1 /*
2 * Copyright (c) 2011, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation.
8 *
9 * This code is distributed in the hope that it will be useful, but WITHOUT
10 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
11 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
12 * version 2 for more details (a copy is included in the LICENSE file that
13 * accompanied this code).
14 *
15 * You should have received a copy of the GNU General Public License version
16 * 2 along with this work; if not, write to the Free Software Foundation,
17 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
18 *
19 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
20 * or visit www.oracle.com if you need additional information or have any
21 * questions.
22 */
23
24 /*
25 * @test
26 * @bug 4900206
27 * @summary Test worst case behavior of exp, log, sin, cos, etc.
28 * @build Tests
29 * @build WorstCaseTests
30 * @run main WorstCaseTests
31 * @run main/othervm -Xcomp WorstCaseTests
32 * @author Joseph D. Darcy
33 */
34
35 /**
36 * Use "Table Maker's Dilemma" results from Jean-Michel Muller and
37 * Vincent Lefèvre, to test the math library. See
38 * http://perso.ens-lyon.fr/jean-michel.muller/TMD.html for original
39 * test vectors from 2000 and see
40 * http://perso.ens-lyon.fr/jean-michel.muller/TMDworstcases.pdf with
41 * additional test vectors from 2003. The latter link also contains
42 * some information about the methodology used to produce the test
43 * vectors.
44 *
45 * Most of the Java math library methods tested here have a 1-ulp
46 * error bound from their specifications. This implies the returned
47 * value must be one of the two representable floating-point numbers
48 * bracketing the exact result. The expected value in the test
49 * vectors below is the truncation of the exact value. Therefore, the
50 * computed result must either be that value or the value next larger
51 * in magnitude. The hyperbolic transcendental functions sinh and cosh
52 * have a larger 2.5 ulp error bound in their specification, but the
53 * JDK implementation complies with a 1 ulp bound on the worst-case
54 * values. Therefore, no addition leeway is afforded when testing
55 * sinh and cosh.
56 */
57 public class WorstCaseTests {
58 private WorstCaseTests() {throw new AssertionError("No instances for you.");}
59
60 public static void main(String... args) {
61 int failures = 0;
62
63 failures += testWorstExp();
64 failures += testWorstLog();
65 failures += testWorstSin();
66 failures += testWorstAsin();
67 failures += testWorstCos();
68 failures += testWorstAcos();
69 failures += testWorstTan();
70 failures += testWorstAtan();
71 failures += testWorstPow2();
72 failures += testWorstSinh();
73 failures += testWorstCosh();
74
75 if (failures > 0) {
76 System.err.printf("Testing worst cases incurred %d failures.%n", failures);
77 throw new RuntimeException();
78 }
79 }
80
81 private static int testWorstExp() {
82 int failures = 0;
83 double [][] testCases = {
84 {-0x1.E8BDBFCD9144Ep3, 0x1.F3E558CF4DE54p-23},
85 {-0x1.71E0B869B5E79p2, 0x1.951C6DC5D24E2p-9},
86 {-0x1.02393D5976769p1, 0x1.1064B2C103DDAp-3},
87 {-0x1.2A9CAD9998262p0, 0x1.3EF1E9B3A81C7p-2},
88 {-0x1.CC37EF7DE7501p0, 0x1.534D4DE870713p-3},
89 {-0x1.22E24FA3D5CF9p-1, 0x1.2217147B85EA9p-1},
90 {-0x1.DC2B5DF1F7D3Dp-1, 0x1.9403FD0EE51C8p-2},
91 {-0x1.290EA09E36479p-3, 0x1.BADED30CBF1C3p-1},
92 {-0x1.A2FEFEFD580DFp-13, 0x1.FFE5D0BB7EABFp-1},
93 {-0x1.ED318EFB627EAp-27, 0x1.FFFFFF84B39C4p-1},
94 {-0x1.4BD46601AE1EFp-31, 0x1.FFFFFFFAD0AE6p-1},
95 {-0x1.1000000000242p-42, 0x1.FFFFFFFFFF780p-1},
96 {-0x1.2000000000288p-42, 0x1.FFFFFFFFFF700p-1},
97 {-0x1.8000000000012p-48, 0x1.FFFFFFFFFFFD0p-1},
98 {-0x1.0000000000001p-51, 0x1.FFFFFFFFFFFFCp-1},
99
100 {+0x1.FFFFFFFFFFFFFp-53, 0x1.0000000000000p0},
101 {+0x1.FFFFFFFFFFFE0p-48, 0x1.000000000001Fp0},
102 {+0x1.7FFE7FFEE0024p-32, 0x1.000000017FFE8p0},
103 {+0x1.80017FFEDFFDCp-32, 0x1.0000000180017p0},
104 {+0x1.9E9CBBFD6080Bp-31, 0x1.000000033D397p0},
105 {+0x1.D7A7D893609E5p-26, 0x1.00000075E9F64p0},
106 {+0x1.BA07D73250DE7p-14, 0x1.0006E83736F8Cp0},
107 {+0x1.D77FD13D27FFFp-11, 0x1.003AF6C37C1D3p0},
108 {+0x1.6A4D1AF9CC989p-8, 0x1.016B4DF3299D7p0},
109 {+0x1.ACCFBE46B4EF0p-1, 0x2.4F85C9783DCE0p0},
110 {+0x1.ACA7AE8DA5A7Bp0, 0x5.55F52B35F955Ap0},
111 {+0x1.D6336A88077AAp0, 0x6.46A37FD503FDCp0},
112 {+0x2.85DC78FB8928Cp0, 0xC.76F2496CB038Fp0},
113 {+0x1.76E7E5D7B6EACp3, 0x1.DE7CD6751029Ap16},
114 {+0x1.A8EAD058BC6B8p3, 0x1.1D71965F516ADp19},
115 {+0x1.1D5C2DAEBE367p4, 0x1.A8C02E974C314p25},
116 {+0x1.C44CE0D716A1Ap4, 0x1.B890CA8637AE1p40},
117 };
118
119 for(double[] testCase: testCases) {
120 failures += testExpCase(testCase[0], testCase[1]);
121 }
122
123 return failures;
124 }
125
126 private static int testExpCase(double input, double expected) {
127 int failures = 0;
128 double out = Tests.nextOut(expected);
129 failures += Tests.testBounds("Math.exp", input, Math.exp(input), expected, out);
130 failures += Tests.testBounds("StrictMath.exp", input, StrictMath.exp(input), expected, out);
131 return failures;
132 }
133
134 private static int testWorstLog() {
135 int failures = 0;
136 double [][] testCases = {
137 {+0x1.0000000000001p0, +0x1.FFFFFFFFFFFFFp-53},
138 {+0x2.0012ECB039C9Cp0, +0x1.62F71C4656B60p-1},
139 {+0x6.46A37FD503FDCp0, +0x1.D6336A88077A9p+0},
140 {+0x7.78DFECC7F57Fp0, +0x2.02DD059DB46Bp+0},
141 {+0x9.588CCF24BB9C8p0, +0x2.3C24DEBB2BE7p+0},
142 {+0xA.AF87550D97E4p0, +0x2.5E706595A7ABEp+0},
143 {+0xC.76F2496CB039p0, +0x2.85DC78FB8928Cp+0},
144 {+0x11.1867637CBD03p0, +0x2.D6BBEFC79A842p+0},
145 {+0x13.D9D7D597A9DDp0, +0x2.FCFE12AE07DDCp+0},
146 {+0x17.F3825778AAAFp0, +0x3.2D0F907F5E00Cp+0},
147 {+0x1AC.50B409C8AEEp0, +0x6.0F52F37AECFCCp+0},
148 {+0x1.DE7CD6751029Ap16, +0x1.76E7E5D7B6EABp+3},
149 };
150
151 for(double[] testCase: testCases) {
152 failures += testLogCase(testCase[0], testCase[1]);
153 }
154
155 return failures;
156 }
157
158 private static int testLogCase(double input, double expected) {
159 int failures = 0;
160 double out = Tests.nextOut(expected);
161 failures += Tests.testBounds("Math.log", input, Math.log(input), expected, out);
162 failures += Tests.testBounds("StrictMath.log", input, StrictMath.log(input), expected, out);
163 return failures;
164 }
165
166 private static int testWorstSin() {
167 int failures = 0;
168 double [][] testCases = {
169 {+0x1.E0000000001C2p-20, +0x1.DFFFFFFFFF02Ep-20},
170 {+0x1.598BAE9E632F6p-7, +0x1.598A0AEA48996p-7},
171
172 {+0x1.9283586503FEp-5, +0x1.9259E3708BD39p-5},
173 {+0x1.D7BDCD778049Fp-5, +0x1.D77B117F230D5p-5},
174 {+0x1.A202B3FB84788p-4, +0x1.A1490C8C06BA6p-4},
175 {+0x1.D037CB27EE6DFp-3, +0x1.CC40C3805229Ap-3},
176 {+0x1.D5064E6FE82C5p-3, +0x1.D0EF799001BA9p-3},
177 {+0x1.FE767739D0F6Dp-2, +0x1.E9950730C4695p-2},
178 {+0x1.D98C4C612718Dp-1, +0x1.98DCD09337792p-1},
179 {+0x1.921FB54442D18p-0, +0x1.FFFFFFFFFFFFFp-1},
180
181 {+0x1.6756745770A51p+1, +0x1.4FF350E412821p-2},
182 };
183
184 for(double[] testCase: testCases) {
185 failures += testSinCase(testCase[0], testCase[1]);
186 }
187
188 return failures;
189 }
190
191 private static int testSinCase(double input, double expected) {
192 int failures = 0;
193 double out = Tests.nextOut(expected);
194 failures += Tests.testBounds("Math.sin", input, Math.sin(input), expected, out);
195 failures += Tests.testBounds("StrictMath.sin", input, StrictMath.sin(input), expected, out);
196 return failures;
197 }
198
199 private static int testWorstAsin() {
200 int failures = 0;
201 double [][] testCases = {
202 {+0x1.DFFFFFFFFF02Ep-20, +0x1.E0000000001C1p-20},
203 {+0x1.DFFFFFFFFC0B8p-19, +0x1.E000000000707p-19},
204
205 {+0x1.9259E3708BD3Ap-5, +0x1.9283586503FEp-5},
206 {+0x1.D77B117F230D6p-5, +0x1.D7BDCD778049Fp-5},
207 {+0x1.A1490C8C06BA7p-4, +0x1.A202B3FB84788p-4},
208 {+0x1.9697CB602C582p-3, +0x1.994FFB5DAF0F9p-3},
209 {+0x1.D0EF799001BA9p-3, +0x1.D5064E6FE82C4p-3},
210 {+0x1.E9950730C4696p-2, +0x1.FE767739D0F6Dp-2},
211 {+0x1.1ED06D50F7E88p-1, +0x1.30706F699466Dp-1},
212 {+0x1.D5B05A89D3E77p-1, +0x1.29517AB4C132Ap+0},
213 {+0x1.E264357EA0E29p-1, +0x1.3AA301F6EBB1Dp+0},
214 };
215
216 for(double[] testCase: testCases) {
217 failures += testAsinCase(testCase[0], testCase[1]);
218 }
219
220 return failures;
221 }
222
223 private static int testAsinCase(double input, double expected) {
224 int failures = 0;
225 double out = Tests.nextOut(expected);
226 failures += Tests.testBounds("Math.asin", input, Math.asin(input), expected, out);
227 failures += Tests.testBounds("StrictMath.asin", input, StrictMath.asin(input), expected, out);
228 return failures;
229 }
230
231 private static int testWorstCos() {
232 int failures = 0;
233 double [][] testCases = {
234 {+0x1.8000000000009p-23, +0x0.FFFFFFFFFFFB8p+0},
235 {+0x1.8000000000024p-22, +0x0.FFFFFFFFFFEE0p+0},
236 {+0x1.2000000000F30p-18, +0x0.FFFFFFFFF5E00p+0},
237 {+0x1.06B505550E6B2p-9, +0x0.FFFFDE4D1FDFFp+0},
238 {+0x1.97CCD3D2C438Fp-6, +0x0.FFEBB35D43854p+0},
239
240 {+0x1.549EC0C0C5AFAp-5, +0x1.FF8EB6A91ECB0p-1},
241 {+0x1.16E534EE36580p-4, +0x1.FED0476FC75C9p-1},
242 {+0x1.EFEEF61D39AC2p-3, +0x1.F10FC61E2C78Ep-1},
243 {+0x1.FEB1F7920E248p-2, +0x1.C1A27AE836F12p-1},
244 {+0x1.7CB7648526F99p-1, +0x1.78DAF01036D0Cp-1},
245 {+0x1.C65A170474549p-1, +0x1.434A3645BE208p-1},
246 {+0x1.6B8A6273D7C21p+0, +0x1.337FC5B072C52p-3},
247 };
248
249 for(double[] testCase: testCases) {
250 failures += testCosCase(testCase[0], testCase[1]);
251 }
252
253 return failures;
254 }
255
256 private static int testCosCase(double input, double expected) {
257 int failures = 0;
258 double out = Tests.nextOut(expected);
259 failures += Tests.testBounds("Math.cos", input, Math.cos(input), expected, out);
260 failures += Tests.testBounds("StrictMath.cos", input, StrictMath.cos(input), expected, out);
261 return failures;
262 }
263
264 private static int testWorstAcos() {
265 int failures = 0;
266 double [][] testCases = {
267 {+0x1.FD737BE914578p-11, +0x1.91E006D41D8D8p+0},
268 {+0x1.4182199998587p-1, +0x1.C8A538AE83D1Fp-1},
269 {+0x1.E45A1C93651ECp-1, +0x1.520DC553F6B23p-2},
270 {+0x1.F10FC61E2C78Fp-1, +0x1.EFEEF61D39AC1p-3},
271 };
272
273 for(double[] testCase: testCases) {
274 failures += testAcosCase(testCase[0], testCase[1]);
275 }
276
277 return failures;
278 }
279
280 private static int testAcosCase(double input, double expected) {
281 int failures = 0;
282 double out = Tests.nextOut(expected);
283 failures += Tests.testBounds("Math.acos", input, Math.acos(input), expected, out);
284 failures += Tests.testBounds("StrictMath.acos", input, StrictMath.acos(input), expected, out);
285 return failures;
286 }
287
288 private static int testWorstTan() {
289 int failures = 0;
290 double [][] testCases = {
291 {+0x1.DFFFFFFFFFF1Fp-22, +0x1.E000000000151p-22},
292 {+0x1.67FFFFFFFA114p-18, +0x1.6800000008E61p-18},
293
294 {+0x1.50486B2F87014p-5, +0x1.5078CEBFF9C72p-5},
295 {+0x1.52C39EF070CADp-4, +0x1.5389E6DF41978p-4},
296 {+0x1.A33F32AC5CEB5p-3, +0x1.A933FE176B375p-3},
297 {+0x1.D696BFA988DB9p-2, +0x1.FAC71CD34EEA6p-2},
298 {+0x1.46AC372243536p-1, +0x1.7BA49F739829Ep-1},
299 {+0x0.A3561B9121A9Bp+0, +0x0.BDD24FB9CC14Fp+0},
300 };
301
302 for(double[] testCase: testCases) {
303 failures += testTanCase(testCase[0], testCase[1]);
304 }
305
306 return failures;
307 }
308
309 private static int testTanCase(double input, double expected) {
310 int failures = 0;
311 double out = Tests.nextOut(expected);
312 failures += Tests.testBounds("Math.tan", input, Math.tan(input), expected, out);
313 failures += Tests.testBounds("StrictMath.tan", input, StrictMath.tan(input), expected, out);
314 return failures;
315 }
316
317 private static int testWorstAtan() {
318 int failures = 0;
319 double [][] testCases = {
320 {+0x1.E000000000546p-21, +0x1.DFFFFFFFFFC7Cp-21},
321 {+0x1.22E8D75E2BC7Fp-11, +0x1.22E8D5694AD2Bp-11},
322
323 {+0x1.0FC9F1FABE658p-5, +0x1.0FB06EDE9973Ap-5},
324 {+0x1.1BBE9C255698Dp-5, +0x1.1BA1951DB1D6Dp-5},
325 {+0x1.8DDD25AB90CA1p-5, +0x1.8D8D2D4BD6FA2p-5},
326 {+0x1.5389E6DF41979p-4, +0x1.52C39EF070CADp-4},
327 {+0x1.A933FE176B375p-3, +0x1.A33F32AC5CEB4p-3},
328 {+0x1.0F6E5D9960397p-2, +0x1.09544B71AD4A6p-2},
329 {+0x1.7BA49F739829Fp-1, +0x1.46AC372243536p-1},
330
331 {+0x0.BDD24FB9CC14F8p+0, +0x0.A3561B9121A9Bp+0},
332 };
333
334 for(double[] testCase: testCases) {
335 failures += testAtanCase(testCase[0], testCase[1]);
336 }
337
338 return failures;
339 }
340
341 private static int testAtanCase(double input, double expected) {
342 int failures = 0;
343 double out = Tests.nextOut(expected);
344 failures += Tests.testBounds("Math.atan", input, Math.atan(input), expected, out);
345 failures += Tests.testBounds("StrictMath.atan", input, StrictMath.atan(input), expected, out);
346 return failures;
347 }
348
349 private static int testWorstPow2() {
350 int failures = 0;
351 double [][] testCases = {
352 {+0x1.16A76EC41B516p-1, +0x1.7550685A42C63p+0},
353 {+0x1.3E34FA6AB969Ep-1, +0x1.89D948A94FE16p+0},
354 {+0x1.4A63FF1D53F53p-1, +0x1.90661DA12D528p+0},
355 {+0x1.B32A6C92D1185p-1, +0x1.CD6B37EDECEAFp+0},
356
357 {+0x1.25DD9EEDAC79Ap+0, +0x1.1BA39FF28E3E9p+1},
358 };
359
360 for(double[] testCase: testCases) {
361 failures += testPow2Case(testCase[0], testCase[1]);
362 }
363
364 return failures;
365 }
366
367 private static int testPow2Case(double input, double expected) {
368 int failures = 0;
369 double out = Tests.nextOut(expected);
370 failures += Tests.testBounds("Math.pow2", input, Math.pow(2, input), expected, out);
371 failures += Tests.testBounds("StrictMath.pow2", input, StrictMath.pow(2, input), expected, out);
372 return failures;
373 }
374
375 // 2.5 ulp error bound in the specification; the implementation
376 // does better on the tested values.
377 private static int testWorstSinh() {
378 int failures = 0;
379 double [][] testCases = {
380 {+0x1.DFFFFFFFFFE3Ep-20, +0x1.E000000000FD1p-20},
381 {+0x1.DFFFFFFFFE3E0p-18, +0x1.E00000000FD1Fp-18},
382 {+0x1.135E31FDD05D3p-5, +0x1.136B78B25CC57p-5},
383 {+0x1.0DC68D5E8F959p-3, +0x1.0E8E73DC4FEE3p-3},
384 {+0x1.616CC75D49226p-2, +0x1.687BD068C1C1Ep-2},
385 {+0x1.3FFC12B81CBC2p+0, +0x1.9A0FF413A1AF2p+0},
386 {+0x2.FE008C44BACA2p+0, +0x9.F08A43ED03AEp+0},
387 {+0x1.C089FCF166171p+4, +0x1.5C452E0E37569p+39},
388 {+0x1.E07E71BFCF06Fp+5, +0x1.91EC4412C344Fp+85},
389 {+0x1.54CD1FEA7663Ap+7, +0x1.C90810D354618p+244},
390 {+0x1.D6479EBA7C971p+8, +0x1.62A88613629B5p+677},
391 };
392
393 for(double[] testCase: testCases) {
394 failures += testSinhCase(testCase[0], testCase[1]);
395 }
396
397 return failures;
398 }
399
400 private static int testSinhCase(double input, double expected) {
401 int failures = 0;
402 double out = Tests.nextOut(expected);
403 failures += Tests.testBounds("Math.sinh", input, Math.sinh(input), expected, out);
404 failures += Tests.testBounds("StrictMath.sinh", input, StrictMath.sinh(input), expected, out);
405 return failures;
406 }
407
408 // 2.5 ulp error bound in the specification; the implementation
409 // does better on the tested values.
410 private static int testWorstCosh() {
411 int failures = 0;
412 double [][] testCases = {
413 {+0x1.17D8A9F206217p-6, +0x1.00098F5F09BE3p+0},
414 {+0x1.BF0305E2C6C37p-3, +0x1.061F4C39E16F2p+0},
415 {+0x1.03923F2B47C07p-1, +0x1.219C1989E3372p+0},
416 {+0x1.A6031CD5F93BAp-1, +0x1.5BFF041B260FDp+0},
417 {+0x1.104B648F113A1p+0, +0x1.9EFDCA62B7009p+0},
418 {+0x1.EA5F2F2E4B0C5p+1, +0x17.10DB0CD0FED5p+0},
419 };
420
421 for(double[] testCase: testCases) {
422 failures += testCoshCase(testCase[0], testCase[1]);
423 }
424
425 return failures;
426 }
427
428 private static int testCoshCase(double input, double expected) {
429 int failures = 0;
430 double out = Tests.nextOut(expected);
431 failures += Tests.testBounds("Math.cosh", input, Math.cosh(input), expected, out);
432 failures += Tests.testBounds("StrictMath.cosh", input, StrictMath.cosh(input), expected, out);
433 return failures;
434 }
435 }