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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      https://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  
18  /*
19   * This is not the original file distributed by the Apache Software Foundation
20   * It has been modified by the Hipparchus project
21   */
22  package org.hipparchus.special;
23  
24  import org.hipparchus.UnitTestUtils;
25  import org.hipparchus.exception.MathIllegalArgumentException;
26  import org.hipparchus.util.FastMath;
27  import org.junit.jupiter.api.Test;
28  
29  import java.lang.reflect.InvocationTargetException;
30  import java.lang.reflect.Method;
31  import java.util.concurrent.atomic.AtomicReference;
32  
33  import static org.junit.jupiter.api.Assertions.assertDoesNotThrow;
34  import static org.junit.jupiter.api.Assertions.assertEquals;
35  import static org.junit.jupiter.api.Assertions.assertThrows;
36  import static org.junit.jupiter.api.Assertions.fail;
37  
38  /**
39   */
40  class BetaTest {
41  
42      /*
43       * Use reflection to test private methods.
44       */
45      private static final Method LOG_GAMMA_SUM_METHOD;
46  
47      private static final Method LOG_GAMMA_MINUS_LOG_GAMMA_SUM_METHOD;
48  
49      private static final Method SUM_DELTA_MINUS_DELTA_SUM_METHOD;
50  
51      static {
52          final Class<Beta> b;
53          final Class<Double> d = Double.TYPE;
54          b = Beta.class;
55          AtomicReference<Method> m = new AtomicReference<>();
56          assertDoesNotThrow(() -> {
57              m.set(b.getDeclaredMethod("logGammaSum", d, d));
58          });
59          LOG_GAMMA_SUM_METHOD = m.get();
60          LOG_GAMMA_SUM_METHOD.setAccessible(true);
61  
62          m.set(null);
63          assertDoesNotThrow(() -> {
64              m.set(b.getDeclaredMethod("logGammaMinusLogGammaSum", d, d));
65          });
66          LOG_GAMMA_MINUS_LOG_GAMMA_SUM_METHOD = m.get();
67          LOG_GAMMA_MINUS_LOG_GAMMA_SUM_METHOD.setAccessible(true);
68  
69          m.set(null);
70          assertDoesNotThrow(() -> {
71              m.set(b.getDeclaredMethod("sumDeltaMinusDeltaSum", d, d));
72          });
73          SUM_DELTA_MINUS_DELTA_SUM_METHOD = m.get();
74          SUM_DELTA_MINUS_DELTA_SUM_METHOD.setAccessible(true);
75      }
76  
77      private void testRegularizedBeta(double expected, double x,
78                                       double a, double b) {
79          double actual = Beta.regularizedBeta(x, a, b);
80          UnitTestUtils.customAssertEquals(expected, actual, 10e-15);
81      }
82  
83      private void testLogBeta(double expected, double a, double b) {
84          double actual = Beta.logBeta(a, b);
85          UnitTestUtils.customAssertEquals(expected, actual, 10e-15);
86      }
87  
88      @Test
89      void testRegularizedBetaNanPositivePositive() {
90          testRegularizedBeta(Double.NaN, Double.NaN, 1.0, 1.0);
91      }
92  
93      @Test
94      void testRegularizedBetaPositiveNanPositive() {
95          testRegularizedBeta(Double.NaN, 0.5, Double.NaN, 1.0);
96      }
97  
98      @Test
99      void testRegularizedBetaPositivePositiveNan() {
100         testRegularizedBeta(Double.NaN, 0.5, 1.0, Double.NaN);
101     }
102 
103     @Test
104     void testRegularizedBetaNegativePositivePositive() {
105         testRegularizedBeta(Double.NaN, -0.5, 1.0, 2.0);
106     }
107 
108     @Test
109     void testRegularizedBetaPositiveNegativePositive() {
110         testRegularizedBeta(Double.NaN, 0.5, -1.0, 2.0);
111     }
112 
113     @Test
114     void testRegularizedBetaPositivePositiveNegative() {
115         testRegularizedBeta(Double.NaN, 0.5, 1.0, -2.0);
116     }
117 
118     @Test
119     void testRegularizedBetaZeroPositivePositive() {
120         testRegularizedBeta(0.0, 0.0, 1.0, 2.0);
121     }
122 
123     @Test
124     void testRegularizedBetaPositiveZeroPositive() {
125         testRegularizedBeta(Double.NaN, 0.5, 0.0, 2.0);
126     }
127 
128     @Test
129     void testRegularizedBetaPositivePositiveZero() {
130         testRegularizedBeta(Double.NaN, 0.5, 1.0, 0.0);
131     }
132 
133     @Test
134     void testRegularizedBetaPositivePositivePositive() {
135         testRegularizedBeta(0.75, 0.5, 1.0, 2.0);
136     }
137 
138     @Test
139     void testRegularizedBetaTinyArgument() {
140         double actual = Beta.regularizedBeta(1e-17, 1.0, 1e12);
141         // This value is from R: pbeta(1e-17,1,1e12)
142         UnitTestUtils.customAssertEquals(9.999950000166648e-6, actual, 1e-16);
143     }
144 
145     @Test
146     void testMath1067() {
147         final double x = 0.22580645161290325;
148         final double a = 64.33333333333334;
149         final double b = 223;
150 
151         assertDoesNotThrow(() -> {
152             Beta.regularizedBeta(x, a, b, 1e-14, 10000);
153         }, "Infinite recursion");
154     }
155 
156     @Test
157     void testLogBetaNanPositive() {
158         testLogBeta(Double.NaN, Double.NaN, 2.0);
159     }
160 
161     @Test
162     void testLogBetaPositiveNan() {
163         testLogBeta(Double.NaN, 1.0, Double.NaN);
164     }
165 
166     @Test
167     void testLogBetaNegativePositive() {
168         testLogBeta(Double.NaN, -1.0, 2.0);
169     }
170 
171     @Test
172     void testLogBetaPositiveNegative() {
173         testLogBeta(Double.NaN, 1.0, -2.0);
174     }
175 
176     @Test
177     void testLogBetaZeroPositive() {
178         testLogBeta(Double.NaN, 0.0, 2.0);
179     }
180 
181     @Test
182     void testLogBetaPositiveZero() {
183         testLogBeta(Double.NaN, 1.0, 0.0);
184     }
185 
186     @Test
187     void testLogBetaPositivePositive() {
188         testLogBeta(-0.693147180559945, 1.0, 2.0);
189     }
190 
191     /**
192      * Reference data for the {@link #logGammaSum(double, double)}
193      * function. This data was generated with the following
194      * <a href="http://maxima.sourceforge.net/">Maxima</a> script.
195      *
196      * <pre>
197      * kill(all);
198      *
199      * fpprec : 64;
200      * gsumln(a, b) := log(gamma(a + b));
201      *
202      * x : [1.0b0, 1.125b0, 1.25b0, 1.375b0, 1.5b0, 1.625b0, 1.75b0, 1.875b0, 2.0b0];
203      *
204      * for i : 1 while i <= length(x) do
205      *   for j : 1 while j <= length(x) do block(
206      *     a : x[i],
207      *     b : x[j],
208      *     print("{", float(a), ",", float(b), ",", float(gsumln(a, b)), "},")
209      *   );
210      * </pre>
211      */
212     private static final double[][] LOG_GAMMA_SUM_REF = {
213         { 1.0 , 1.0 , 0.0 },
214         { 1.0 , 1.125 , .05775985153034387 },
215         { 1.0 , 1.25 , .1248717148923966 },
216         { 1.0 , 1.375 , .2006984603774558 },
217         { 1.0 , 1.5 , .2846828704729192 },
218         { 1.0 , 1.625 , .3763336820249054 },
219         { 1.0 , 1.75 , .4752146669149371 },
220         { 1.0 , 1.875 , .5809359740231859 },
221         { 1.0 , 2.0 , .6931471805599453 },
222         { 1.125 , 1.0 , .05775985153034387 },
223         { 1.125 , 1.125 , .1248717148923966 },
224         { 1.125 , 1.25 , .2006984603774558 },
225         { 1.125 , 1.375 , .2846828704729192 },
226         { 1.125 , 1.5 , .3763336820249054 },
227         { 1.125 , 1.625 , .4752146669149371 },
228         { 1.125 , 1.75 , .5809359740231859 },
229         { 1.125 , 1.875 , .6931471805599453 },
230         { 1.125 , 2.0 , 0.811531653906724 },
231         { 1.25 , 1.0 , .1248717148923966 },
232         { 1.25 , 1.125 , .2006984603774558 },
233         { 1.25 , 1.25 , .2846828704729192 },
234         { 1.25 , 1.375 , .3763336820249054 },
235         { 1.25 , 1.5 , .4752146669149371 },
236         { 1.25 , 1.625 , .5809359740231859 },
237         { 1.25 , 1.75 , .6931471805599453 },
238         { 1.25 , 1.875 , 0.811531653906724 },
239         { 1.25 , 2.0 , .9358019311087253 },
240         { 1.375 , 1.0 , .2006984603774558 },
241         { 1.375 , 1.125 , .2846828704729192 },
242         { 1.375 , 1.25 , .3763336820249054 },
243         { 1.375 , 1.375 , .4752146669149371 },
244         { 1.375 , 1.5 , .5809359740231859 },
245         { 1.375 , 1.625 , .6931471805599453 },
246         { 1.375 , 1.75 , 0.811531653906724 },
247         { 1.375 , 1.875 , .9358019311087253 },
248         { 1.375 , 2.0 , 1.06569589786406 },
249         { 1.5 , 1.0 , .2846828704729192 },
250         { 1.5 , 1.125 , .3763336820249054 },
251         { 1.5 , 1.25 , .4752146669149371 },
252         { 1.5 , 1.375 , .5809359740231859 },
253         { 1.5 , 1.5 , .6931471805599453 },
254         { 1.5 , 1.625 , 0.811531653906724 },
255         { 1.5 , 1.75 , .9358019311087253 },
256         { 1.5 , 1.875 , 1.06569589786406 },
257         { 1.5 , 2.0 , 1.200973602347074 },
258         { 1.625 , 1.0 , .3763336820249054 },
259         { 1.625 , 1.125 , .4752146669149371 },
260         { 1.625 , 1.25 , .5809359740231859 },
261         { 1.625 , 1.375 , .6931471805599453 },
262         { 1.625 , 1.5 , 0.811531653906724 },
263         { 1.625 , 1.625 , .9358019311087253 },
264         { 1.625 , 1.75 , 1.06569589786406 },
265         { 1.625 , 1.875 , 1.200973602347074 },
266         { 1.625 , 2.0 , 1.341414578068493 },
267         { 1.75 , 1.0 , .4752146669149371 },
268         { 1.75 , 1.125 , .5809359740231859 },
269         { 1.75 , 1.25 , .6931471805599453 },
270         { 1.75 , 1.375 , 0.811531653906724 },
271         { 1.75 , 1.5 , .9358019311087253 },
272         { 1.75 , 1.625 , 1.06569589786406 },
273         { 1.75 , 1.75 , 1.200973602347074 },
274         { 1.75 , 1.875 , 1.341414578068493 },
275         { 1.75 , 2.0 , 1.486815578593417 },
276         { 1.875 , 1.0 , .5809359740231859 },
277         { 1.875 , 1.125 , .6931471805599453 },
278         { 1.875 , 1.25 , 0.811531653906724 },
279         { 1.875 , 1.375 , .9358019311087253 },
280         { 1.875 , 1.5 , 1.06569589786406 },
281         { 1.875 , 1.625 , 1.200973602347074 },
282         { 1.875 , 1.75 , 1.341414578068493 },
283         { 1.875 , 1.875 , 1.486815578593417 },
284         { 1.875 , 2.0 , 1.6369886482725 },
285         { 2.0 , 1.0 , .6931471805599453 },
286         { 2.0 , 1.125 , 0.811531653906724 },
287         { 2.0 , 1.25 , .9358019311087253 },
288         { 2.0 , 1.375 , 1.06569589786406 },
289         { 2.0 , 1.5 , 1.200973602347074 },
290         { 2.0 , 1.625 , 1.341414578068493 },
291         { 2.0 , 1.75 , 1.486815578593417 },
292         { 2.0 , 1.875 , 1.6369886482725 },
293         { 2.0 , 2.0 , 1.791759469228055 },
294     };
295 
296     private static double logGammaSum(final double a, final double b) {
297 
298         /*
299          * Use reflection to access private method.
300          */
301         try {
302             return ((Double) LOG_GAMMA_SUM_METHOD.invoke(null, a, b)).doubleValue();
303         } catch (final IllegalAccessException e) {
304             fail(e.getMessage());
305         } catch (final IllegalArgumentException e) {
306             fail(e.getMessage());
307         } catch (final InvocationTargetException e) {
308             final Throwable te = e.getTargetException();
309             if (te instanceof MathIllegalArgumentException) {
310                 throw (MathIllegalArgumentException) te;
311             }
312             fail(e.getMessage());
313         }
314         return Double.NaN;
315     }
316 
317     @Test
318     void testLogGammaSum() {
319         final int ulps = 2;
320         for (int i = 0; i < LOG_GAMMA_SUM_REF.length; i++) {
321             final double[] ref = LOG_GAMMA_SUM_REF[i];
322             final double a = ref[0];
323             final double b = ref[1];
324             final double expected = ref[2];
325             final double actual = logGammaSum(a, b);
326             final double tol = ulps * FastMath.ulp(expected);
327             final StringBuilder builder = new StringBuilder();
328             builder.append(a).append(", ").append(b);
329             assertEquals(expected, actual, tol, builder.toString());
330         }
331     }
332 
333     @Test
334     void testLogGammaSumPrecondition1() {
335         assertThrows(MathIllegalArgumentException.class, () -> {
336 
337             logGammaSum(0.0, 1.0);
338         });
339     }
340 
341     @Test
342     void testLogGammaSumPrecondition2() {
343         assertThrows(MathIllegalArgumentException.class, () -> {
344 
345             logGammaSum(3.0, 1.0);
346         });
347     }
348 
349     @Test
350     void testLogGammaSumPrecondition3() {
351         assertThrows(MathIllegalArgumentException.class, () -> {
352 
353             logGammaSum(1.0, 0.0);
354         });
355     }
356 
357     @Test
358     void testLogGammaSumPrecondition4() {
359         assertThrows(MathIllegalArgumentException.class, () -> {
360 
361             logGammaSum(1.0, 3.0);
362         });
363     }
364 
365     private static final double[][] LOG_GAMMA_MINUS_LOG_GAMMA_SUM_REF = {
366 //        { 0.0 , 8.0 , 0.0 },
367 //        { 0.0 , 9.0 , 0.0 },
368         { 0.0 , 10.0 , 0.0 },
369         { 0.0 , 11.0 , 0.0 },
370         { 0.0 , 12.0 , 0.0 },
371         { 0.0 , 13.0 , 0.0 },
372         { 0.0 , 14.0 , 0.0 },
373         { 0.0 , 15.0 , 0.0 },
374         { 0.0 , 16.0 , 0.0 },
375         { 0.0 , 17.0 , 0.0 },
376         { 0.0 , 18.0 , 0.0 },
377 //        { 1.0 , 8.0 , - 2.079441541679836 },
378 //        { 1.0 , 9.0 , - 2.19722457733622 },
379         { 1.0 , 10.0 , - 2.302585092994046 },
380         { 1.0 , 11.0 , - 2.397895272798371 },
381         { 1.0 , 12.0 , - 2.484906649788 },
382         { 1.0 , 13.0 , - 2.564949357461537 },
383         { 1.0 , 14.0 , - 2.639057329615258 },
384         { 1.0 , 15.0 , - 2.70805020110221 },
385         { 1.0 , 16.0 , - 2.772588722239781 },
386         { 1.0 , 17.0 , - 2.833213344056216 },
387         { 1.0 , 18.0 , - 2.890371757896165 },
388 //        { 2.0 , 8.0 , - 4.276666119016055 },
389 //        { 2.0 , 9.0 , - 4.499809670330265 },
390         { 2.0 , 10.0 , - 4.700480365792417 },
391         { 2.0 , 11.0 , - 4.882801922586371 },
392         { 2.0 , 12.0 , - 5.049856007249537 },
393         { 2.0 , 13.0 , - 5.204006687076795 },
394         { 2.0 , 14.0 , - 5.347107530717468 },
395         { 2.0 , 15.0 , - 5.480638923341991 },
396         { 2.0 , 16.0 , - 5.605802066295998 },
397         { 2.0 , 17.0 , - 5.723585101952381 },
398         { 2.0 , 18.0 , - 5.834810737062605 },
399 //        { 3.0 , 8.0 , - 6.579251212010101 },
400 //        { 3.0 , 9.0 , - 6.897704943128636 },
401         { 3.0 , 10.0 , - 7.185387015580416 },
402         { 3.0 , 11.0 , - 7.447751280047908 },
403         { 3.0 , 12.0 , - 7.688913336864796 },
404         { 3.0 , 13.0 , - 7.912056888179006 },
405         { 3.0 , 14.0 , - 8.11969625295725 },
406         { 3.0 , 15.0 , - 8.313852267398207 },
407         { 3.0 , 16.0 , - 8.496173824192162 },
408         { 3.0 , 17.0 , - 8.668024081118821 },
409         { 3.0 , 18.0 , - 8.830543010616596 },
410 //        { 4.0 , 8.0 , - 8.977146484808472 },
411 //        { 4.0 , 9.0 , - 9.382611592916636 },
412         { 4.0 , 10.0 , - 9.750336373041954 },
413         { 4.0 , 11.0 , - 10.08680860966317 },
414         { 4.0 , 12.0 , - 10.39696353796701 },
415         { 4.0 , 13.0 , - 10.68464561041879 },
416         { 4.0 , 14.0 , - 10.95290959701347 },
417         { 4.0 , 15.0 , - 11.20422402529437 },
418         { 4.0 , 16.0 , - 11.4406128033586 },
419         { 4.0 , 17.0 , - 11.66375635467281 },
420         { 4.0 , 18.0 , - 11.87506544834002 },
421 //        { 5.0 , 8.0 , - 11.46205313459647 },
422 //        { 5.0 , 9.0 , - 11.94756095037817 },
423         { 5.0 , 10.0 , - 12.38939370265721 },
424         { 5.0 , 11.0 , - 12.79485881076538 },
425         { 5.0 , 12.0 , - 13.16955226020679 },
426         { 5.0 , 13.0 , - 13.517858954475 },
427         { 5.0 , 14.0 , - 13.84328135490963 },
428         { 5.0 , 15.0 , - 14.14866300446081 },
429         { 5.0 , 16.0 , - 14.43634507691259 },
430         { 5.0 , 17.0 , - 14.70827879239624 },
431         { 5.0 , 18.0 , - 14.96610790169833 },
432 //        { 6.0 , 8.0 , - 14.02700249205801 },
433 //        { 6.0 , 9.0 , - 14.58661827999343 },
434         { 6.0 , 10.0 , - 15.09744390375942 },
435         { 6.0 , 11.0 , - 15.56744753300516 },
436         { 6.0 , 12.0 , - 16.002765604263 },
437         { 6.0 , 13.0 , - 16.40823071237117 },
438         { 6.0 , 14.0 , - 16.78772033407607 },
439         { 6.0 , 15.0 , - 17.14439527801481 },
440         { 6.0 , 16.0 , - 17.48086751463602 },
441         { 6.0 , 17.0 , - 17.79932124575455 },
442         { 6.0 , 18.0 , - 18.10160211762749 },
443 //        { 7.0 , 8.0 , - 16.66605982167327 },
444 //        { 7.0 , 9.0 , - 17.29466848109564 },
445         { 7.0 , 10.0 , - 17.8700326259992 },
446         { 7.0 , 11.0 , - 18.40066087706137 },
447         { 7.0 , 12.0 , - 18.89313736215917 },
448         { 7.0 , 13.0 , - 19.35266969153761 },
449         { 7.0 , 14.0 , - 19.78345260763006 },
450         { 7.0 , 15.0 , - 20.18891771573823 },
451         { 7.0 , 16.0 , - 20.57190996799433 },
452         { 7.0 , 17.0 , - 20.9348154616837 },
453         { 7.0 , 18.0 , - 21.27965594797543 },
454 //        { 8.0 , 8.0 , - 19.37411002277548 },
455 //        { 8.0 , 9.0 , - 20.06725720333542 },
456         { 8.0 , 10.0 , - 20.70324597005542 },
457         { 8.0 , 11.0 , - 21.29103263495754 },
458         { 8.0 , 12.0 , - 21.83757634132561 },
459         { 8.0 , 13.0 , - 22.3484019650916 },
460         { 8.0 , 14.0 , - 22.82797504535349 },
461         { 8.0 , 15.0 , - 23.27996016909654 },
462         { 8.0 , 16.0 , - 23.70740418392348 },
463         { 8.0 , 17.0 , - 24.11286929203165 },
464         { 8.0 , 18.0 , - 24.49853177284363 },
465 //        { 9.0 , 8.0 , - 22.14669874501526 },
466 //        { 9.0 , 9.0 , - 22.90047054739164 },
467         { 9.0 , 10.0 , - 23.59361772795159 },
468         { 9.0 , 11.0 , - 24.23547161412398 },
469         { 9.0 , 12.0 , - 24.8333086148796 },
470         { 9.0 , 13.0 , - 25.39292440281502 },
471         { 9.0 , 14.0 , - 25.9190174987118 },
472         { 9.0 , 15.0 , - 26.41545438502569 },
473         { 9.0 , 16.0 , - 26.88545801427143 },
474         { 9.0 , 17.0 , - 27.33174511689985 },
475         { 9.0 , 18.0 , - 27.75662831086511 },
476 //        { 10.0 , 8.0 , - 24.97991208907148 },
477 //        { 10.0 , 9.0 , - 25.7908423052878 },
478         { 10.0 , 10.0 , - 26.53805670711802 },
479         { 10.0 , 11.0 , - 27.23120388767797 },
480         { 10.0 , 12.0 , - 27.87783105260302 },
481         { 10.0 , 13.0 , - 28.48396685617334 },
482         { 10.0 , 14.0 , - 29.05451171464095 },
483         { 10.0 , 15.0 , - 29.59350821537364 },
484         { 10.0 , 16.0 , - 30.10433383913963 },
485         { 10.0 , 17.0 , - 30.58984165492133 },
486         { 10.0 , 18.0 , - 31.05246517686944 },
487     };
488 
489     private static double logGammaMinusLogGammaSum(final double a, final double b) {
490 
491         /*
492          * Use reflection to access private method.
493          */
494         try {
495             final Method m = LOG_GAMMA_MINUS_LOG_GAMMA_SUM_METHOD;
496             return ((Double) m.invoke(null, a, b)).doubleValue();
497         } catch (final IllegalAccessException e) {
498             fail(e.getMessage());
499         } catch (final IllegalArgumentException e) {
500             fail(e.getMessage());
501         } catch (final InvocationTargetException e) {
502             final Throwable te = e.getTargetException();
503             if (te instanceof MathIllegalArgumentException) {
504                 throw (MathIllegalArgumentException) te;
505             }
506             fail(e.getMessage());
507         }
508         return Double.NaN;
509     }
510 
511     @Test
512     void testLogGammaMinusLogGammaSum() {
513         final int ulps = 4;
514         for (int i = 0; i < LOG_GAMMA_MINUS_LOG_GAMMA_SUM_REF.length; i++) {
515             final double[] ref = LOG_GAMMA_MINUS_LOG_GAMMA_SUM_REF[i];
516             final double a = ref[0];
517             final double b = ref[1];
518             final double expected = ref[2];
519             final double actual = logGammaMinusLogGammaSum(a, b);
520             final double tol = ulps * FastMath.ulp(expected);
521             final StringBuilder builder = new StringBuilder();
522             builder.append(a).append(", ").append(b);
523             assertEquals(expected, actual, tol, builder.toString());
524         }
525     }
526 
527     @Test
528     void testLogGammaMinusLogGammaSumPrecondition1() {
529         assertThrows(MathIllegalArgumentException.class, () -> {
530             logGammaMinusLogGammaSum(-1.0, 8.0);
531         });
532     }
533 
534     @Test
535     void testLogGammaMinusLogGammaSumPrecondition2() {
536         assertThrows(MathIllegalArgumentException.class, () -> {
537             logGammaMinusLogGammaSum(1.0, 7.0);
538         });
539     }
540 
541     private static final double[][] SUM_DELTA_MINUS_DELTA_SUM_REF = {
542         { 10.0 , 10.0 , .01249480717472882 },
543         { 10.0 , 11.0 , .01193628470267385 },
544         { 10.0 , 12.0 , .01148578547212797 },
545         { 10.0 , 13.0 , .01111659739668398 },
546         { 10.0 , 14.0 , .01080991216314295 },
547         { 10.0 , 15.0 , .01055214134859758 },
548         { 10.0 , 16.0 , .01033324912491747 },
549         { 10.0 , 17.0 , .01014568069918883 },
550         { 10.0 , 18.0 , .009983653199146491 },
551         { 10.0 , 19.0 , .009842674320242729 },
552         { 10.0 , 20.0 , 0.0097192081956071 },
553         { 11.0 , 10.0 , .01193628470267385 },
554         { 11.0 , 11.0 , .01135973290745925 },
555         { 11.0 , 12.0 , .01089355537047828 },
556         { 11.0 , 13.0 , .01051064829297728 },
557         { 11.0 , 14.0 , 0.0101918899639826 },
558         { 11.0 , 15.0 , .009923438811859604 },
559         { 11.0 , 16.0 , .009695052724952705 },
560         { 11.0 , 17.0 , 0.00949900745283617 },
561         { 11.0 , 18.0 , .009329379874933402 },
562         { 11.0 , 19.0 , 0.00918156080743147 },
563         { 11.0 , 20.0 , 0.00905191635141762 },
564         { 12.0 , 10.0 , .01148578547212797 },
565         { 12.0 , 11.0 , .01089355537047828 },
566         { 12.0 , 12.0 , .01041365883144029 },
567         { 12.0 , 13.0 , .01001867865848564 },
568         { 12.0 , 14.0 , 0.00968923999191334 },
569         { 12.0 , 15.0 , .009411294976563555 },
570         { 12.0 , 16.0 , .009174432043268762 },
571         { 12.0 , 17.0 , .008970786693291802 },
572         { 12.0 , 18.0 , .008794318926790865 },
573         { 12.0 , 19.0 , .008640321527910711 },
574         { 12.0 , 20.0 , .008505077879954796 },
575         { 13.0 , 10.0 , .01111659739668398 },
576         { 13.0 , 11.0 , .01051064829297728 },
577         { 13.0 , 12.0 , .01001867865848564 },
578         { 13.0 , 13.0 , .009613018147953376 },
579         { 13.0 , 14.0 , .009274085618154277 },
580         { 13.0 , 15.0 , 0.0089876637564166 },
581         { 13.0 , 16.0 , .008743200745261382 },
582         { 13.0 , 17.0 , .008532715206686251 },
583         { 13.0 , 18.0 , .008350069108807093 },
584         { 13.0 , 19.0 , .008190472517984874 },
585         { 13.0 , 20.0 , .008050138630244345 },
586         { 14.0 , 10.0 , .01080991216314295 },
587         { 14.0 , 11.0 , 0.0101918899639826 },
588         { 14.0 , 12.0 , 0.00968923999191334 },
589         { 14.0 , 13.0 , .009274085618154277 },
590         { 14.0 , 14.0 , .008926676241967286 },
591         { 14.0 , 15.0 , .008632654302369184 },
592         { 14.0 , 16.0 , .008381351102615795 },
593         { 14.0 , 17.0 , .008164687232662443 },
594         { 14.0 , 18.0 , .007976441942841219 },
595         { 14.0 , 19.0 , .007811755112234388 },
596         { 14.0 , 20.0 , .007666780069317652 },
597         { 15.0 , 10.0 , .01055214134859758 },
598         { 15.0 , 11.0 , .009923438811859604 },
599         { 15.0 , 12.0 , .009411294976563555 },
600         { 15.0 , 13.0 , 0.0089876637564166 },
601         { 15.0 , 14.0 , .008632654302369184 },
602         { 15.0 , 15.0 , 0.00833179217417291 },
603         { 15.0 , 16.0 , .008074310643041299 },
604         { 15.0 , 17.0 , .007852047581145882 },
605         { 15.0 , 18.0 , .007658712051540045 },
606         { 15.0 , 19.0 , .007489384065757007 },
607         { 15.0 , 20.0 , .007340165635725612 },
608         { 16.0 , 10.0 , .01033324912491747 },
609         { 16.0 , 11.0 , .009695052724952705 },
610         { 16.0 , 12.0 , .009174432043268762 },
611         { 16.0 , 13.0 , .008743200745261382 },
612         { 16.0 , 14.0 , .008381351102615795 },
613         { 16.0 , 15.0 , .008074310643041299 },
614         { 16.0 , 16.0 , .007811229919967624 },
615         { 16.0 , 17.0 , .007583876618287594 },
616         { 16.0 , 18.0 , .007385899933505551 },
617         { 16.0 , 19.0 , .007212328560607852 },
618         { 16.0 , 20.0 , .007059220321091879 },
619         { 17.0 , 10.0 , .01014568069918883 },
620         { 17.0 , 11.0 , 0.00949900745283617 },
621         { 17.0 , 12.0 , .008970786693291802 },
622         { 17.0 , 13.0 , .008532715206686251 },
623         { 17.0 , 14.0 , .008164687232662443 },
624         { 17.0 , 15.0 , .007852047581145882 },
625         { 17.0 , 16.0 , .007583876618287594 },
626         { 17.0 , 17.0 , .007351882161431358 },
627         { 17.0 , 18.0 , .007149662089534654 },
628         { 17.0 , 19.0 , .006972200907152378 },
629         { 17.0 , 20.0 , .006815518216094137 },
630         { 18.0 , 10.0 , .009983653199146491 },
631         { 18.0 , 11.0 , .009329379874933402 },
632         { 18.0 , 12.0 , .008794318926790865 },
633         { 18.0 , 13.0 , .008350069108807093 },
634         { 18.0 , 14.0 , .007976441942841219 },
635         { 18.0 , 15.0 , .007658712051540045 },
636         { 18.0 , 16.0 , .007385899933505551 },
637         { 18.0 , 17.0 , .007149662089534654 },
638         { 18.0 , 18.0 , .006943552208153373 },
639         { 18.0 , 19.0 , .006762516574228829 },
640         { 18.0 , 20.0 , .006602541598043117 },
641         { 19.0 , 10.0 , .009842674320242729 },
642         { 19.0 , 11.0 , 0.00918156080743147 },
643         { 19.0 , 12.0 , .008640321527910711 },
644         { 19.0 , 13.0 , .008190472517984874 },
645         { 19.0 , 14.0 , .007811755112234388 },
646         { 19.0 , 15.0 , .007489384065757007 },
647         { 19.0 , 16.0 , .007212328560607852 },
648         { 19.0 , 17.0 , .006972200907152378 },
649         { 19.0 , 18.0 , .006762516574228829 },
650         { 19.0 , 19.0 , .006578188655176814 },
651         { 19.0 , 20.0 , .006415174623476747 },
652         { 20.0 , 10.0 , 0.0097192081956071 },
653         { 20.0 , 11.0 , 0.00905191635141762 },
654         { 20.0 , 12.0 , .008505077879954796 },
655         { 20.0 , 13.0 , .008050138630244345 },
656         { 20.0 , 14.0 , .007666780069317652 },
657         { 20.0 , 15.0 , .007340165635725612 },
658         { 20.0 , 16.0 , .007059220321091879 },
659         { 20.0 , 17.0 , .006815518216094137 },
660         { 20.0 , 18.0 , .006602541598043117 },
661         { 20.0 , 19.0 , .006415174623476747 },
662         { 20.0 , 20.0 , .006249349445691423 },
663     };
664 
665     private static double sumDeltaMinusDeltaSum(final double a,
666                                                 final double b) {
667 
668         /*
669          * Use reflection to access private method.
670          */
671         try {
672             final Method m = SUM_DELTA_MINUS_DELTA_SUM_METHOD;
673             return ((Double) m.invoke(null, a, b)).doubleValue();
674         } catch (final IllegalAccessException e) {
675             fail(e.getMessage());
676         } catch (final IllegalArgumentException e) {
677             fail(e.getMessage());
678         } catch (final InvocationTargetException e) {
679             final Throwable te = e.getTargetException();
680             if (te instanceof MathIllegalArgumentException) {
681                 throw (MathIllegalArgumentException) te;
682             }
683             fail(e.getMessage());
684         }
685         return Double.NaN;
686     }
687 
688     @Test
689     void testSumDeltaMinusDeltaSum() {
690 
691         final int ulps = 3;
692         for (int i = 0; i < SUM_DELTA_MINUS_DELTA_SUM_REF.length; i++) {
693             final double[] ref = SUM_DELTA_MINUS_DELTA_SUM_REF[i];
694             final double a = ref[0];
695             final double b = ref[1];
696             final double expected = ref[2];
697             final double actual = sumDeltaMinusDeltaSum(a, b);
698             final double tol = ulps * FastMath.ulp(expected);
699             final StringBuilder builder = new StringBuilder();
700             builder.append(a).append(", ").append(b);
701             assertEquals(expected, actual, tol, builder.toString());
702         }
703     }
704 
705     @Test
706     void testSumDeltaMinusDeltaSumPrecondition1() {
707         assertThrows(MathIllegalArgumentException.class, () -> {
708 
709             sumDeltaMinusDeltaSum(9.0, 10.0);
710         });
711     }
712 
713     @Test
714     void testSumDeltaMinusDeltaSumPrecondition2() {
715         assertThrows(MathIllegalArgumentException.class, () -> {
716 
717             sumDeltaMinusDeltaSum(10.0, 9.0);
718         });
719     }
720 
721     private static final double[][] LOG_BETA_REF = {
722         { 0.125 , 0.125 , 2.750814190409515 },
723         { 0.125 , 0.25 , 2.444366899981226 },
724         { 0.125 , 0.5 , 2.230953804989556 },
725         { 0.125 , 1.0 , 2.079441541679836 },
726         { 0.125 , 2.0 , 1.961658506023452 },
727         { 0.125 , 3.0 , 1.901033884207018 },
728         { 0.125 , 4.0 , 1.860211889686763 },
729         { 0.125 , 5.0 , 1.829440231020009 },
730         { 0.125 , 6.0 , 1.804747618429637 },
731         { 0.125 , 7.0 , 1.784128331226902 },
732         { 0.125 , 8.0 , 1.766428754127501 },
733         { 0.125 , 9.0 , 1.750924567591535 },
734         { 0.125 , 10.0 , 1.7371312454592 },
735         { 0.125 , 1000.0 , 1.156003642015969 },
736         { 0.125 , 1001.0 , 1.155878649827818 },
737         { 0.125 , 10000.0 , .8681312798751318 },
738         { 0.25 , 0.125 , 2.444366899981226 },
739         { 0.25 , 0.25 , 2.003680106471455 },
740         { 0.25 , 0.5 , 1.657106516191482 },
741         { 0.25 , 1.0 , 1.386294361119891 },
742         { 0.25 , 2.0 , 1.163150809805681 },
743         { 0.25 , 3.0 , 1.045367774149297 },
744         { 0.25 , 4.0 , 0.965325066475761 },
745         { 0.25 , 5.0 , .9047004446593261 },
746         { 0.25 , 6.0 , .8559102804898941 },
747         { 0.25 , 7.0 , 0.815088285969639 },
748         { 0.25 , 8.0 , .7799969661583689 },
749         { 0.25 , 9.0 , .7492253074916152 },
750         { 0.25 , 10.0 , .7218263333035008 },
751         { 0.25 , 1000.0 , - .4388225372378877 },
752         { 0.25 , 1001.0 , - .4390725059930951 },
753         { 0.25 , 10000.0 , - 1.014553193217846 },
754         { 0.5 , 0.125 , 2.230953804989556 },
755         { 0.5 , 0.25 , 1.657106516191482 },
756         { 0.5 , 0.5 , 1.1447298858494 },
757         { 0.5 , 1.0 , .6931471805599453 },
758         { 0.5 , 2.0 , .2876820724517809 },
759         { 0.5 , 3.0 , .06453852113757118 },
760 //        { 0.5 , 4.0 , - .08961215868968714 },
761         { 0.5 , 5.0 , - .2073951943460706 },
762         { 0.5 , 6.0 , - .3027053741503954 },
763         { 0.5 , 7.0 , - .3827480818239319 },
764         { 0.5 , 8.0 , - .4517409533108833 },
765         { 0.5 , 9.0 , - .5123655751273182 },
766         { 0.5 , 10.0 , - .5664327963975939 },
767         { 0.5 , 1000.0 , - 2.881387696571577 },
768         { 0.5 , 1001.0 , - 2.881887571613228 },
769         { 0.5 , 10000.0 , - 4.032792743063396 },
770         { 1.0 , 0.125 , 2.079441541679836 },
771         { 1.0 , 0.25 , 1.386294361119891 },
772         { 1.0 , 0.5 , .6931471805599453 },
773         { 1.0 , 1.0 , 0.0 },
774         { 1.0 , 2.0 , - .6931471805599453 },
775         { 1.0 , 3.0 , - 1.09861228866811 },
776         { 1.0 , 4.0 , - 1.386294361119891 },
777         { 1.0 , 5.0 , - 1.6094379124341 },
778         { 1.0 , 6.0 , - 1.791759469228055 },
779         { 1.0 , 7.0 , - 1.945910149055313 },
780         { 1.0 , 8.0 , - 2.079441541679836 },
781         { 1.0 , 9.0 , - 2.19722457733622 },
782         { 1.0 , 10.0 , - 2.302585092994046 },
783         { 1.0 , 1000.0 , - 6.907755278982137 },
784         { 1.0 , 1001.0 , - 6.90875477931522 },
785         { 1.0 , 10000.0 , - 9.210340371976184 },
786         { 2.0 , 0.125 , 1.961658506023452 },
787         { 2.0 , 0.25 , 1.163150809805681 },
788         { 2.0 , 0.5 , .2876820724517809 },
789         { 2.0 , 1.0 , - .6931471805599453 },
790         { 2.0 , 2.0 , - 1.791759469228055 },
791         { 2.0 , 3.0 , - 2.484906649788 },
792         { 2.0 , 4.0 , - 2.995732273553991 },
793         { 2.0 , 5.0 , - 3.401197381662155 },
794         { 2.0 , 6.0 , - 3.737669618283368 },
795         { 2.0 , 7.0 , - 4.02535169073515 },
796         { 2.0 , 8.0 , - 4.276666119016055 },
797         { 2.0 , 9.0 , - 4.499809670330265 },
798         { 2.0 , 10.0 , - 4.700480365792417 },
799         { 2.0 , 1000.0 , - 13.81651005829736 },
800         { 2.0 , 1001.0 , - 13.81850806096003 },
801         { 2.0 , 10000.0 , - 18.4207807389527 },
802         { 3.0 , 0.125 , 1.901033884207018 },
803         { 3.0 , 0.25 , 1.045367774149297 },
804         { 3.0 , 0.5 , .06453852113757118 },
805         { 3.0 , 1.0 , - 1.09861228866811 },
806         { 3.0 , 2.0 , - 2.484906649788 },
807         { 3.0 , 3.0 , - 3.401197381662155 },
808         { 3.0 , 4.0 , - 4.0943445622221 },
809         { 3.0 , 5.0 , - 4.653960350157523 },
810         { 3.0 , 6.0 , - 5.123963979403259 },
811         { 3.0 , 7.0 , - 5.529429087511423 },
812         { 3.0 , 8.0 , - 5.886104031450156 },
813         { 3.0 , 9.0 , - 6.20455776256869 },
814         { 3.0 , 10.0 , - 6.492239835020471 },
815         { 3.0 , 1000.0 , - 20.03311615938222 },
816         { 3.0 , 1001.0 , - 20.03611166836202 },
817         { 3.0 , 10000.0 , - 26.9381739103716 },
818         { 4.0 , 0.125 , 1.860211889686763 },
819         { 4.0 , 0.25 , 0.965325066475761 },
820 //        { 4.0 , 0.5 , - .08961215868968714 },
821         { 4.0 , 1.0 , - 1.386294361119891 },
822         { 4.0 , 2.0 , - 2.995732273553991 },
823         { 4.0 , 3.0 , - 4.0943445622221 },
824         { 4.0 , 4.0 , - 4.941642422609304 },
825         { 4.0 , 5.0 , - 5.634789603169249 },
826         { 4.0 , 6.0 , - 6.222576268071369 },
827         { 4.0 , 7.0 , - 6.733401891837359 },
828         { 4.0 , 8.0 , - 7.185387015580416 },
829         { 4.0 , 9.0 , - 7.590852123688581 },
830         { 4.0 , 10.0 , - 7.958576903813898 },
831         { 4.0 , 1000.0 , - 25.84525465867605 },
832         { 4.0 , 1001.0 , - 25.84924667994559 },
833         { 4.0 , 10000.0 , - 35.05020194868867 },
834         { 5.0 , 0.125 , 1.829440231020009 },
835         { 5.0 , 0.25 , .9047004446593261 },
836         { 5.0 , 0.5 , - .2073951943460706 },
837         { 5.0 , 1.0 , - 1.6094379124341 },
838         { 5.0 , 2.0 , - 3.401197381662155 },
839         { 5.0 , 3.0 , - 4.653960350157523 },
840         { 5.0 , 4.0 , - 5.634789603169249 },
841         { 5.0 , 5.0 , - 6.445719819385578 },
842         { 5.0 , 6.0 , - 7.138866999945524 },
843         { 5.0 , 7.0 , - 7.745002803515839 },
844         { 5.0 , 8.0 , - 8.283999304248526 },
845         { 5.0 , 9.0 , - 8.769507120030227 },
846         { 5.0 , 10.0 , - 9.211339872309265 },
847         { 5.0 , 1000.0 , - 31.37070759780783 },
848         { 5.0 , 1001.0 , - 31.37569513931887 },
849         { 5.0 , 10000.0 , - 42.87464787956629 },
850         { 6.0 , 0.125 , 1.804747618429637 },
851         { 6.0 , 0.25 , .8559102804898941 },
852         { 6.0 , 0.5 , - .3027053741503954 },
853         { 6.0 , 1.0 , - 1.791759469228055 },
854         { 6.0 , 2.0 , - 3.737669618283368 },
855         { 6.0 , 3.0 , - 5.123963979403259 },
856         { 6.0 , 4.0 , - 6.222576268071369 },
857         { 6.0 , 5.0 , - 7.138866999945524 },
858         { 6.0 , 6.0 , - 7.927324360309794 },
859         { 6.0 , 7.0 , - 8.620471540869739 },
860         { 6.0 , 8.0 , - 9.239510749275963 },
861         { 6.0 , 9.0 , - 9.799126537211386 },
862         { 6.0 , 10.0 , - 10.30995216097738 },
863         { 6.0 , 1000.0 , - 36.67401250586691 },
864         { 6.0 , 1001.0 , - 36.67999457754446 },
865         { 6.0 , 10000.0 , - 50.47605021415003 },
866         { 7.0 , 0.125 , 1.784128331226902 },
867         { 7.0 , 0.25 , 0.815088285969639 },
868         { 7.0 , 0.5 , - .3827480818239319 },
869         { 7.0 , 1.0 , - 1.945910149055313 },
870         { 7.0 , 2.0 , - 4.02535169073515 },
871         { 7.0 , 3.0 , - 5.529429087511423 },
872         { 7.0 , 4.0 , - 6.733401891837359 },
873         { 7.0 , 5.0 , - 7.745002803515839 },
874         { 7.0 , 6.0 , - 8.620471540869739 },
875         { 7.0 , 7.0 , - 9.39366142910322 },
876         { 7.0 , 8.0 , - 10.08680860966317 },
877         { 7.0 , 9.0 , - 10.71541726908554 },
878         { 7.0 , 10.0 , - 11.2907814139891 },
879         { 7.0 , 1000.0 , - 41.79599038729854 },
880         { 7.0 , 1001.0 , - 41.80296600103496 },
881         { 7.0 , 10000.0 , - 57.89523093697012 },
882         { 8.0 , 0.125 , 1.766428754127501 },
883         { 8.0 , 0.25 , .7799969661583689 },
884         { 8.0 , 0.5 , - .4517409533108833 },
885         { 8.0 , 1.0 , - 2.079441541679836 },
886         { 8.0 , 2.0 , - 4.276666119016055 },
887         { 8.0 , 3.0 , - 5.886104031450156 },
888         { 8.0 , 4.0 , - 7.185387015580416 },
889         { 8.0 , 5.0 , - 8.283999304248526 },
890         { 8.0 , 6.0 , - 9.239510749275963 },
891         { 8.0 , 7.0 , - 10.08680860966317 },
892         { 8.0 , 8.0 , - 10.84894866171006 },
893         { 8.0 , 9.0 , - 11.54209584227001 },
894         { 8.0 , 10.0 , - 12.17808460899001 },
895         { 8.0 , 1000.0 , - 46.76481113096179 },
896         { 8.0 , 1001.0 , - 46.77277930061096 },
897         { 8.0 , 10000.0 , - 65.16036091500527 },
898         { 9.0 , 0.125 , 1.750924567591535 },
899         { 9.0 , 0.25 , .7492253074916152 },
900         { 9.0 , 0.5 , - .5123655751273182 },
901         { 9.0 , 1.0 , - 2.19722457733622 },
902         { 9.0 , 2.0 , - 4.499809670330265 },
903         { 9.0 , 3.0 , - 6.20455776256869 },
904         { 9.0 , 4.0 , - 7.590852123688581 },
905         { 9.0 , 5.0 , - 8.769507120030227 },
906         { 9.0 , 6.0 , - 9.799126537211386 },
907         { 9.0 , 7.0 , - 10.71541726908554 },
908         { 9.0 , 8.0 , - 11.54209584227001 },
909         { 9.0 , 9.0 , - 12.29586764464639 },
910         { 9.0 , 10.0 , - 12.98901482520633 },
911         { 9.0 , 1000.0 , - 51.60109303791327 },
912         { 9.0 , 1001.0 , - 51.61005277928474 },
913         { 9.0 , 10000.0 , - 72.29205942547217 },
914         { 10.0 , 0.125 , 1.7371312454592 },
915         { 10.0 , 0.25 , .7218263333035008 },
916         { 10.0 , 0.5 , - .5664327963975939 },
917         { 10.0 , 1.0 , - 2.302585092994046 },
918         { 10.0 , 2.0 , - 4.700480365792417 },
919         { 10.0 , 3.0 , - 6.492239835020471 },
920         { 10.0 , 4.0 , - 7.958576903813898 },
921         { 10.0 , 5.0 , - 9.211339872309265 },
922         { 10.0 , 6.0 , - 10.30995216097738 },
923         { 10.0 , 7.0 , - 11.2907814139891 },
924         { 10.0 , 8.0 , - 12.17808460899001 },
925         { 10.0 , 9.0 , - 12.98901482520633 },
926         { 10.0 , 10.0 , - 13.73622922703655 },
927         { 10.0 , 1000.0 , - 56.32058348093065 },
928         { 10.0 , 1001.0 , - 56.33053381178382 },
929         { 10.0 , 10000.0 , - 79.30607481535498 },
930         { 1000.0 , 0.125 , 1.156003642015969 },
931         { 1000.0 , 0.25 , - .4388225372378877 },
932         { 1000.0 , 0.5 , - 2.881387696571577 },
933         { 1000.0 , 1.0 , - 6.907755278982137 },
934         { 1000.0 , 2.0 , - 13.81651005829736 },
935         { 1000.0 , 3.0 , - 20.03311615938222 },
936         { 1000.0 , 4.0 , - 25.84525465867605 },
937         { 1000.0 , 5.0 , - 31.37070759780783 },
938         { 1000.0 , 6.0 , - 36.67401250586691 },
939         { 1000.0 , 7.0 , - 41.79599038729854 },
940         { 1000.0 , 8.0 , - 46.76481113096179 },
941         { 1000.0 , 9.0 , - 51.60109303791327 },
942         { 1000.0 , 10.0 , - 56.32058348093065 },
943         { 1000.0 , 1000.0 , - 1388.482601635902 },
944         { 1000.0 , 1001.0 , - 1389.175748816462 },
945         { 1000.0 , 10000.0 , - 3353.484270767097 },
946         { 1001.0 , 0.125 , 1.155878649827818 },
947         { 1001.0 , 0.25 , - .4390725059930951 },
948         { 1001.0 , 0.5 , - 2.881887571613228 },
949         { 1001.0 , 1.0 , - 6.90875477931522 },
950         { 1001.0 , 2.0 , - 13.81850806096003 },
951         { 1001.0 , 3.0 , - 20.03611166836202 },
952         { 1001.0 , 4.0 , - 25.84924667994559 },
953         { 1001.0 , 5.0 , - 31.37569513931887 },
954         { 1001.0 , 6.0 , - 36.67999457754446 },
955         { 1001.0 , 7.0 , - 41.80296600103496 },
956         { 1001.0 , 8.0 , - 46.77277930061096 },
957         { 1001.0 , 9.0 , - 51.61005277928474 },
958         { 1001.0 , 10.0 , - 56.33053381178382 },
959         { 1001.0 , 1000.0 , - 1389.175748816462 },
960         { 1001.0 , 1001.0 , - 1389.869395872064 },
961         { 1001.0 , 10000.0 , - 3355.882166039895 },
962         { 10000.0 , 0.125 , .8681312798751318 },
963         { 10000.0 , 0.25 , - 1.014553193217846 },
964         { 10000.0 , 0.5 , - 4.032792743063396 },
965         { 10000.0 , 1.0 , - 9.210340371976184 },
966         { 10000.0 , 2.0 , - 18.4207807389527 },
967         { 10000.0 , 3.0 , - 26.9381739103716 },
968         { 10000.0 , 4.0 , - 35.05020194868867 },
969         { 10000.0 , 5.0 , - 42.87464787956629 },
970         { 10000.0 , 6.0 , - 50.47605021415003 },
971         { 10000.0 , 7.0 , - 57.89523093697012 },
972         { 10000.0 , 8.0 , - 65.16036091500527 },
973         { 10000.0 , 9.0 , - 72.29205942547217 },
974         { 10000.0 , 10.0 , - 79.30607481535498 },
975         { 10000.0 , 1000.0 , - 3353.484270767097 },
976         { 10000.0 , 1001.0 , - 3355.882166039895 },
977         { 10000.0 , 10000.0 , - 13866.28325676141 },
978     };
979 
980     @Test
981     void testLogBeta() {
982         final int ulps = 3;
983         for (int i = 0; i < LOG_BETA_REF.length; i++) {
984             final double[] ref = LOG_BETA_REF[i];
985             final double a = ref[0];
986             final double b = ref[1];
987             final double expected = ref[2];
988             final double actual = Beta.logBeta(a, b);
989             final double tol = ulps * FastMath.ulp(expected);
990             final StringBuilder builder = new StringBuilder();
991             builder.append(a).append(", ").append(b);
992             assertEquals(expected, actual, tol, builder.toString());
993         }
994     }}