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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

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 *

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 * 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

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 *

 * 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

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 */

/*

 * @test

 * @bug 4851638 4900189 4939441

 * @summary Tests for {Math, StrictMath}.expm1

 * @author Joseph D. Darcy

 */

import sun.misc.DoubleConsts;

/*

 * The Taylor expansion of expxm1(x) = exp(x) -1 is

 *

 * 1 + x/1! + x^2/2! + x^3/3| + ... -1 =

 *

 * x + x^2/2! + x^3/3 + ...

 *

 * Therefore, for small values of x, expxm1 ~= x.

 *

 * For large values of x, expxm1(x) ~= exp(x)

 *

 * For large negative x, expxm1(x) ~= -1.

 */

public class Expm1Tests {

    private Expm1Tests(){}

    static final double infinityD = Double.POSITIVE_INFINITY;

    static final double NaNd = Double.NaN;

    static int testExpm1() {

        int failures = 0;

        double [][] testCases = {

            {Double.NaN,                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},

            {infinityD,                 infinityD},

            {-infinityD,                -1.0},

            {-0.0,                      -0.0},

            {+0.0,                      +0.0},

        };

        // Test special cases

        for(int i = 0; i < testCases.length; i++) {

            failures += testExpm1CaseWithUlpDiff(testCases[i][0],

                                                 testCases[i][1], 0, null);

        }

        // For |x| < 2^-54 expm1(x) ~= x

        for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) {

            double d = Math.scalb(2, i);

            failures += testExpm1Case(d, d);

            failures += testExpm1Case(-d, -d);

        }

        // For values of y where exp(y) > 2^54, expm1(x) ~= exp(x).

        // The least such y is ln(2^54) ~= 37.42994775023705; exp(x)

        // overflows for x > ~= 709.8

        // Use a 2-ulp error threshold to account for errors in the

        // exp implementation; the increments of d in the loop will be

        // exact.

        for(double d = 37.5; d <= 709.5; d += 1.0) {

            failures += testExpm1CaseWithUlpDiff(d, StrictMath.exp(d), 2, null);

        }

        // For x > 710, expm1(x) should be infinity

        for(int i = 10; i <= DoubleConsts.MAX_EXPONENT; i++) {

            double d = Math.scalb(2, i);

            failures += testExpm1Case(d, infinityD);

        }

        // By monotonicity, once the limit is reached, the

        // implemenation should return the limit for all smaller

        // values.

        boolean reachedLimit [] = {false, false};

        // Once exp(y) < 0.5 * ulp(1), expm1(y) ~= -1.0;

        // The greatest such y is ln(2^-53) ~= -36.7368005696771.

        for(double d = -36.75; d >= -127.75; d -= 1.0) {

            failures += testExpm1CaseWithUlpDiff(d, -1.0, 1,

                                                 reachedLimit);

        }

        for(int i = 7; i <= DoubleConsts.MAX_EXPONENT; i++) {

            double d = -Math.scalb(2, i);

            failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit);

        }

        // Test for monotonicity failures near multiples of log(2).

        // Test two numbers before and two numbers after each chosen

        // value; i.e.

        //

        // pcNeighbors[] =

        // {nextDown(nextDown(pc)),

        // nextDown(pc),

        // pc,

        // nextUp(pc),

        // nextUp(nextUp(pc))}

        //

        // and we test that expm1(pcNeighbors[i]) <= expm1(pcNeighbors[i+1])

        {

            double pcNeighbors[] = new double[5];

            double pcNeighborsExpm1[] = new double[5];

            double pcNeighborsStrictExpm1[] = new double[5];

            for(int i = -50; i <= 50; i++) {

                double pc = StrictMath.log(2)*i;

                pcNeighbors[2] = pc;

                pcNeighbors[1] = Math.nextDown(pc);

                pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);

                pcNeighbors[3] = Math.nextUp(pc);

                pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);

                for(int j = 0; j < pcNeighbors.length; j++) {

                    pcNeighborsExpm1[j]       =       Math.expm1(pcNeighbors[j]);

                    pcNeighborsStrictExpm1[j] = StrictMath.expm1(pcNeighbors[j]);

                }

                for(int j = 0; j < pcNeighborsExpm1.length-1; j++) {

                    if(pcNeighborsExpm1[j] >  pcNeighborsExpm1[j+1] ) {

                        failures++;

                        System.err.println("Monotonicity failure for Math.expm1 on " +

                                          pcNeighbors[j] + " and "  +

                                          pcNeighbors[j+1] + "\n\treturned " +

                                          pcNeighborsExpm1[j] + " and " +

                                          pcNeighborsExpm1[j+1] );

                    }

                    if(pcNeighborsStrictExpm1[j] >  pcNeighborsStrictExpm1[j+1] ) {

                        failures++;

                        System.err.println("Monotonicity failure for StrictMath.expm1 on " +

                                          pcNeighbors[j] + " and "  +

                                          pcNeighbors[j+1] + "\n\treturned " +

                                          pcNeighborsStrictExpm1[j] + " and " +

                                          pcNeighborsStrictExpm1[j+1] );

                    }

                }

            }

        }

        return failures;

    }

    public static int testExpm1Case(double input,

                                    double expected) {

        return testExpm1CaseWithUlpDiff(input, expected, 1, null);

    }

    public static int testExpm1CaseWithUlpDiff(double input,

                                               double expected,

                                               double ulps,

                                               boolean [] reachedLimit) {

        int failures = 0;

        double mathUlps = ulps, strictUlps = ulps;

        double mathOutput;

        double strictOutput;

        if (reachedLimit != null) {

            if (reachedLimit[0])

                mathUlps = 0;

            if (reachedLimit[1])

                strictUlps = 0;

        }

        failures += Tests.testUlpDiffWithLowerBound("Math.expm1(double)",

                                                    input, mathOutput=Math.expm1(input),

                                                    expected, mathUlps, -1.0);

        failures += Tests.testUlpDiffWithLowerBound("StrictMath.expm1(double)",

                                                    input, strictOutput=StrictMath.expm1(input),

                                                    expected, strictUlps, -1.0);

        if (reachedLimit != null) {

            reachedLimit[0] |= (mathOutput   == -1.0);

            reachedLimit[1] |= (strictOutput == -1.0);

        }

        return failures;

    }

    public static void main(String argv[]) {

        int failures = 0;

        failures += testExpm1();

        if (failures > 0) {

            System.err.println("Testing expm1 incurred "

                               + failures + " failures.");

            throw new RuntimeException();

        }

    }

}