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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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 * 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 CubeRootTests
 * @bug 4347132 4939441 8078672
 * @summary Tests for {Math, StrictMath}.cbrt (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 CubeRootTests {

    private CubeRootTests() {
    }

    static final double infinityD = Double.POSITIVE_INFINITY;
    static final double NaNd = Double.NaN;

    // Initialize shared random number generator
    static java.util.Random rand = new Random();

    static void testCubeRootCase(double input, double expected) {
        double minus_input = -input;
        double minus_expected = -expected;

        Tests.test("Math.cbrt(double)", input,
                Math.cbrt(input), expected);
        Tests.test("Math.cbrt(double)", minus_input,
                Math.cbrt(minus_input), minus_expected);
        Tests.test("StrictMath.cbrt(double)", input,
                StrictMath.cbrt(input), expected);
        Tests.test("StrictMath.cbrt(double)", minus_input,
                StrictMath.cbrt(minus_input), minus_expected);
    }

    @Test
    public void testCubeRoot() {
        double[][] testCases = {
                {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},
                {Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY},
                {+0.0, +0.0},
                {-0.0, -0.0},
                {+1.0, +1.0},
                {-1.0, -1.0},
                {+8.0, +2.0},
                {-8.0, -2.0}
        };

        for (double[] testCase : testCases) {
            testCubeRootCase(testCase[0], testCase[1]);
        }

        // Test integer perfect cubes less than 2^53.
        // Android-changed: reduce test run time testing every 100th of original
        // for (int i = 0; i <= 208063; i++) {
        for (int i = 0; i <= 208063; i += 100) {
            double d = i;
            testCubeRootCase(d * d * d, (double) i);
        }

        // Test cbrt(2^(3n)) = 2^n.
        for (int i = 18; i <= Double.MAX_EXPONENT / 3; i++) {
            testCubeRootCase(Math.scalb(1.0, 3 * i), Math.scalb(1.0, i));
        }

        // Test cbrt(2^(-3n)) = 2^-n.
        for (int i = -1; i >= DoubleConsts.MIN_SUB_EXPONENT / 3; i--) {
            testCubeRootCase(Math.scalb(1.0, 3 * i), Math.scalb(1.0, i));
        }

        // Test random perfect cubes.  Create double values with
        // modest exponents but only have at most the 17 most
        // significant bits in the significand set; 17*3 = 51, which
        // is less than the number of bits in a double's significand.
        long exponentBits1 =
                Double.doubleToLongBits(Math.scalb(1.0, 55)) &
                        DoubleConsts.EXP_BIT_MASK;
        long exponentBits2 =
                Double.doubleToLongBits(Math.scalb(1.0, -55)) &
                        DoubleConsts.EXP_BIT_MASK;
        for (int i = 0; i < 100; i++) {
            // Take 16 bits since the 17th bit is implicit in the
            // exponent
            double input1 =
                    Double.longBitsToDouble(exponentBits1 |
                            // Significand bits
                            ((long) (rand.nextInt() & 0xFFFF)) <<
                                    (DoubleConsts.SIGNIFICAND_WIDTH - 1 - 16));
            testCubeRootCase(input1 * input1 * input1, input1);

            double input2 =
                    Double.longBitsToDouble(exponentBits2 |
                            // Significand bits
                            ((long) (rand.nextInt() & 0xFFFF)) <<
                                    (DoubleConsts.SIGNIFICAND_WIDTH - 1 - 16));
            testCubeRootCase(input2 * input2 * input2, input2);
        }

        // Directly test quality of implementation properties of cbrt
        // for values that aren't perfect cubes.  Verify returned
        // result meets the 1 ulp test.  That is, we want to verify
        // that for positive x > 1,
        // y = cbrt(x),
        //
        // if (err1=x - y^3 ) < 0, abs((y_pp^3 -x )) < err1
        // if (err1=x - y^3 ) > 0, abs((y_mm^3 -x )) < err1
        //
        // where y_mm and y_pp are the next smaller and next larger
        // floating-point value to y.  In other words, if y^3 is too
        // big, making y larger does not improve the result; likewise,
        // if y^3 is too small, making y smaller does not improve the
        // result.
        //
        // ...-----|--?--|--?--|-----... Where is the true result?
        //         y_mm  y     y_pp
        //
        // The returned value y should be one of the floating-point
        // values braketing the true result.  However, given y, a
        // priori we don't know if the true result falls in [y_mm, y]
        // or [y, y_pp].  The above test looks at the error in x-y^3
        // to determine which region the true result is in; e.g. if
        // y^3 is smaller than x, the true result should be in [y,
        // y_pp].  Therefore, it would be an error for y_mm to be a
        // closer approximation to x^(1/3).  In this case, it is
        // permissible, although not ideal, for y_pp^3 to be a closer
        // approximation to x^(1/3) than y^3.
        //
        // We will use pow(y,3) to compute y^3.  Although pow is not
        // correctly rounded, StrictMath.pow should have at most 1 ulp
        // error.  For y > 1, pow(y_mm,3) and pow(y_pp,3) will differ
        // from pow(y,3) by more than one ulp so the comparison of
        // errors should still be valid.

        for (int i = 0; i < 1000; i++) {
            double d = 1.0 + rand.nextDouble();
            double err, err_adjacent;

            double y1 = Math.cbrt(d);
            double y2 = StrictMath.cbrt(d);

            err = d - StrictMath.pow(y1, 3);
            if (err != 0.0) {
                if (Double.isNaN(err)) {
                    Assert.fail("Encountered unexpected NaN value: d = " + d +
                            "\tcbrt(d) = " + y1);
                } else {
                    if (err < 0.0) {
                        err_adjacent = StrictMath.pow(Math.nextUp(y1), 3) - d;
                    } else { // (err > 0.0)
                        err_adjacent = StrictMath.pow(Math.nextAfter(y1, 0.0), 3) - d;
                    }

                    if (Math.abs(err) > Math.abs(err_adjacent)) {
                        Assert.fail("For Math.cbrt(" + d + "), returned result " +
                                y1 + "is not as good as adjacent value.");
                    }
                }
            }

            err = d - StrictMath.pow(y2, 3);
            if (err != 0.0) {
                if (Double.isNaN(err)) {
                    Assert.fail("Encountered unexpected NaN value: d = " + d +
                            "\tcbrt(d) = " + y2);
                } else {
                    if (err < 0.0) {
                        err_adjacent = StrictMath.pow(Math.nextUp(y2), 3) - d;
                    } else { // (err > 0.0)
                        err_adjacent = StrictMath.pow(Math.nextAfter(y2, 0.0), 3) - d;
                    }

                    if (Math.abs(err) > Math.abs(err_adjacent)) {
                        Assert.fail("For StrictMath.cbrt(" + d + "), returned result " +
                                y2 + "is not as good as adjacent value.");
                    }
                }
            }


        }

        // Test monotonicity properties near perfect cubes; test two
        // numbers before and two numbers after; i.e. for
        //
        // pcNeighbors[] =
        // {nextDown(nextDown(pc)),
        // nextDown(pc),
        // pc,
        // nextUp(pc),
        // nextUp(nextUp(pc))}
        //
        // test that cbrt(pcNeighbors[i]) <= cbrt(pcNeighbors[i+1])
        {

            double[] pcNeighbors = new double[5];
            double[] pcNeighborsCbrt = new double[5];
            double[] pcNeighborsStrictCbrt = new double[5];

            // Test near cbrt(2^(3n)) = 2^n.
            for (int i = 18; i <= Double.MAX_EXPONENT / 3; i++) {
                double pc = Math.scalb(1.0, 3 * 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++) {
                    pcNeighborsCbrt[j] = Math.cbrt(pcNeighbors[j]);
                    pcNeighborsStrictCbrt[j] = StrictMath.cbrt(pcNeighbors[j]);
                }

                for (int j = 0; j < pcNeighborsCbrt.length - 1; j++) {
                    if (pcNeighborsCbrt[j] > pcNeighborsCbrt[j + 1]) {
                        Assert.fail("Monotonicity failure for Math.cbrt on " +
                                pcNeighbors[j] + " and " +
                                pcNeighbors[j + 1] + "\n\treturned " +
                                pcNeighborsCbrt[j] + " and " +
                                pcNeighborsCbrt[j + 1]);
                    }

                    if (pcNeighborsStrictCbrt[j] > pcNeighborsStrictCbrt[j + 1]) {
                        Assert.fail("Monotonicity failure for StrictMath.cbrt on " +
                                pcNeighbors[j] + " and " +
                                pcNeighbors[j + 1] + "\n\treturned " +
                                pcNeighborsStrictCbrt[j] + " and " +
                                pcNeighborsStrictCbrt[j + 1]);
                    }


                }

            }

            // Test near cbrt(2^(-3n)) = 2^-n.
            for (int i = -1; i >= DoubleConsts.MIN_SUB_EXPONENT / 3; i--) {
                double pc = Math.scalb(1.0, 3 * 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++) {
                    pcNeighborsCbrt[j] = Math.cbrt(pcNeighbors[j]);
                    pcNeighborsStrictCbrt[j] = StrictMath.cbrt(pcNeighbors[j]);
                }

                for (int j = 0; j < pcNeighborsCbrt.length - 1; j++) {
                    if (pcNeighborsCbrt[j] > pcNeighborsCbrt[j + 1]) {
                        Assert.fail("Monotonicity failure for Math.cbrt on " +
                                pcNeighbors[j] + " and " +
                                pcNeighbors[j + 1] + "\n\treturned " +
                                pcNeighborsCbrt[j] + " and " +
                                pcNeighborsCbrt[j + 1]);
                    }

                    if (pcNeighborsStrictCbrt[j] > pcNeighborsStrictCbrt[j + 1]) {
                        Assert.fail("Monotonicity failure for StrictMath.cbrt on " +
                                pcNeighbors[j] + " and " +
                                pcNeighbors[j + 1] + "\n\treturned " +
                                pcNeighborsStrictCbrt[j] + " and " +
                                pcNeighborsStrictCbrt[j + 1]);
                    }


                }
            }
        }
    }

}
