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

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 * This code is distributed in the hope that it will be useful, but WITHOUT

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 * 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,

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 */

/*

 * @test

 * @library /lib/testlibrary/

 * @build jdk.testlibrary.*

 * @run main Log1pTests

 * @bug 4851638 4939441 8078672

 * @summary Tests for {Math, StrictMath}.log1p (use -Dseed=X to set PRNG seed)

 * @author Joseph D. Darcy

 * @key randomness

 */

public class Log1pTests {

    private Log1pTests(){}

    static final double infinityD = Double.POSITIVE_INFINITY;

    static final double NaNd = Double.NaN;

    /**

     * Formulation taken from HP-15C Advanced Functions Handbook, part

     * number HP 0015-90011, p 181.  This is accurate to a few ulps.

     */

    static double hp15cLogp(double x) {

        double u = 1.0 + x;

        return (u==1.0? x : StrictMath.log(u)*x/(u-1) );

    }

    /*

     * The Taylor expansion of ln(1 + x) for -1 < x <= 1 is:

     *

     * x - x^2/2 + x^3/3 - ... -(-x^j)/j

     *

     * Therefore, for small values of x, log1p(x) ~= x.  For large

     * values of x, log1p(x) ~= log(x).

     *

     * Also x/(x+1) < ln(1+x) < x

     */

    static int testLog1p() {

        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},

            {Double.NEGATIVE_INFINITY,  NaNd},

            {-8.0,                      NaNd},

            {-1.0,                      -infinityD},

            {-0.0,                      -0.0},

            {+0.0,                      +0.0},

            {infinityD,                 infinityD},

        };

        // Test special cases

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

            failures += testLog1pCaseWithUlpDiff(testCases[i][0],

                                                 testCases[i][1], 0);

        }

        // For |x| < 2^-54 log1p(x) ~= x

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

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

            failures += testLog1pCase(d, d);

            failures += testLog1pCase(-d, -d);

        }

        // For x > 2^53 log1p(x) ~= log(x)

        for(int i = 53; i <= Double.MAX_EXPONENT; i++) {

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

            failures += testLog1pCaseWithUlpDiff(d, StrictMath.log(d), 2.001);

        }

        // Construct random values with exponents ranging from -53 to

        // 52 and compare against HP-15C formula.

        java.util.Random rand = RandomFactory.getRandom();

        for(int i = 0; i < 1000; i++) {

            double d = rand.nextDouble();

            d = Math.scalb(d, -53 - Tests.ilogb(d));

            for(int j = -53; j <= 52; j++) {

                failures += testLog1pCaseWithUlpDiff(d, hp15cLogp(d), 5);

                d *= 2.0; // increase exponent by 1

            }

        }

        // Test for monotonicity failures near values y-1 where y ~=

        // e^x.  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 log1p(pcNeighbors[i]) <= log1p(pcNeighbors[i+1])

        {

            double pcNeighbors[] = new double[5];

            double pcNeighborsLog1p[] = new double[5];

            double pcNeighborsStrictLog1p[] = new double[5];

            for(int i = -36; i <= 36; i++) {

                double pc = StrictMath.pow(Math.E, i) - 1;

                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++) {

                    pcNeighborsLog1p[j]       =       Math.log1p(pcNeighbors[j]);

                    pcNeighborsStrictLog1p[j] = StrictMath.log1p(pcNeighbors[j]);

                }

                for(int j = 0; j < pcNeighborsLog1p.length-1; j++) {

                    if(pcNeighborsLog1p[j] >  pcNeighborsLog1p[j+1] ) {

                        failures++;

                        System.err.println("Monotonicity failure for Math.log1p on " +

                                          pcNeighbors[j] + " and "  +

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

                                          pcNeighborsLog1p[j] + " and " +

                                          pcNeighborsLog1p[j+1] );

                    }

                    if(pcNeighborsStrictLog1p[j] >  pcNeighborsStrictLog1p[j+1] ) {

                        failures++;

                        System.err.println("Monotonicity failure for StrictMath.log1p on " +

                                          pcNeighbors[j] + " and "  +

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

                                          pcNeighborsStrictLog1p[j] + " and " +

                                          pcNeighborsStrictLog1p[j+1] );

                    }

                }

            }

        }

        return failures;

    }

    public static int testLog1pCase(double input,

                                    double expected) {

        return testLog1pCaseWithUlpDiff(input, expected, 1);

    }

    public static int testLog1pCaseWithUlpDiff(double input,

                                               double expected,

                                               double ulps) {

        int failures = 0;

        failures += Tests.testUlpDiff("Math.lop1p(double",

                                      input, Math.log1p(input),

                                      expected, ulps);

        failures += Tests.testUlpDiff("StrictMath.log1p(double",

                                      input, StrictMath.log1p(input),

                                      expected, ulps);

        return failures;

    }

    public static void main(String argv[]) {

        int failures = 0;

        failures += testLog1p();

        if (failures > 0) {

            System.err.println("Testing log1p incurred "

                               + failures + " failures.");

            throw new RuntimeException();

        }

    }

}