HyperbolicTests.java revision 9330:8b1f1c2a400f
1/* 2 * Copyright (c) 2003, 2012, 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 4851625 4900189 4939441 27 * @summary Tests for {Math, StrictMath}.{sinh, cosh, tanh} 28 * @author Joseph D. Darcy 29 */ 30 31import sun.misc.DoubleConsts; 32 33public class HyperbolicTests { 34 private HyperbolicTests(){} 35 36 static final double NaNd = Double.NaN; 37 38 /** 39 * Test accuracy of {Math, StrictMath}.sinh. The specified 40 * accuracy is 2.5 ulps. 41 * 42 * The defintion of sinh(x) is 43 * 44 * (e^x - e^(-x))/2 45 * 46 * The series expansion of sinh(x) = 47 * 48 * x + x^3/3! + x^5/5! + x^7/7! +... 49 * 50 * Therefore, 51 * 52 * 1. For large values of x sinh(x) ~= signum(x)*exp(|x|)/2 53 * 54 * 2. For small values of x, sinh(x) ~= x. 55 * 56 * Additionally, sinh is an odd function; sinh(-x) = -sinh(x). 57 * 58 */ 59 static int testSinh() { 60 int failures = 0; 61 /* 62 * Array elements below generated using a quad sinh 63 * implementation. Rounded to a double, the quad result 64 * *should* be correctly rounded, unless we are quite unlucky. 65 * Assuming the quad value is a correctly rounded double, the 66 * allowed error is 3.0 ulps instead of 2.5 since the quad 67 * value rounded to double can have its own 1/2 ulp error. 68 */ 69 double [][] testCases = { 70 // x sinh(x) 71 {0.0625, 0.06254069805219182172183988501029229}, 72 {0.1250, 0.12532577524111545698205754229137154}, 73 {0.1875, 0.18860056562029018382047025055167585}, 74 {0.2500, 0.25261231680816830791412515054205787}, 75 {0.3125, 0.31761115611357728583959867611490292}, 76 {0.3750, 0.38385106791361456875429567642050245}, 77 {0.4375, 0.45159088610312053032509815226723017}, 78 {0.5000, 0.52109530549374736162242562641149155}, 79 {0.5625, 0.59263591611468777373870867338492247}, 80 {0.6250, 0.66649226445661608227260655608302908}, 81 {0.6875, 0.74295294580567543571442036910465007}, 82 {0.7500, 0.82231673193582998070366163444691386}, 83 {0.8125, 0.90489373856606433650504536421491368}, 84 {0.8750, 0.99100663714429475605317427568995231}, 85 {0.9375, 1.08099191569306394011007867453992548}, 86 {1.0000, 1.17520119364380145688238185059560082}, 87 {1.0625, 1.27400259579739321279181130344911907}, 88 {1.1250, 1.37778219077984075760379987065228373}, 89 {1.1875, 1.48694549961380717221109202361777593}, 90 {1.2500, 1.60191908030082563790283030151221415}, 91 {1.3125, 1.72315219460596010219069206464391528}, 92 {1.3750, 1.85111856355791532419998548438506416}, 93 {1.4375, 1.98631821852425112898943304217629457}, 94 {1.5000, 2.12927945509481749683438749467763195}, 95 {1.5625, 2.28056089740825247058075476705718764}, 96 {1.6250, 2.44075368098794353221372986997161132}, 97 {1.6875, 2.61048376261693140366028569794027603}, 98 {1.7500, 2.79041436627764265509289122308816092}, 99 {1.8125, 2.98124857471401377943765253243875520}, 100 {1.8750, 3.18373207674259205101326780071803724}, 101 {1.9375, 3.39865608104779099764440244167531810}, 102 {2.0000, 3.62686040784701876766821398280126192}, 103 {2.0625, 3.86923677050642806693938384073620450}, 104 {2.1250, 4.12673225993027252260441410537905269}, 105 {2.1875, 4.40035304533919660406976249684469164}, 106 {2.2500, 4.69116830589833069188357567763552003}, 107 {2.3125, 5.00031440855811351554075363240262157}, 108 {2.3750, 5.32899934843284576394645856548481489}, 109 {2.4375, 5.67850746906785056212578751630266858}, 110 {2.5000, 6.05020448103978732145032363835040319}, 111 {2.5625, 6.44554279850040875063706020260185553}, 112 {2.6250, 6.86606721451642172826145238779845813}, 113 {2.6875, 7.31342093738196587585692115636603571}, 114 {2.7500, 7.78935201149073201875513401029935330}, 115 {2.8125, 8.29572014785741787167717932988491961}, 116 {2.8750, 8.83450399097893197351853322827892144}, 117 {2.9375, 9.40780885043076394429977972921690859}, 118 {3.0000, 10.01787492740990189897459361946582867}, 119 {3.0625, 10.66708606836969224165124519209968368}, 120 {3.1250, 11.35797907995166028304704128775698426}, 121 {3.1875, 12.09325364161259019614431093344260209}, 122 {3.2500, 12.87578285468067003959660391705481220}, 123 {3.3125, 13.70862446906136798063935858393686525}, 124 {3.3750, 14.59503283146163690015482636921657975}, 125 {3.4375, 15.53847160182039311025096666980558478}, 126 {3.5000, 16.54262728763499762495673152901249743}, 127 {3.5625, 17.61142364906941482858466494889121694}, 128 {3.6250, 18.74903703113232171399165788088277979}, 129 {3.6875, 19.95991268283598684128844120984214675}, 130 {3.7500, 21.24878212710338697364101071825171163}, 131 {3.8125, 22.62068164929685091969259499078125023}, 132 {3.8750, 24.08097197661255803883403419733891573}, 133 {3.9375, 25.63535922523855307175060244757748997}, 134 {4.0000, 27.28991719712775244890827159079382096}, 135 {4.0625, 29.05111111351106713777825462100160185}, 136 {4.1250, 30.92582287788986031725487699744107092}, 137 {4.1875, 32.92137796722343190618721270937061472}, 138 {4.2500, 35.04557405638942942322929652461901154}, 139 {4.3125, 37.30671148776788628118833357170042385}, 140 {4.3750, 39.71362570500944929025069048612806024}, 141 {4.4375, 42.27572177772344954814418332587050658}, 142 {4.5000, 45.00301115199178562180965680564371424}, 143 {4.5625, 47.90615077031205065685078058248081891}, 144 {4.6250, 50.99648471383193131253995134526177467}, 145 {4.6875, 54.28608852959281437757368957713936555}, 146 {4.7500, 57.78781641599226874961859781628591635}, 147 {4.8125, 61.51535145084362283008545918273109379}, 148 {4.8750, 65.48325905829987165560146562921543361}, 149 {4.9375, 69.70704392356508084094318094283346381}, 150 {5.0000, 74.20321057778875897700947199606456364}, 151 {5.0625, 78.98932788987998983462810080907521151}, 152 {5.1250, 84.08409771724448958901392613147384951}, 153 {5.1875, 89.50742798369883598816307922895346849}, 154 {5.2500, 95.28051047011540739630959111303975956}, 155 {5.3125, 101.42590362176666730633859252034238987}, 156 {5.3750, 107.96762069594029162704530843962700133}, 157 {5.4375, 114.93122359426386042048760580590182604}, 158 {5.5000, 122.34392274639096192409774240457730721}, 159 {5.5625, 130.23468343534638291488502321709913206}, 160 {5.6250, 138.63433897999898233879574111119546728}, 161 {5.6875, 147.57571121692522056519568264304815790}, 162 {5.7500, 157.09373875244884423880085377625986165}, 163 {5.8125, 167.22561348600435888568183143777868662}, 164 {5.8750, 178.01092593829229887752609866133883987}, 165 {5.9375, 189.49181995209921964640216682906501778}, 166 {6.0000, 201.71315737027922812498206768797872263}, 167 {6.0625, 214.72269333437984291483666459592578915}, 168 {6.1250, 228.57126288889537420461281285729970085}, 169 {6.1875, 243.31297962030799867970551767086092471}, 170 {6.2500, 259.00544710710289911522315435345489966}, 171 {6.3125, 275.70998400700299790136562219920451185}, 172 {6.3750, 293.49186366095654566861661249898332253}, 173 {6.4375, 312.42056915013535342987623229485223434}, 174 {6.5000, 332.57006480258443156075705566965111346}, 175 {6.5625, 354.01908521044116928437570109827956007}, 176 {6.6250, 376.85144288706511933454985188849781703}, 177 {6.6875, 401.15635576625530823119100750634165252}, 178 {6.7500, 427.02879582326538080306830640235938517}, 179 {6.8125, 454.56986017986077163530945733572724452}, 180 {6.8750, 483.88716614351897894746751705315210621}, 181 {6.9375, 515.09527172439720070161654727225752288}, 182 {7.0000, 548.31612327324652237375611757601851598}, 183 {7.0625, 583.67953198942753384680988096024373270}, 184 {7.1250, 621.32368116099280160364794462812762880}, 185 {7.1875, 661.39566611888784148449430491465857519}, 186 {7.2500, 704.05206901515336623551137120663358760}, 187 {7.3125, 749.45957067108712382864538206200700256}, 188 {7.3750, 797.79560188617531521347351754559776282}, 189 {7.4375, 849.24903675279739482863565789325699416}, 190 {7.5000, 904.02093068584652953510919038935849651}, 191 {7.5625, 962.32530605113249628368993221570636328}, 192 {7.6250, 1024.38998846242707559349318193113614698}, 193 {7.6875, 1090.45749701500081956792547346904792325}, 194 {7.7500, 1160.78599193425808533255719118417856088}, 195 {7.8125, 1235.65028334242796895820912936318532502}, 196 {7.8750, 1315.34290508508890654067255740428824014}, 197 {7.9375, 1400.17525781352742299995139486063802583}, 198 {8.0000, 1490.47882578955018611587663903188144796}, 199 {8.0625, 1586.60647216744061169450001100145859236}, 200 {8.1250, 1688.93381781440241350635231605477507900}, 201 {8.1875, 1797.86070905726094477721128358866360644}, 202 {8.2500, 1913.81278009067446281883262689250118009}, 203 {8.3125, 2037.24311615199935553277163192983440062}, 204 {8.3750, 2168.63402396170125867037749369723761636}, 205 {8.4375, 2308.49891634734644432370720900969004306}, 206 {8.5000, 2457.38431841538268239359965370719928775}, 207 {8.5625, 2615.87200310986940554256648824234335262}, 208 {8.6250, 2784.58126450289932429469130598902487336}, 209 {8.6875, 2964.17133769964321637973459949999057146}, 210 {8.7500, 3155.34397481384944060352507473513108710}, 211 {8.8125, 3358.84618707947841898217318996045550438}, 212 {8.8750, 3575.47316381333288862617411467285480067}, 213 {8.9375, 3806.07137963459383403903729660349293583}, 214 {9.0000, 4051.54190208278996051522359589803425598}, 215 {9.0625, 4312.84391255878980330955246931164633615}, 216 {9.1250, 4590.99845434696991399363282718106006883}, 217 {9.1875, 4887.09242236403719571363798584676797558}, 218 {9.2500, 5202.28281022453561319352901552085348309}, 219 {9.3125, 5537.80123121853803935727335892054791265}, 220 {9.3750, 5894.95873086734181634245918412592155656}, 221 {9.4375, 6275.15090986233399457103055108344546942}, 222 {9.5000, 6679.86337740502119410058225086262108741}, 223 {9.5625, 7110.67755625726876329967852256934334025}, 224 {9.6250, 7569.27686218510919585241049433331592115}, 225 {9.6875, 8057.45328194243077504648484392156371121}, 226 {9.7500, 8577.11437549816065709098061006273039092}, 227 {9.8125, 9130.29072986829727910801024120918114778}, 228 {9.8750, 9719.14389367880274015504995181862860062}, 229 {9.9375, 10345.97482346383208590278839409938269134}, 230 {10.0000, 11013.23287470339337723652455484636420303}, 231 }; 232 233 for(int i = 0; i < testCases.length; i++) { 234 double [] testCase = testCases[i]; 235 failures += testSinhCaseWithUlpDiff(testCase[0], 236 testCase[1], 237 3.0); 238 } 239 240 double [][] specialTestCases = { 241 {0.0, 0.0}, 242 {NaNd, NaNd}, 243 {Double.longBitsToDouble(0x7FF0000000000001L), NaNd}, 244 {Double.longBitsToDouble(0xFFF0000000000001L), NaNd}, 245 {Double.longBitsToDouble(0x7FF8555555555555L), NaNd}, 246 {Double.longBitsToDouble(0xFFF8555555555555L), NaNd}, 247 {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd}, 248 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd}, 249 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, 250 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, 251 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, 252 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, 253 {Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY} 254 }; 255 256 for(int i = 0; i < specialTestCases.length; i++) { 257 failures += testSinhCaseWithUlpDiff(specialTestCases[i][0], 258 specialTestCases[i][1], 259 0.0); 260 } 261 262 // For powers of 2 less than 2^(-27), the second and 263 // subsequent terms of the Taylor series expansion will get 264 // rounded away since |n-n^3| > 53, the binary precision of a 265 // double significand. 266 267 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i < -27; i++) { 268 double d = Math.scalb(2.0, i); 269 270 // Result and expected are the same. 271 failures += testSinhCaseWithUlpDiff(d, d, 2.5); 272 } 273 274 // For values of x larger than 22, the e^(-x) term is 275 // insignificant to the floating-point result. Util exp(x) 276 // overflows around 709.8, sinh(x) ~= exp(x)/2; will will test 277 // 10000 values in this range. 278 279 long trans22 = Double.doubleToLongBits(22.0); 280 // (approximately) largest value such that exp shouldn't 281 // overflow 282 long transExpOvfl = Double.doubleToLongBits(Math.nextDown(709.7827128933841)); 283 284 for(long i = trans22; 285 i < transExpOvfl; 286 i +=(transExpOvfl-trans22)/10000) { 287 288 double d = Double.longBitsToDouble(i); 289 290 // Allow 3.5 ulps of error to deal with error in exp. 291 failures += testSinhCaseWithUlpDiff(d, StrictMath.exp(d)*0.5, 3.5); 292 } 293 294 // (approximately) largest value such that sinh shouldn't 295 // overflow. 296 long transSinhOvfl = Double.doubleToLongBits(710.4758600739439); 297 298 // Make sure sinh(x) doesn't overflow as soon as exp(x) 299 // overflows. 300 301 /* 302 * For large values of x, sinh(x) ~= 0.5*(e^x). Therefore, 303 * 304 * sinh(x) ~= e^(ln 0.5) * e^x = e^(x + ln 0.5) 305 * 306 * So, we can calculate the approximate expected result as 307 * exp(x + -0.693147186). However, this sum suffers from 308 * roundoff, limiting the accuracy of the approximation. The 309 * accuracy can be improved by recovering the rounded-off 310 * information. Since x is larger than ln(0.5), the trailing 311 * bits of ln(0.5) get rounded away when the two values are 312 * added. However, high-order bits of ln(0.5) that 313 * contribute to the sum can be found: 314 * 315 * offset = log(0.5); 316 * effective_offset = (x + offset) - x; // exact subtraction 317 * rounded_away_offset = offset - effective_offset; // exact subtraction 318 * 319 * Therefore, the product 320 * 321 * exp(x + offset)*exp(rounded_away_offset) 322 * 323 * will be a better approximation to the exact value of 324 * 325 * e^(x + offset) 326 * 327 * than exp(x+offset) alone. (The expected result cannot be 328 * computed as exp(x)*exp(offset) since exp(x) by itself would 329 * overflow to infinity.) 330 */ 331 double offset = StrictMath.log(0.5); 332 for(long i = transExpOvfl+1; i < transSinhOvfl; 333 i += (transSinhOvfl-transExpOvfl)/1000 ) { 334 double input = Double.longBitsToDouble(i); 335 336 double expected = 337 StrictMath.exp(input + offset) * 338 StrictMath.exp( offset - ((input + offset) - input) ); 339 340 failures += testSinhCaseWithUlpDiff(input, expected, 4.0); 341 } 342 343 // sinh(x) overflows for values greater than 710; in 344 // particular, it overflows for all 2^i, i > 10. 345 for(int i = 10; i <= DoubleConsts.MAX_EXPONENT; i++) { 346 double d = Math.scalb(2.0, i); 347 348 // Result and expected are the same. 349 failures += testSinhCaseWithUlpDiff(d, 350 Double.POSITIVE_INFINITY, 0.0); 351 } 352 353 return failures; 354 } 355 356 public static int testSinhCaseWithTolerance(double input, 357 double expected, 358 double tolerance) { 359 int failures = 0; 360 failures += Tests.testTolerance("Math.sinh(double)", 361 input, Math.sinh(input), 362 expected, tolerance); 363 failures += Tests.testTolerance("Math.sinh(double)", 364 -input, Math.sinh(-input), 365 -expected, tolerance); 366 367 failures += Tests.testTolerance("StrictMath.sinh(double)", 368 input, StrictMath.sinh(input), 369 expected, tolerance); 370 failures += Tests.testTolerance("StrictMath.sinh(double)", 371 -input, StrictMath.sinh(-input), 372 -expected, tolerance); 373 return failures; 374 } 375 376 public static int testSinhCaseWithUlpDiff(double input, 377 double expected, 378 double ulps) { 379 int failures = 0; 380 failures += Tests.testUlpDiff("Math.sinh(double)", 381 input, Math.sinh(input), 382 expected, ulps); 383 failures += Tests.testUlpDiff("Math.sinh(double)", 384 -input, Math.sinh(-input), 385 -expected, ulps); 386 387 failures += Tests.testUlpDiff("StrictMath.sinh(double)", 388 input, StrictMath.sinh(input), 389 expected, ulps); 390 failures += Tests.testUlpDiff("StrictMath.sinh(double)", 391 -input, StrictMath.sinh(-input), 392 -expected, ulps); 393 return failures; 394 } 395 396 397 /** 398 * Test accuracy of {Math, StrictMath}.cosh. The specified 399 * accuracy is 2.5 ulps. 400 * 401 * The defintion of cosh(x) is 402 * 403 * (e^x + e^(-x))/2 404 * 405 * The series expansion of cosh(x) = 406 * 407 * 1 + x^2/2! + x^4/4! + x^6/6! +... 408 * 409 * Therefore, 410 * 411 * 1. For large values of x cosh(x) ~= exp(|x|)/2 412 * 413 * 2. For small values of x, cosh(x) ~= 1. 414 * 415 * Additionally, cosh is an even function; cosh(-x) = cosh(x). 416 * 417 */ 418 static int testCosh() { 419 int failures = 0; 420 /* 421 * Array elements below generated using a quad cosh 422 * implementation. Rounded to a double, the quad result 423 * *should* be correctly rounded, unless we are quite unlucky. 424 * Assuming the quad value is a correctly rounded double, the 425 * allowed error is 3.0 ulps instead of 2.5 since the quad 426 * value rounded to double can have its own 1/2 ulp error. 427 */ 428 double [][] testCases = { 429 // x cosh(x) 430 {0.0625, 1.001953760865667607841550709632597376}, 431 {0.1250, 1.007822677825710859846949685520422223}, 432 {0.1875, 1.017629683800690526835115759894757615}, 433 {0.2500, 1.031413099879573176159295417520378622}, 434 {0.3125, 1.049226785060219076999158096606305793}, 435 {0.3750, 1.071140346704586767299498015567016002}, 436 {0.4375, 1.097239412531012567673453832328262160}, 437 {0.5000, 1.127625965206380785226225161402672030}, 438 {0.5625, 1.162418740845610783505338363214045218}, 439 {0.6250, 1.201753692975606324229229064105075301}, 440 {0.6875, 1.245784523776616395403056980542275175}, 441 {0.7500, 1.294683284676844687841708185390181730}, 442 {0.8125, 1.348641048647144208352285714214372703}, 443 {0.8750, 1.407868656822803158638471458026344506}, 444 {0.9375, 1.472597542369862933336886403008640891}, 445 {1.0000, 1.543080634815243778477905620757061497}, 446 {1.0625, 1.619593348374367728682469968448090763}, 447 {1.1250, 1.702434658138190487400868008124755757}, 448 {1.1875, 1.791928268324866464246665745956119612}, 449 {1.2500, 1.888423877161015738227715728160051696}, 450 {1.3125, 1.992298543335143985091891077551921106}, 451 {1.3750, 2.103958159362661802010972984204389619}, 452 {1.4375, 2.223839037619709260803023946704272699}, 453 {1.5000, 2.352409615243247325767667965441644201}, 454 {1.5625, 2.490172284559350293104864895029231913}, 455 {1.6250, 2.637665356192137582275019088061812951}, 456 {1.6875, 2.795465162524235691253423614360562624}, 457 {1.7500, 2.964188309728087781773608481754531801}, 458 {1.8125, 3.144494087167972176411236052303565201}, 459 {1.8750, 3.337087043587520514308832278928116525}, 460 {1.9375, 3.542719740149244276729383650503145346}, 461 {2.0000, 3.762195691083631459562213477773746099}, 462 {2.0625, 3.996372503438463642260225717607554880}, 463 {2.1250, 4.246165228196992140600291052990934410}, 464 {2.1875, 4.512549935859540340856119781585096760}, 465 {2.2500, 4.796567530460195028666793366876218854}, 466 {2.3125, 5.099327816921939817643745917141739051}, 467 {2.3750, 5.422013837643509250646323138888569746}, 468 {2.4375, 5.765886495263270945949271410819116399}, 469 {2.5000, 6.132289479663686116619852312817562517}, 470 {2.5625, 6.522654518468725462969589397439224177}, 471 {2.6250, 6.938506971550673190999796241172117288}, 472 {2.6875, 7.381471791406976069645686221095397137}, 473 {2.7500, 7.853279872697439591457564035857305647}, 474 {2.8125, 8.355774815752725814638234943192709129}, 475 {2.8750, 8.890920130482709321824793617157134961}, 476 {2.9375, 9.460806908834119747071078865866737196}, 477 {3.0000, 10.067661995777765841953936035115890343}, 478 {3.0625, 10.713856690753651225304006562698007312}, 479 {3.1250, 11.401916013575067700373788969458446177}, 480 {3.1875, 12.134528570998387744547733730974713055}, 481 {3.2500, 12.914557062512392049483503752322408761}, 482 {3.3125, 13.745049466398732213877084541992751273}, 483 {3.3750, 14.629250949773302934853381428660210721}, 484 {3.4375, 15.570616549147269180921654324879141947}, 485 {3.5000, 16.572824671057316125696517821376119469}, 486 {3.5625, 17.639791465519127930722105721028711044}, 487 {3.6250, 18.775686128468677200079039891415789429}, 488 {3.6875, 19.984947192985946987799359614758598457}, 489 {3.7500, 21.272299872959396081877161903352144126}, 490 {3.8125, 22.642774526961913363958587775566619798}, 491 {3.8750, 24.101726314486257781049388094955970560}, 492 {3.9375, 25.654856121347151067170940701379544221}, 493 {4.0000, 27.308232836016486629201989612067059978}, 494 {4.0625, 29.068317063936918520135334110824828950}, 495 {4.1250, 30.941986372478026192360480044849306606}, 496 {4.1875, 32.936562165180269851350626768308756303}, 497 {4.2500, 35.059838290298428678502583470475012235}, 498 {4.3125, 37.320111495433027109832850313172338419}, 499 {4.3750, 39.726213847251883288518263854094284091}, 500 {4.4375, 42.287547242982546165696077854963452084}, 501 {4.5000, 45.014120148530027928305799939930642658}, 502 {4.5625, 47.916586706774825161786212701923307169}, 503 {4.6250, 51.006288368867753140854830589583165950}, 504 {4.6875, 54.295298211196782516984520211780624960}, 505 {4.7500, 57.796468111195389383795669320243166117}, 506 {4.8125, 61.523478966332915041549750463563672435}, 507 {4.8750, 65.490894152518731617237739112888213645}, 508 {4.9375, 69.714216430810089539924900313140922323}, 509 {5.0000, 74.209948524787844444106108044487704798}, 510 {5.0625, 78.995657605307475581204965926043112946}, 511 {5.1250, 84.090043934600961683400343038519519678}, 512 {5.1875, 89.513013937957834087706670952561002466}, 513 {5.2500, 95.285757988514588780586084642381131013}, 514 {5.3125, 101.430833209098212357990123684449846912}, 515 {5.3750, 107.972251614673824873137995865940755392}, 516 {5.4375, 114.935573939814969189535554289886848550}, 517 {5.5000, 122.348009517829425991091207107262038316}, 518 {5.5625, 130.238522601820409078244923165746295574}, 519 {5.6250, 138.637945543134998069351279801575968875}, 520 {5.6875, 147.579099269447055276899288971207106581}, 521 {5.7500, 157.096921533245353905868840194264636395}, 522 {5.8125, 167.228603431860671946045256541679445836}, 523 {5.8750, 178.013734732486824390148614309727161925}, 524 {5.9375, 189.494458570056311567917444025807275896}, 525 {6.0000, 201.715636122455894483405112855409538488}, 526 {6.0625, 214.725021906554080628430756558271312513}, 527 {6.1250, 228.573450380013557089736092321068279231}, 528 {6.1875, 243.315034578039208138752165587134488645}, 529 {6.2500, 259.007377561239126824465367865430519592}, 530 {6.3125, 275.711797500835732516530131577254654076}, 531 {6.3750, 293.493567280752348242602902925987643443}, 532 {6.4375, 312.422169552825597994104814531010579387}, 533 {6.5000, 332.571568241777409133204438572983297292}, 534 {6.5625, 354.020497560858198165985214519757890505}, 535 {6.6250, 376.852769667496146326030849450983914197}, 536 {6.6875, 401.157602161123700280816957271992998156}, 537 {6.7500, 427.029966702886171977469256622451185850}, 538 {6.8125, 454.570960119471524953536004647195906721}, 539 {6.8750, 483.888199441157626584508920036981010995}, 540 {6.9375, 515.096242417696720610477570797503766179}, 541 {7.0000, 548.317035155212076889964120712102928484}, 542 {7.0625, 583.680388623257719787307547662358502345}, 543 {7.1250, 621.324485894002926216918634755431456031}, 544 {7.1875, 661.396422095589629755266517362992812037}, 545 {7.2500, 704.052779189542208784574955807004218856}, 546 {7.3125, 749.460237818184878095966335081928645934}, 547 {7.3750, 797.796228612873763671070863694973560629}, 548 {7.4375, 849.249625508044731271830060572510241864}, 549 {7.5000, 904.021483770216677368692292389446994987}, 550 {7.5625, 962.325825625814651122171697031114091993}, 551 {7.6250, 1024.390476557670599008492465853663578558}, 552 {7.6875, 1090.457955538048482588540574008226583335}, 553 {7.7500, 1160.786422676798661020094043586456606003}, 554 {7.8125, 1235.650687987597295222707689125107720568}, 555 {7.8750, 1315.343285214046776004329388551335841550}, 556 {7.9375, 1400.175614911635999247504386054087931958}, 557 {8.0000, 1490.479161252178088627715460421007179728}, 558 {8.0625, 1586.606787305415349050508956232945539108}, 559 {8.1250, 1688.934113859132470361718199038326340668}, 560 {8.1875, 1797.860987165547537276364148450577336075}, 561 {8.2500, 1913.813041349231764486365114317586148767}, 562 {8.3125, 2037.243361581700856522236313401822532385}, 563 {8.3750, 2168.634254521568851112005905503069409349}, 564 {8.4375, 2308.499132938297821208734949028296170563}, 565 {8.5000, 2457.384521883751693037774022640629666294}, 566 {8.5625, 2615.872194250713123494312356053193077854}, 567 {8.6250, 2784.581444063104750127653362960649823247}, 568 {8.6875, 2964.171506380845754878370650565756538203}, 569 {8.7500, 3155.344133275174556354775488913749659006}, 570 {8.8125, 3358.846335940117183452010789979584950102}, 571 {8.8750, 3575.473303654961482727206202358956274888}, 572 {8.9375, 3806.071511003646460448021740303914939059}, 573 {9.0000, 4051.542025492594047194773093534725371440}, 574 {9.0625, 4312.844028491571841588188869958240355518}, 575 {9.1250, 4590.998563255739769060078863130940205710}, 576 {9.1875, 4887.092524674358252509551443117048351290}, 577 {9.2500, 5202.282906336187674588222835339193136030}, 578 {9.3125, 5537.801321507079474415176386655744387251}, 579 {9.3750, 5894.958815685577062811620236195525504885}, 580 {9.4375, 6275.150989541692149890530417987358096221}, 581 {9.5000, 6679.863452256851081801173722051940058824}, 582 {9.5625, 7110.677626574055535297758456126491707647}, 583 {9.6250, 7569.276928241617224537226019600213961572}, 584 {9.6875, 8057.453343996777301036241026375049070162}, 585 {9.7500, 8577.114433792824387959788368429252257664}, 586 {9.8125, 9130.290784631065880205118262838330689429}, 587 {9.8750, 9719.143945123662919857326995631317996715}, 588 {9.9375, 10345.974871791805753327922796701684092861}, 589 {10.0000, 11013.232920103323139721376090437880844591}, 590 }; 591 592 for(int i = 0; i < testCases.length; i++) { 593 double [] testCase = testCases[i]; 594 failures += testCoshCaseWithUlpDiff(testCase[0], 595 testCase[1], 596 3.0); 597 } 598 599 600 double [][] specialTestCases = { 601 {0.0, 1.0}, 602 {NaNd, NaNd}, 603 {Double.longBitsToDouble(0x7FF0000000000001L), NaNd}, 604 {Double.longBitsToDouble(0xFFF0000000000001L), NaNd}, 605 {Double.longBitsToDouble(0x7FF8555555555555L), NaNd}, 606 {Double.longBitsToDouble(0xFFF8555555555555L), NaNd}, 607 {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd}, 608 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd}, 609 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, 610 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, 611 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, 612 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, 613 {Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY} 614 }; 615 616 for(int i = 0; i < specialTestCases.length; i++ ) { 617 failures += testCoshCaseWithUlpDiff(specialTestCases[i][0], 618 specialTestCases[i][1], 619 0.0); 620 } 621 622 // For powers of 2 less than 2^(-27), the second and 623 // subsequent terms of the Taylor series expansion will get 624 // rounded. 625 626 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i < -27; i++) { 627 double d = Math.scalb(2.0, i); 628 629 // Result and expected are the same. 630 failures += testCoshCaseWithUlpDiff(d, 1.0, 2.5); 631 } 632 633 // For values of x larger than 22, the e^(-x) term is 634 // insignificant to the floating-point result. Util exp(x) 635 // overflows around 709.8, cosh(x) ~= exp(x)/2; will will test 636 // 10000 values in this range. 637 638 long trans22 = Double.doubleToLongBits(22.0); 639 // (approximately) largest value such that exp shouldn't 640 // overflow 641 long transExpOvfl = Double.doubleToLongBits(Math.nextDown(709.7827128933841)); 642 643 for(long i = trans22; 644 i < transExpOvfl; 645 i +=(transExpOvfl-trans22)/10000) { 646 647 double d = Double.longBitsToDouble(i); 648 649 // Allow 3.5 ulps of error to deal with error in exp. 650 failures += testCoshCaseWithUlpDiff(d, StrictMath.exp(d)*0.5, 3.5); 651 } 652 653 // (approximately) largest value such that cosh shouldn't 654 // overflow. 655 long transCoshOvfl = Double.doubleToLongBits(710.4758600739439); 656 657 // Make sure sinh(x) doesn't overflow as soon as exp(x) 658 // overflows. 659 660 /* 661 * For large values of x, cosh(x) ~= 0.5*(e^x). Therefore, 662 * 663 * cosh(x) ~= e^(ln 0.5) * e^x = e^(x + ln 0.5) 664 * 665 * So, we can calculate the approximate expected result as 666 * exp(x + -0.693147186). However, this sum suffers from 667 * roundoff, limiting the accuracy of the approximation. The 668 * accuracy can be improved by recovering the rounded-off 669 * information. Since x is larger than ln(0.5), the trailing 670 * bits of ln(0.5) get rounded away when the two values are 671 * added. However, high-order bits of ln(0.5) that 672 * contribute to the sum can be found: 673 * 674 * offset = log(0.5); 675 * effective_offset = (x + offset) - x; // exact subtraction 676 * rounded_away_offset = offset - effective_offset; // exact subtraction 677 * 678 * Therefore, the product 679 * 680 * exp(x + offset)*exp(rounded_away_offset) 681 * 682 * will be a better approximation to the exact value of 683 * 684 * e^(x + offset) 685 * 686 * than exp(x+offset) alone. (The expected result cannot be 687 * computed as exp(x)*exp(offset) since exp(x) by itself would 688 * overflow to infinity.) 689 */ 690 double offset = StrictMath.log(0.5); 691 for(long i = transExpOvfl+1; i < transCoshOvfl; 692 i += (transCoshOvfl-transExpOvfl)/1000 ) { 693 double input = Double.longBitsToDouble(i); 694 695 double expected = 696 StrictMath.exp(input + offset) * 697 StrictMath.exp( offset - ((input + offset) - input) ); 698 699 failures += testCoshCaseWithUlpDiff(input, expected, 4.0); 700 } 701 702 // cosh(x) overflows for values greater than 710; in 703 // particular, it overflows for all 2^i, i > 10. 704 for(int i = 10; i <= DoubleConsts.MAX_EXPONENT; i++) { 705 double d = Math.scalb(2.0, i); 706 707 // Result and expected are the same. 708 failures += testCoshCaseWithUlpDiff(d, 709 Double.POSITIVE_INFINITY, 0.0); 710 } 711 return failures; 712 } 713 714 public static int testCoshCaseWithTolerance(double input, 715 double expected, 716 double tolerance) { 717 int failures = 0; 718 failures += Tests.testTolerance("Math.cosh(double)", 719 input, Math.cosh(input), 720 expected, tolerance); 721 failures += Tests.testTolerance("Math.cosh(double)", 722 -input, Math.cosh(-input), 723 expected, tolerance); 724 725 failures += Tests.testTolerance("StrictMath.cosh(double)", 726 input, StrictMath.cosh(input), 727 expected, tolerance); 728 failures += Tests.testTolerance("StrictMath.cosh(double)", 729 -input, StrictMath.cosh(-input), 730 expected, tolerance); 731 return failures; 732 } 733 734 public static int testCoshCaseWithUlpDiff(double input, 735 double expected, 736 double ulps) { 737 int failures = 0; 738 failures += Tests.testUlpDiff("Math.cosh(double)", 739 input, Math.cosh(input), 740 expected, ulps); 741 failures += Tests.testUlpDiff("Math.cosh(double)", 742 -input, Math.cosh(-input), 743 expected, ulps); 744 745 failures += Tests.testUlpDiff("StrictMath.cosh(double)", 746 input, StrictMath.cosh(input), 747 expected, ulps); 748 failures += Tests.testUlpDiff("StrictMath.cosh(double)", 749 -input, StrictMath.cosh(-input), 750 expected, ulps); 751 return failures; 752 } 753 754 755 /** 756 * Test accuracy of {Math, StrictMath}.tanh. The specified 757 * accuracy is 2.5 ulps. 758 * 759 * The defintion of tanh(x) is 760 * 761 * (e^x - e^(-x))/(e^x + e^(-x)) 762 * 763 * The series expansion of tanh(x) = 764 * 765 * x - x^3/3 + 2x^5/15 - 17x^7/315 + ... 766 * 767 * Therefore, 768 * 769 * 1. For large values of x tanh(x) ~= signum(x) 770 * 771 * 2. For small values of x, tanh(x) ~= x. 772 * 773 * Additionally, tanh is an odd function; tanh(-x) = -tanh(x). 774 * 775 */ 776 static int testTanh() { 777 int failures = 0; 778 /* 779 * Array elements below generated using a quad sinh 780 * implementation. Rounded to a double, the quad result 781 * *should* be correctly rounded, unless we are quite unlucky. 782 * Assuming the quad value is a correctly rounded double, the 783 * allowed error is 3.0 ulps instead of 2.5 since the quad 784 * value rounded to double can have its own 1/2 ulp error. 785 */ 786 double [][] testCases = { 787 // x tanh(x) 788 {0.0625, 0.06241874674751251449014289119421133}, 789 {0.1250, 0.12435300177159620805464727580589271}, 790 {0.1875, 0.18533319990813951753211997502482787}, 791 {0.2500, 0.24491866240370912927780113149101697}, 792 {0.3125, 0.30270972933210848724239738970991712}, 793 {0.3750, 0.35835739835078594631936023155315807}, 794 {0.4375, 0.41157005567402245143207555859415687}, 795 {0.5000, 0.46211715726000975850231848364367256}, 796 {0.5625, 0.50982997373525658248931213507053130}, 797 {0.6250, 0.55459972234938229399903909532308371}, 798 {0.6875, 0.59637355547924233984437303950726939}, 799 {0.7500, 0.63514895238728731921443435731249638}, 800 {0.8125, 0.67096707420687367394810954721913358}, 801 {0.8750, 0.70390560393662106058763026963135371}, 802 {0.9375, 0.73407151960434149263991588052503660}, 803 {1.0000, 0.76159415595576488811945828260479366}, 804 {1.0625, 0.78661881210869761781941794647736081}, 805 {1.1250, 0.80930107020178101206077047354332696}, 806 {1.1875, 0.82980190998595952708572559629034476}, 807 {1.2500, 0.84828363995751289761338764670750445}, 808 {1.3125, 0.86490661772074179125443141102709751}, 809 {1.3750, 0.87982669965198475596055310881018259}, 810 {1.4375, 0.89319334040035153149249598745889365}, 811 {1.5000, 0.90514825364486643824230369645649557}, 812 {1.5625, 0.91582454416876231820084311814416443}, 813 {1.6250, 0.92534622531174107960457166792300374}, 814 {1.6875, 0.93382804322259173763570528576138652}, 815 {1.7500, 0.94137553849728736226942088377163687}, 816 {1.8125, 0.94808528560440629971240651310180052}, 817 {1.8750, 0.95404526017994877009219222661968285}, 818 {1.9375, 0.95933529331468249183399461756952555}, 819 {2.0000, 0.96402758007581688394641372410092317}, 820 {2.0625, 0.96818721657637057702714316097855370}, 821 {2.1250, 0.97187274591350905151254495374870401}, 822 {2.1875, 0.97513669829362836159665586901156483}, 823 {2.2500, 0.97802611473881363992272924300618321}, 824 {2.3125, 0.98058304703705186541999427134482061}, 825 {2.3750, 0.98284502917257603002353801620158861}, 826 {2.4375, 0.98484551746427837912703608465407824}, 827 {2.5000, 0.98661429815143028888127603923734964}, 828 {2.5625, 0.98817786228751240824802592958012269}, 829 {2.6250, 0.98955974861288320579361709496051109}, 830 {2.6875, 0.99078085564125158320311117560719312}, 831 {2.7500, 0.99185972456820774534967078914285035}, 832 {2.8125, 0.99281279483715982021711715899682324}, 833 {2.8750, 0.99365463431502962099607366282699651}, 834 {2.9375, 0.99439814606575805343721743822723671}, 835 {3.0000, 0.99505475368673045133188018525548849}, 836 {3.0625, 0.99563456710930963835715538507891736}, 837 {3.1250, 0.99614653067334504917102591131792951}, 838 {3.1875, 0.99659855517712942451966113109487039}, 839 {3.2500, 0.99699763548652601693227592643957226}, 840 {3.3125, 0.99734995516557367804571991063376923}, 841 {3.3750, 0.99766097946988897037219469409451602}, 842 {3.4375, 0.99793553792649036103161966894686844}, 843 {3.5000, 0.99817789761119870928427335245061171}, 844 {3.5625, 0.99839182812874152902001617480606320}, 845 {3.6250, 0.99858065920179882368897879066418294}, 846 {3.6875, 0.99874733168378115962760304582965538}, 847 {3.7500, 0.99889444272615280096784208280487888}, 848 {3.8125, 0.99902428575443546808677966295308778}, 849 {3.8750, 0.99913888583735077016137617231569011}, 850 {3.9375, 0.99924003097049627100651907919688313}, 851 {4.0000, 0.99932929973906704379224334434172499}, 852 {4.0625, 0.99940808577297384603818654530731215}, 853 {4.1250, 0.99947761936180856115470576756499454}, 854 {4.1875, 0.99953898655601372055527046497863955}, 855 {4.2500, 0.99959314604388958696521068958989891}, 856 {4.3125, 0.99964094406130644525586201091350343}, 857 {4.3750, 0.99968312756179494813069349082306235}, 858 {4.4375, 0.99972035584870534179601447812936151}, 859 {4.5000, 0.99975321084802753654050617379050162}, 860 {4.5625, 0.99978220617994689112771768489030236}, 861 {4.6250, 0.99980779516900105210240981251048167}, 862 {4.6875, 0.99983037791655283849546303868853396}, 863 {4.7500, 0.99985030754497877753787358852000255}, 864 {4.8125, 0.99986789571029070417475400133989992}, 865 {4.8750, 0.99988341746867772271011794614780441}, 866 {4.9375, 0.99989711557251558205051185882773206}, 867 {5.0000, 0.99990920426259513121099044753447306}, 868 {5.0625, 0.99991987261554158551063867262784721}, 869 {5.1250, 0.99992928749851651137225712249720606}, 870 {5.1875, 0.99993759617721206697530526661105307}, 871 {5.2500, 0.99994492861777083305830639416802036}, 872 {5.3125, 0.99995139951851344080105352145538345}, 873 {5.3750, 0.99995711010315817210152906092289064}, 874 {5.4375, 0.99996214970350792531554669737676253}, 875 {5.5000, 0.99996659715630380963848952941756868}, 876 {5.5625, 0.99997052203605101013786592945475432}, 877 {5.6250, 0.99997398574306704793434088941484766}, 878 {5.6875, 0.99997704246374583929961850444364696}, 879 {5.7500, 0.99997974001803825215761760428815437}, 880 {5.8125, 0.99998212060739040166557477723121777}, 881 {5.8750, 0.99998422147482750993344503195672517}, 882 {5.9375, 0.99998607548749972326220227464612338}, 883 {6.0000, 0.99998771165079557056434885235523206}, 884 {6.0625, 0.99998915556205996764518917496149338}, 885 {6.1250, 0.99999042981101021976277974520745310}, 886 {6.1875, 0.99999155433311068015449574811497719}, 887 {6.2500, 0.99999254672143162687722782398104276}, 888 {6.3125, 0.99999342250186907900400800240980139}, 889 {6.3750, 0.99999419537602957780612639767025158}, 890 {6.4375, 0.99999487743557848265406225515388994}, 891 {6.5000, 0.99999547935140419285107893831698753}, 892 {6.5625, 0.99999601054055694588617385671796346}, 893 {6.6250, 0.99999647931357331502887600387959900}, 894 {6.6875, 0.99999689300449080997594368612277442}, 895 {6.7500, 0.99999725808558628431084200832778748}, 896 {6.8125, 0.99999758026863294516387464046135924}, 897 {6.8750, 0.99999786459425991170635407313276785}, 898 {6.9375, 0.99999811551081218572759991597586905}, 899 {7.0000, 0.99999833694394467173571641595066708}, 900 {7.0625, 0.99999853235803894918375164252059190}, 901 {7.1250, 0.99999870481040359014665019356422927}, 902 {7.1875, 0.99999885699910593255108365463415411}, 903 {7.2500, 0.99999899130518359709674536482047025}, 904 {7.3125, 0.99999910982989611769943303422227663}, 905 {7.3750, 0.99999921442759946591163427422888252}, 906 {7.4375, 0.99999930673475777603853435094943258}, 907 {7.5000, 0.99999938819554614875054970643513124}, 908 {7.5625, 0.99999946008444508183970109263856958}, 909 {7.6250, 0.99999952352618001331402589096040117}, 910 {7.6875, 0.99999957951331792817413683491979752}, 911 {7.7500, 0.99999962892179632633374697389145081}, 912 {7.8125, 0.99999967252462750190604116210421169}, 913 {7.8750, 0.99999971100399253750324718031574484}, 914 {7.9375, 0.99999974496191422474977283863588658}, 915 {8.0000, 0.99999977492967588981001883295636840}, 916 {8.0625, 0.99999980137613348259726597081723424}, 917 {8.1250, 0.99999982471505097353529823063673263}, 918 {8.1875, 0.99999984531157382142423402736529911}, 919 {8.2500, 0.99999986348794179107425910499030547}, 920 {8.3125, 0.99999987952853049895833839645847571}, 921 {8.3750, 0.99999989368430056302584289932834041}, 922 {8.4375, 0.99999990617672396471542088609051728}, 923 {8.5000, 0.99999991720124905211338798152800748}, 924 {8.5625, 0.99999992693035839516545287745322387}, 925 {8.6250, 0.99999993551626733394129009365703767}, 926 {8.6875, 0.99999994309330543951799157347876934}, 927 {8.7500, 0.99999994978001814614368429416607424}, 928 {8.8125, 0.99999995568102143535399207289008504}, 929 {8.8750, 0.99999996088863858914831986187674522}, 930 {8.9375, 0.99999996548434461974481685677429908}, 931 {9.0000, 0.99999996954004097447930211118358244}, 932 {9.0625, 0.99999997311918045901919121395899372}, 933 {9.1250, 0.99999997627775997868467948564005257}, 934 {9.1875, 0.99999997906519662964368381583648379}, 935 {9.2500, 0.99999998152510084671976114264303159}, 936 {9.3125, 0.99999998369595870397054673668361266}, 937 {9.3750, 0.99999998561173404286033236040150950}, 938 {9.4375, 0.99999998730239984852716512979473289}, 939 {9.5000, 0.99999998879440718770812040917618843}, 940 {9.5625, 0.99999999011109904501789298212541698}, 941 {9.6250, 0.99999999127307553219220251303121960}, 942 {9.6875, 0.99999999229851618412119275358396363}, 943 {9.7500, 0.99999999320346438410630581726217930}, 944 {9.8125, 0.99999999400207836827291739324060736}, 945 {9.8750, 0.99999999470685273619047001387577653}, 946 {9.9375, 0.99999999532881393331131526966058758}, 947 {10.0000, 0.99999999587769276361959283713827574}, 948 }; 949 950 for(int i = 0; i < testCases.length; i++) { 951 double [] testCase = testCases[i]; 952 failures += testTanhCaseWithUlpDiff(testCase[0], 953 testCase[1], 954 3.0); 955 } 956 957 958 double [][] specialTestCases = { 959 {0.0, 0.0}, 960 {NaNd, NaNd}, 961 {Double.longBitsToDouble(0x7FF0000000000001L), NaNd}, 962 {Double.longBitsToDouble(0xFFF0000000000001L), NaNd}, 963 {Double.longBitsToDouble(0x7FF8555555555555L), NaNd}, 964 {Double.longBitsToDouble(0xFFF8555555555555L), NaNd}, 965 {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd}, 966 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd}, 967 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, 968 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, 969 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, 970 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, 971 {Double.POSITIVE_INFINITY, 1.0} 972 }; 973 974 for(int i = 0; i < specialTestCases.length; i++) { 975 failures += testTanhCaseWithUlpDiff(specialTestCases[i][0], 976 specialTestCases[i][1], 977 0.0); 978 } 979 980 // For powers of 2 less than 2^(-27), the second and 981 // subsequent terms of the Taylor series expansion will get 982 // rounded away since |n-n^3| > 53, the binary precision of a 983 // double significand. 984 985 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i < -27; i++) { 986 double d = Math.scalb(2.0, i); 987 988 // Result and expected are the same. 989 failures += testTanhCaseWithUlpDiff(d, d, 2.5); 990 } 991 992 // For values of x larger than 22, tanh(x) is 1.0 in double 993 // floating-point arithmetic. 994 995 for(int i = 22; i < 32; i++) { 996 failures += testTanhCaseWithUlpDiff(i, 1.0, 2.5); 997 } 998 999 for(int i = 5; i <= DoubleConsts.MAX_EXPONENT; i++) { 1000 double d = Math.scalb(2.0, i); 1001 1002 failures += testTanhCaseWithUlpDiff(d, 1.0, 2.5); 1003 } 1004 1005 return failures; 1006 } 1007 1008 public static int testTanhCaseWithTolerance(double input, 1009 double expected, 1010 double tolerance) { 1011 int failures = 0; 1012 failures += Tests.testTolerance("Math.tanh(double", 1013 input, Math.tanh(input), 1014 expected, tolerance); 1015 failures += Tests.testTolerance("Math.tanh(double", 1016 -input, Math.tanh(-input), 1017 -expected, tolerance); 1018 1019 failures += Tests.testTolerance("StrictMath.tanh(double", 1020 input, StrictMath.tanh(input), 1021 expected, tolerance); 1022 failures += Tests.testTolerance("StrictMath.tanh(double", 1023 -input, StrictMath.tanh(-input), 1024 -expected, tolerance); 1025 return failures; 1026 } 1027 1028 public static int testTanhCaseWithUlpDiff(double input, 1029 double expected, 1030 double ulps) { 1031 int failures = 0; 1032 1033 failures += Tests.testUlpDiffWithAbsBound("Math.tanh(double)", 1034 input, Math.tanh(input), 1035 expected, ulps, 1.0); 1036 failures += Tests.testUlpDiffWithAbsBound("Math.tanh(double)", 1037 -input, Math.tanh(-input), 1038 -expected, ulps, 1.0); 1039 1040 failures += Tests.testUlpDiffWithAbsBound("StrictMath.tanh(double)", 1041 input, StrictMath.tanh(input), 1042 expected, ulps, 1.0); 1043 failures += Tests.testUlpDiffWithAbsBound("StrictMath.tanh(double)", 1044 -input, StrictMath.tanh(-input), 1045 -expected, ulps, 1.0); 1046 return failures; 1047 } 1048 1049 1050 public static void main(String argv[]) { 1051 int failures = 0; 1052 1053 failures += testSinh(); 1054 failures += testCosh(); 1055 failures += testTanh(); 1056 1057 if (failures > 0) { 1058 System.err.println("Testing the hyperbolic functions incurred " 1059 + failures + " failures."); 1060 throw new RuntimeException(); 1061 } 1062 } 1063 1064} 1065