test/jdk/java/lang/Math/HyperbolicTests.java - master - githubmirror/panama-vector

test/jdk/java/lang/Math/HyperbolicTests.java
2 488 строк180 KB
Anton Artemov
8377603: Review worst-case testing of inverse hyperbolic methods
13 мар 2026, 18:28
13 мар 2026, 18:2892fafa4
/*
 * Copyright (c) 2003, 2026, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

/*
 * @test
 * @bug 4851625 4900189 4939441
 * @build Tests
 * @build HyperbolicTests
 * @run main HyperbolicTests
 * @summary Tests for {Math, StrictMath}.{sinh, cosh, tanh, asinh, acosh, atanh}
 */

import static java.lang.Double.longBitsToDouble;

public class HyperbolicTests {
    private HyperbolicTests(){}

    static final double NaNd = Double.NaN;

    public static void main(String... argv) {
        int failures = 0;

        failures += testSinh();
        failures += testCosh();
        failures += testTanh();
        failures += testAsinh();
        failures += testAcosh();
        failures += testAtanh();

        if (failures > 0) {
            System.err.println("Testing the hyperbolic functions incurred "
                               + failures + " failures.");
            throw new RuntimeException();
        }
    }

    /**
     * Test accuracy of {Math, StrictMath}.sinh.  The specified
     * accuracy is 2.5 ulps.
     *
     * The defintion of sinh(x) is
     *
     * (e^x - e^(-x))/2
     *
     * The series expansion of sinh(x) =
     *
     * x + x^3/3! + x^5/5! + x^7/7! +...
     *
     * Therefore,
     *
     * 1. For large values of x sinh(x) ~= signum(x)*exp(|x|)/2
     *
     * 2. For small values of x, sinh(x) ~= x.
     *
     * Additionally, sinh is an odd function; sinh(-x) = -sinh(x).
     *
     */
    static int testSinh() {
        int failures = 0;
        /*
         * Array elements below generated using a quad sinh
         * implementation.  Rounded to a double, the quad result
         * *should* be correctly rounded, unless we are quite unlucky.
         * Assuming the quad value is a correctly rounded double, the
         * allowed error is 3.0 ulps instead of 2.5 since the quad
         * value rounded to double can have its own 1/2 ulp error.
         */
        double [][] testCases = {
            // x                sinh(x)
            {0.0625,            0.06254069805219182172183988501029229},
            {0.1250,            0.12532577524111545698205754229137154},
            {0.1875,            0.18860056562029018382047025055167585},
            {0.2500,            0.25261231680816830791412515054205787},
            {0.3125,            0.31761115611357728583959867611490292},
            {0.3750,            0.38385106791361456875429567642050245},
            {0.4375,            0.45159088610312053032509815226723017},
            {0.5000,            0.52109530549374736162242562641149155},
            {0.5625,            0.59263591611468777373870867338492247},
            {0.6250,            0.66649226445661608227260655608302908},
            {0.6875,            0.74295294580567543571442036910465007},
            {0.7500,            0.82231673193582998070366163444691386},
            {0.8125,            0.90489373856606433650504536421491368},
            {0.8750,            0.99100663714429475605317427568995231},
            {0.9375,            1.08099191569306394011007867453992548},
            {1.0000,            1.17520119364380145688238185059560082},
            {1.0625,            1.27400259579739321279181130344911907},
            {1.1250,            1.37778219077984075760379987065228373},
            {1.1875,            1.48694549961380717221109202361777593},
            {1.2500,            1.60191908030082563790283030151221415},
            {1.3125,            1.72315219460596010219069206464391528},
            {1.3750,            1.85111856355791532419998548438506416},
            {1.4375,            1.98631821852425112898943304217629457},
            {1.5000,            2.12927945509481749683438749467763195},
            {1.5625,            2.28056089740825247058075476705718764},
            {1.6250,            2.44075368098794353221372986997161132},
            {1.6875,            2.61048376261693140366028569794027603},
            {1.7500,            2.79041436627764265509289122308816092},
            {1.8125,            2.98124857471401377943765253243875520},
            {1.8750,            3.18373207674259205101326780071803724},
            {1.9375,            3.39865608104779099764440244167531810},
            {2.0000,            3.62686040784701876766821398280126192},
            {2.0625,            3.86923677050642806693938384073620450},
            {2.1250,            4.12673225993027252260441410537905269},
            {2.1875,            4.40035304533919660406976249684469164},
            {2.2500,            4.69116830589833069188357567763552003},
            {2.3125,            5.00031440855811351554075363240262157},
            {2.3750,            5.32899934843284576394645856548481489},
            {2.4375,            5.67850746906785056212578751630266858},
            {2.5000,            6.05020448103978732145032363835040319},
            {2.5625,            6.44554279850040875063706020260185553},
            {2.6250,            6.86606721451642172826145238779845813},
            {2.6875,            7.31342093738196587585692115636603571},
            {2.7500,            7.78935201149073201875513401029935330},
            {2.8125,            8.29572014785741787167717932988491961},
            {2.8750,            8.83450399097893197351853322827892144},
            {2.9375,            9.40780885043076394429977972921690859},
            {3.0000,            10.01787492740990189897459361946582867},
            {3.0625,            10.66708606836969224165124519209968368},
            {3.1250,            11.35797907995166028304704128775698426},
            {3.1875,            12.09325364161259019614431093344260209},
            {3.2500,            12.87578285468067003959660391705481220},
            {3.3125,            13.70862446906136798063935858393686525},
            {3.3750,            14.59503283146163690015482636921657975},
            {3.4375,            15.53847160182039311025096666980558478},
            {3.5000,            16.54262728763499762495673152901249743},
            {3.5625,            17.61142364906941482858466494889121694},
            {3.6250,            18.74903703113232171399165788088277979},
            {3.6875,            19.95991268283598684128844120984214675},
            {3.7500,            21.24878212710338697364101071825171163},
            {3.8125,            22.62068164929685091969259499078125023},
            {3.8750,            24.08097197661255803883403419733891573},
            {3.9375,            25.63535922523855307175060244757748997},
            {4.0000,            27.28991719712775244890827159079382096},
            {4.0625,            29.05111111351106713777825462100160185},
            {4.1250,            30.92582287788986031725487699744107092},
            {4.1875,            32.92137796722343190618721270937061472},
            {4.2500,            35.04557405638942942322929652461901154},
            {4.3125,            37.30671148776788628118833357170042385},
            {4.3750,            39.71362570500944929025069048612806024},
            {4.4375,            42.27572177772344954814418332587050658},
            {4.5000,            45.00301115199178562180965680564371424},
            {4.5625,            47.90615077031205065685078058248081891},
            {4.6250,            50.99648471383193131253995134526177467},
            {4.6875,            54.28608852959281437757368957713936555},
            {4.7500,            57.78781641599226874961859781628591635},
            {4.8125,            61.51535145084362283008545918273109379},
            {4.8750,            65.48325905829987165560146562921543361},
            {4.9375,            69.70704392356508084094318094283346381},
            {5.0000,            74.20321057778875897700947199606456364},
            {5.0625,            78.98932788987998983462810080907521151},
            {5.1250,            84.08409771724448958901392613147384951},
            {5.1875,            89.50742798369883598816307922895346849},
            {5.2500,            95.28051047011540739630959111303975956},
            {5.3125,            101.42590362176666730633859252034238987},
            {5.3750,            107.96762069594029162704530843962700133},
            {5.4375,            114.93122359426386042048760580590182604},
            {5.5000,            122.34392274639096192409774240457730721},
            {5.5625,            130.23468343534638291488502321709913206},
            {5.6250,            138.63433897999898233879574111119546728},
            {5.6875,            147.57571121692522056519568264304815790},
            {5.7500,            157.09373875244884423880085377625986165},
            {5.8125,            167.22561348600435888568183143777868662},
            {5.8750,            178.01092593829229887752609866133883987},
            {5.9375,            189.49181995209921964640216682906501778},
            {6.0000,            201.71315737027922812498206768797872263},
            {6.0625,            214.72269333437984291483666459592578915},
            {6.1250,            228.57126288889537420461281285729970085},
            {6.1875,            243.31297962030799867970551767086092471},
            {6.2500,            259.00544710710289911522315435345489966},
            {6.3125,            275.70998400700299790136562219920451185},
            {6.3750,            293.49186366095654566861661249898332253},
            {6.4375,            312.42056915013535342987623229485223434},
            {6.5000,            332.57006480258443156075705566965111346},
            {6.5625,            354.01908521044116928437570109827956007},
            {6.6250,            376.85144288706511933454985188849781703},
            {6.6875,            401.15635576625530823119100750634165252},
            {6.7500,            427.02879582326538080306830640235938517},
            {6.8125,            454.56986017986077163530945733572724452},
            {6.8750,            483.88716614351897894746751705315210621},
            {6.9375,            515.09527172439720070161654727225752288},
            {7.0000,            548.31612327324652237375611757601851598},
            {7.0625,            583.67953198942753384680988096024373270},
            {7.1250,            621.32368116099280160364794462812762880},
            {7.1875,            661.39566611888784148449430491465857519},
            {7.2500,            704.05206901515336623551137120663358760},
            {7.3125,            749.45957067108712382864538206200700256},
            {7.3750,            797.79560188617531521347351754559776282},
            {7.4375,            849.24903675279739482863565789325699416},
            {7.5000,            904.02093068584652953510919038935849651},
            {7.5625,            962.32530605113249628368993221570636328},
            {7.6250,            1024.38998846242707559349318193113614698},
            {7.6875,            1090.45749701500081956792547346904792325},
            {7.7500,            1160.78599193425808533255719118417856088},
            {7.8125,            1235.65028334242796895820912936318532502},
            {7.8750,            1315.34290508508890654067255740428824014},
            {7.9375,            1400.17525781352742299995139486063802583},
            {8.0000,            1490.47882578955018611587663903188144796},
            {8.0625,            1586.60647216744061169450001100145859236},
            {8.1250,            1688.93381781440241350635231605477507900},
            {8.1875,            1797.86070905726094477721128358866360644},
            {8.2500,            1913.81278009067446281883262689250118009},
            {8.3125,            2037.24311615199935553277163192983440062},
            {8.3750,            2168.63402396170125867037749369723761636},
            {8.4375,            2308.49891634734644432370720900969004306},
            {8.5000,            2457.38431841538268239359965370719928775},
            {8.5625,            2615.87200310986940554256648824234335262},
            {8.6250,            2784.58126450289932429469130598902487336},
            {8.6875,            2964.17133769964321637973459949999057146},
            {8.7500,            3155.34397481384944060352507473513108710},
            {8.8125,            3358.84618707947841898217318996045550438},
            {8.8750,            3575.47316381333288862617411467285480067},
            {8.9375,            3806.07137963459383403903729660349293583},
            {9.0000,            4051.54190208278996051522359589803425598},
            {9.0625,            4312.84391255878980330955246931164633615},
            {9.1250,            4590.99845434696991399363282718106006883},
            {9.1875,            4887.09242236403719571363798584676797558},
            {9.2500,            5202.28281022453561319352901552085348309},
            {9.3125,            5537.80123121853803935727335892054791265},
            {9.3750,            5894.95873086734181634245918412592155656},
            {9.4375,            6275.15090986233399457103055108344546942},
            {9.5000,            6679.86337740502119410058225086262108741},
            {9.5625,            7110.67755625726876329967852256934334025},
            {9.6250,            7569.27686218510919585241049433331592115},
            {9.6875,            8057.45328194243077504648484392156371121},
            {9.7500,            8577.11437549816065709098061006273039092},
            {9.8125,            9130.29072986829727910801024120918114778},
            {9.8750,            9719.14389367880274015504995181862860062},
            {9.9375,            10345.97482346383208590278839409938269134},
            {10.0000,           11013.23287470339337723652455484636420303},
        };

        for(int i = 0; i < testCases.length; i++) {
            double [] testCase = testCases[i];
            failures += testSinhCaseWithUlpDiff(testCase[0],
                                                testCase[1],
                                                3.0);
        }

        for(double nan : Tests.NaNs) {
            failures += testSinhCaseWithUlpDiff(nan, NaNd, 0);
        }

        double [][] specialTestCases = {
            {0.0,                       0.0},
            {Double.POSITIVE_INFINITY,  Double.POSITIVE_INFINITY}
        };

        for(int i = 0; i < specialTestCases.length; i++) {
            failures += testSinhCaseWithUlpDiff(specialTestCases[i][0],
                                                specialTestCases[i][1],
                                                0.0);
        }

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

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

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

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

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

        for(long i = trans22;
            i < transExpOvfl;
            i +=(transExpOvfl-trans22)/10000) {

            double d = Double.longBitsToDouble(i);

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

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

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

        /*
         * For large values of x, sinh(x) ~= 0.5*(e^x).  Therefore,
         *
         * sinh(x) ~= e^(ln 0.5) * e^x = e^(x + ln 0.5)
         *
         * So, we can calculate the approximate expected result as
         * exp(x + -0.693147186).  However, this sum suffers from
         * roundoff, limiting the accuracy of the approximation.  The
         * accuracy can be improved by recovering the rounded-off
         * information.  Since x is larger than ln(0.5), the trailing
         * bits of ln(0.5) get rounded away when the two values are
         * added.  However, high-order bits of ln(0.5) that
         * contribute to the sum can be found:
         *
         * offset = log(0.5);
         * effective_offset = (x + offset) - x; // exact subtraction
         * rounded_away_offset = offset - effective_offset; // exact subtraction
         *
         * Therefore, the product
         *
         * exp(x + offset)*exp(rounded_away_offset)
         *
         * will be a better approximation to the exact value of
         *
         * e^(x + offset)
         *
         * than exp(x+offset) alone.  (The expected result cannot be
         * computed as exp(x)*exp(offset) since exp(x) by itself would
         * overflow to infinity.)
         */
        double offset = StrictMath.log(0.5);
        for(long i = transExpOvfl+1; i < transSinhOvfl;
            i += (transSinhOvfl-transExpOvfl)/1000 ) {
            double input = Double.longBitsToDouble(i);

            double expected =
                StrictMath.exp(input + offset) *
                StrictMath.exp( offset - ((input + offset) - input) );

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

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

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

        return failures;
    }

    public static int testSinhCaseWithTolerance(double input,
                                                double expected,
                                                double tolerance) {
        int failures = 0;
        failures += Tests.testTolerance("Math.sinh",        input, Math::sinh,        expected, tolerance);
        failures += Tests.testTolerance("Math.sinh",       -input, Math::sinh,       -expected, tolerance);

        failures += Tests.testTolerance("StrictMath.sinh",  input, StrictMath::sinh,  expected, tolerance);
        failures += Tests.testTolerance("StrictMath.sinh", -input, StrictMath::sinh, -expected, tolerance);
        return failures;
    }

    public static int testSinhCaseWithUlpDiff(double input,
                                              double expected,
                                              double ulps) {
        int failures = 0;
        failures += Tests.testUlpDiff("Math.sinh",        input, Math::sinh,        expected, ulps);
        failures += Tests.testUlpDiff("Math.sinh",       -input, Math::sinh,       -expected, ulps);

        failures += Tests.testUlpDiff("StrictMath.sinh",  input, StrictMath::sinh,  expected, ulps);
        failures += Tests.testUlpDiff("StrictMath.sinh", -input, StrictMath::sinh, -expected, ulps);
        return failures;
    }

    /**
     * Test accuracy of {Math, StrictMath}.cosh.  The specified
     * accuracy is 2.5 ulps.
     *
     * The defintion of cosh(x) is
     *
     * (e^x + e^(-x))/2
     *
     * The series expansion of cosh(x) =
     *
     * 1 + x^2/2! + x^4/4! + x^6/6! +...
     *
     * Therefore,
     *
     * 1. For large values of x cosh(x) ~= exp(|x|)/2
     *
     * 2. For small values of x, cosh(x) ~= 1.
     *
     * Additionally, cosh is an even function; cosh(-x) = cosh(x).
     *
     */
    static int testCosh() {
        int failures = 0;
        /*
         * Array elements below generated using a quad cosh
         * implementation.  Rounded to a double, the quad result
         * *should* be correctly rounded, unless we are quite unlucky.
         * Assuming the quad value is a correctly rounded double, the
         * allowed error is 3.0 ulps instead of 2.5 since the quad
         * value rounded to double can have its own 1/2 ulp error.
         */
        double [][] testCases = {
            // x                cosh(x)
            {0.0625,            1.001953760865667607841550709632597376},
            {0.1250,            1.007822677825710859846949685520422223},
            {0.1875,            1.017629683800690526835115759894757615},
            {0.2500,            1.031413099879573176159295417520378622},
            {0.3125,            1.049226785060219076999158096606305793},
            {0.3750,            1.071140346704586767299498015567016002},
            {0.4375,            1.097239412531012567673453832328262160},
            {0.5000,            1.127625965206380785226225161402672030},
            {0.5625,            1.162418740845610783505338363214045218},
            {0.6250,            1.201753692975606324229229064105075301},
            {0.6875,            1.245784523776616395403056980542275175},
            {0.7500,            1.294683284676844687841708185390181730},
            {0.8125,            1.348641048647144208352285714214372703},
            {0.8750,            1.407868656822803158638471458026344506},
            {0.9375,            1.472597542369862933336886403008640891},
            {1.0000,            1.543080634815243778477905620757061497},
            {1.0625,            1.619593348374367728682469968448090763},
            {1.1250,            1.702434658138190487400868008124755757},
            {1.1875,            1.791928268324866464246665745956119612},
            {1.2500,            1.888423877161015738227715728160051696},
            {1.3125,            1.992298543335143985091891077551921106},
            {1.3750,            2.103958159362661802010972984204389619},
            {1.4375,            2.223839037619709260803023946704272699},
            {1.5000,            2.352409615243247325767667965441644201},
            {1.5625,            2.490172284559350293104864895029231913},
            {1.6250,            2.637665356192137582275019088061812951},
            {1.6875,            2.795465162524235691253423614360562624},
            {1.7500,            2.964188309728087781773608481754531801},
            {1.8125,            3.144494087167972176411236052303565201},
            {1.8750,            3.337087043587520514308832278928116525},
            {1.9375,            3.542719740149244276729383650503145346},
            {2.0000,            3.762195691083631459562213477773746099},
            {2.0625,            3.996372503438463642260225717607554880},
            {2.1250,            4.246165228196992140600291052990934410},
            {2.1875,            4.512549935859540340856119781585096760},
            {2.2500,            4.796567530460195028666793366876218854},
            {2.3125,            5.099327816921939817643745917141739051},
            {2.3750,            5.422013837643509250646323138888569746},
            {2.4375,            5.765886495263270945949271410819116399},
            {2.5000,            6.132289479663686116619852312817562517},
            {2.5625,            6.522654518468725462969589397439224177},
            {2.6250,            6.938506971550673190999796241172117288},
            {2.6875,            7.381471791406976069645686221095397137},
            {2.7500,            7.853279872697439591457564035857305647},
            {2.8125,            8.355774815752725814638234943192709129},
            {2.8750,            8.890920130482709321824793617157134961},
            {2.9375,            9.460806908834119747071078865866737196},
            {3.0000,            10.067661995777765841953936035115890343},
            {3.0625,            10.713856690753651225304006562698007312},
            {3.1250,            11.401916013575067700373788969458446177},
            {3.1875,            12.134528570998387744547733730974713055},
            {3.2500,            12.914557062512392049483503752322408761},
            {3.3125,            13.745049466398732213877084541992751273},
            {3.3750,            14.629250949773302934853381428660210721},
            {3.4375,            15.570616549147269180921654324879141947},
            {3.5000,            16.572824671057316125696517821376119469},
            {3.5625,            17.639791465519127930722105721028711044},
            {3.6250,            18.775686128468677200079039891415789429},
            {3.6875,            19.984947192985946987799359614758598457},
            {3.7500,            21.272299872959396081877161903352144126},
            {3.8125,            22.642774526961913363958587775566619798},
            {3.8750,            24.101726314486257781049388094955970560},
            {3.9375,            25.654856121347151067170940701379544221},
            {4.0000,            27.308232836016486629201989612067059978},
            {4.0625,            29.068317063936918520135334110824828950},
            {4.1250,            30.941986372478026192360480044849306606},
            {4.1875,            32.936562165180269851350626768308756303},
            {4.2500,            35.059838290298428678502583470475012235},
            {4.3125,            37.320111495433027109832850313172338419},
            {4.3750,            39.726213847251883288518263854094284091},
            {4.4375,            42.287547242982546165696077854963452084},
            {4.5000,            45.014120148530027928305799939930642658},
            {4.5625,            47.916586706774825161786212701923307169},
            {4.6250,            51.006288368867753140854830589583165950},
            {4.6875,            54.295298211196782516984520211780624960},
            {4.7500,            57.796468111195389383795669320243166117},
            {4.8125,            61.523478966332915041549750463563672435},
            {4.8750,            65.490894152518731617237739112888213645},
            {4.9375,            69.714216430810089539924900313140922323},
            {5.0000,            74.209948524787844444106108044487704798},
            {5.0625,            78.995657605307475581204965926043112946},
            {5.1250,            84.090043934600961683400343038519519678},
            {5.1875,            89.513013937957834087706670952561002466},
            {5.2500,            95.285757988514588780586084642381131013},
            {5.3125,            101.430833209098212357990123684449846912},
            {5.3750,            107.972251614673824873137995865940755392},
            {5.4375,            114.935573939814969189535554289886848550},
            {5.5000,            122.348009517829425991091207107262038316},
            {5.5625,            130.238522601820409078244923165746295574},
            {5.6250,            138.637945543134998069351279801575968875},
            {5.6875,            147.579099269447055276899288971207106581},
            {5.7500,            157.096921533245353905868840194264636395},
            {5.8125,            167.228603431860671946045256541679445836},
            {5.8750,            178.013734732486824390148614309727161925},
            {5.9375,            189.494458570056311567917444025807275896},
            {6.0000,            201.715636122455894483405112855409538488},
            {6.0625,            214.725021906554080628430756558271312513},
            {6.1250,            228.573450380013557089736092321068279231},
            {6.1875,            243.315034578039208138752165587134488645},
            {6.2500,            259.007377561239126824465367865430519592},
            {6.3125,            275.711797500835732516530131577254654076},
            {6.3750,            293.493567280752348242602902925987643443},
            {6.4375,            312.422169552825597994104814531010579387},
            {6.5000,            332.571568241777409133204438572983297292},
            {6.5625,            354.020497560858198165985214519757890505},
            {6.6250,            376.852769667496146326030849450983914197},
            {6.6875,            401.157602161123700280816957271992998156},
            {6.7500,            427.029966702886171977469256622451185850},
            {6.8125,            454.570960119471524953536004647195906721},
            {6.8750,            483.888199441157626584508920036981010995},
            {6.9375,            515.096242417696720610477570797503766179},
            {7.0000,            548.317035155212076889964120712102928484},
            {7.0625,            583.680388623257719787307547662358502345},
            {7.1250,            621.324485894002926216918634755431456031},
            {7.1875,            661.396422095589629755266517362992812037},
            {7.2500,            704.052779189542208784574955807004218856},
            {7.3125,            749.460237818184878095966335081928645934},
            {7.3750,            797.796228612873763671070863694973560629},
            {7.4375,            849.249625508044731271830060572510241864},
            {7.5000,            904.021483770216677368692292389446994987},
            {7.5625,            962.325825625814651122171697031114091993},
            {7.6250,            1024.390476557670599008492465853663578558},
            {7.6875,            1090.457955538048482588540574008226583335},
            {7.7500,            1160.786422676798661020094043586456606003},
            {7.8125,            1235.650687987597295222707689125107720568},
            {7.8750,            1315.343285214046776004329388551335841550},
            {7.9375,            1400.175614911635999247504386054087931958},
            {8.0000,            1490.479161252178088627715460421007179728},
            {8.0625,            1586.606787305415349050508956232945539108},
            {8.1250,            1688.934113859132470361718199038326340668},
            {8.1875,            1797.860987165547537276364148450577336075},
            {8.2500,            1913.813041349231764486365114317586148767},
            {8.3125,            2037.243361581700856522236313401822532385},
            {8.3750,            2168.634254521568851112005905503069409349},
            {8.4375,            2308.499132938297821208734949028296170563},
            {8.5000,            2457.384521883751693037774022640629666294},
            {8.5625,            2615.872194250713123494312356053193077854},
            {8.6250,            2784.581444063104750127653362960649823247},
            {8.6875,            2964.171506380845754878370650565756538203},
            {8.7500,            3155.344133275174556354775488913749659006},
            {8.8125,            3358.846335940117183452010789979584950102},
            {8.8750,            3575.473303654961482727206202358956274888},
            {8.9375,            3806.071511003646460448021740303914939059},
            {9.0000,            4051.542025492594047194773093534725371440},
            {9.0625,            4312.844028491571841588188869958240355518},
            {9.1250,            4590.998563255739769060078863130940205710},
            {9.1875,            4887.092524674358252509551443117048351290},
            {9.2500,            5202.282906336187674588222835339193136030},
            {9.3125,            5537.801321507079474415176386655744387251},
            {9.3750,            5894.958815685577062811620236195525504885},
            {9.4375,            6275.150989541692149890530417987358096221},
            {9.5000,            6679.863452256851081801173722051940058824},
            {9.5625,            7110.677626574055535297758456126491707647},
            {9.6250,            7569.276928241617224537226019600213961572},
            {9.6875,            8057.453343996777301036241026375049070162},
            {9.7500,            8577.114433792824387959788368429252257664},
            {9.8125,            9130.290784631065880205118262838330689429},
            {9.8750,            9719.143945123662919857326995631317996715},
            {9.9375,            10345.974871791805753327922796701684092861},
            {10.0000,           11013.232920103323139721376090437880844591},
        };

        for(int i = 0; i < testCases.length; i++) {
            double [] testCase = testCases[i];
            failures += testCoshCaseWithUlpDiff(testCase[0],
                                                testCase[1],
                                                3.0);
        }

        for(double nan : Tests.NaNs) {
            failures += testCoshCaseWithUlpDiff(nan, NaNd, 0);
        }

        double [][] specialTestCases = {
            {0.0,                       1.0},
            {Double.POSITIVE_INFINITY,  Double.POSITIVE_INFINITY}
        };

        for(int i = 0; i < specialTestCases.length; i++ ) {
            failures += testCoshCaseWithUlpDiff(specialTestCases[i][0],
                                                specialTestCases[i][1],
                                                0.0);
        }

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

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

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

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

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

        for(long i = trans22;
            i < transExpOvfl;
            i +=(transExpOvfl-trans22)/10000) {

            double d = Double.longBitsToDouble(i);

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

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

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

        /*
         * For large values of x, cosh(x) ~= 0.5*(e^x).  Therefore,
         *
         * cosh(x) ~= e^(ln 0.5) * e^x = e^(x + ln 0.5)
         *
         * So, we can calculate the approximate expected result as
         * exp(x + -0.693147186).  However, this sum suffers from
         * roundoff, limiting the accuracy of the approximation.  The
         * accuracy can be improved by recovering the rounded-off
         * information.  Since x is larger than ln(0.5), the trailing
         * bits of ln(0.5) get rounded away when the two values are
         * added.  However, high-order bits of ln(0.5) that
         * contribute to the sum can be found:
         *
         * offset = log(0.5);
         * effective_offset = (x + offset) - x; // exact subtraction
         * rounded_away_offset = offset - effective_offset; // exact subtraction
         *
         * Therefore, the product
         *
         * exp(x + offset)*exp(rounded_away_offset)
         *
         * will be a better approximation to the exact value of
         *
         * e^(x + offset)
         *
         * than exp(x+offset) alone.  (The expected result cannot be
         * computed as exp(x)*exp(offset) since exp(x) by itself would
         * overflow to infinity.)
         */
        double offset = StrictMath.log(0.5);
        for(long i = transExpOvfl+1; i < transCoshOvfl;
            i += (transCoshOvfl-transExpOvfl)/1000 ) {
            double input = Double.longBitsToDouble(i);

            double expected =
                StrictMath.exp(input + offset) *
                StrictMath.exp( offset - ((input + offset) - input) );

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

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

            // Result and expected are the same.
            failures += testCoshCaseWithUlpDiff(d,
                                                Double.POSITIVE_INFINITY, 0.0);
        }
        return failures;
    }

    public static int testCoshCaseWithTolerance(double input,
                                                double expected,
                                                double tolerance) {
        int failures = 0;
        failures += Tests.testTolerance("Math.cosh(double)",
                                        input, Math.cosh(input),
                                        expected, tolerance);
        failures += Tests.testTolerance("Math.cosh(double)",
                                        -input, Math.cosh(-input),
                                        expected, tolerance);

        failures += Tests.testTolerance("StrictMath.cosh(double)",
                                        input, StrictMath.cosh(input),
                                        expected, tolerance);
        failures += Tests.testTolerance("StrictMath.cosh(double)",
                                        -input, StrictMath.cosh(-input),
                                        expected, tolerance);
        return failures;
    }

    public static int testCoshCaseWithUlpDiff(double input,
                                              double expected,
                                              double ulps) {
        int failures = 0;
        failures += Tests.testUlpDiff("Math.cosh",        input, Math::cosh,       expected, ulps);
        failures += Tests.testUlpDiff("Math.cosh",       -input, Math::cosh,       expected, ulps);

        failures += Tests.testUlpDiff("StrictMath.cosh",  input, StrictMath::cosh, expected, ulps);
        failures += Tests.testUlpDiff("StrictMath.cosh", -input, StrictMath::cosh, expected, ulps);
        return failures;
    }

    /**
     * Test accuracy of {Math, StrictMath}.tanh.  The specified
     * accuracy is 2.5 ulps.
     *
     * The defintion of tanh(x) is
     *
     * (e^x - e^(-x))/(e^x + e^(-x))
     *
     * The series expansion of tanh(x) =
     *
     * x - x^3/3 + 2x^5/15 - 17x^7/315 + ...
     *
     * Therefore,
     *
     * 1. For large values of x tanh(x) ~= signum(x)
     *
     * 2. For small values of x, tanh(x) ~= x.
     *
     * Additionally, tanh is an odd function; tanh(-x) = -tanh(x).
     *
     */
    static int testTanh() {
        int failures = 0;
        /*
         * Array elements below generated using a quad sinh
         * implementation.  Rounded to a double, the quad result
         * *should* be correctly rounded, unless we are quite unlucky.
         * Assuming the quad value is a correctly rounded double, the
         * allowed error is 3.0 ulps instead of 2.5 since the quad
         * value rounded to double can have its own 1/2 ulp error.
         */
        double [][] testCases = {
            // x                tanh(x)
            {0.0625,            0.06241874674751251449014289119421133},
            {0.1250,            0.12435300177159620805464727580589271},
            {0.1875,            0.18533319990813951753211997502482787},
            {0.2500,            0.24491866240370912927780113149101697},
            {0.3125,            0.30270972933210848724239738970991712},
            {0.3750,            0.35835739835078594631936023155315807},
            {0.4375,            0.41157005567402245143207555859415687},
            {0.5000,            0.46211715726000975850231848364367256},
            {0.5625,            0.50982997373525658248931213507053130},
            {0.6250,            0.55459972234938229399903909532308371},
            {0.6875,            0.59637355547924233984437303950726939},
            {0.7500,            0.63514895238728731921443435731249638},
            {0.8125,            0.67096707420687367394810954721913358},
            {0.8750,            0.70390560393662106058763026963135371},
            {0.9375,            0.73407151960434149263991588052503660},
            {1.0000,            0.76159415595576488811945828260479366},
            {1.0625,            0.78661881210869761781941794647736081},
            {1.1250,            0.80930107020178101206077047354332696},
            {1.1875,            0.82980190998595952708572559629034476},
            {1.2500,            0.84828363995751289761338764670750445},
            {1.3125,            0.86490661772074179125443141102709751},
            {1.3750,            0.87982669965198475596055310881018259},
            {1.4375,            0.89319334040035153149249598745889365},
            {1.5000,            0.90514825364486643824230369645649557},
            {1.5625,            0.91582454416876231820084311814416443},
            {1.6250,            0.92534622531174107960457166792300374},
            {1.6875,            0.93382804322259173763570528576138652},
            {1.7500,            0.94137553849728736226942088377163687},
            {1.8125,            0.94808528560440629971240651310180052},
            {1.8750,            0.95404526017994877009219222661968285},
            {1.9375,            0.95933529331468249183399461756952555},
            {2.0000,            0.96402758007581688394641372410092317},
            {2.0625,            0.96818721657637057702714316097855370},
            {2.1250,            0.97187274591350905151254495374870401},
            {2.1875,            0.97513669829362836159665586901156483},
            {2.2500,            0.97802611473881363992272924300618321},
            {2.3125,            0.98058304703705186541999427134482061},
            {2.3750,            0.98284502917257603002353801620158861},
            {2.4375,            0.98484551746427837912703608465407824},
            {2.5000,            0.98661429815143028888127603923734964},
            {2.5625,            0.98817786228751240824802592958012269},
            {2.6250,            0.98955974861288320579361709496051109},
            {2.6875,            0.99078085564125158320311117560719312},
            {2.7500,            0.99185972456820774534967078914285035},
            {2.8125,            0.99281279483715982021711715899682324},
            {2.8750,            0.99365463431502962099607366282699651},
            {2.9375,            0.99439814606575805343721743822723671},
            {3.0000,            0.99505475368673045133188018525548849},
            {3.0625,            0.99563456710930963835715538507891736},
            {3.1250,            0.99614653067334504917102591131792951},
            {3.1875,            0.99659855517712942451966113109487039},
            {3.2500,            0.99699763548652601693227592643957226},
            {3.3125,            0.99734995516557367804571991063376923},
            {3.3750,            0.99766097946988897037219469409451602},
            {3.4375,            0.99793553792649036103161966894686844},
            {3.5000,            0.99817789761119870928427335245061171},
            {3.5625,            0.99839182812874152902001617480606320},
            {3.6250,            0.99858065920179882368897879066418294},
            {3.6875,            0.99874733168378115962760304582965538},
            {3.7500,            0.99889444272615280096784208280487888},
            {3.8125,            0.99902428575443546808677966295308778},
            {3.8750,            0.99913888583735077016137617231569011},
            {3.9375,            0.99924003097049627100651907919688313},
            {4.0000,            0.99932929973906704379224334434172499},
            {4.0625,            0.99940808577297384603818654530731215},
            {4.1250,            0.99947761936180856115470576756499454},
            {4.1875,            0.99953898655601372055527046497863955},
            {4.2500,            0.99959314604388958696521068958989891},
            {4.3125,            0.99964094406130644525586201091350343},
            {4.3750,            0.99968312756179494813069349082306235},
            {4.4375,            0.99972035584870534179601447812936151},
            {4.5000,            0.99975321084802753654050617379050162},
            {4.5625,            0.99978220617994689112771768489030236},
            {4.6250,            0.99980779516900105210240981251048167},
            {4.6875,            0.99983037791655283849546303868853396},
            {4.7500,            0.99985030754497877753787358852000255},
            {4.8125,            0.99986789571029070417475400133989992},
            {4.8750,            0.99988341746867772271011794614780441},
            {4.9375,            0.99989711557251558205051185882773206},
            {5.0000,            0.99990920426259513121099044753447306},
            {5.0625,            0.99991987261554158551063867262784721},
            {5.1250,            0.99992928749851651137225712249720606},
            {5.1875,            0.99993759617721206697530526661105307},
            {5.2500,            0.99994492861777083305830639416802036},
            {5.3125,            0.99995139951851344080105352145538345},
            {5.3750,            0.99995711010315817210152906092289064},
            {5.4375,            0.99996214970350792531554669737676253},
            {5.5000,            0.99996659715630380963848952941756868},
            {5.5625,            0.99997052203605101013786592945475432},
            {5.6250,            0.99997398574306704793434088941484766},
            {5.6875,            0.99997704246374583929961850444364696},
            {5.7500,            0.99997974001803825215761760428815437},
            {5.8125,            0.99998212060739040166557477723121777},
            {5.8750,            0.99998422147482750993344503195672517},
            {5.9375,            0.99998607548749972326220227464612338},
            {6.0000,            0.99998771165079557056434885235523206},
            {6.0625,            0.99998915556205996764518917496149338},
            {6.1250,            0.99999042981101021976277974520745310},
            {6.1875,            0.99999155433311068015449574811497719},
            {6.2500,            0.99999254672143162687722782398104276},
            {6.3125,            0.99999342250186907900400800240980139},
            {6.3750,            0.99999419537602957780612639767025158},
            {6.4375,            0.99999487743557848265406225515388994},
            {6.5000,            0.99999547935140419285107893831698753},
            {6.5625,            0.99999601054055694588617385671796346},
            {6.6250,            0.99999647931357331502887600387959900},
            {6.6875,            0.99999689300449080997594368612277442},
            {6.7500,            0.99999725808558628431084200832778748},
            {6.8125,            0.99999758026863294516387464046135924},
            {6.8750,            0.99999786459425991170635407313276785},
            {6.9375,            0.99999811551081218572759991597586905},
            {7.0000,            0.99999833694394467173571641595066708},
            {7.0625,            0.99999853235803894918375164252059190},
            {7.1250,            0.99999870481040359014665019356422927},
            {7.1875,            0.99999885699910593255108365463415411},
            {7.2500,            0.99999899130518359709674536482047025},
            {7.3125,            0.99999910982989611769943303422227663},
            {7.3750,            0.99999921442759946591163427422888252},
            {7.4375,            0.99999930673475777603853435094943258},
            {7.5000,            0.99999938819554614875054970643513124},
            {7.5625,            0.99999946008444508183970109263856958},
            {7.6250,            0.99999952352618001331402589096040117},
            {7.6875,            0.99999957951331792817413683491979752},
            {7.7500,            0.99999962892179632633374697389145081},
            {7.8125,            0.99999967252462750190604116210421169},
            {7.8750,            0.99999971100399253750324718031574484},
            {7.9375,            0.99999974496191422474977283863588658},
            {8.0000,            0.99999977492967588981001883295636840},
            {8.0625,            0.99999980137613348259726597081723424},
            {8.1250,            0.99999982471505097353529823063673263},
            {8.1875,            0.99999984531157382142423402736529911},
            {8.2500,            0.99999986348794179107425910499030547},
            {8.3125,            0.99999987952853049895833839645847571},
            {8.3750,            0.99999989368430056302584289932834041},
            {8.4375,            0.99999990617672396471542088609051728},
            {8.5000,            0.99999991720124905211338798152800748},
            {8.5625,            0.99999992693035839516545287745322387},
            {8.6250,            0.99999993551626733394129009365703767},
            {8.6875,            0.99999994309330543951799157347876934},
            {8.7500,            0.99999994978001814614368429416607424},
            {8.8125,            0.99999995568102143535399207289008504},
            {8.8750,            0.99999996088863858914831986187674522},
            {8.9375,            0.99999996548434461974481685677429908},
            {9.0000,            0.99999996954004097447930211118358244},
            {9.0625,            0.99999997311918045901919121395899372},
            {9.1250,            0.99999997627775997868467948564005257},
            {9.1875,            0.99999997906519662964368381583648379},
            {9.2500,            0.99999998152510084671976114264303159},
            {9.3125,            0.99999998369595870397054673668361266},
            {9.3750,            0.99999998561173404286033236040150950},
            {9.4375,            0.99999998730239984852716512979473289},
            {9.5000,            0.99999998879440718770812040917618843},
            {9.5625,            0.99999999011109904501789298212541698},
            {9.6250,            0.99999999127307553219220251303121960},
            {9.6875,            0.99999999229851618412119275358396363},
            {9.7500,            0.99999999320346438410630581726217930},
            {9.8125,            0.99999999400207836827291739324060736},
            {9.8750,            0.99999999470685273619047001387577653},
            {9.9375,            0.99999999532881393331131526966058758},
            {10.0000,           0.99999999587769276361959283713827574},
        };

        for(int i = 0; i < testCases.length; i++) {
            double [] testCase = testCases[i];
            failures += testTanhCaseWithUlpDiff(testCase[0],
                                                testCase[1],
                                                3.0);
        }

        for(double nan : Tests.NaNs) {
            failures += testTanhCaseWithUlpDiff(nan, NaNd, 0);
        }

        double [][] specialTestCases = {
            {0.0,                       0.0},
            {Double.POSITIVE_INFINITY,  1.0}
        };

        for(int i = 0; i < specialTestCases.length; i++) {
            failures += testTanhCaseWithUlpDiff(specialTestCases[i][0],
                                                specialTestCases[i][1],
                                                0.0);
        }

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

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

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

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

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

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

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

        failures += testTanhAdditionalTests();

        return failures;
    }

    /**
     * Test accuracy of {Math, StrictMath}.tanh using quad precision
     * tanh implementation as the reference. There are additional tests.
     * The specified accuracy is 2.5 ulps.
     *
     */
    static int testTanhAdditionalTests() {
        int failures = 0;
        /*
         * Array elements below are generated using a quad precision tanh
         * implementation (libquadmath). Rounded to a double, the quad result
         * *should* be correctly rounded, unless we are quite unlucky.
         * Assuming the quad value is a correctly rounded double, the
         * allowed error is 3.0 ulps instead of 2.5 since the quad
         * value rounded to double can have its own 1/2 ulp error.
         */
        double[][] testCases = {
            // x                                                   tanh(x)
            {1.09951162777600024414062500000000000e+12,            1.00000000000000000000000000000000000e+00},
            {1.56250000000000416333634234433702659e-02,            1.56237285584089068255495133849899136e-02},
            {1.61254882812500000000000000000000000e+01,            9.99999999999980293529906376885389048e-01},
            {2.53165043529127054000582575099542737e-01,            2.47891535884497437358843835970604812e-01},
            {2.05669906337718799704816774465143681e+00,            9.67821952180774991463712302156014956e-01},
            {8.73243486124784240587359818164259195e+00,            9.99999947984421044859570034536492937e-01},
            {1.35302734375000000000000000000000000e+00,            8.74765946489987955543753077657414741e-01},
            {7.51299319580434721288497712521348149e-01,            6.35923468395323117288273690770900477e-01},
            {9.53088818012631927567568368431238923e-02,            9.50213381512267711017656118902912332e-02},
            {7.64443165964961757197215774795040488e-01,            6.43686625696507143760198874608796949e-01},
            {9.80772770147126660145175947036477737e-02,            9.77640088885469645387119927980991050e-02},
            {8.00000000000000044408920985006261617e-01,            6.64036770267848988511881426480887109e-01},
            {6.58800443825626694943631278533757722e-03,            6.58790912948844334160953310959647563e-03},
            {3.50634723606509357551885841530747712e+00,            9.98200861366828007281302037717336212e-01},
            {8.80951107580675074615328412619419396e-01,            7.06895478355484050029724917425086249e-01},
            {9.41693953354077795125931515940465033e-01,            7.35999567964351009171211613664845735e-01},
            {4.86714106743433794211028953213826753e-01,            4.51604571680788935707314000261162601e-01},
            {4.99999999970896114032115065128891729e-01,            4.62117157237121073362068671381593592e-01},
            {1.27999999999999971578290569595992565e+02,            1.00000000000000000000000000000000000e+00},
            {1.00000000000000022204460492503130808e+00,            7.61594155955764981372495044941331753e-01},
            {1.09951162777600024414062500000000000e+12,            1.00000000000000000000000000000000000e+00},
            {5.00000000000000777156117237609578297e-01,            4.62117157260010369694985045764006657e-01},
            {3.90625000000001474514954580286030250e-03,            3.90623013190635482599726614938805467e-03},
            {1.56250000000000659194920871186695877e-02,            1.56237285584089311057499113400637264e-02},
            {1.25000000000001332267629550187848508e-01,            1.24353001771597519720531117125519878e-01},
            {1.56250000000005169475958410885141348e-02,            1.56237285584093820237573019342883109e-02},
            {2.00000000000022737367544323205947876e+00,            9.64027580075832948084133680630298643e-01},
            {6.25000000000080352391407245704613160e-02,            6.24187467475205184231888372622987839e-02},
            {2.50000000000049737991503207013010979e-01,            2.44918662403755883728363950973251081e-01},
            {2.50000000000454747350886464118957520e-01,            2.44918662404136598540089724354621762e-01},
            {7.81250000001537658889105841808486730e-03,            7.81234105817638947180855590780540396e-03},
            {8.00000000002179945113311987370252609e+00,            9.99999774929675899622836792366347278e-01},
            {8.00000000002182787284255027770996094e+00,            9.99999774929675899635630557632573807e-01},
            {1.00000000004506106598967107856879011e+00,            7.61594155974689379640247120538425632e-01},
            {5.00000000024432678102925819985102862e-01,            4.62117157279224782806433798595181278e-01},
            {5.00000000124148025193449029757175595e-01,            4.62117157357645691462301850285961295e-01},
            {1.25000000043655745685100555419921875e-01,            1.24353001814576875736126314329404676e-01},
            {1.56250130385160446166992187500000000e-02,            1.56237415937421937398207048034470765e-02},
            {6.25000596046447753906250000000000000e-02,            6.24188061199314157260056878713262148e-02},
            {6.25001570879248902201652526855468750e-02,            6.24189032234056148184566765458350515e-02},
            {3.12509536743164062500000000000000000e-02,            3.12407841896026978197614959195842857e-02},
            {1.00024414062500000000000000000000000e+00,            7.61696669690972358277739369649969500e-01},
            {1.25091552734375000000000000000000000e-01,            1.24443137738349286849917747910445080e-01},
            {6.25703578334750876166481248219497502e-02,            6.24888301519391612116796252071905868e-02},
            {2.52525252525252597024518763646483421e-01,            2.47290965006585965880182136581880733e-01},
            {1.00000000164410457817454336293394590e-03,            9.99999668310902934017090322313224382e-04},
            {1.00000000966720672609944209341392707e-03,            9.99999676333997058845099107943491685e-04},
            {5.13687551499984795810860305209644139e-01,            4.72813376851263299460550751434331149e-01},
            {1.03125000000000000000000000000000000e+00,            7.74409187434213568286703209738132986e-01},
            {1.03372912114974835340319714305223897e+00,            7.75399652279487427958938283855319050e-01},
            {8.73243486124791523650401359191164374e+00,            9.99999947984421044867146689152891277e-01},
            {5.46364074509520181166521979321260005e-01,            4.97790203319363272413440879555555135e-01},
            {5.48776992118357842542764046811498702e-01,            4.99603030846724465253358333732665160e-01},
            {8.62884521484375000000000000000000000e-03,            8.62863106199946057455229821459862778e-03},
            {5.56840723899044820477399753144709393e-01,            5.05629619734278492036257594911833276e-01},
            {1.12042968912429174999090264464030042e+00,            8.07718324543002512898290101804260243e-01},
            {2.80761718750000000000000000000000000e-01,            2.73609921989813966516244201735889906e-01},
            {4.50982142857161694138312668655999005e+00,            9.99758010610690750512553927515350523e-01},
            {1.79803946803892764072507759465224808e-02,            1.79784572761372499903768063141254578e-02},
            {2.90674624105783541150316295897937380e-01,            2.82755618405959946459876962574827861e-01},
            {3.00000000019552404140199541870970279e-01,            2.91312612469484033539387970973996561e-01},
            {1.52306844600212459850396840010944288e-01,            1.51139964502163284820786391222343666e-01},
            {1.21913138136517762433186362613923848e+00,            8.39397762830401796350294214789399315e-01},
            {1.91612901016097944562055488404439529e-02,            1.91589453912240029886209020645693670e-02},
            {1.23194037796136601770058405236341059e+00,            8.43141232466373734055029303451281784e-01},
            {5.14544145441922751160745974630117416e+00,            9.99932120037417992977353814124626761e-01},
            {1.29608715898613313655118872702587396e+00,            8.60712461444305632100271902930674052e-01},
            {1.35302734375000000000000000000000000e+00,            8.74765946489987955543753077657414741e-01},
            {6.89141205308152926534148718928918242e-01,            5.97430012402391408227990740295335202e-01},
            {2.16702398900134561576802383342510439e-02,            2.16668484172600518601166701940771309e-02},
            {6.95330121814107471323040954302996397e-01,            6.01395252733578654705526153849150843e-01},
            {1.70127028180982076566857275068400668e-04,            1.70127026539641570641832179464678521e-04},
            {6.98731899876564921392230189667316154e-01,            6.03562246839061712657431798989209285e-01},
            {2.82308042901865396956395670713391155e+00,            9.92962754889608618611084237181745775e-01},
            {8.85009765625000000000000000000000000e-02,            8.82706391518277914218106043840064600e-02},
            {1.44086021505376304929768593865446746e+00,            8.93870759190524111186764508137227647e-01},
            {4.52708479240923750142044923450157512e-02,            4.52399464814195843886615749285771251e-02},
            {7.42434201630502221824770003877347335e-01,            6.30613596749571014884527941122811076e-01},
            {7.47314453125000000000000000000000000e-01,            6.33544059591028741704251380359792317e-01},
            {2.33572976827208893257914468222224968e-02,            2.33530509808936286709795071423335732e-02},
            {7.51392746195329142011587464367039502e-01,            6.35979110106607807348963004903609067e-01},
            {7.51649175412362091641682582121575251e-01,            6.36131796640758591543062918907122080e-01},
            {7.62560692649938864917658065678551793e-01,            6.42582785959772486552828548950126373e-01},
            {7.64660852335945273594575155584607273e-01,            6.43814099671361386286313072270915932e-01},
            {1.92871093750000000000000000000000000e-01,            1.90514597602311764623059750704793759e-01},
            {2.43864313521849479515779535176989157e-02,            2.43815983142663741885939851467013521e-02},
            {3.97705078125000000000000000000000000e-01,            3.77983627858614640283948547303348236e-01},
            {7.98034667968750000000000000000000000e-01,            6.62936606884708330125541187161682941e-01},
            {7.99316406250000000000000000000000000e-01,            6.63654430152659513562528989372441102e-01},
            {1.99890136718750000000000000000000000e-01,            1.97269734600247465099938891830640889e-01},
            {2.00000000008910994164779140191967599e-01,            1.97375320233467849151455260287892058e-01},
            {4.00000000093461316463816501709516160e-01,            3.79948962335194012629557116519596150e-01},
            {2.00000000069810862646235705142316874e-01,            1.97375320291995240418209079080646997e-01},
            {1.00000000056612609045103567950718571e-01,            9.96679946810060529704707312198636589e-02},
            {1.00000000080404896629637789828848327e-01,            9.96679947045619948897444345018478492e-02},
            {1.66666666666666696272613990004174411e+00,            9.31109608667577693190680177920119455e-01},
            {1.31034851074218750000000000000000000e-02,            1.31027351970209980614612589861988504e-02},
            {8.43444227005861080215254332870244980e-01,            6.87629045782656322925865941652078512e-01},
            {4.25596815032856623517432126391213387e-01,            4.01634947321531793299729470086813678e-01},
            {8.54614885269050605920426733064232394e-01,            6.93472710492835200064966331725774025e-01},
            {8.63777419830865200722769259300548583e-01,            6.98198780318331041148483592329099127e-01},
            {2.70117449276632004551146337689715438e-02,            2.70051772786722224566765342032635559e-02},
            {2.16282487792377908775165451515931636e-01,            2.12971988592557031781365419455581001e-01},
            {1.73204653003120601084674490266479552e+00,            9.39297315789076214802641716736658105e-01},
            {2.71436010781672190650404274947504746e-02,            2.71369367992428389623549774823710978e-02},
            {8.69092640155437079485523099720012397e-01,            7.00912831250687651307196017605464473e-01},
            {2.78015136718750000000000000000000000e-02,            2.77943530651526982827985645341156701e-02},
            {9.10156250000000000000000000000000000e-01,            7.21207240669352050307412688531998165e-01},
            {2.27787862235060922788676407435559668e-01,            2.23928183342045426304404589794035157e-01},
            {5.71524498377538048288215577485971153e-02,            5.70903033991663026980553749418981725e-02},
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            {2.00000000000000000000000000000000000e+00,            9.64027580075816883946413724100923171e-01},
            {2.00000000000000044408920985006261617e+00,            9.64027580075816915321682708397883469e-01},
            {9.99999999999999888977697537484345958e-01,            7.61594155955764841492939901436512668e-01},
            {1.00000000000000000000000000000000000e+00,            7.61594155955764888119458282604793657e-01},
            {1.00000000000000022204460492503130808e+00,            7.61594155955764981372495044941331753e-01},
            {4.99999999999999944488848768742172979e-01,            4.62117157260009714845699443492203290e-01},
            {5.00000000000000000000000000000000000e-01,            4.62117157260009758502318483643672557e-01},
            {5.00000000000000111022302462515654042e-01,            4.62117157260009845815556563946604302e-01},
            {2.49999999999999972244424384371086489e-01,            2.44918662403709103187147915631612892e-01},
            {2.50000000000000000000000000000000000e-01,            2.44918662403709129277801131491016945e-01},
            {2.50000000000000055511151231257827021e-01,            2.44918662403709181459107563209824042e-01},
            {1.24999999999999986122212192185543245e-01,            1.24353001771596194391460985792144305e-01},
            {1.25000000000000000000000000000000000e-01,            1.24353001771596208054647275805892707e-01},
            {1.25000000000000027755575615628913511e-01,            1.24353001771596235381019855833389378e-01},
            {6.24999999999999930611060960927716224e-02,            6.24187467475125075782836114480350829e-02},
            {6.25000000000000000000000000000000000e-02,            6.24187467475125144901428911942113317e-02},
            {6.25000000000000138777878078144567553e-02,            6.24187467475125283138614506865638292e-02},
            {3.12499999999999965305530480463858112e-02,            3.12398314460312533021176543496182149e-02},
            {3.12500000000000000000000000000000000e-02,            3.12398314460312567681786791091369499e-02},
            {3.12500000000000069388939039072283776e-02,            3.12398314460312637003007286281744168e-02},
            {1.56249999999999982652765240231929056e-02,            1.56237285584088634680488027509294906e-02},
            {1.56250000000000000000000000000000000e-02,            1.56237285584088652023488311762919065e-02},
            {1.56250000000000034694469519536141888e-02,            1.56237285584088686709488880270167445e-02},
            {6.10351562499999932237364219655972875e-05,            6.10351561742087681889301535131725312e-05},
            {6.10351562500000000000000000000000000e-05,            6.10351561742087749651937063040263414e-05},
            {6.10351562500000135525271560688054251e-05,            6.10351561742087885177208118857339557e-05},
            {9.31322574615478412227423430871540641e-10,            9.31322574615478411958158908556102005e-10},
            {9.31322574615478515625000000000000000e-10,            9.31322574615478515355735477684561274e-10},
            {9.31322574615478722420153138256918718e-10,            9.31322574615478722150888615941479902e-10},
            {2.77555756156289104291028806826931429e-17,            2.77555756156289104291028806826931349e-17},
            {2.77555756156289135105907917022705078e-17,            2.77555756156289135105907917022704998e-17},
            {2.77555756156289196735666137414252376e-17,            2.77555756156289196735666137414252322e-17},
            {1.79769313486231570814527423731704357e+308,           1.00000000000000000000000000000000000e+00},
            {1.79769313486231570814527423731704357e+308,           1.00000000000000000000000000000000000e+00},
            {1.79769313486231570814527423731704357e+308,           1.00000000000000000000000000000000000e+00},
            {1.79769313486231550856124328384506240e+308,           1.00000000000000000000000000000000000e+00},
            {3.14159265358979311599796346854418516e+00,            9.96272076220749943353314537833579484e-01},
            {1.57079632679489655799898173427209258e+00,            9.17152335667274336647462811870662140e-01},
            {1.00000000000000022204460492503130808e+00,            7.61594155955764981372495044941331753e-01},
            {1.00000000000000000000000000000000000e+00,            7.61594155955764888119458282604793657e-01},
            {9.99999999999999888977697537484345958e-01,            7.61594155955764841492939901436512668e-01},
            {7.85398163397448278999490867136046290e-01,            6.55794202632672418203926030568705821e-01},
            {2.22507385850720187715587855857894824e-308,           2.22507385850720187715587855857894824e-308},
            {2.22507385850720138309023271733240406e-308,           2.22507385850720138309023271733240406e-308},
            {2.22507385850720088902458687608585989e-308,           2.22507385850720088902458687608585989e-308},
            {2.22507385850720039495894103483931571e-308,           2.22507385850720039495894103483931571e-308},
            {9.88131291682493088353137585736442745e-324,           9.88131291682493088353137585736442745e-324},
            {4.94065645841246544176568792868221372e-324,           4.94065645841246544176568792868221372e-324},
        };

        for (int i = 0; i < testCases.length; i++) {
            double[] testCase = testCases[i];
            failures += testTanhCaseWithUlpDiff(testCase[0],
                    testCase[1],
                    3.0);
        }

        return failures;
    }

    public static int testTanhCaseWithTolerance(double input,
                                                double expected,
                                                double tolerance) {
        int failures = 0;
        failures += Tests.testTolerance("Math.tanh",       input, Math::tanh,         expected, tolerance);
        failures += Tests.testTolerance("Math.tanh",      -input, Math::tanh,        -expected, tolerance);

        failures += Tests.testTolerance("StrictMath.tanh",  input, StrictMath::tanh,  expected, tolerance);
        failures += Tests.testTolerance("StrictMath.tanh", -input, StrictMath::tanh, -expected, tolerance);
        return failures;
    }

    public static int testTanhCaseWithUlpDiff(double input,
                                              double expected,
                                              double ulps) {
        int failures = 0;

        failures += Tests.testUlpDiffWithAbsBound("Math.tanh",       input,  Math::tanh,       expected, ulps, 1.0);
        failures += Tests.testUlpDiffWithAbsBound("Math.tanh",      -input,  Math::tanh,      -expected, ulps, 1.0);

        failures += Tests.testUlpDiffWithAbsBound("StrictMath.tanh",  input, StrictMath::tanh,  expected, ulps, 1.0);
        failures += Tests.testUlpDiffWithAbsBound("StrictMath.tanh", -input, StrictMath::tanh, -expected, ulps, 1.0);
        return failures;
    }

    /**
     * Test accuracy of {Math, StrictMath}.asinh.  The specified
     * accuracy is 2.5 ulps.
     *
     * The defintion of asinh(x) is
     *
     * asinh(sinh(x)) = x
     *
     * Can be also written as
     *
     * asinh(x) = ln(x + sqrt(x*x + 1))
     *
     * The series expansion of asinh(x) =
     *
     * x - x^3/6 + 3x^5/40 - 15x^7/336 + ...
     *
     * Therefore,
     *
     * 1. For small values of x, asinh(x) ~= x.
     *
     * Additionally, asinh is an odd function; asinh(-x) = -asinh(x).
     *
     */
    static int testAsinh() {
        int failures = 0;
        /*
         * Array elements below generated using a quad asinh
         * implementation.  Rounded to a double, the quad result
         * *should* be correctly rounded, unless we are quite unlucky.
         * Assuming the quad value is a correctly rounded double, the
         * allowed error is 3.0 ulps instead of 2.5 since the quad
         * value rounded to double can have its own 1/2 ulp error.
         */
        double [][] testCases = {
                // x                                              asinh(x)
                {+8.08576586004706676646947016706690192e+00    , +2.78705446940175084037519072068240843e+00    },
                {+5.71198448718283557923314219806343317e+00    , +2.44328951112537869179362382769224610e+00    },
                {+5.13969133196956207143557548988610506e+00    , +2.33947242588811531576718987896918712e+00    },
                {+2.95996078504353032911922127823345363e+00    , +1.80570832446450945675615676944433187e+00    },
                {+4.16200980791957864113328469102270901e+00    , +2.13327472868053919998765640756092875e+00    },
                {+3.69545071772785460595400763850193471e+00    , +2.01807302682646291458685219028816252e+00    },
                {+1.37724078256330018099617973348358646e+00    , +1.12468193910119796648577714130477538e+00    },
                {+8.42544369040329677034151245607063174e+00    , +2.82790657643842246518401899587920414e+00    },
                {+3.91229039061375782893037467147223651e+00    , +2.07321736531667549827684130235156669e+00    },
                {+5.73782778462038400846267904853448272e+00    , +2.44773637486997939825874893068408245e+00    },
                {+4.99855755102017340618658636230975389e+00    , +2.31215541451092776291779112133540281e+00    },
                {+8.10100320171622989562365546589717269e+00    , +2.78892295229049846951081695322303143e+00    },
                {+6.40711498894297992734436775208450854e+00    , +2.55659134739804960225496541857063844e+00    },
                {+4.25639664782793492037171745323576033e+00    , +2.15509221067754853744881157535735520e+00    },
                {+2.65061122655180847473843641637358814e+00    , +1.70175906719364776650786532519668576e+00    },
                {+3.14233404262031967846269253641366959e+00    , +1.86252059324271515969573278167449533e+00    },
                {+9.13083295141416328988270834088325500e+00    , +2.90778930976529177537743330080053959e+00    },
                {+9.34996922888940673601609887555241585e+00    , +2.93136773795688457445658002134152253e+00    },
                {+9.35132773574746245515143527882173657e+00    , +2.93151219897178112284587212807769745e+00    },
                {+1.47453686867873412502660812606336549e+00    , +1.18055530917929730380021873702412893e+00    },
                {+2.93708318858647077220780374773312360e+00    , +1.79836038745797816082436481350298220e+00    },
                {+4.09105467685985679793247982161119580e+00    , +2.11656320434131763040467250984368994e+00    },
                {+4.65121160775030162426446622703224421e+00    , +2.24163561547669988062740649953739512e+00    },
                {+8.83128600332669755346159945474937558e+00    , +2.87463799399744068863572725409458990e+00    },
                {+1.66240543263013162977870251779677346e+00    , +1.28160121300334421559587040333022048e+00    },
                {+4.58372145493984728403802364482544363e+00    , +2.22735027800562207352532152241704895e+00    },
                {+8.50271775332108248335316602606326342e+00    , +2.83697322459569158510957272430255446e+00    },
                {+8.82962635800362249938189052045345306e+00    , +2.87445124207064977822740131999732509e+00    },
                {+8.84552264926561093716372852213680744e+00    , +2.87623855339831018046947582541398439e+00    },
                {+3.12516324361785047258877057174686342e+00    , +1.85730059825198435603813107760370448e+00    },
                {+8.26480987017928114823916985187679529e+00    , +2.80879391905067271939218423695889677e+00    },
                {+9.68117403887023186825899756513535976e+00    , +2.96598712423961990106836581021055404e+00    },
                {+3.05372997660021550103692788979969919e+00    , +1.83530180662998049991392377010746750e+00    },
                {+4.40157829954937795946534606628119946e+00    , +2.18777148553475610871290743261274356e+00    },
                {+6.88055177977352627749496605247259140e+00    , +2.62708540897893209827881652490154282e+00    },
                {+5.98475681846005524988640900119207799e+00    , +2.48927078678959642161006322827411013e+00    },
                {+8.92994029487849694248779996996745467e+00    , +2.88567728733406656162446662917506943e+00    },
                {+3.12419716639021327608816136489622295e+00    , +1.85700613402604977963039277274730202e+00    },
                {+7.51161063055123179310612613335251808e+00    , +2.71399864345854847918135863803957037e+00    },
                {+1.17944590788822001314883891609497368e+00    , +1.00274792631001937429660854217557106e+00    },
                {+1.36421200272156672994583459512796253e+00    , +1.11700316010328101318941761315262905e+00    },
                {+6.88888479910741580169997178018093109e+00    , +2.62828320452398770553274423944254222e+00    },
                {+3.64699814082431839068476620013825595e+00    , +2.00533888971591775569462526134655508e+00    },
                {+1.41057156993997545590957543026888743e+00    , +1.14411132290221221244416446367286189e+00    },
                {+6.14945472638136703125155690941028297e+00    , +2.51605697935151660544323868421618014e+00    },
                {+6.02996213994895136067952989833429456e+00    , +2.49669366977555745163814756818745494e+00    },
                {+9.65271660518461160904735152143985033e+00    , +2.96305895992701909105343212587439308e+00    },
                {+3.48339981002946785793028539046645164e+00    , +1.96115002199047863383320140967526859e+00    },
                {+6.07995920803143352628694628947414458e+00    , +2.50484056235894688250578712446408489e+00    },
                {+6.00204567486939666309808671940118074e+00    , +2.49211610375224051369293822349155577e+00    },
                {+1.38833519546032624347731143643613905e+00    , +1.13118326188543957732445742827584178e+00    },
                {+4.52480967383013776839106867555528879e+00    , +2.21471559269073802833304398595496088e+00    },
                {+6.11810275538071746126433936296962202e+00    , +2.51101220932060589427300910397289711e+00    },
                {+7.50648056792778461954185331705957651e+00    , +2.71332143777867740825109248925661428e+00    },
                {+4.89658239129396388733539424720220268e+00    , +2.29195213807282224382341089459270833e+00    },
                {+2.79265817118974496446881516931171063e-02    , +2.79229530231546570990366385479747555e-02    },
                {+9.69315108025863381158160336781293154e+00    , +2.96721697176250274577477693915618144e+00    },
                {+7.83910637998812109827895255875773728e+00    , +2.75631566551255789285879320458504177e+00    },
                {+2.76576984498692324265789466153364629e+00    , +1.74165321687466923031477628544545184e+00    },
                {+4.99754435738235347486124737770296633e+00    , +2.31195663638515281361584735869808938e+00    },
                {+4.88922334987356776991873630322515965e+00    , +2.29047857490944287858591282873426921e+00    },
                {+2.78689754339832429508305722265504301e+00    , +1.74881289991707628903792141369254180e+00    },
                {+7.20931795462930935514123120810836554e+00    , +2.67329726418547732793921189411944602e+00    },
                {+8.33063517511005890980868571205064654e+00    , +2.81666990685356361031034871477442414e+00    },
                {+3.61188437237348836106320959515869617e+00    , +1.99601167970722876532263572785839092e+00    },
                {+5.32263649620131218398455530405044556e+00    , +2.37382580077770566473979021057511520e+00    },
                {+8.00366962656528002639788610395044088e+00    , +2.77692733912554343763823757722995583e+00    },
                {+4.59751681469834139193153532687574625e+00    , +2.23028654083102682106197643909523811e+00    },
                {+8.20253764279967612083055428229272366e+00    , +2.80128593985583624900402694440723735e+00    },
                {+8.81590969774593169461240904638543725e+00    , +2.87290644386803298326256037256286587e+00    },
                {+9.00323408655057377814046049024909735e+00    , +2.89380106762776953348709842638973283e+00    },
                {+7.21533058010746941590696224011480808e+00    , +2.67412302459536699184126235350224069e+00    },
                {+8.23695914498319758934030687669292092e+00    , +2.80544295419888555964661400747277886e+00    },
                {+9.66912482942344198022510681767016649e+00    , +2.96474834621717039972248353595994898e+00    },
                {+3.17602315814959101913927952409721911e+00    , +1.87268737666193382172385150977422494e+00    },
                {+6.90930101488594594627556944033131003e+00    , +2.63121186253032074408677485367709385e+00    },
                {+6.52386312488162189993090578354895115e+00    , +2.57443674633460769002260368508028529e+00    },
                {+8.33701897902340283152966549096163362e-01    , +7.58769250678348128717944053061372995e-01    },
                {+1.84073794668312284983358040335588157e+00    , +1.37005541332928719568137972151743439e+00    },
                {+3.74278586498477183752697783347684890e+00    , +2.03036413719335448282150464654423886e+00    },
                {+1.24005876679504356552286026271758601e+00    , +1.04136768247874493368196676622778561e+00    },
                {+5.46039591734140294931876269401982427e+00    , +2.39894972726732001224686289699275119e+00    },
                {+2.05576175637293001585703677847050130e+00    , +1.46829835554351749799178251325101620e+00    },
                {+8.14075272140118322283797169802710414e+00    , +2.79378100004325258561034629239868920e+00    },
                {+1.83236824312878154863426516385516152e+00    , +1.36605297794115641494849841805273118e+00    },
                {+3.75374287549383511830569659650791436e+00    , +2.03318857169224539730556063537088565e+00    },
                {+6.43073501869452779367009043198777363e-01    , +6.05407648939611618428355730173212664e-01    },
                {+3.48621711345758855671306264412123710e+00    , +1.96192711264291527976588288592889484e+00    },
                {+3.91549582965699016767757711932063103e+00    , +2.07401086477835132988304884524188567e+00    },
                {+8.71307615958979297943187702912837267e+00    , +2.86124897639861530832907097356321837e+00    },
                {+9.25125528837059185605085076531395316e+00    , +2.92081476128803069384228991876733421e+00    },
                {+1.39894257949993688905365729624463711e-01    , +1.39441932379308919610017101598940231e-01    },
                {+2.13018467023163493578863381117116660e+00    , +1.50038473636497909802939352641033551e+00    },
                {+9.11338663647286573166184098226949573e+00    , +2.90588816775704749530976417485641794e+00    },
                {+2.13672753800762960096903952944558114e+00    , +1.50316162138023144213989303271149548e+00    },
                {+1.84662954052762628975870029535144567e+00    , +1.37286438673796624203424974151164008e+00    },
                {+2.27538767726088808629469895095098764e+00    , +1.56042056675324794384613128836997008e+00    },
                {+2.25459809157452584216230206948239356e+00    , +1.55202382694053013875493092338973536e+00    },
                {+6.43951067826539436111943359719589353e+00    , +2.56157478187883218395455558699771338e+00    },
                {+2.38928979360439708301555583602748811e+00    , +1.60531075239512338397498990117642106e+00    }
        };


        for (double [] testCase : testCases) {
            failures += testAsinhCaseWithUlpDiff(testCase[0],
                    testCase[1],
                    3.0);
        }



        for (double nan : Tests.NaNs) {
            failures += testAsinhCaseWithUlpDiff(nan, NaNd, 0);
        }



        double [][] specialTestCases = {
                {0.0,                       0.0},
                {-0.0,                     -0.0},
                {Double.POSITIVE_INFINITY,  Double.POSITIVE_INFINITY},
                {Double.NEGATIVE_INFINITY,  Double.NEGATIVE_INFINITY}
        };



        for (double [] specialTestCase : specialTestCases) {
            failures += testAsinhCaseWithUlpDiff(specialTestCase[0],
                    specialTestCase[1],
                    0.0);
        }



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

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

            // Result and expected are the same.
            failures += testAsinhCaseWithUlpDiff(d, d, 3.0);
        }

        failures += testAsinhAdditionalTests();

        return failures;
    }

    /**
     * Test accuracy of {Math, StrictMath}.asinh using quad precision
     * asinh implementation as the reference. There are additional tests.
     * The specified accuracy is 2.5 ulps.
     *
     */
    static int testAsinhAdditionalTests() {
        int failures = 0;
        /*
         * Array elements below are generated using a quad precision asinh
         * implementation (libquadmath). Rounded to a double, the quad result
         * *should* be correctly rounded, unless we are quite unlucky.
         * Assuming the quad value is a correctly rounded double, the
         * allowed error is 3.0 ulps instead of 2.5 since the quad
         * value rounded to double can have its own 1/2 ulp error.
         */
        double[][] testCases = {
                // x                                              asinh(x)
                {+9.29888520047217510822168407003118773e-03    , +9.29875119439016991620829879950089510e-03    },
                {+8.99606577522583765460506555200481671e-03    , +8.99594443891109052619951669093253709e-03    },
                {+1.14699795207729403345719987328266143e-03    , +1.14699770057820289010729363443748979e-03    },
                {-7.40424146583510897623447988280531717e-03    , -7.40417381397284073003520743847398090e-03    },
                {+5.49488608694304568602628791040842771e-03    , +5.49485843542812296005405619611903743e-03    },
                {-2.52116366329231764847884633695684897e-03    , -2.52116099243538701654807174519941378e-03    },
                {+8.06768422999586641564118139058336965e-03    , +8.06759671495411237747532966838824601e-03    },
                {+9.88178277836134454081840061689945287e-03    , +9.88162196002118907735979091611455166e-03    },
                {-9.74812907680771244256501262270830921e-03    , -9.74797469575697378811862965186905034e-03    },
                {+1.28957646989550853144912423431378556e-03    , +1.28957611246655855199674391222106077e-03    },
                {-3.58837408582282288427300898092653370e-03    , -3.58836638496033900344918006245058062e-03    },
                {+4.13062959563161372078532451723731356e-03    , +4.13061784951867272487598247250853139e-03    },
                {-2.51244549635140212301420703511212196e-03    , -2.51244285310613342444371438470610248e-03    },
                {+9.68636675928437156091188597883956390e-03    , +9.68621529398750501339156647788267837e-03    },
                {-5.46432162869262862125996349504930549e-03    , -5.46429443603366704988023092426655825e-03    },
                {-1.83386276898741575058782160567716346e-03    , -1.83386174109279550088776833959567103e-03    },
                {+4.29194713096967862819841599275605404e-03    , +4.29193395422167505495925421977757693e-03    },
                {-9.98345193989031744197237827620483586e-03    , -9.98328610669592860197569944928865818e-03    },
                {-2.77682511858849418590056146172173612e-03    , -2.77682155002991423153566829770018797e-03    },
                {-9.27080565792574341765774903478813940e-03    , -9.27067286211199059124030266083673465e-03    },
                {+2.13343832085455265001883162767626345e-03    , +2.13343670244611127381061946915639278e-03    },
                {+1.86531796573603282640707590189776965e-03    , +1.86531688403638317794548160776476123e-03    },
                {+7.59089952706850680519412577496041195e-03    , +7.59082662879913430594165031269929038e-03    },
                {-7.23221864571126256404642873576449347e-03    , -7.23215560034534649276205014022842148e-03    },
                {-4.85379569260787659124023463164121495e-03    , -4.85377663411205855718020189862812411e-03    },
                {+2.06427745583616026325834980070794700e-03    , +2.06427598977487382238201754110142048e-03    },
                {-9.05864273164906988466960058303811820e-03    , -9.05851884568408865775918913306811448e-03    },
                {+8.14126659074132334736884075709895114e-03    , +8.14117665926450847350600785486541236e-03    },
                {-1.18703607276676031956341716977476608e-03    , -1.18703579400048976745061906381442506e-03    },
                {-3.72556727069004237073990282169688726e-03    , -3.72555865235713390047416035972567655e-03    },
                {+3.20078632768614965153908258344017668e-03    , +3.20078086235102579132641956617880741e-03    },
                {-3.64652695868728470018904630478573381e-03    , -3.64651887732759812624780495337361570e-03    },
                {-4.37271109890237635181575726051050879e-03    , -4.37269716421058504020032749615645348e-03    },
                {-4.53954699201700607319454050525564526e-03    , -4.53953140071906668014572342681250395e-03    },
                {-7.71410922638161335174178390161614516e-03    , -7.71403272056205844933819193169521112e-03    },
                {-4.14748385016995048391041933655287721e-03    , -4.14747195968688563991362285984749351e-03    },
                {+2.16239643776180469336711809091866598e-03    , +2.16239475255273602474341490749538226e-03    },
                {+1.70867505939914857138184345330955693e-04    , +1.70867505108481996929933792720554316e-04    },
                {+4.45468038573873341412490134416657384e-03    , +4.45466565262570403928813346774794963e-03    },
                {+5.02848450175214997659445259614585666e-04    , +5.02848428983795534702560585886961806e-04    },
                {+3.27121347478520618778929929248988628e-03    , +3.27120764069260936386068328808026876e-03    },
                {-3.02035237923277844612757192521712568e-03    , -3.02034778704318937598236175985252813e-03    },
                {+1.83493544153568409471599665039320826e-03    , +1.83493441183628601773262459027151432e-03    },
                {-3.57742891707456961425393160425301176e-03    , -3.57742128646403200576149317708586166e-03    },
                {+4.07461518018882584701856330866576172e-04    , +4.07461506744091232910512108590665082e-04    },
                {+8.93213245095503781401102827430804609e-03    , +8.93201368317984717551252673740071605e-03    },
                {+4.83633433470810093768310622408534982e-03    , +4.83631548115857258701091393657125083e-03    },
                {+4.41941080408745669283465673515820527e-03    , +4.41939641815384450220145838057678415e-03    },
                {-7.40905574125878471636319488879962591e-03    , -7.40898795735011644277922058251845971e-03    },
                {+5.86417821400006013254913028731607483e-03    , +5.86414460438723375893640532030031887e-03    },
                {+6.40143962390532852979596611930901418e-04    , +6.40143918670384118303282950462728667e-04    },
                {-6.62414482978957927516994175221043406e-03    , -6.62409638694556116425732364897473820e-03    },
                {+2.32034013904017406837443360245742952e-03    , +2.32033805693503550464566970496041304e-03    },
                {-1.70037238711657177903102677873903303e-03    , -1.70037156774608724006177273975196346e-03    },
                {-2.41007559448008345376335270771051000e-03    , -2.41007326134647811152942503146226815e-03    },
                {-4.88371906557288470301925187300184916e-03    , -4.88369965241849364892773140816442366e-03    },
                {+5.45353417327115556900718473798406194e-03    , +5.45350714134116714399404074418610335e-03    },
                {+1.82127472834406854695910027430727496e-03    , +1.82127372147155402291508536733347481e-03    },
                {+3.08464771244317328968698177504847990e-03    , +3.08464282070047297125571891308421168e-03    },
                {+8.64099586698139320029010690404902562e-03    , +8.64088833799551442516038310825829002e-03    },
                {+5.55586600363066999974659410099775414e-03    , +5.55583742127587993316327594170344732e-03    },
                {+8.72688321697448303460031837630594964e-03    , +8.72677244972821936872995155020997092e-03    },
                {+8.67310115846320860144569309113649069e-03    , +8.67299242648623772707657889109267822e-03    },
                {-6.14210531791088872044515056813906995e-03    , -6.14206669961072319996743834488437463e-03    },
                {+8.88625749891074935560286718327915878e-03    , +8.88614055166480866111859091126682642e-03    },
                {-1.43504119833010382323301712403917918e-03    , -1.43504070579016156191011766070535043e-03    },
                {+8.88630021979499445938799340183322784e-04    , +8.88629905026452701546356648558325925e-04    },
                {+3.93780142608554303840229238176107174e-03    , +3.93779124938125782164719425287579139e-03    },
                {+5.97434710953371854447180311353804427e-03    , +5.97431156988517485964304752157241804e-03    },
                {-7.98875566707221360096546902695990866e-03    , -7.98867069549231529699110336543851522e-03    },
                {-7.35260998042218307663153709086145682e-03    , -7.35254373394740372183361138755444401e-03    },
                {-1.21452151194481779150624589647122775e-03    , -1.21452121336249242914680975845323467e-03    },
                {+4.98481949753720385287714123023761204e-04    , +4.98481929109570105039386663388380124e-04    },
                {+4.91985816350236880578616904813316069e-03    , +4.91983831618717601288972307767102048e-03    },
                {+7.68796449908712258014542584305672790e-03    , +7.68788876850302034489862036714171394e-03    },
                {-1.49188964399755812084702455422302592e-03    , -1.49188909057301843050666760106824645e-03    },
                {-6.73163270527497858974896871586679481e-03    , -6.73158186579155909561057079482268382e-03    },
                {+8.73326787816911150053034162965559517e-03    , +8.73315686763575988088834491175495305e-03    },
                {+7.81885100909627574206073319373899722e-03    , +7.81877134445315065535398733750043537e-03    },
                {+5.17883696377165365920536288513176260e-03    , +5.17881381434573686588090532152532759e-03    },
                {+5.94443020139156542980263253639350296e-03    , +5.94439519296920978949883610708856872e-03    },
                {+6.20408692607689153664107806207539397e-03    , +6.20404712683039987243003869674263039e-03    },
                {-4.13924636982772493898341537033047643e-03    , -4.13923455005213957426577773895357676e-03    },
                {-3.71140287747976152510354097557865316e-03    , -3.71139435707241790669973810798603847e-03    },
                {-8.37941685260259506995428324671593145e-03    , -8.37931879609631048090526043629803007e-03    },
                {+8.48517293301665094518160259440264781e-03    , +8.48507111684271940482025173385456325e-03    },
                {+8.52827781082153742187035305732933921e-03    , +8.52817443510010657036791986083451790e-03    },
                {-4.07416024108964158756407414330169559e-03    , -4.07414897015777394146227881635448891e-03    },
                {+4.33240979016216026797891913702187594e-03    , +4.33239623721743479728849041379241354e-03    },
                {-4.89052581083683143847729013486969052e-04    , -4.89052561589036445343259711601066150e-04    },
                {-9.62974650385375885441874288517283276e-05    , -9.62974648897066185792218187524452666e-05    },
                {-9.26529020589744040092838872624270152e-04    , -9.26528888025725086174151901318195528e-04    },
                {+1.39965317129459553002757132844635635e-03    , +1.39965271430147299997462291249440004e-03    },
                {-7.12079193844885119379917171045235591e-03    , -7.12073176239158986696262840488189056e-03    },
                {-3.62621830991397085114380516301935131e-03    , -3.62621036282602413990843595245483708e-03    },
                {-7.11170226471406416446363607519742800e-03    , -7.11164231880305326913177834599584014e-03    },
                {-1.07788116725225993630665755063091638e-04    , -1.07788116516507275261580974984359313e-04    },
                {-2.51343271020868386927960003163207148e-03    , -2.51343006384636979438035563375611134e-03    },
                {-9.70989675056706420808172453007500735e-03    , -9.70974417880563379443605277365308469e-03    },
                {+7.17488567146307328059595675995296915e-03    , +7.17482411358449384368065167506580475e-03    }
        };

        for (int i = 0; i < testCases.length; i++) {
            double[] testCase = testCases[i];
            failures += testAsinhCaseWithUlpDiff(testCase[0],
                    testCase[1],
                    3.0);
        }

        return failures;
    }

    public static int testAsinhCaseWithTolerance(double input,
                                                double expected,
                                                double tolerance) {
        int failures = 0;
        failures += Tests.testTolerance("Math.asinh",       input, Math::asinh,         expected, tolerance);
        failures += Tests.testTolerance("Math.asinh",      -input, Math::asinh,        -expected, tolerance);

        failures += Tests.testTolerance("StrictMath.asinh",  input, StrictMath::asinh,  expected, tolerance);
        failures += Tests.testTolerance("StrictMath.asinh", -input, StrictMath::asinh, -expected, tolerance);
        return failures;
    }

    public static int testAsinhCaseWithUlpDiff(double input,
                                              double expected,
                                              double ulps) {
        int failures = 0;

        failures += Tests.testUlpDiffWithAbsBound("Math.asinh",       input,  Math::asinh,       expected, ulps, Double.POSITIVE_INFINITY);
        failures += Tests.testUlpDiffWithAbsBound("Math.asinh",      -input,  Math::asinh,      -expected, ulps, Double.NEGATIVE_INFINITY);

        failures += Tests.testUlpDiffWithAbsBound("StrictMath.asinh",  input, StrictMath::asinh,  expected, ulps, Double.POSITIVE_INFINITY);
        failures += Tests.testUlpDiffWithAbsBound("StrictMath.asinh", -input, StrictMath::asinh, -expected, ulps, Double.NEGATIVE_INFINITY);
        return failures;
    }

    /**
     * Test accuracy of {Math, StrictMath}.acosh.  The specified
     * accuracy is 2.5 ulps.
     *
     * The defintion of acosh(x) is
     *
     * acosh(cosh(x)) = x
     *
     * Can be also written as
     *
     * acosh(x) = ln(x + sqrt(x * x - 1))
     *
     * The series expansion of acosh(x) =
     *
     * ln(2 * x) - (x^-2 / 4 + 3 * x^-4 / 32 + 15 * x^-6 / 288 ...)
     *
     * Therefore,
     *
     * 1. acosh(1) = 0.
     *
     * 2. The domain is x >= 1.
     *
     * 3. The function is neither odd nor even.
     *
     */
    static int testAcosh() {
        int failures = 0;
        /*
         * Array elements below generated using a quad acosh
         * implementation.  Rounded to a double, the quad result
         * *should* be correctly rounded, unless we are quite unlucky.
         * Assuming the quad value is a correctly rounded double, the
         * allowed error is 3.0 ulps instead of 2.5 since the quad
         * value rounded to double can have its own 1/2 ulp error.
         */
        double [][] testCases = {
                // x     acosh(x)
                {1.0000, +0.00000000000000000000000000000000000e+00    },
                {1.0625, +3.51737390043260579770744786121122844e-01    },
                {1.1250, +4.94932923094526905889563099576718556e-01    },
                {1.1875, +6.03186598686334413155297365190676416e-01    },
                {1.2500, +6.93147180559945309417232121458176575e-01    },
                {1.3125, +7.71307459173256653700937951825817144e-01    },
                {1.3750, +8.41019322011445738489485196126304665e-01    },
                {1.4375, +9.04286762705515769042139988689583282e-01    },
                {1.5000, +9.62423650119206894995517826848736845e-01    },
                {1.5625, +1.01634809667840380541358127166594224e+00    },
                {1.6250, +1.06673243190143557362309154628644597e+00    },
                {1.6875, +1.11408700135293645158376433073169476e+00    },
                {1.7500, +1.15881036042994681173087299087873020e+00    },
                {1.8125, +1.20122101997969472087682270695675759e+00    },
                {1.8750, +1.24157842330772117651284669611837885e+00    },
                {1.9375, +1.28009731675807455651225000558265526e+00    },
                {2.0000, +1.31695789692481670862504634730796848e+00    },
                {2.0625, +1.35231316261931093541047819670045078e+00    },
                {2.1250, +1.38629436111989061883446424291635315e+00    },
                {2.1875, +1.41901510140371506613255066437684651e+00    },
                {2.2500, +1.45057451382258020872826178236677635e+00    },
                {2.3125, +1.48105971405608381331792780208719133e+00    },
                {2.3750, +1.51054775047320739150161777699985299e+00    },
                {2.4375, +1.53910716184424377297903295285722198e+00    },
                {2.5000, +1.56679923697241107866405686258048358e+00    },
                {2.5625, +1.59367904336440765353731339657532894e+00    },
                {2.6250, +1.61979627485649999465013597110633349e+00    },
                {2.6875, +1.64519595581279452177517379518794699e+00    },
                {2.7500, +1.66991903058776998677838891147712239e+00    },
                {2.8125, +1.69400286038199600062127876942753998e+00    },
                {2.8750, +1.71748164473336519458386901818676709e+00    },
                {2.9375, +1.74038678120611400701568860843885133e+00    },
                {3.0000, +1.76274717403908605046521864995958460e+00    },
                {3.0625, +1.78458950036205246630242932084698860e+00    },
                {3.1250, +1.80593844091928647006641838950547765e+00    },
                {3.1875, +1.82681688093354809536648865402886324e+00    },
                {3.2500, +1.84724608571383784130004129627716938e+00    },
                {3.3125, +1.86724585479221893347421970944127165e+00    },
                {3.3750, +1.88683465772058517690549455261749833e+00    },
                {3.4375, +1.90602975413127236084850555002346490e+00    },
                {3.5000, +1.92484730023841378999103565369747369e+00    },
                {3.5625, +1.94330244360892107348697778473632964e+00    },
                {3.6250, +1.96140940774674480423275041043129955e+00    },
                {3.6875, +1.97918156779907568924375778194574535e+00    },
                {3.7500, +1.99663151849857170393899871209510294e+00    },
                {3.8125, +2.01377113529382496280930762219993708e+00    },
                {3.8750, +2.03061162948500957172739654092925159e+00    },
                {3.9375, +2.04716359806812267677620352283230977e+00    },
                {4.0000, +2.06343706889556054672728117262013178e+00    },
                {4.0625, +2.07944154167983592825169636437452953e+00    },
                {4.1250, +2.09518602529851747179664246793750599e+00    },
                {4.1875, +2.11067907179990670152964344211957784e+00    },
                {4.2500, +2.12592880745889053593506179143141713e+00    },
                {4.3125, +2.14094296118944770996055814756135545e+00    },
                {4.3750, +2.15572889058331846311473049052403906e+00    },
                {4.4375, +2.17029360581243752070499251797833202e+00    },
                {4.5000, +2.18464379160510872667627813307212784e+00    },
                {4.5625, +2.19878582748192321247116242073983256e+00    },
                {4.6250, +2.21272580641655511554559532685274022e+00    },
                {4.6875, +2.22646955206835990390469193746457694e+00    },
                {4.7500, +2.24002263471777221819301091423172581e+00    },
                {4.8125, +2.25339038602153389445857144762743321e+00    },
                {4.8750, +2.26657791269250866199452039018610592e+00    },
                {4.9375, +2.27959010919802897270925407255393153e+00    },
                {5.0000, +2.29243166956117768780078731134801529e+00    },
                {5.0625, +2.30510709834096668441430402487399027e+00    },
                {5.1250, +2.31762072085989362346174598175746039e+00    },
                {5.1875, +2.32997669274071514661824152082627607e+00    },
                {5.2500, +2.34217900880836474718960439585388779e+00    },
                {5.3125, +2.35423151140767607019354831300009086e+00    },
                {5.3750, +2.36613789818286932753788120137389157e+00    },
                {5.4375, +2.37790172936055222645518871553565388e+00    },
                {5.5000, +2.38952643457421860822386165703818122e+00    },
                {5.5625, +2.40101531926484683717268315699636478e+00    },
                {5.6250, +2.41237157068916138816151585667001780e+00    },
                {5.6875, +2.42359826356438621752612199535640197e+00    },
                {5.7500, +2.43469836537585339202679859270163341e+00    },
                {5.8125, +2.44567474137160531324234100032920604e+00    },
                {5.8750, +2.45653015926611756205299063862500772e+00    },
                {5.9375, +2.46726729367344889723552955806057589e+00    },
                {6.0000, +2.47788873028847500481395074507450545e+00    },
                {6.0625, +2.48839696983336532007430913631752335e+00    },
                {6.1250, +2.49879443178510181484789673802222733e+00    },
                {6.1875, +2.50908345789860105234876846349648239e+00    },
                {6.2500, +2.51926631553887363826303725428234388e+00    },
                {6.3125, +2.52934520083462740598919885177286592e+00    },
                {6.3750, +2.53932224166478245066792464622248188e+00    },
                {6.4375, +2.54919950048850872717547586051387259e+00    },
                {6.5000, +2.55897897702861255144554182625683448e+00    },
                {6.5625, +2.56866261081738002442374329274624674e+00    },
                {6.6250, +2.57825228361332690085894009323471199e+00    },
                {6.6875, +2.58774982169670016849316580209717247e+00    },
                {6.7500, +2.59715699805102158059159611581476354e+00    },
                {6.8125, +2.60647553443745310075195298905494613e+00    },
                {6.8750, +2.61570710336829463210497297146055746e+00    },
                {6.9375, +2.62485332998549187571842397668306463e+00    },
                {7.0000, +2.63391579384963341725009269461593696e+00    },
                {7.0625, +2.64289603064454821939888620389440586e+00    },
                {7.1250, +2.65179553380227492960508448932353394e+00    },
                {7.1875, +2.66061575605286038291043830648413625e+00    },
                {7.2500, +2.66935811090315420323249076787858338e+00    },
                {7.3125, +2.67802397404849750222123152071366765e+00    },
                {7.3750, +2.68661468472095454727243455865687717e+00    },
                {7.4375, +2.69513154697750528856415868272675449e+00    },
                {7.5000, +2.70357583093140231733394963705451385e+00    },
                {7.5625, +2.71194877392969682611305770501597479e+00    },
                {7.6250, +2.72025158167975322903284501674667068e+00    },
                {7.6875, +2.72848542932740015820479864569947040e+00    },
                {7.7500, +2.73665146248920556040148045776356816e+00    },
                {7.8125, +2.74475079824121464549309272530654441e+00    },
                {7.8750, +2.75278452606635063332660947345292156e+00    },
                {7.9375, +2.76075370876254883072567909046267813e+00    },
                {8.0000, +2.76865938331357383273200140938374547e+00    },
                {8.0625, +2.77650256172435692961336760207948251e+00    },
                {8.1250, +2.78428423182258551535630273235901386e+00    },
                {8.1875, +2.79200535802817788553087801705861609e+00    },
                {8.2500, +2.79966688209218477865004528925200022e+00    },
                {8.3125, +2.80726972380657289240925980113428074e+00    },
                {8.3750, +2.81481478168626496869015857854363587e+00    },
                {8.4375, +2.82230293362473549711106510083524230e+00    },
                {8.5000, +2.82973503752439027536610108611637391e+00    },
                {8.5625, +2.83711193190289165307916749543060640e+00    },
                {8.6250, +2.84443443647652896774770544175385075e+00    },
                {8.6875, +2.85170335272167517356988163822694873e+00    },
                {8.7500, +2.85891946441531570520913194770155741e+00    },
                {8.8125, +2.86608353815558396737111566993889866e+00    },
                {8.8750, +2.87319632386318927416511462539646535e+00    },
                {8.9375, +2.88025855526457737300290165271813925e+00    },
                {9.0000, +2.88727095035762068498655348054621044e+00    },
                {9.0625, +2.89423421186059490016531823326821096e+00    },
                {9.1250, +2.90114902764516041745652356473355270e+00    },
                {9.1875, +2.90801607115403116308966232802812480e+00    },
                {9.2500, +2.91483600180397941677005500735563642e+00    },
                {9.3125, +2.92160946537479329008903038647778851e+00    },
                {9.3750, +2.92833709438477331505751565470704144e+00    },
                {9.4375, +2.93501950845332609861824133070706912e+00    },
                {9.5000, +2.94165731465118607612817277397561825e+00    },
                {9.5625, +2.94825110783877095494122437627939968e+00    },
                {9.6250, +2.95480147099315238696389016790268450e+00    },
                {9.6875, +2.96130897552410066125326263536732120e+00    },
                {9.7500, +2.96777418157964068500790378422486329e+00    },
                {9.8125, +2.97419763834153614964672155497739057e+00    },
                {9.8750, +2.98057988431109948901325801645778406e+00    },
                {9.9375, +2.98692144758570696460723739938555692e+00    },
                {10.0000, +2.99322284612638089791266771377418276e+00    },
        };


        for (double [] testCase : testCases) {
            failures += testAcoshCaseWithUlpDiff(testCase[0],
                    testCase[1],
                    3.0);
        }



        for (double nan : Tests.NaNs) {
            failures += testAcoshCaseWithUlpDiff(nan, NaNd, 0);
        }



        double [][] specialTestCases = {
                {0.0,                       NaNd},
                {-0.0,                      NaNd},
                {1.0,                       0.0},
                {Double.POSITIVE_INFINITY,  Double.POSITIVE_INFINITY},
                {Double.NEGATIVE_INFINITY,  NaNd}
        };



        for (double [] specialTestCase : specialTestCases) {
            failures += testAcoshCaseWithUlpDiff(specialTestCase[0],
                    specialTestCase[1],
                    0.0);
        }


        failures += testAcoshAdditionalTests();

        return failures;
    }

    /**
     * Test accuracy of {Math, StrictMath}.acosh using quad precision
     * acosh implementation as the reference. There are additional tests.
     * The specified accuracy is 2.5 ulps.
     *
     */
    static int testAcoshAdditionalTests() {
        int failures = 0;
        /*
         * Array elements below are generated using a quad precision acosh
         * implementation (libquadmath). Rounded to a double, the quad result
         * *should* be correctly rounded, unless we are quite unlucky.
         * Assuming the quad value is a correctly rounded double, the
         * allowed error is 3.0 ulps instead of 2.5 since the quad
         * value rounded to double can have its own 1/2 ulp error.
         */
        double[][] testCases = {
                // x                                              acosh(x)
                {+1.40222409861373051853661308996379375e+01    , +3.33251799248457675610296187717275023e+00    },
                {+4.64063630702987595100239559542387724e+01    , +4.53046765794427717250009108708063951e+00    },
                {+2.26769594350354175560369185404852033e+01    , +3.81401008174403012773998497198756862e+00    },
                {+6.82076069573278687130368780344724655e+01    , +4.91564953670154039555101045371992145e+00    },
                {+9.35345967264471340740783489309251308e+01    , +5.23144999004817476451595194893686997e+00    },
                {+5.24222208302520016331982333213090897e+01    , +4.65238675892723943927493345614044802e+00    },
                {+4.42263893601989721560130419675260782e+00    , +2.16685013650055071552269762531726701e+00    },
                {+5.34403191209646664106003299821168184e+01    , +4.67162513077968730816736013866320559e+00    },
                {+1.76212042009831870714720025716815144e+00    , +1.16720688415256589829633745537084420e+00    },
                {+7.61738148899418732185040425974875689e+00    , +2.71924321506064362327407359954437453e+00    },
                {+6.89904985284954790358824538998305798e+01    , +4.92706344460967378866907640972706781e+00    },
                {+9.31132130019995969405499636195600033e+01    , +5.22693444138174309022758439394131022e+00    },
                {+5.31659489982307036370912101119756699e+01    , +4.66647685890886539018247877652269347e+00    },
                {+6.57379772558717405672723543830215931e+01    , +4.87876612392399046931262815776348806e+00    },
                {+7.04178688554184901704502408392727375e+01    , +4.94754380999195554008986754487841587e+00    },
                {+7.64576059598647788106973166577517986e+01    , +5.02984082858162069509313975886000718e+00    },
                {+5.69898682524488275902285749907605350e+00    , +2.42564775130097776080234839595030019e+00    },
                {+3.34951883898407629658322548493742943e+01    , +4.20432607363489310218001177932001376e+00    },
                {+7.58846381271260241874188068322837353e+01    , +5.02231803118503396528914607189891829e+00    },
                {+3.71685284182660993224089907016605139e+01    , +4.30842856158112686719805147741579474e+00    },
                {+9.82724783457824031529526109807193279e+01    , +5.28086530470046881951663865035216936e+00    },
                {+7.55822276853527057483006501570343971e+01    , +5.01832458735915146090685859231899627e+00    },
                {+8.19590239920287544350685493554919958e+00    , +2.79303880830104526461764198808709567e+00    },
                {+8.85860057527683011358021758496761322e+01    , +5.17708921820009272972577332594088089e+00    },
                {+4.42047291460483080527410493232309818e+01    , +4.48185099473614683233384262644114551e+00    },
                {+4.82954447467224099455052055418491364e+01    , +4.57037722443775069839008053496876858e+00    },
                {+2.82157771675713533454654680099338293e+01    , +4.03271430903366741210592839999395032e+00    },
                {+1.74842128192706276479384541744366288e+01    , +3.55362672330870909254873232512209322e+00    },
                {+8.98679723864892281426364206708967686e+01    , +5.19145784395917044408731940940225234e+00    },
                {+6.99586842581785273154082460678182542e+00    , +2.63331927275597158625520354348567456e+00    },
                {+5.09477665985264778214514080900698900e+01    , +4.62385177612510228171242777653641979e+00    },
                {+3.25842611674598501281252538319677114e+01    , +4.17674101901473628570827854743466486e+00    },
                {+4.99036918354616290116609889082610607e+01    , +4.60314176379122016396592518510391469e+00    },
                {+9.98255656348235120844947232399135828e+00    , +2.99146816849131388203109739268493125e+00    },
                {+8.30115844701927940718633180949836969e+00    , +2.80589439276611715849813780991570715e+00    },
                {+3.90300726488373044276158907450735569e+01    , +4.35731547033614744103231173076054669e+00    },
                {+9.14679267650316347726402455009520054e+01    , +5.20910568139874158502888666687786843e+00    },
                {+4.69801366698952662659394263755530119e+01    , +4.54275878054294975578025810303600533e+00    },
                {+5.95831438716205052941177200409583747e+00    , +2.47081727711668636777886134527797777e+00    },
                {+7.72502501531925105382470064796507359e+01    , +5.04015543904862200893429166398240913e+00    },
                {+1.34111721821950098387787875253707170e+01    , +3.28784240452352224920507313116967307e+00    },
                {+6.91570748043642566926791914738714695e+01    , +4.92947526860125472538045310739830979e+00    },
                {+6.33247983942767831422315794043242931e+01    , +4.84136184327272941501425426966065239e+00    },
                {+7.28157878674183933753738529048860073e+01    , +4.98103282444372675567185179132668151e+00    },
                {+8.89686491926590150569609249942004681e+01    , +5.18139964655774166552638928730792362e+00    },
                {+3.13258612573789463340290240012109280e+01    , +4.13733631620326521460511053592093813e+00    },
                {+5.18140965157089325998640561010688543e+01    , +4.64071629304849263117175976059711265e+00    },
                {+8.47521744710507647369013284333050251e+01    , +5.13284377741645310577993893073249440e+00    },
                {+8.43095533174532931752764852717518806e+01    , +5.12760719138905245783659501854598879e+00    },
                {+4.21240669274286076984026294667273760e+01    , +4.43362549935510675489581351410263443e+00    },
                {+4.73238194816935475728314486332237720e+01    , +4.55004928385543400029944037596031391e+00    },
                {+1.86544426645817758014800347154960036e+01    , +3.61851232034069491499592508470176552e+00    },
                {+5.75938262601410571051019360311329365e+01    , +4.74648718281138202967444216845950983e+00    },
                {+4.27232167589609090896374254953116179e+00    , +2.13131771884641485793724599940809626e+00    },
                {+5.03495317868001706074210233055055141e+01    , +4.61203786952239923442865869830624998e+00    },
                {+7.50809724725515792442820384167134762e+01    , +5.01166999309632169153897035236491293e+00    },
                {+8.91830106756043647919796057976782322e+01    , +5.18380630497515107426424373476548239e+00    },
                {+8.43619216604083419497328577563166618e+01    , +5.12822818585720472109565051928260461e+00    },
                {+2.20623999405381177041363116586580873e+01    , +3.78650797260310183157107999251647380e+00    },
                {+1.39122989185065399908580729970708489e+01    , +3.32462629189603078991830801184905350e+00    },
                {+2.81842266001629120353300095302984118e+01    , +4.03159479043564760795745665884328416e+00    },
                {+4.20150330398823186328627343755215406e+01    , +4.43103301227168439924256715079001048e+00    },
                {+7.12721396815986594219793914817273617e+01    , +4.95960346484961706088932387548050013e+00    },
                {+2.47511696812483386054282163968309760e+01    , +3.90161159523447275422094662483857801e+00    },
                {+3.24364140945400691862232633866369724e+01    , +4.17219116407069688318499622366971673e+00    },
                {+6.55538099356552947938325814902782440e+01    , +4.87596033055444598453664902130389245e+00    },
                {+6.84532751547124860280746361240744591e+01    , +4.91924522217897758728929410442650248e+00    },
                {+3.93848083647737539081390423234552145e+01    , +4.36636613965538581613443666385597861e+00    },
                {+1.56057673113820580823585260077379644e+01    , +3.43975961616459237301460093608428409e+00    },
                {+8.47119903068781923138885758817195892e+01    , +5.13236949468185791854133268753960238e+00    },
                {+9.55854738436600683826327440328896046e+01    , +5.25314067817929358802774910100252994e+00    },
                {+1.56670046394655830823694486753083766e+01    , +3.44368399001615451248068997740627574e+00    },
                {+4.14679026870443507846175634767860174e+01    , +4.41792146385299219920359657474436019e+00    },
                {+5.69249693750823269056127173826098442e+01    , +4.73480409586514749627990327668077645e+00    },
                {+4.93629403713561600852699484676122665e+01    , +4.59224451473128480136302652897840027e+00    },
                {+9.61484189551490686653778539039194584e+01    , +5.25901316478560252169572160735164898e+00    },
                {+2.07759627057374345326934417244046926e+01    , +3.72636417050318935004571518016144611e+00    },
                {+6.32976464844313539970244164578616619e+01    , +4.84093292566853424246928339764776273e+00    },
                {+6.54741204020067897317858296446502209e+01    , +4.87474381391982909784974793043917201e+00    },
                {+8.05042266117176978923453134484589100e+01    , +5.08141829115959617683933639313475601e+00    },
                {+4.81667484910552587962229154072701931e+01    , +4.56770832383321482034955903243661906e+00    },
                {+2.11217831158012465664342016680166125e+01    , +3.74289121691996804899454065396184575e+00    },
                {+9.02656763961261532358548720367252827e+01    , +5.19587377817524068279272963615894387e+00    },
                {+1.50600821596306779781571094645187259e+01    , +3.40409076820438745807924396441229869e+00    },
                {+4.16209905361957765990155166946351528e+01    , +4.42160745328229554045710868854157175e+00    },
                {+8.86791887429291563194055925123393536e+01    , +5.17814062516654447520446624771754712e+00    },
                {+1.70576566142218695176779874600470066e+01    , +3.52888602841986989717710320391598297e+00    },
                {+3.71685638271143758970538328867405653e+01    , +4.30842951458236820308439636796433560e+00    },
                {+1.43758274343816250251393284997902811e+01    , +3.35748343469042965382754422758946510e+00    },
                {+4.60754211385189549332608294207602739e+01    , +4.52330904257767828148397295029679237e+00    },
                {+4.57777167466274974572115752380341291e+01    , +4.51682530040123678433942314310447564e+00    },
                {+9.32357656650976593937230063602328300e+01    , +5.22824982009254837221678766114741857e+00    },
                {+2.23095900244694895775410259375348687e+01    , +3.79766114099573434402313460678612040e+00    },
                {+9.09832666680431856320865335874259472e+01    , +5.20379258533493176911574496349341434e+00    },
                {+8.62251237613208019183730357326567173e+01    , +5.15007514723643448859452771190406728e+00    },
                {+5.10896316393437928127241320908069611e+01    , +4.62663296015956482467254446322296917e+00    },
                {+8.19385868289117524909670464694499969e+01    , +5.09907996803279765921917143342322948e+00    },
                {+4.67622529628467802353952720295637846e+01    , +4.53810915071314717336273606975590283e+00    },
                {+6.36411313235143367705859418492764235e+01    , +4.84634542963631730817381276671897779e+00    },
                {+8.26450413110590460519233602099120617e+01    , +5.10766540264697663339669119714720544e+00    },
        };

        for (double[] testCase : testCases) {
            failures += testAcoshCaseWithUlpDiff(testCase[0],
                    testCase[1],
                    3.0);
        }

        return failures;
    }

    public static int testAcoshCaseWithTolerance(double input,
                                                 double expected,
                                                 double tolerance) {
        int failures = 0;
        failures += Tests.testTolerance("Math.acosh",        input, Math::acosh,         expected, tolerance);
        failures += Tests.testTolerance("StrictMath.acosh",  input, StrictMath::acosh,   expected, tolerance);
        return failures;
    }

    public static int testAcoshCaseWithUlpDiff(double input,
                                               double expected,
                                               double ulps) {
        int failures = 0;
        failures += Tests.testUlpDiffWithAbsBound("Math.acosh",        input,  Math::acosh,       expected, ulps, Double.POSITIVE_INFINITY);
        failures += Tests.testUlpDiffWithAbsBound("StrictMath.acosh",  input,  StrictMath::acosh, expected, ulps, Double.POSITIVE_INFINITY);
        return failures;
    }

    /**
     * Test accuracy of {Math, StrictMath}.atanh.  The specified
     * accuracy is 2.5 ulps.
     *
     * The defintion of atanh(x) is
     *
     * atanh(tanh(x)) = x
     *
     * Can be also written as
     *
     * 0.5 * log1p(2 * x / (1-x0))
     *
     * Taylor expansion:
     *
     * x + x^3 / 3 + x^5 / 5 + ...
     *
     * Therefore,
     *
     * 1. For small values of x, tanh(x) ~= x.
     *
     * Additionally, atanh is an odd function; atanh(-x) = -atanh(x).
     *
     */
    static int testAtanh() {
        int failures = 0;
        /*
         * Array elements below generated using a quad atanh
         * implementation.  Rounded to a double, the quad result
         * *should* be correctly rounded, unless we are quite unlucky.
         * Assuming the quad value is a correctly rounded double, the
         * allowed error is 3.0 ulps instead of 2.5 since the quad
         * value rounded to double can have its own 1/2 ulp error.
         */
        double [][] testCases = {
                // x                                            atanh(x)
                {+0.00000000000000000000000000000000000e+00    , +0.00000000000000000000000000000000000e+00    },
                {+2.00000000000000004163336342344337027e-02    , +2.00026673068495811335374182828113576e-02    },
                {+4.00000000000000008326672684688674053e-02    , +4.00213538367682137458906520059156020e-02    },
                {+5.99999999999999977795539507496869192e-02    , +6.00721559210316214332906986486015264e-02    },
                {+8.00000000000000016653345369377348106e-02    , +8.01713250375896933655527689248809233e-02    },
                {+1.00000000000000005551115123125782702e-01    , +1.00335347731075586242913545116385118e-01    },
                {+1.20000000000000009436895709313830594e-01    , +1.20581028408444044805093075807633198e-01    },
                {+1.40000000000000013322676295501878485e-01    , +1.40925576070493877554736186975308236e-01    },
                {+1.60000000000000003330669073875469621e-01    , +1.61386696131525518759511362898215609e-01    },
                {+1.79999999999999993338661852249060757e-01    , +1.81982688600705816490251036770517457e-01    },
                {+1.99999999999999983346654630622651894e-01    , +2.02732554054082173641771797964103718e-01    },
                {+2.19999999999999973354647408996243030e-01    , +2.23656109021832382650747515743625830e-01    },
                {+2.39999999999999963362640187369834166e-01    , +2.44774112659352854083413297101694196e-01    },
                {+2.59999999999999953370632965743425302e-01    , +2.66108406873654071753827618842061943e-01    },
                {+2.79999999999999971134201359745929949e-01    , +2.87682072451780896117822911968144088e-01    },
                {+2.99999999999999988897769753748434596e-01    , +3.09519604203111703273814331202206426e-01    },
                {+3.20000000000000006661338147750939243e-01    , +3.31647108705132085025104001081840030e-01    },
                {+3.40000000000000024424906541753443889e-01    , +3.54092528962242939723929765493171945e-01    },
                {+3.60000000000000042188474935755948536e-01    , +3.76885901188190124469133896689497444e-01    },
                {+3.80000000000000059952043329758453183e-01    , +4.00059650056056638206593741845596981e-01    },
                {+4.00000000000000077715611723760957830e-01    , +4.23648930193601899373639138690042112e-01    },
                {+4.20000000000000095479180117763462476e-01    , +4.47692023527420813002158901561072580e-01    },
                {+4.40000000000000113242748511765967123e-01    , +4.72230804420425833981180600242988051e-01    },
                {+4.60000000000000131006316905768471770e-01    , +4.97311287572031193620508878977899997e-01    },
                {+4.80000000000000148769885299770976417e-01    , +5.22984277591344047465367134186014130e-01    },
                {+5.00000000000000111022302462515654042e-01    , +5.49306144334054993727359235148812474e-01    },
                {+5.20000000000000128785870856518158689e-01    , +5.76339754969192906113997153691857594e-01    },
                {+5.40000000000000146549439250520663336e-01    , +6.04155602962267286054127265014583953e-01    },
                {+5.60000000000000164313007644523167983e-01    , +6.32833186665638181077146946128475799e-01    },
                {+5.80000000000000182076576038525672629e-01    , +6.62462707371799523213172030295196960e-01    },
                {+6.00000000000000199840144432528177276e-01    , +6.93147180559945621667457797283512021e-01    },
                {+6.20000000000000217603712826530681923e-01    , +7.25005087752999506268291290927001216e-01    },
                {+6.40000000000000235367281220533186570e-01    , +7.58173744684044609195455590065769225e-01    },
                {+6.60000000000000253130849614535691217e-01    , +7.92813631870191370108450047457113058e-01    },
                {+6.80000000000000270894418008538195863e-01    , +8.29114038301766692728933700083100051e-01    },
                {+7.00000000000000288657986402540700510e-01    , +8.67300527694053760423196460163172710e-01    },
                {+7.20000000000000306421554796543205157e-01    , +9.07644983319125195441126107009775370e-01    },
                {+7.40000000000000324185123190545709804e-01    , +9.50479380596524207852088721432242171e-01    },
                {+7.60000000000000341948691584548214450e-01    , +9.96215082345103890579587353760865510e-01    },
                {+7.80000000000000359712259978550719097e-01    , +1.04537054846688556569856922586455819e+00    },
                {+8.00000000000000377475828372553223744e-01    , +1.09861228866811073993921293846013796e+00    },
                {+8.20000000000000395239396766555728391e-01    , +1.15681746459031653565363995495937725e+00    },
                {+8.40000000000000413002965160558233038e-01    , +1.22117351768460359355809310163905228e+00    },
                {+8.60000000000000430766533554560737684e-01    , +1.29334467204897297035888921761818841e+00    },
                {+8.80000000000000448530101948563242331e-01    , +1.37576765652097643587819823310934128e+00    },
                {+9.00000000000000466293670342565746978e-01    , +1.47221948958322268418172604524275263e+00    },
                {+9.20000000000000484057238736568251625e-01    , +1.58902691517397596123778549185721945e+00    },
                {+9.40000000000000501820807130570756271e-01    , +1.73804934491764087653605718356588900e+00    },
                {+9.60000000000000519584375524573260918e-01    , +1.94591014905531993245708137324632564e+00    },
                {+9.80000000000000537347943918575765565e-01    , +2.29755992506730853281874022244325249e+00    },
        };

        for(double [] testCase : testCases) {
            failures += testAtanhCaseWithUlpDiff(testCase[0],
                    testCase[1],
                    3.0);
        }

        for(double nan : Tests.NaNs) {
            failures += testAtanhCaseWithUlpDiff(nan, NaNd, 0);
        }

        double [][] specialTestCases = {
                {0.0,                       0.0},
                {-0.0,                      -0.0},
                {1.0,                       Double.POSITIVE_INFINITY},
                {-1.0,                      Double.NEGATIVE_INFINITY},
                {2.0,                       NaNd},
                {-2.0,                      NaNd},
        };

        for(double [] specialTestCase : specialTestCases) {
            failures += testAtanhCaseWithUlpDiff(specialTestCase[0],
                    specialTestCase[1],
                    0.0);
        }

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

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

            // Result and expected are the same.
            failures += testAtanhCaseWithUlpDiff(d, d, 2.5);
        }

        failures += testAtanhAdditionalTests();

        return failures;
    }

    /**
     * Test accuracy of {Math, StrictMath}.atanh using quad precision
     * tanh implementation as the reference. There are additional tests.
     * The specified accuracy is 2.5 ulps.
     *
     */
    static int testAtanhAdditionalTests() {
        int failures = 0;
        /*
         * Array elements below are generated using a quad precision tanh
         * implementation (libquadmath). Rounded to a double, the quad result
         * *should* be correctly rounded, unless we are quite unlucky.
         * Assuming the quad value is a correctly rounded double, the
         * allowed error is 3.0 ulps instead of 2.5 since the quad
         * value rounded to double can have its own 1/2 ulp error.
         */
        double[][] testCases = {
                // x                                             atanh(x)
                {+9.39017107929201566562937841808889061e-01    , +1.72967155564501022599234830162276798e+00    },
                {+4.56590977869321346105380143853835762e-01    , +4.92995868916526654745557405930485720e-01    },
                {-6.57855028101722583144805867050308734e-01    , -7.89022676186288902931611202476188124e-01    },
                {+4.62405425240985490376033339998684824e-01    , +5.00366606474614321339885208418466006e-01    },
                {-9.83365261789753697385663144814316183e-01    , -2.39052856803141716223262787771779768e+00    },
                {-6.27582201138608741786129030515439808e-01    , -7.37417270574716377975381198846020522e-01    },
                {-9.83196938676588638728048863413278013e-01    , -2.38545217282555498582477166161511345e+00    },
                {+7.36681396907350904967870519612915814e-01    , +9.43183305171108845024940622694003154e-01    },
                {-7.68733978209885648880117514636367559e-01    , -1.01722532284268312448347897782273734e+00    },
                {-8.99650279001481090190850409271661192e-01    , -1.47038189478731874369381319202006168e+00    },
                {+6.23383381659472490810003364458680153e-02    , +6.24192773197774301522605242534216118e-02    },
                {-8.14139384718910008587045012973248959e-01    , -1.13918472673420532816505691112579313e+00    },
                {-4.89518635342238050967011986358556896e-01    , -5.35427075187260852558782518094419668e-01    },
                {-6.08295892536873550326959048106800765e-01    , -7.06211859359034873213744847874549993e-01    },
                {+9.36079053287340978606323460553539917e-01    , +1.70538649403259128938060088254525967e+00    },
                {+8.31593360663532843446432707423809916e-01    , +1.19328001443669418326658153597705593e+00    },
                {+6.56422583223821076714443734090309590e-01    , +7.86501511439435312578862353672697253e-01    },
                {-3.45789522181036979020518629113212228e-01    , -3.60653496973375779632391162421477716e-01    },
                {+5.32079052777165939502879155043046921e-01    , +5.93040792269778100045583612458499490e-01    },
                {-3.36182931512335247958844774984754622e-01    , -3.49782828626977949006925091676664461e-01    },
                {+6.13630231412017335124176042882027104e-01    , +7.14723430606319696079463920489037224e-01    },
                {+7.39217182016670415478643008100334555e-01    , +9.48751224833067617682882507817093541e-01    },
                {-7.64409441646018983362864673836156726e-03    , -7.64424330871250337925427639013540391e-03    },
                {-9.74816033382744917545892349153291434e-01    , -2.18101148933100542106171185218910695e+00    },
                {+5.52687515297161868765840608830330893e-01    , +6.22242584006598996817110126253907160e-01    },
                {+9.93416759200363430615254856093088165e-01    , +2.85653913150680081054657418761203993e+00    },
                {+9.07659865436335255850508474395610392e-01    , +1.51407684709244159021847264731507603e+00    },
                {+6.60272764758356833780794659105595201e-01    , +7.93297068812459385386864151954890303e-01    },
                {+9.63130814953695568725322573300218210e-01    , +1.98745986190671136058731587311090272e+00    },
                {-5.70877067883640121337407435930799693e-01    , -6.48822975697686437517619163352737241e-01    },
                {-8.11543971448019485492864077968988568e-01    , -1.13153503707350652581786706338031953e+00    },
                {+6.25363929368137561048968109389534220e-01    , +7.33765974893577300297563917687072047e-01    },
                {-2.98846490310910706256208868580870330e-01    , -3.08252492314447063039336121789383998e-01    },
                {-5.97049745291272859759601487894542515e-01    , -6.88550090030688204308547683807415861e-01    },
                {+8.32383827085564576009346637874841690e-01    , +1.19584817769769645815260824209818595e+00    },
                {-6.63715390745103883674005373904947191e-01    , -7.99425357382537999237287552090479860e-01    },
                {-3.94238412786191538828006741823628545e-01    , -4.16808558150307726736043589182851417e-01    },
                {-9.76759747274416945117536670295521617e-01    , -2.22166424268955747060822814557733573e+00    },
                {+8.57442746954987455865193624049425125e-01    , +1.28360612935435243492898897724236702e+00    },
                {-4.24565955117479187919116156990639865e-01    , -4.53248918353154620159372526887584647e-01    },
                {+3.42862260746481295470289296645205468e-01    , +3.57332492545316699435359810051341636e-01    },
                {+9.34459049867542246303742103918921202e-01    , +1.69245393271799745831802454769856267e+00    },
                {+7.64520478549035598092586951679550111e-01    , +1.00700514849153029184678063244721996e+00    },
                {-9.63864704576277597780631367641035467e-01    , -1.99769974929677935746994673118167405e+00    },
                {-1.63366842704400605512660149543080479e-01    , -1.64843919557971079920329622870569601e-01    },
                {+9.94878693411232140064726081618573517e-01    , +2.98246446127683966842287869896800818e+00    },
                {+7.97196021651951247655176757689332590e-01    , +1.09087153746565597453258159715989760e+00    },
                {+8.42371664350162419054868223611265421e-01    , +1.22928450632196951329839160548759750e+00    },
                {+6.96520087724423975217291626904625446e-01    , +8.60509501716176099565750762116593117e-01    },
                {+2.01836732473232416396058397367596626e-01    , +2.04646551779576522368238234135183581e-01    },
                {+5.05939365449320055390103334502782673e-01    , +5.57256946951148119219566387597645954e-01    },
                {-6.01430574320412913991162895399611443e-01    , -6.95385458565007214254554832195678104e-01    },
                {-4.47649318961238940062230540206655860e-01    , -4.81756612137591759595253632500957881e-01    },
                {+3.37215361458020113083478008775273338e-01    , +3.50947266793232870614512911957588554e-01    },
                {+5.14125575037364890285118690371746197e-01    , +5.68321583728012649428480801619053327e-01    },
                {-2.15214858343344861424384362180717289e-01    , -2.18633101430445893274568498462426012e-01    },
                {-9.20630621904034773805847180483397096e-01    , -1.59314811621779716899638118653946385e+00    },
                {+9.19047868224296293782060729427030310e-01    , +1.58286321290197920098639225270320808e+00    },
                {-2.90913484009795997309311132994480431e-01    , -2.99563914714840125917110413508169726e-01    },
                {+3.17993101000002553746526245959103107e-03    , +3.17994172851141737533171613593260162e-03    },
                {-7.16021961571153608971940229821484536e-01    , -8.99433586194582637259073931486986768e-01    },
                {+9.92926371376932737078391255636233836e-01    , +2.82049289268529672262432232518141968e+00    },
                {-7.42199723778889541847547661745920777e-01    , -9.55359320438959545982214260560204172e-01    },
                {+4.01228574786033020949105321051320061e-01    , +4.25112376436892578257996500834612471e-01    },
                {-4.41626489426403034954660142830107361e-01    , -4.74249574732580717257665801841627296e-01    },
                {-7.21334187852223251979921769816428423e-01    , -9.10420850885118135075313207007968241e-01    },
                {+2.82138790772897052328005429444601759e-01    , +2.90004322151609047453793285881602424e-01    },
                {+9.42986643599090679224161704041762277e-01    , +1.76434800601646585550841462860153977e+00    },
                {-5.29497382099672897481923428131267428e-01    , -5.89446464446382266025999977702386855e-01    },
                {+8.90579204675862490248050562513526529e-01    , +1.42471878072594370872155352848645131e+00    },
                {+7.91047774827229877026013582508312538e-01    , +1.07422521925289214702426279427778303e+00    },
                {+4.75836513423619322793456376530230045e-01    , +5.17588301409701923326927500834908347e-01    },
                {+9.32576831661000027473562568047782406e-01    , +1.67781041728427657120484424620161805e+00    },
                {+4.49528137196881449888508086587535217e-01    , +4.84108758524071045231641283604748208e-01    },
                {-6.26946229789648867836149292998015881e-01    , -7.36368746336877301544734566556181860e-01    },
                {+9.58777722962137812778848910966189578e-01    , +1.93054856596755898497650787204101231e+00    },
                {-9.52075725696122754371231167169753462e-01    , -1.85351320681716370080636444991087747e+00    },
                {+9.66628065084665144546249848644947633e-01    , +2.03818021917486263862909093415522483e+00    },
                {-9.90577960901121823411585864960215986e-01    , -2.67656438907628996596144534201915287e+00    },
                {-4.29129153811968588883019037893973291e-01    , -4.58828779570547333956754968138122237e-01    },
                {+9.21075240738198020018501210870454088e-01    , +1.59607267263080478465215862819487820e+00    },
                {-3.36155477527195101217216688382904977e-01    , -3.49751876782073295503516199927519371e-01    },
                {-4.48919523178084922676589485490694642e-01    , -4.83346273396370947315596684554195125e-01    },
                {-7.74714213440744980943009068141691387e-01    , -1.03201246185914269057125935805127686e+00    },
                {-9.33695607057150489538344118045642972e-01    , -1.68646605985566878841417421790327581e+00    },
                {-9.70495709947644780157816057908348739e-01    , -2.10075237060881671900628221642575807e+00    },
                {-9.36541591900329706277261720970273018e-01    , -1.70913713792726775520494333833202263e+00    },
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                {-8.13140811836136734314095519948750734e-01    , -1.13623027343457311746522665305747518e+00    },
                {-9.09625945665704094267312029842287302e-03    , -9.09651034981903612229998860206266111e-03    },
                {+7.11723260837115345722736492461990565e-01    , +8.90667489144918362129731310184000150e-01    },
                {-8.83729688568336113618784111167769879e-01    , -1.39254560811946769303745792066561506e+00    },
                {+2.81119771587539202251093684026272967e-01    , +2.88897516488748428420498810336047168e-01    },
                {+8.67969571335847511761585337808355689e-01    , +1.32478745650884654793737485679177607e+00    },
                {+3.71711284421433640901000217127148062e-01    , +3.90407276521447439801268385319531263e-01    },
                {-5.53264526894389874200896883849054575e-01    , -6.23073752400105167233817313285610373e-01    },
                {-7.50972436681106358946635737083852291e-01    , -9.75181502145488477599896301261990367e-01    },
                {+6.22632428081477007353328190220054239e-01    , +7.29292680370939598849165484001382202e-01    },
                {-5.93039523143406244187758602492976934e-01    , -6.82341523923040079633725976448706286e-01    },
                {-6.21804927349977942796499519317876548e-01    , -7.27942416494347815893737620840227454e-01    },
                {-5.91667199221579398482617762056179345e-01    , -6.80227384371192279205589233595913495e-01    },
        };

        for (double[] testCase : testCases) {
            failures += testAtanhCaseWithUlpDiff(testCase[0],
                    testCase[1],
                    3.0);
        }

        return failures;
    }

    public static int testAtanhCaseWithTolerance(double input,
                                                double expected,
                                                double tolerance) {
        int failures = 0;
        failures += Tests.testTolerance("Math.atanh",       input, Math::atanh,         expected, tolerance);
        failures += Tests.testTolerance("Math.atanh",      -input, Math::atanh,        -expected, tolerance);

        failures += Tests.testTolerance("StrictMath.atanh",  input, StrictMath::atanh,  expected, tolerance);
        failures += Tests.testTolerance("StrictMath.atanh", -input, StrictMath::atanh, -expected, tolerance);
        return failures;
    }

    public static int testAtanhCaseWithUlpDiff(double input,
                                              double expected,
                                              double ulps) {
        int failures = 0;

        failures += Tests.testUlpDiffWithAbsBound("Math.atanh",       input,  Math::atanh,       expected, ulps, Double.POSITIVE_INFINITY);
        failures += Tests.testUlpDiffWithAbsBound("Math.atanh",      -input,  Math::atanh,      -expected, ulps, Double.POSITIVE_INFINITY);

        failures += Tests.testUlpDiffWithAbsBound("StrictMath.atanh",  input, StrictMath::atanh,  expected, ulps, Double.POSITIVE_INFINITY);
        failures += Tests.testUlpDiffWithAbsBound("StrictMath.atanh", -input, StrictMath::atanh, -expected, ulps, Double.POSITIVE_INFINITY);
        return failures;
    }
}