CoCalc -- HyperbolicTests.java

GitHub Repository: PojavLauncherTeam/openjdk-multiarch-jdk8u
Path: blob/aarch64-shenandoah-jdk8u272-b10/jdk/test/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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import sun.misc.DoubleConsts;
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public class HyperbolicTests {
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    private HyperbolicTests(){}
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36
    static final double NaNd = Double.NaN;
37

38
    /**
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     * Test accuracy of {Math, StrictMath}.sinh.  The specified
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     * accuracy is 2.5 ulps.
41
     *
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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,
51
     *
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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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     *
58
     */
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    static int testSinh() {
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        int failures = 0;
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        /*
62
         * 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.
68
         */
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        double [][] testCases = {
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            // x                sinh(x)
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            {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

1066
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