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  * @library /lib/testlibrary
  29  * @build jdk.testlibrary.DoubleUtils jdk.testlibrary.FloatUtils
  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 }