CoCalc -- HyperbolicTests.java

GitHub Repository: PojavLauncherTeam/mobile
Path: blob/master/test/jdk/java/lang/Math/HyperbolicTests.java
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/*
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 * Copyright (c) 2003, 2012, Oracle and/or its affiliates. All rights reserved.
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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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 *
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 * This code is free software; you can redistribute it and/or modify it
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 * under the terms of the GNU General Public License version 2 only, as
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 * published by the Free Software Foundation.
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 *
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 * This code is distributed in the hope that it will be useful, but WITHOUT
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 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
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 * version 2 for more details (a copy is included in the LICENSE file that
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 * accompanied this code).
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 *
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 * You should have received a copy of the GNU General Public License version
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 * 2 along with this work; if not, write to the Free Software Foundation,
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 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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 *
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 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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 * or visit www.oracle.com if you need additional information or have any
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 * questions.
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 */
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/*
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 * @test
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 * @bug 4851625 4900189 4939441
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 * @summary Tests for {Math, StrictMath}.{sinh, cosh, tanh}
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 * @author Joseph D. Darcy
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 */
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public class HyperbolicTests {
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    private HyperbolicTests(){}
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    static final double NaNd = Double.NaN;
35

36
    /**
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     * Test accuracy of {Math, StrictMath}.sinh.  The specified
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     * accuracy is 2.5 ulps.
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     *
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     * The defintion of sinh(x) is
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     *
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     * (e^x - e^(-x))/2
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     *
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     * The series expansion of sinh(x) =
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     *
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     * x + x^3/3! + x^5/5! + x^7/7! +...
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     *
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     * Therefore,
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     *
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     * 1. For large values of x sinh(x) ~= signum(x)*exp(|x|)/2
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     *
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     * 2. For small values of x, sinh(x) ~= x.
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     *
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     * Additionally, sinh is an odd function; sinh(-x) = -sinh(x).
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     *
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     */
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    static int testSinh() {
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        int failures = 0;
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        /*
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         * Array elements below generated using a quad sinh
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         * implementation.  Rounded to a double, the quad result
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         * *should* be correctly rounded, unless we are quite unlucky.
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         * Assuming the quad value is a correctly rounded double, the
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         * allowed error is 3.0 ulps instead of 2.5 since the quad
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         * value rounded to double can have its own 1/2 ulp error.
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         */
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        double [][] testCases = {
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            // x                sinh(x)
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            {0.0625,            0.06254069805219182172183988501029229},
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            {0.1250,            0.12532577524111545698205754229137154},
71
            {0.1875,            0.18860056562029018382047025055167585},
72
            {0.2500,            0.25261231680816830791412515054205787},
73
            {0.3125,            0.31761115611357728583959867611490292},
74
            {0.3750,            0.38385106791361456875429567642050245},
75
            {0.4375,            0.45159088610312053032509815226723017},
76
            {0.5000,            0.52109530549374736162242562641149155},
77
            {0.5625,            0.59263591611468777373870867338492247},
78
            {0.6250,            0.66649226445661608227260655608302908},
79
            {0.6875,            0.74295294580567543571442036910465007},
80
            {0.7500,            0.82231673193582998070366163444691386},
81
            {0.8125,            0.90489373856606433650504536421491368},
82
            {0.8750,            0.99100663714429475605317427568995231},
83
            {0.9375,            1.08099191569306394011007867453992548},
84
            {1.0000,            1.17520119364380145688238185059560082},
85
            {1.0625,            1.27400259579739321279181130344911907},
86
            {1.1250,            1.37778219077984075760379987065228373},
87
            {1.1875,            1.48694549961380717221109202361777593},
88
            {1.2500,            1.60191908030082563790283030151221415},
89
            {1.3125,            1.72315219460596010219069206464391528},
90
            {1.3750,            1.85111856355791532419998548438506416},
91
            {1.4375,            1.98631821852425112898943304217629457},
92
            {1.5000,            2.12927945509481749683438749467763195},
93
            {1.5625,            2.28056089740825247058075476705718764},
94
            {1.6250,            2.44075368098794353221372986997161132},
95
            {1.6875,            2.61048376261693140366028569794027603},
96
            {1.7500,            2.79041436627764265509289122308816092},
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            {1.8125,            2.98124857471401377943765253243875520},
98
            {1.8750,            3.18373207674259205101326780071803724},
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            {1.9375,            3.39865608104779099764440244167531810},
100
            {2.0000,            3.62686040784701876766821398280126192},
101
            {2.0625,            3.86923677050642806693938384073620450},
102
            {2.1250,            4.12673225993027252260441410537905269},
103
            {2.1875,            4.40035304533919660406976249684469164},
104
            {2.2500,            4.69116830589833069188357567763552003},
105
            {2.3125,            5.00031440855811351554075363240262157},
106
            {2.3750,            5.32899934843284576394645856548481489},
107
            {2.4375,            5.67850746906785056212578751630266858},
108
            {2.5000,            6.05020448103978732145032363835040319},
109
            {2.5625,            6.44554279850040875063706020260185553},
110
            {2.6250,            6.86606721451642172826145238779845813},
111
            {2.6875,            7.31342093738196587585692115636603571},
112
            {2.7500,            7.78935201149073201875513401029935330},
113
            {2.8125,            8.29572014785741787167717932988491961},
114
            {2.8750,            8.83450399097893197351853322827892144},
115
            {2.9375,            9.40780885043076394429977972921690859},
116
            {3.0000,            10.01787492740990189897459361946582867},
117
            {3.0625,            10.66708606836969224165124519209968368},
118
            {3.1250,            11.35797907995166028304704128775698426},
119
            {3.1875,            12.09325364161259019614431093344260209},
120
            {3.2500,            12.87578285468067003959660391705481220},
121
            {3.3125,            13.70862446906136798063935858393686525},
122
            {3.3750,            14.59503283146163690015482636921657975},
123
            {3.4375,            15.53847160182039311025096666980558478},
124
            {3.5000,            16.54262728763499762495673152901249743},
125
            {3.5625,            17.61142364906941482858466494889121694},
126
            {3.6250,            18.74903703113232171399165788088277979},
127
            {3.6875,            19.95991268283598684128844120984214675},
128
            {3.7500,            21.24878212710338697364101071825171163},
129
            {3.8125,            22.62068164929685091969259499078125023},
130
            {3.8750,            24.08097197661255803883403419733891573},
131
            {3.9375,            25.63535922523855307175060244757748997},
132
            {4.0000,            27.28991719712775244890827159079382096},
133
            {4.0625,            29.05111111351106713777825462100160185},
134
            {4.1250,            30.92582287788986031725487699744107092},
135
            {4.1875,            32.92137796722343190618721270937061472},
136
            {4.2500,            35.04557405638942942322929652461901154},
137
            {4.3125,            37.30671148776788628118833357170042385},
138
            {4.3750,            39.71362570500944929025069048612806024},
139
            {4.4375,            42.27572177772344954814418332587050658},
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            {4.5000,            45.00301115199178562180965680564371424},
141
            {4.5625,            47.90615077031205065685078058248081891},
142
            {4.6250,            50.99648471383193131253995134526177467},
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            {4.6875,            54.28608852959281437757368957713936555},
144
            {4.7500,            57.78781641599226874961859781628591635},
145
            {4.8125,            61.51535145084362283008545918273109379},
146
            {4.8750,            65.48325905829987165560146562921543361},
147
            {4.9375,            69.70704392356508084094318094283346381},
148
            {5.0000,            74.20321057778875897700947199606456364},
149
            {5.0625,            78.98932788987998983462810080907521151},
150
            {5.1250,            84.08409771724448958901392613147384951},
151
            {5.1875,            89.50742798369883598816307922895346849},
152
            {5.2500,            95.28051047011540739630959111303975956},
153
            {5.3125,            101.42590362176666730633859252034238987},
154
            {5.3750,            107.96762069594029162704530843962700133},
155
            {5.4375,            114.93122359426386042048760580590182604},
156
            {5.5000,            122.34392274639096192409774240457730721},
157
            {5.5625,            130.23468343534638291488502321709913206},
158
            {5.6250,            138.63433897999898233879574111119546728},
159
            {5.6875,            147.57571121692522056519568264304815790},
160
            {5.7500,            157.09373875244884423880085377625986165},
161
            {5.8125,            167.22561348600435888568183143777868662},
162
            {5.8750,            178.01092593829229887752609866133883987},
163
            {5.9375,            189.49181995209921964640216682906501778},
164
            {6.0000,            201.71315737027922812498206768797872263},
165
            {6.0625,            214.72269333437984291483666459592578915},
166
            {6.1250,            228.57126288889537420461281285729970085},
167
            {6.1875,            243.31297962030799867970551767086092471},
168
            {6.2500,            259.00544710710289911522315435345489966},
169
            {6.3125,            275.70998400700299790136562219920451185},
170
            {6.3750,            293.49186366095654566861661249898332253},
171
            {6.4375,            312.42056915013535342987623229485223434},
172
            {6.5000,            332.57006480258443156075705566965111346},
173
            {6.5625,            354.01908521044116928437570109827956007},
174
            {6.6250,            376.85144288706511933454985188849781703},
175
            {6.6875,            401.15635576625530823119100750634165252},
176
            {6.7500,            427.02879582326538080306830640235938517},
177
            {6.8125,            454.56986017986077163530945733572724452},
178
            {6.8750,            483.88716614351897894746751705315210621},
179
            {6.9375,            515.09527172439720070161654727225752288},
180
            {7.0000,            548.31612327324652237375611757601851598},
181
            {7.0625,            583.67953198942753384680988096024373270},
182
            {7.1250,            621.32368116099280160364794462812762880},
183
            {7.1875,            661.39566611888784148449430491465857519},
184
            {7.2500,            704.05206901515336623551137120663358760},
185
            {7.3125,            749.45957067108712382864538206200700256},
186
            {7.3750,            797.79560188617531521347351754559776282},
187
            {7.4375,            849.24903675279739482863565789325699416},
188
            {7.5000,            904.02093068584652953510919038935849651},
189
            {7.5625,            962.32530605113249628368993221570636328},
190
            {7.6250,            1024.38998846242707559349318193113614698},
191
            {7.6875,            1090.45749701500081956792547346904792325},
192
            {7.7500,            1160.78599193425808533255719118417856088},
193
            {7.8125,            1235.65028334242796895820912936318532502},
194
            {7.8750,            1315.34290508508890654067255740428824014},
195
            {7.9375,            1400.17525781352742299995139486063802583},
196
            {8.0000,            1490.47882578955018611587663903188144796},
197
            {8.0625,            1586.60647216744061169450001100145859236},
198
            {8.1250,            1688.93381781440241350635231605477507900},
199
            {8.1875,            1797.86070905726094477721128358866360644},
200
            {8.2500,            1913.81278009067446281883262689250118009},
201
            {8.3125,            2037.24311615199935553277163192983440062},
202
            {8.3750,            2168.63402396170125867037749369723761636},
203
            {8.4375,            2308.49891634734644432370720900969004306},
204
            {8.5000,            2457.38431841538268239359965370719928775},
205
            {8.5625,            2615.87200310986940554256648824234335262},
206
            {8.6250,            2784.58126450289932429469130598902487336},
207
            {8.6875,            2964.17133769964321637973459949999057146},
208
            {8.7500,            3155.34397481384944060352507473513108710},
209
            {8.8125,            3358.84618707947841898217318996045550438},
210
            {8.8750,            3575.47316381333288862617411467285480067},
211
            {8.9375,            3806.07137963459383403903729660349293583},
212
            {9.0000,            4051.54190208278996051522359589803425598},
213
            {9.0625,            4312.84391255878980330955246931164633615},
214
            {9.1250,            4590.99845434696991399363282718106006883},
215
            {9.1875,            4887.09242236403719571363798584676797558},
216
            {9.2500,            5202.28281022453561319352901552085348309},
217
            {9.3125,            5537.80123121853803935727335892054791265},
218
            {9.3750,            5894.95873086734181634245918412592155656},
219
            {9.4375,            6275.15090986233399457103055108344546942},
220
            {9.5000,            6679.86337740502119410058225086262108741},
221
            {9.5625,            7110.67755625726876329967852256934334025},
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            {9.6250,            7569.27686218510919585241049433331592115},
223
            {9.6875,            8057.45328194243077504648484392156371121},
224
            {9.7500,            8577.11437549816065709098061006273039092},
225
            {9.8125,            9130.29072986829727910801024120918114778},
226
            {9.8750,            9719.14389367880274015504995181862860062},
227
            {9.9375,            10345.97482346383208590278839409938269134},
228
            {10.0000,           11013.23287470339337723652455484636420303},
229
        };
230

231
        for(int i = 0; i < testCases.length; i++) {
232
            double [] testCase = testCases[i];
233
            failures += testSinhCaseWithUlpDiff(testCase[0],
234
                                                testCase[1],
235
                                                3.0);
236
        }
237

238
        double [][] specialTestCases = {
239
            {0.0,                       0.0},
240
            {NaNd,                      NaNd},
241
            {Double.longBitsToDouble(0x7FF0000000000001L),      NaNd},
242
            {Double.longBitsToDouble(0xFFF0000000000001L),      NaNd},
243
            {Double.longBitsToDouble(0x7FF8555555555555L),      NaNd},
244
            {Double.longBitsToDouble(0xFFF8555555555555L),      NaNd},
245
            {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL),      NaNd},
246
            {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL),      NaNd},
247
            {Double.longBitsToDouble(0x7FFDeadBeef00000L),      NaNd},
248
            {Double.longBitsToDouble(0xFFFDeadBeef00000L),      NaNd},
249
            {Double.longBitsToDouble(0x7FFCafeBabe00000L),      NaNd},
250
            {Double.longBitsToDouble(0xFFFCafeBabe00000L),      NaNd},
251
            {Double.POSITIVE_INFINITY,  Double.POSITIVE_INFINITY}
252
        };
253

254
        for(int i = 0; i < specialTestCases.length; i++) {
255
            failures += testSinhCaseWithUlpDiff(specialTestCases[i][0],
256
                                                specialTestCases[i][1],
257
                                                0.0);
258
        }
259

260
        // For powers of 2 less than 2^(-27), the second and
261
        // subsequent terms of the Taylor series expansion will get
262
        // rounded away since |n-n^3| > 53, the binary precision of a
263
        // double significand.
264

265
        for(int i = DoubleConsts.MIN_SUB_EXPONENT; i < -27; i++) {
266
            double d = Math.scalb(2.0, i);
267

268
            // Result and expected are the same.
269
            failures += testSinhCaseWithUlpDiff(d, d, 2.5);
270
        }
271

272
        // For values of x larger than 22, the e^(-x) term is
273
        // insignificant to the floating-point result.  Util exp(x)
274
        // overflows around 709.8, sinh(x) ~= exp(x)/2; will will test
275
        // 10000 values in this range.
276

277
        long trans22 = Double.doubleToLongBits(22.0);
278
        // (approximately) largest value such that exp shouldn't
279
        // overflow
280
        long transExpOvfl = Double.doubleToLongBits(Math.nextDown(709.7827128933841));
281

282
        for(long i = trans22;
283
            i < transExpOvfl;
284
            i +=(transExpOvfl-trans22)/10000) {
285

286
            double d = Double.longBitsToDouble(i);
287

288
            // Allow 3.5 ulps of error to deal with error in exp.
289
            failures += testSinhCaseWithUlpDiff(d, StrictMath.exp(d)*0.5, 3.5);
290
        }
291

292
        // (approximately) largest value such that sinh shouldn't
293
        // overflow.
294
        long transSinhOvfl = Double.doubleToLongBits(710.4758600739439);
295

296
        // Make sure sinh(x) doesn't overflow as soon as exp(x)
297
        // overflows.
298

299
        /*
300
         * For large values of x, sinh(x) ~= 0.5*(e^x).  Therefore,
301
         *
302
         * sinh(x) ~= e^(ln 0.5) * e^x = e^(x + ln 0.5)
303
         *
304
         * So, we can calculate the approximate expected result as
305
         * exp(x + -0.693147186).  However, this sum suffers from
306
         * roundoff, limiting the accuracy of the approximation.  The
307
         * accuracy can be improved by recovering the rounded-off
308
         * information.  Since x is larger than ln(0.5), the trailing
309
         * bits of ln(0.5) get rounded away when the two values are
310
         * added.  However, high-order bits of ln(0.5) that
311
         * contribute to the sum can be found:
312
         *
313
         * offset = log(0.5);
314
         * effective_offset = (x + offset) - x; // exact subtraction
315
         * rounded_away_offset = offset - effective_offset; // exact subtraction
316
         *
317
         * Therefore, the product
318
         *
319
         * exp(x + offset)*exp(rounded_away_offset)
320
         *
321
         * will be a better approximation to the exact value of
322
         *
323
         * e^(x + offset)
324
         *
325
         * than exp(x+offset) alone.  (The expected result cannot be
326
         * computed as exp(x)*exp(offset) since exp(x) by itself would
327
         * overflow to infinity.)
328
         */
329
        double offset = StrictMath.log(0.5);
330
        for(long i = transExpOvfl+1; i < transSinhOvfl;
331
            i += (transSinhOvfl-transExpOvfl)/1000 ) {
332
            double input = Double.longBitsToDouble(i);
333

334
            double expected =
335
                StrictMath.exp(input + offset) *
336
                StrictMath.exp( offset - ((input + offset) - input) );
337

338
            failures += testSinhCaseWithUlpDiff(input, expected, 4.0);
339
        }
340

341
        // sinh(x) overflows for values greater than 710; in
342
        // particular, it overflows for all 2^i, i > 10.
343
        for(int i = 10; i <= Double.MAX_EXPONENT; i++) {
344
            double d = Math.scalb(2.0, i);
345

346
            // Result and expected are the same.
347
            failures += testSinhCaseWithUlpDiff(d,
348
                                                Double.POSITIVE_INFINITY, 0.0);
349
        }
350

351
        return failures;
352
    }
353

354
    public static int testSinhCaseWithTolerance(double input,
355
                                                double expected,
356
                                                double tolerance) {
357
        int failures = 0;
358
        failures += Tests.testTolerance("Math.sinh(double)",
359
                                        input, Math.sinh(input),
360
                                        expected, tolerance);
361
        failures += Tests.testTolerance("Math.sinh(double)",
362
                                        -input, Math.sinh(-input),
363
                                        -expected, tolerance);
364

365
        failures += Tests.testTolerance("StrictMath.sinh(double)",
366
                                        input, StrictMath.sinh(input),
367
                                        expected, tolerance);
368
        failures += Tests.testTolerance("StrictMath.sinh(double)",
369
                                        -input, StrictMath.sinh(-input),
370
                                        -expected, tolerance);
371
        return failures;
372
    }
373

374
    public static int testSinhCaseWithUlpDiff(double input,
375
                                              double expected,
376
                                              double ulps) {
377
        int failures = 0;
378
        failures += Tests.testUlpDiff("Math.sinh(double)",
379
                                      input, Math.sinh(input),
380
                                      expected, ulps);
381
        failures += Tests.testUlpDiff("Math.sinh(double)",
382
                                      -input, Math.sinh(-input),
383
                                      -expected, ulps);
384

385
        failures += Tests.testUlpDiff("StrictMath.sinh(double)",
386
                                      input, StrictMath.sinh(input),
387
                                      expected, ulps);
388
        failures += Tests.testUlpDiff("StrictMath.sinh(double)",
389
                                      -input, StrictMath.sinh(-input),
390
                                      -expected, ulps);
391
        return failures;
392
    }
393

394

395
    /**
396
     * Test accuracy of {Math, StrictMath}.cosh.  The specified
397
     * accuracy is 2.5 ulps.
398
     *
399
     * The defintion of cosh(x) is
400
     *
401
     * (e^x + e^(-x))/2
402
     *
403
     * The series expansion of cosh(x) =
404
     *
405
     * 1 + x^2/2! + x^4/4! + x^6/6! +...
406
     *
407
     * Therefore,
408
     *
409
     * 1. For large values of x cosh(x) ~= exp(|x|)/2
410
     *
411
     * 2. For small values of x, cosh(x) ~= 1.
412
     *
413
     * Additionally, cosh is an even function; cosh(-x) = cosh(x).
414
     *
415
     */
416
    static int testCosh() {
417
        int failures = 0;
418
        /*
419
         * Array elements below generated using a quad cosh
420
         * implementation.  Rounded to a double, the quad result
421
         * *should* be correctly rounded, unless we are quite unlucky.
422
         * Assuming the quad value is a correctly rounded double, the
423
         * allowed error is 3.0 ulps instead of 2.5 since the quad
424
         * value rounded to double can have its own 1/2 ulp error.
425
         */
426
        double [][] testCases = {
427
            // x                cosh(x)
428
            {0.0625,            1.001953760865667607841550709632597376},
429
            {0.1250,            1.007822677825710859846949685520422223},
430
            {0.1875,            1.017629683800690526835115759894757615},
431
            {0.2500,            1.031413099879573176159295417520378622},
432
            {0.3125,            1.049226785060219076999158096606305793},
433
            {0.3750,            1.071140346704586767299498015567016002},
434
            {0.4375,            1.097239412531012567673453832328262160},
435
            {0.5000,            1.127625965206380785226225161402672030},
436
            {0.5625,            1.162418740845610783505338363214045218},
437
            {0.6250,            1.201753692975606324229229064105075301},
438
            {0.6875,            1.245784523776616395403056980542275175},
439
            {0.7500,            1.294683284676844687841708185390181730},
440
            {0.8125,            1.348641048647144208352285714214372703},
441
            {0.8750,            1.407868656822803158638471458026344506},
442
            {0.9375,            1.472597542369862933336886403008640891},
443
            {1.0000,            1.543080634815243778477905620757061497},
444
            {1.0625,            1.619593348374367728682469968448090763},
445
            {1.1250,            1.702434658138190487400868008124755757},
446
            {1.1875,            1.791928268324866464246665745956119612},
447
            {1.2500,            1.888423877161015738227715728160051696},
448
            {1.3125,            1.992298543335143985091891077551921106},
449
            {1.3750,            2.103958159362661802010972984204389619},
450
            {1.4375,            2.223839037619709260803023946704272699},
451
            {1.5000,            2.352409615243247325767667965441644201},
452
            {1.5625,            2.490172284559350293104864895029231913},
453
            {1.6250,            2.637665356192137582275019088061812951},
454
            {1.6875,            2.795465162524235691253423614360562624},
455
            {1.7500,            2.964188309728087781773608481754531801},
456
            {1.8125,            3.144494087167972176411236052303565201},
457
            {1.8750,            3.337087043587520514308832278928116525},
458
            {1.9375,            3.542719740149244276729383650503145346},
459
            {2.0000,            3.762195691083631459562213477773746099},
460
            {2.0625,            3.996372503438463642260225717607554880},
461
            {2.1250,            4.246165228196992140600291052990934410},
462
            {2.1875,            4.512549935859540340856119781585096760},
463
            {2.2500,            4.796567530460195028666793366876218854},
464
            {2.3125,            5.099327816921939817643745917141739051},
465
            {2.3750,            5.422013837643509250646323138888569746},
466
            {2.4375,            5.765886495263270945949271410819116399},
467
            {2.5000,            6.132289479663686116619852312817562517},
468
            {2.5625,            6.522654518468725462969589397439224177},
469
            {2.6250,            6.938506971550673190999796241172117288},
470
            {2.6875,            7.381471791406976069645686221095397137},
471
            {2.7500,            7.853279872697439591457564035857305647},
472
            {2.8125,            8.355774815752725814638234943192709129},
473
            {2.8750,            8.890920130482709321824793617157134961},
474
            {2.9375,            9.460806908834119747071078865866737196},
475
            {3.0000,            10.067661995777765841953936035115890343},
476
            {3.0625,            10.713856690753651225304006562698007312},
477
            {3.1250,            11.401916013575067700373788969458446177},
478
            {3.1875,            12.134528570998387744547733730974713055},
479
            {3.2500,            12.914557062512392049483503752322408761},
480
            {3.3125,            13.745049466398732213877084541992751273},
481
            {3.3750,            14.629250949773302934853381428660210721},
482
            {3.4375,            15.570616549147269180921654324879141947},
483
            {3.5000,            16.572824671057316125696517821376119469},
484
            {3.5625,            17.639791465519127930722105721028711044},
485
            {3.6250,            18.775686128468677200079039891415789429},
486
            {3.6875,            19.984947192985946987799359614758598457},
487
            {3.7500,            21.272299872959396081877161903352144126},
488
            {3.8125,            22.642774526961913363958587775566619798},
489
            {3.8750,            24.101726314486257781049388094955970560},
490
            {3.9375,            25.654856121347151067170940701379544221},
491
            {4.0000,            27.308232836016486629201989612067059978},
492
            {4.0625,            29.068317063936918520135334110824828950},
493
            {4.1250,            30.941986372478026192360480044849306606},
494
            {4.1875,            32.936562165180269851350626768308756303},
495
            {4.2500,            35.059838290298428678502583470475012235},
496
            {4.3125,            37.320111495433027109832850313172338419},
497
            {4.3750,            39.726213847251883288518263854094284091},
498
            {4.4375,            42.287547242982546165696077854963452084},
499
            {4.5000,            45.014120148530027928305799939930642658},
500
            {4.5625,            47.916586706774825161786212701923307169},
501
            {4.6250,            51.006288368867753140854830589583165950},
502
            {4.6875,            54.295298211196782516984520211780624960},
503
            {4.7500,            57.796468111195389383795669320243166117},
504
            {4.8125,            61.523478966332915041549750463563672435},
505
            {4.8750,            65.490894152518731617237739112888213645},
506
            {4.9375,            69.714216430810089539924900313140922323},
507
            {5.0000,            74.209948524787844444106108044487704798},
508
            {5.0625,            78.995657605307475581204965926043112946},
509
            {5.1250,            84.090043934600961683400343038519519678},
510
            {5.1875,            89.513013937957834087706670952561002466},
511
            {5.2500,            95.285757988514588780586084642381131013},
512
            {5.3125,            101.430833209098212357990123684449846912},
513
            {5.3750,            107.972251614673824873137995865940755392},
514
            {5.4375,            114.935573939814969189535554289886848550},
515
            {5.5000,            122.348009517829425991091207107262038316},
516
            {5.5625,            130.238522601820409078244923165746295574},
517
            {5.6250,            138.637945543134998069351279801575968875},
518
            {5.6875,            147.579099269447055276899288971207106581},
519
            {5.7500,            157.096921533245353905868840194264636395},
520
            {5.8125,            167.228603431860671946045256541679445836},
521
            {5.8750,            178.013734732486824390148614309727161925},
522
            {5.9375,            189.494458570056311567917444025807275896},
523
            {6.0000,            201.715636122455894483405112855409538488},
524
            {6.0625,            214.725021906554080628430756558271312513},
525
            {6.1250,            228.573450380013557089736092321068279231},
526
            {6.1875,            243.315034578039208138752165587134488645},
527
            {6.2500,            259.007377561239126824465367865430519592},
528
            {6.3125,            275.711797500835732516530131577254654076},
529
            {6.3750,            293.493567280752348242602902925987643443},
530
            {6.4375,            312.422169552825597994104814531010579387},
531
            {6.5000,            332.571568241777409133204438572983297292},
532
            {6.5625,            354.020497560858198165985214519757890505},
533
            {6.6250,            376.852769667496146326030849450983914197},
534
            {6.6875,            401.157602161123700280816957271992998156},
535
            {6.7500,            427.029966702886171977469256622451185850},
536
            {6.8125,            454.570960119471524953536004647195906721},
537
            {6.8750,            483.888199441157626584508920036981010995},
538
            {6.9375,            515.096242417696720610477570797503766179},
539
            {7.0000,            548.317035155212076889964120712102928484},
540
            {7.0625,            583.680388623257719787307547662358502345},
541
            {7.1250,            621.324485894002926216918634755431456031},
542
            {7.1875,            661.396422095589629755266517362992812037},
543
            {7.2500,            704.052779189542208784574955807004218856},
544
            {7.3125,            749.460237818184878095966335081928645934},
545
            {7.3750,            797.796228612873763671070863694973560629},
546
            {7.4375,            849.249625508044731271830060572510241864},
547
            {7.5000,            904.021483770216677368692292389446994987},
548
            {7.5625,            962.325825625814651122171697031114091993},
549
            {7.6250,            1024.390476557670599008492465853663578558},
550
            {7.6875,            1090.457955538048482588540574008226583335},
551
            {7.7500,            1160.786422676798661020094043586456606003},
552
            {7.8125,            1235.650687987597295222707689125107720568},
553
            {7.8750,            1315.343285214046776004329388551335841550},
554
            {7.9375,            1400.175614911635999247504386054087931958},
555
            {8.0000,            1490.479161252178088627715460421007179728},
556
            {8.0625,            1586.606787305415349050508956232945539108},
557
            {8.1250,            1688.934113859132470361718199038326340668},
558
            {8.1875,            1797.860987165547537276364148450577336075},
559
            {8.2500,            1913.813041349231764486365114317586148767},
560
            {8.3125,            2037.243361581700856522236313401822532385},
561
            {8.3750,            2168.634254521568851112005905503069409349},
562
            {8.4375,            2308.499132938297821208734949028296170563},
563
            {8.5000,            2457.384521883751693037774022640629666294},
564
            {8.5625,            2615.872194250713123494312356053193077854},
565
            {8.6250,            2784.581444063104750127653362960649823247},
566
            {8.6875,            2964.171506380845754878370650565756538203},
567
            {8.7500,            3155.344133275174556354775488913749659006},
568
            {8.8125,            3358.846335940117183452010789979584950102},
569
            {8.8750,            3575.473303654961482727206202358956274888},
570
            {8.9375,            3806.071511003646460448021740303914939059},
571
            {9.0000,            4051.542025492594047194773093534725371440},
572
            {9.0625,            4312.844028491571841588188869958240355518},
573
            {9.1250,            4590.998563255739769060078863130940205710},
574
            {9.1875,            4887.092524674358252509551443117048351290},
575
            {9.2500,            5202.282906336187674588222835339193136030},
576
            {9.3125,            5537.801321507079474415176386655744387251},
577
            {9.3750,            5894.958815685577062811620236195525504885},
578
            {9.4375,            6275.150989541692149890530417987358096221},
579
            {9.5000,            6679.863452256851081801173722051940058824},
580
            {9.5625,            7110.677626574055535297758456126491707647},
581
            {9.6250,            7569.276928241617224537226019600213961572},
582
            {9.6875,            8057.453343996777301036241026375049070162},
583
            {9.7500,            8577.114433792824387959788368429252257664},
584
            {9.8125,            9130.290784631065880205118262838330689429},
585
            {9.8750,            9719.143945123662919857326995631317996715},
586
            {9.9375,            10345.974871791805753327922796701684092861},
587
            {10.0000,           11013.232920103323139721376090437880844591},
588
        };
589

590
        for(int i = 0; i < testCases.length; i++) {
591
            double [] testCase = testCases[i];
592
            failures += testCoshCaseWithUlpDiff(testCase[0],
593
                                                testCase[1],
594
                                                3.0);
595
        }
596

597

598
        double [][] specialTestCases = {
599
            {0.0,                       1.0},
600
            {NaNd,                      NaNd},
601
            {Double.longBitsToDouble(0x7FF0000000000001L),      NaNd},
602
            {Double.longBitsToDouble(0xFFF0000000000001L),      NaNd},
603
            {Double.longBitsToDouble(0x7FF8555555555555L),      NaNd},
604
            {Double.longBitsToDouble(0xFFF8555555555555L),      NaNd},
605
            {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL),      NaNd},
606
            {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL),      NaNd},
607
            {Double.longBitsToDouble(0x7FFDeadBeef00000L),      NaNd},
608
            {Double.longBitsToDouble(0xFFFDeadBeef00000L),      NaNd},
609
            {Double.longBitsToDouble(0x7FFCafeBabe00000L),      NaNd},
610
            {Double.longBitsToDouble(0xFFFCafeBabe00000L),      NaNd},
611
            {Double.POSITIVE_INFINITY,  Double.POSITIVE_INFINITY}
612
        };
613

614
        for(int i = 0; i < specialTestCases.length; i++ ) {
615
            failures += testCoshCaseWithUlpDiff(specialTestCases[i][0],
616
                                                specialTestCases[i][1],
617
                                                0.0);
618
        }
619

620
        // For powers of 2 less than 2^(-27), the second and
621
        // subsequent terms of the Taylor series expansion will get
622
        // rounded.
623

624
        for(int i = DoubleConsts.MIN_SUB_EXPONENT; i < -27; i++) {
625
            double d = Math.scalb(2.0, i);
626

627
            // Result and expected are the same.
628
            failures += testCoshCaseWithUlpDiff(d, 1.0, 2.5);
629
        }
630

631
        // For values of x larger than 22, the e^(-x) term is
632
        // insignificant to the floating-point result.  Util exp(x)
633
        // overflows around 709.8, cosh(x) ~= exp(x)/2; will will test
634
        // 10000 values in this range.
635

636
        long trans22 = Double.doubleToLongBits(22.0);
637
        // (approximately) largest value such that exp shouldn't
638
        // overflow
639
        long transExpOvfl = Double.doubleToLongBits(Math.nextDown(709.7827128933841));
640

641
        for(long i = trans22;
642
            i < transExpOvfl;
643
            i +=(transExpOvfl-trans22)/10000) {
644

645
            double d = Double.longBitsToDouble(i);
646

647
            // Allow 3.5 ulps of error to deal with error in exp.
648
            failures += testCoshCaseWithUlpDiff(d, StrictMath.exp(d)*0.5, 3.5);
649
        }
650

651
        // (approximately) largest value such that cosh shouldn't
652
        // overflow.
653
        long transCoshOvfl = Double.doubleToLongBits(710.4758600739439);
654

655
        // Make sure sinh(x) doesn't overflow as soon as exp(x)
656
        // overflows.
657

658
        /*
659
         * For large values of x, cosh(x) ~= 0.5*(e^x).  Therefore,
660
         *
661
         * cosh(x) ~= e^(ln 0.5) * e^x = e^(x + ln 0.5)
662
         *
663
         * So, we can calculate the approximate expected result as
664
         * exp(x + -0.693147186).  However, this sum suffers from
665
         * roundoff, limiting the accuracy of the approximation.  The
666
         * accuracy can be improved by recovering the rounded-off
667
         * information.  Since x is larger than ln(0.5), the trailing
668
         * bits of ln(0.5) get rounded away when the two values are
669
         * added.  However, high-order bits of ln(0.5) that
670
         * contribute to the sum can be found:
671
         *
672
         * offset = log(0.5);
673
         * effective_offset = (x + offset) - x; // exact subtraction
674
         * rounded_away_offset = offset - effective_offset; // exact subtraction
675
         *
676
         * Therefore, the product
677
         *
678
         * exp(x + offset)*exp(rounded_away_offset)
679
         *
680
         * will be a better approximation to the exact value of
681
         *
682
         * e^(x + offset)
683
         *
684
         * than exp(x+offset) alone.  (The expected result cannot be
685
         * computed as exp(x)*exp(offset) since exp(x) by itself would
686
         * overflow to infinity.)
687
         */
688
        double offset = StrictMath.log(0.5);
689
        for(long i = transExpOvfl+1; i < transCoshOvfl;
690
            i += (transCoshOvfl-transExpOvfl)/1000 ) {
691
            double input = Double.longBitsToDouble(i);
692

693
            double expected =
694
                StrictMath.exp(input + offset) *
695
                StrictMath.exp( offset - ((input + offset) - input) );
696

697
            failures += testCoshCaseWithUlpDiff(input, expected, 4.0);
698
        }
699

700
        // cosh(x) overflows for values greater than 710; in
701
        // particular, it overflows for all 2^i, i > 10.
702
        for(int i = 10; i <= Double.MAX_EXPONENT; i++) {
703
            double d = Math.scalb(2.0, i);
704

705
            // Result and expected are the same.
706
            failures += testCoshCaseWithUlpDiff(d,
707
                                                Double.POSITIVE_INFINITY, 0.0);
708
        }
709
        return failures;
710
    }
711

712
    public static int testCoshCaseWithTolerance(double input,
713
                                                double expected,
714
                                                double tolerance) {
715
        int failures = 0;
716
        failures += Tests.testTolerance("Math.cosh(double)",
717
                                        input, Math.cosh(input),
718
                                        expected, tolerance);
719
        failures += Tests.testTolerance("Math.cosh(double)",
720
                                        -input, Math.cosh(-input),
721
                                        expected, tolerance);
722

723
        failures += Tests.testTolerance("StrictMath.cosh(double)",
724
                                        input, StrictMath.cosh(input),
725
                                        expected, tolerance);
726
        failures += Tests.testTolerance("StrictMath.cosh(double)",
727
                                        -input, StrictMath.cosh(-input),
728
                                        expected, tolerance);
729
        return failures;
730
    }
731

732
    public static int testCoshCaseWithUlpDiff(double input,
733
                                              double expected,
734
                                              double ulps) {
735
        int failures = 0;
736
        failures += Tests.testUlpDiff("Math.cosh(double)",
737
                                      input, Math.cosh(input),
738
                                      expected, ulps);
739
        failures += Tests.testUlpDiff("Math.cosh(double)",
740
                                      -input, Math.cosh(-input),
741
                                      expected, ulps);
742

743
        failures += Tests.testUlpDiff("StrictMath.cosh(double)",
744
                                      input, StrictMath.cosh(input),
745
                                      expected, ulps);
746
        failures += Tests.testUlpDiff("StrictMath.cosh(double)",
747
                                      -input, StrictMath.cosh(-input),
748
                                      expected, ulps);
749
        return failures;
750
    }
751

752

753
    /**
754
     * Test accuracy of {Math, StrictMath}.tanh.  The specified
755
     * accuracy is 2.5 ulps.
756
     *
757
     * The defintion of tanh(x) is
758
     *
759
     * (e^x - e^(-x))/(e^x + e^(-x))
760
     *
761
     * The series expansion of tanh(x) =
762
     *
763
     * x - x^3/3 + 2x^5/15 - 17x^7/315 + ...
764
     *
765
     * Therefore,
766
     *
767
     * 1. For large values of x tanh(x) ~= signum(x)
768
     *
769
     * 2. For small values of x, tanh(x) ~= x.
770
     *
771
     * Additionally, tanh is an odd function; tanh(-x) = -tanh(x).
772
     *
773
     */
774
    static int testTanh() {
775
        int failures = 0;
776
        /*
777
         * Array elements below generated using a quad sinh
778
         * implementation.  Rounded to a double, the quad result
779
         * *should* be correctly rounded, unless we are quite unlucky.
780
         * Assuming the quad value is a correctly rounded double, the
781
         * allowed error is 3.0 ulps instead of 2.5 since the quad
782
         * value rounded to double can have its own 1/2 ulp error.
783
         */
784
        double [][] testCases = {
785
            // x                tanh(x)
786
            {0.0625,            0.06241874674751251449014289119421133},
787
            {0.1250,            0.12435300177159620805464727580589271},
788
            {0.1875,            0.18533319990813951753211997502482787},
789
            {0.2500,            0.24491866240370912927780113149101697},
790
            {0.3125,            0.30270972933210848724239738970991712},
791
            {0.3750,            0.35835739835078594631936023155315807},
792
            {0.4375,            0.41157005567402245143207555859415687},
793
            {0.5000,            0.46211715726000975850231848364367256},
794
            {0.5625,            0.50982997373525658248931213507053130},
795
            {0.6250,            0.55459972234938229399903909532308371},
796
            {0.6875,            0.59637355547924233984437303950726939},
797
            {0.7500,            0.63514895238728731921443435731249638},
798
            {0.8125,            0.67096707420687367394810954721913358},
799
            {0.8750,            0.70390560393662106058763026963135371},
800
            {0.9375,            0.73407151960434149263991588052503660},
801
            {1.0000,            0.76159415595576488811945828260479366},
802
            {1.0625,            0.78661881210869761781941794647736081},
803
            {1.1250,            0.80930107020178101206077047354332696},
804
            {1.1875,            0.82980190998595952708572559629034476},
805
            {1.2500,            0.84828363995751289761338764670750445},
806
            {1.3125,            0.86490661772074179125443141102709751},
807
            {1.3750,            0.87982669965198475596055310881018259},
808
            {1.4375,            0.89319334040035153149249598745889365},
809
            {1.5000,            0.90514825364486643824230369645649557},
810
            {1.5625,            0.91582454416876231820084311814416443},
811
            {1.6250,            0.92534622531174107960457166792300374},
812
            {1.6875,            0.93382804322259173763570528576138652},
813
            {1.7500,            0.94137553849728736226942088377163687},
814
            {1.8125,            0.94808528560440629971240651310180052},
815
            {1.8750,            0.95404526017994877009219222661968285},
816
            {1.9375,            0.95933529331468249183399461756952555},
817
            {2.0000,            0.96402758007581688394641372410092317},
818
            {2.0625,            0.96818721657637057702714316097855370},
819
            {2.1250,            0.97187274591350905151254495374870401},
820
            {2.1875,            0.97513669829362836159665586901156483},
821
            {2.2500,            0.97802611473881363992272924300618321},
822
            {2.3125,            0.98058304703705186541999427134482061},
823
            {2.3750,            0.98284502917257603002353801620158861},
824
            {2.4375,            0.98484551746427837912703608465407824},
825
            {2.5000,            0.98661429815143028888127603923734964},
826
            {2.5625,            0.98817786228751240824802592958012269},
827
            {2.6250,            0.98955974861288320579361709496051109},
828
            {2.6875,            0.99078085564125158320311117560719312},
829
            {2.7500,            0.99185972456820774534967078914285035},
830
            {2.8125,            0.99281279483715982021711715899682324},
831
            {2.8750,            0.99365463431502962099607366282699651},
832
            {2.9375,            0.99439814606575805343721743822723671},
833
            {3.0000,            0.99505475368673045133188018525548849},
834
            {3.0625,            0.99563456710930963835715538507891736},
835
            {3.1250,            0.99614653067334504917102591131792951},
836
            {3.1875,            0.99659855517712942451966113109487039},
837
            {3.2500,            0.99699763548652601693227592643957226},
838
            {3.3125,            0.99734995516557367804571991063376923},
839
            {3.3750,            0.99766097946988897037219469409451602},
840
            {3.4375,            0.99793553792649036103161966894686844},
841
            {3.5000,            0.99817789761119870928427335245061171},
842
            {3.5625,            0.99839182812874152902001617480606320},
843
            {3.6250,            0.99858065920179882368897879066418294},
844
            {3.6875,            0.99874733168378115962760304582965538},
845
            {3.7500,            0.99889444272615280096784208280487888},
846
            {3.8125,            0.99902428575443546808677966295308778},
847
            {3.8750,            0.99913888583735077016137617231569011},
848
            {3.9375,            0.99924003097049627100651907919688313},
849
            {4.0000,            0.99932929973906704379224334434172499},
850
            {4.0625,            0.99940808577297384603818654530731215},
851
            {4.1250,            0.99947761936180856115470576756499454},
852
            {4.1875,            0.99953898655601372055527046497863955},
853
            {4.2500,            0.99959314604388958696521068958989891},
854
            {4.3125,            0.99964094406130644525586201091350343},
855
            {4.3750,            0.99968312756179494813069349082306235},
856
            {4.4375,            0.99972035584870534179601447812936151},
857
            {4.5000,            0.99975321084802753654050617379050162},
858
            {4.5625,            0.99978220617994689112771768489030236},
859
            {4.6250,            0.99980779516900105210240981251048167},
860
            {4.6875,            0.99983037791655283849546303868853396},
861
            {4.7500,            0.99985030754497877753787358852000255},
862
            {4.8125,            0.99986789571029070417475400133989992},
863
            {4.8750,            0.99988341746867772271011794614780441},
864
            {4.9375,            0.99989711557251558205051185882773206},
865
            {5.0000,            0.99990920426259513121099044753447306},
866
            {5.0625,            0.99991987261554158551063867262784721},
867
            {5.1250,            0.99992928749851651137225712249720606},
868
            {5.1875,            0.99993759617721206697530526661105307},
869
            {5.2500,            0.99994492861777083305830639416802036},
870
            {5.3125,            0.99995139951851344080105352145538345},
871
            {5.3750,            0.99995711010315817210152906092289064},
872
            {5.4375,            0.99996214970350792531554669737676253},
873
            {5.5000,            0.99996659715630380963848952941756868},
874
            {5.5625,            0.99997052203605101013786592945475432},
875
            {5.6250,            0.99997398574306704793434088941484766},
876
            {5.6875,            0.99997704246374583929961850444364696},
877
            {5.7500,            0.99997974001803825215761760428815437},
878
            {5.8125,            0.99998212060739040166557477723121777},
879
            {5.8750,            0.99998422147482750993344503195672517},
880
            {5.9375,            0.99998607548749972326220227464612338},
881
            {6.0000,            0.99998771165079557056434885235523206},
882
            {6.0625,            0.99998915556205996764518917496149338},
883
            {6.1250,            0.99999042981101021976277974520745310},
884
            {6.1875,            0.99999155433311068015449574811497719},
885
            {6.2500,            0.99999254672143162687722782398104276},
886
            {6.3125,            0.99999342250186907900400800240980139},
887
            {6.3750,            0.99999419537602957780612639767025158},
888
            {6.4375,            0.99999487743557848265406225515388994},
889
            {6.5000,            0.99999547935140419285107893831698753},
890
            {6.5625,            0.99999601054055694588617385671796346},
891
            {6.6250,            0.99999647931357331502887600387959900},
892
            {6.6875,            0.99999689300449080997594368612277442},
893
            {6.7500,            0.99999725808558628431084200832778748},
894
            {6.8125,            0.99999758026863294516387464046135924},
895
            {6.8750,            0.99999786459425991170635407313276785},
896
            {6.9375,            0.99999811551081218572759991597586905},
897
            {7.0000,            0.99999833694394467173571641595066708},
898
            {7.0625,            0.99999853235803894918375164252059190},
899
            {7.1250,            0.99999870481040359014665019356422927},
900
            {7.1875,            0.99999885699910593255108365463415411},
901
            {7.2500,            0.99999899130518359709674536482047025},
902
            {7.3125,            0.99999910982989611769943303422227663},
903
            {7.3750,            0.99999921442759946591163427422888252},
904
            {7.4375,            0.99999930673475777603853435094943258},
905
            {7.5000,            0.99999938819554614875054970643513124},
906
            {7.5625,            0.99999946008444508183970109263856958},
907
            {7.6250,            0.99999952352618001331402589096040117},
908
            {7.6875,            0.99999957951331792817413683491979752},
909
            {7.7500,            0.99999962892179632633374697389145081},
910
            {7.8125,            0.99999967252462750190604116210421169},
911
            {7.8750,            0.99999971100399253750324718031574484},
912
            {7.9375,            0.99999974496191422474977283863588658},
913
            {8.0000,            0.99999977492967588981001883295636840},
914
            {8.0625,            0.99999980137613348259726597081723424},
915
            {8.1250,            0.99999982471505097353529823063673263},
916
            {8.1875,            0.99999984531157382142423402736529911},
917
            {8.2500,            0.99999986348794179107425910499030547},
918
            {8.3125,            0.99999987952853049895833839645847571},
919
            {8.3750,            0.99999989368430056302584289932834041},
920
            {8.4375,            0.99999990617672396471542088609051728},
921
            {8.5000,            0.99999991720124905211338798152800748},
922
            {8.5625,            0.99999992693035839516545287745322387},
923
            {8.6250,            0.99999993551626733394129009365703767},
924
            {8.6875,            0.99999994309330543951799157347876934},
925
            {8.7500,            0.99999994978001814614368429416607424},
926
            {8.8125,            0.99999995568102143535399207289008504},
927
            {8.8750,            0.99999996088863858914831986187674522},
928
            {8.9375,            0.99999996548434461974481685677429908},
929
            {9.0000,            0.99999996954004097447930211118358244},
930
            {9.0625,            0.99999997311918045901919121395899372},
931
            {9.1250,            0.99999997627775997868467948564005257},
932
            {9.1875,            0.99999997906519662964368381583648379},
933
            {9.2500,            0.99999998152510084671976114264303159},
934
            {9.3125,            0.99999998369595870397054673668361266},
935
            {9.3750,            0.99999998561173404286033236040150950},
936
            {9.4375,            0.99999998730239984852716512979473289},
937
            {9.5000,            0.99999998879440718770812040917618843},
938
            {9.5625,            0.99999999011109904501789298212541698},
939
            {9.6250,            0.99999999127307553219220251303121960},
940
            {9.6875,            0.99999999229851618412119275358396363},
941
            {9.7500,            0.99999999320346438410630581726217930},
942
            {9.8125,            0.99999999400207836827291739324060736},
943
            {9.8750,            0.99999999470685273619047001387577653},
944
            {9.9375,            0.99999999532881393331131526966058758},
945
            {10.0000,           0.99999999587769276361959283713827574},
946
        };
947

948
        for(int i = 0; i < testCases.length; i++) {
949
            double [] testCase = testCases[i];
950
            failures += testTanhCaseWithUlpDiff(testCase[0],
951
                                                testCase[1],
952
                                                3.0);
953
        }
954

955

956
        double [][] specialTestCases = {
957
            {0.0,                       0.0},
958
            {NaNd,                      NaNd},
959
            {Double.longBitsToDouble(0x7FF0000000000001L),      NaNd},
960
            {Double.longBitsToDouble(0xFFF0000000000001L),      NaNd},
961
            {Double.longBitsToDouble(0x7FF8555555555555L),      NaNd},
962
            {Double.longBitsToDouble(0xFFF8555555555555L),      NaNd},
963
            {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL),      NaNd},
964
            {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL),      NaNd},
965
            {Double.longBitsToDouble(0x7FFDeadBeef00000L),      NaNd},
966
            {Double.longBitsToDouble(0xFFFDeadBeef00000L),      NaNd},
967
            {Double.longBitsToDouble(0x7FFCafeBabe00000L),      NaNd},
968
            {Double.longBitsToDouble(0xFFFCafeBabe00000L),      NaNd},
969
            {Double.POSITIVE_INFINITY,  1.0}
970
        };
971

972
        for(int i = 0; i < specialTestCases.length; i++) {
973
            failures += testTanhCaseWithUlpDiff(specialTestCases[i][0],
974
                                                specialTestCases[i][1],
975
                                                0.0);
976
        }
977

978
        // For powers of 2 less than 2^(-27), the second and
979
        // subsequent terms of the Taylor series expansion will get
980
        // rounded away since |n-n^3| > 53, the binary precision of a
981
        // double significand.
982

983
        for(int i = DoubleConsts.MIN_SUB_EXPONENT; i < -27; i++) {
984
            double d = Math.scalb(2.0, i);
985

986
            // Result and expected are the same.
987
            failures += testTanhCaseWithUlpDiff(d, d, 2.5);
988
        }
989

990
        // For values of x larger than 22, tanh(x) is 1.0 in double
991
        // floating-point arithmetic.
992

993
        for(int i = 22; i < 32; i++) {
994
            failures += testTanhCaseWithUlpDiff(i, 1.0, 2.5);
995
        }
996

997
        for(int i = 5; i <= Double.MAX_EXPONENT; i++) {
998
            double d = Math.scalb(2.0, i);
999

1000
            failures += testTanhCaseWithUlpDiff(d, 1.0, 2.5);
1001
        }
1002

1003
        return failures;
1004
    }
1005

1006
    public static int testTanhCaseWithTolerance(double input,
1007
                                                double expected,
1008
                                                double tolerance) {
1009
        int failures = 0;
1010
        failures += Tests.testTolerance("Math.tanh(double",
1011
                                        input, Math.tanh(input),
1012
                                        expected, tolerance);
1013
        failures += Tests.testTolerance("Math.tanh(double",
1014
                                        -input, Math.tanh(-input),
1015
                                        -expected, tolerance);
1016

1017
        failures += Tests.testTolerance("StrictMath.tanh(double",
1018
                                        input, StrictMath.tanh(input),
1019
                                        expected, tolerance);
1020
        failures += Tests.testTolerance("StrictMath.tanh(double",
1021
                                        -input, StrictMath.tanh(-input),
1022
                                        -expected, tolerance);
1023
        return failures;
1024
    }
1025

1026
    public static int testTanhCaseWithUlpDiff(double input,
1027
                                              double expected,
1028
                                              double ulps) {
1029
        int failures = 0;
1030

1031
        failures += Tests.testUlpDiffWithAbsBound("Math.tanh(double)",
1032
                                                  input, Math.tanh(input),
1033
                                                  expected, ulps, 1.0);
1034
        failures += Tests.testUlpDiffWithAbsBound("Math.tanh(double)",
1035
                                                  -input, Math.tanh(-input),
1036
                                                  -expected, ulps, 1.0);
1037

1038
        failures += Tests.testUlpDiffWithAbsBound("StrictMath.tanh(double)",
1039
                                                  input, StrictMath.tanh(input),
1040
                                                  expected, ulps, 1.0);
1041
        failures += Tests.testUlpDiffWithAbsBound("StrictMath.tanh(double)",
1042
                                                  -input, StrictMath.tanh(-input),
1043
                                                  -expected, ulps, 1.0);
1044
        return failures;
1045
    }
1046

1047

1048
    public static void main(String argv[]) {
1049
        int failures = 0;
1050

1051
        failures += testSinh();
1052
        failures += testCosh();
1053
        failures += testTanh();
1054

1055
        if (failures > 0) {
1056
            System.err.println("Testing the hyperbolic functions incurred "
1057
                               + failures + " failures.");
1058
            throw new RuntimeException();
1059
        }
1060
    }
1061

1062
}
1063

1064
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