numbers-gamma/src/site/site.xml
@@ -0,0 +1,35 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<!--
+ 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.
+-->
+<project name="Numbers">
+ <bannerRight>
+ <name>Apache Commons Numbers</name>
+ <src>/images/commons_numbers.small.png</src>
+ <href>/index.html</href>
+ </bannerRight>
+
+ <body>
+ <menu name="Numbers Gamma">
+ <item name="Overview" href="index.html"/>
+ <item name="Latest API docs (development)"
+ href="apidocs/index.html"/>
+ <!--item name="Javadoc (1.0 release)"
+ href="http://commons.apache.org/rng/commons-numbers-gamma/javadocs/api-1.0/index.html"/-->
+ </menu>
+
+ </body>
+</project>
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/site/xdoc/index.xml
----------------------------------------------------------------------
diff --git a/commons-numbers-gamma/src/site/xdoc/index.xml b/commons-numbers-gamma/src/site/xdoc/index.xml
new file mode 100644
index 0000000..29bb57f
--- /dev/null
+++ b/commons-numbers-gamma/src/site/xdoc/index.xml
@@ -0,0 +1,40 @@
+<?xml version="1.0"?>
+
+<!--
+ 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.
+ -->
+
+<document>
+
+ <properties>
+ <title>Commons Numbers Core</title>
+ </properties>
+
+ <body>
+
+ <section name="Apache Commons Numbers: Number types" href="summary">
+ <p>
+ Commons Numbers provides utilities such as complex numbers and fractions.
+ </p>
+
+ <p>
+ The "gamma" module contains utilities related to the "Gamma" function.
+ </p>
+ </section>
+
+ </body>
+
+</document>
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/0c9f1cde/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/DigammaTest.java
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diff --git a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/DigammaTest.java b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/DigammaTest.java
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@@ -0,0 +1,72 @@
+/*
+ * 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.numbers.gamma;
+
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * Tests for {@link Digamma}.
+ */
+public class DigammaTest {
+ @Test
+ public void testDigammaLargeArgs() {
+ double eps = 1e-8;
+ Assert.assertEquals(4.6001618527380874002, Digamma.value(100), eps);
+ Assert.assertEquals(3.9019896734278921970, Digamma.value(50), eps);
+ Assert.assertEquals(2.9705239922421490509, Digamma.value(20), eps);
+ Assert.assertEquals(2.9958363947076465821, Digamma.value(20.5), eps);
+ Assert.assertEquals(2.2622143570941481605, Digamma.value(10.1), eps);
+ Assert.assertEquals(2.1168588189004379233, Digamma.value(8.8), eps);
+ Assert.assertEquals(1.8727843350984671394, Digamma.value(7), eps);
+ Assert.assertEquals(0.42278433509846713939, Digamma.value(2), eps);
+ Assert.assertEquals(-100.56088545786867450, Digamma.value(0.01), eps);
+ Assert.assertEquals(-4.0390398965921882955, Digamma.value(-0.8), eps);
+ Assert.assertEquals(4.2003210041401844726, Digamma.value(-6.3), eps);
+ Assert.assertEquals(-3.110625123035E-5, Digamma.value(1.4616), 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)], Digamma.value(Math.pow(10.0, -n)), 1e-8);
+ }
+ }
+
+ @Test
+ public void testDigammaNonRealArgs() {
+ Assert.assertTrue(Double.isNaN(Digamma.value(Double.NaN)));
+ Assert.assertTrue(Double.isInfinite(Digamma.value(Double.POSITIVE_INFINITY)));
+ Assert.assertTrue(Double.isInfinite(Digamma.value(Double.NEGATIVE_INFINITY)));
+ }
+
+ private void checkRelativeError(String msg,
+ double expected,
+ double actual,
+ double tolerance) {
+ Assert.assertEquals(msg, expected, actual, Math.abs(tolerance * actual));
+ }
+}
+