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

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 *

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 * version 2 for more details (a copy is included in the LICENSE file that

 * accompanied this code).

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 * 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 CubeRootTests

 * @bug 4347132 4939441 8078672

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

 * @author Joseph D. Darcy

 * @key randomness

 */

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 = RandomFactory.getRandom();

    static int testCubeRootCase(double input, double expected) {

        int failures=0;

        double minus_input = -input;

        double minus_expected = -expected;

        failures+=Tests.test("Math.cbrt(double)", input,

                             Math.cbrt(input), expected);

        failures+=Tests.test("Math.cbrt(double)", minus_input,

                             Math.cbrt(minus_input), minus_expected);

        failures+=Tests.test("StrictMath.cbrt(double)", input,

                             StrictMath.cbrt(input), expected);

        failures+=Tests.test("StrictMath.cbrt(double)", minus_input,

                             StrictMath.cbrt(minus_input), minus_expected);

        return failures;

    }

    static int testCubeRoot() {

        int failures = 0;

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

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

                                         testCases[i][1]);

        }

        // Test integer perfect cubes less than 2^53.

        for(int i = 0; i <= 208063; i++) {

            double d = i;

            failures += testCubeRootCase(d*d*d, (double)i);

        }

        // Test cbrt(2^(3n)) = 2^n.

        for(int i = 18; i <= Double.MAX_EXPONENT/3; i++) {

            failures += 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--) {

            failures += 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));

           failures += testCubeRootCase(input1*input1*input1, input1);

           double input2 =

               Double.longBitsToDouble(exponentBits2 |

                                       // Significand bits

                                       ((long) (rand.nextInt() & 0xFFFF))<<

                                       (DoubleConsts.SIGNIFICAND_WIDTH-1-16));

           failures += 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 comparision 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)) {

                    failures++;

                    System.err.println("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)) {

                        failures++;

                        System.err.println("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)) {

                    failures++;

                    System.err.println("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)) {

                        failures++;

                        System.err.println("For StrictMath.cbrt(" + d + "), returned result " +

                                           y2 + "is not as good as adjacent value.");

                    }

                }

            }

        }

        // Test monotonicity properites 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] ) {

                        failures++;

                        System.err.println("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] ) {

                        failures++;

                        System.err.println("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] ) {

                        failures++;

                        System.err.println("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] ) {

                        failures++;

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

                                          pcNeighbors[j] + " and "  +

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

                                          pcNeighborsStrictCbrt[j] + " and " +

                                          pcNeighborsStrictCbrt[j+1] );

                    }

                }

            }

        }

        return failures;

    }

    public static void main(String argv[]) {

        int failures = 0;

        failures += testCubeRoot();

        if (failures > 0) {

            System.err.println("Testing cbrt incurred "

                               + failures + " failures.");

            throw new RuntimeException();

        }

    }

}