/*

 * Copyright (c) 2003, 2011, 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

 * @summary Tests for {Math, StrictMath}.{sinh, cosh, tanh}

 * @author Joseph D. Darcy

 */

import sun.misc.DoubleConsts;

public class HyperbolicTests {

    private HyperbolicTests(){}

    static final double NaNd = Double.NaN;

    /**

     * 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);

        }

        double [][] specialTestCases = {

            {0.0,                       0.0},

            {NaNd,                      NaNd},

            {Double.longBitsToDouble(0x7FF0000000000001L),      NaNd},

            {Double.longBitsToDouble(0xFFF0000000000001L),      NaNd},

            {Double.longBitsToDouble(0x7FF8555555555555L),      NaNd},

            {Double.longBitsToDouble(0xFFF8555555555555L),      NaNd},

            {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL),      NaNd},

            {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL),      NaNd},

            {Double.longBitsToDouble(0x7FFDeadBeef00000L),      NaNd},

            {Double.longBitsToDouble(0xFFFDeadBeef00000L),      NaNd},

            {Double.longBitsToDouble(0x7FFCafeBabe00000L),      NaNd},

            {Double.longBitsToDouble(0xFFFCafeBabe00000L),      NaNd},

            {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 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 <= DoubleConsts.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(double)",

                                        input, Math.sinh(input),

                                        expected, tolerance);

        failures += Tests.testTolerance("Math.sinh(double)",

                                        -input, Math.sinh(-input),

                                        -expected, tolerance);

        failures += Tests.testTolerance("StrictMath.sinh(double)",

                                        input, StrictMath.sinh(input),

                                        expected, tolerance);

        failures += Tests.testTolerance("StrictMath.sinh(double)",

                                        -input, StrictMath.sinh(-input),

                                        -expected, tolerance);

        return failures;

    }

    public static int testSinhCaseWithUlpDiff(double input,

                                              double expected,

                                              double ulps) {

        int failures = 0;

        failures += Tests.testUlpDiff("Math.sinh(double)",

                                      input, Math.sinh(input),

                                      expected, ulps);

        failures += Tests.testUlpDiff("Math.sinh(double)",

                                      -input, Math.sinh(-input),

                                      -expected, ulps);

        failures += Tests.testUlpDiff("StrictMath.sinh(double)",

                                      input, StrictMath.sinh(input),

                                      expected, ulps);

        failures += Tests.testUlpDiff("StrictMath.sinh(double)",

                                      -input, StrictMath.sinh(-input),

                                      -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},