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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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 * This code is free software; you can redistribute it and/or modify it
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 * 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.
 *
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/*
 * @test
 * @library /test/lib
 * @build jdk.test.lib.RandomFactory
 * @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
 */
package test.java.lang.Math;

import java.util.Random;

import org.testng.annotations.Test;
import org.testng.Assert;

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
     */

    @Test
    public void testLog1p() {
        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 (double[] testCase : testCases) {
            testLog1pCaseWithUlpDiff(testCase[0], testCase[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);
            testLog1pCase(d, d);
            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);
            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 = new Random();
        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++) {
                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]) {
                        Assert.fail("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]) {
                        Assert.fail("Monotonicity failure for StrictMath.log1p on " +
                                pcNeighbors[j] + " and " +
                                pcNeighbors[j + 1] + "\n\treturned " +
                                pcNeighborsStrictLog1p[j] + " and " +
                                pcNeighborsStrictLog1p[j + 1]);
                    }


                }

            }
        }
    }

    public static void testLog1pCase(double input, double expected) {
        testLog1pCaseWithUlpDiff(input, expected, 1);
    }

    public static void testLog1pCaseWithUlpDiff(double input, double expected, double ulps) {
        Tests.testUlpDiff("Math.lop1p(double)",
                input, Math.log1p(input),
                expected, ulps);
        Tests.testUlpDiff("StrictMath.log1p(double)",
                input, StrictMath.log1p(input),
                expected, ulps);
    }
}
