Quelle SquareRootTests.java Sprache: JAVA

/*
* Copyright (c) 2016, 2022, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation.
*
* 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.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/

/*
* @test
* @bug 4851777 8233452
* @summary Tests of BigDecimal.sqrt().
*/

import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
import java.math.RoundingMode;
import java.util.List;

import static java.math.BigDecimal.ONE;
import static java.math.BigDecimal.TWO;
import static java.math.BigDecimal.TEN;
import static java.math.BigDecimal.ZERO;
import static java.math.BigDecimal.valueOf;

public class SquareRootTests {
    /**
     * The value 0.1, with a scale of 1.
     */
    private static final BigDecimal ONE_TENTH = valueOf(1L, 1);

    public static void main(String... args) {
        int failures = 0;

        failures += negativeTests();
        failures += zeroTests();
        failures += oneDigitTests();
        failures += twoDigitTests();
        failures += evenPowersOfTenTests();
        failures += squareRootTwoTests();
        failures += lowPrecisionPerfectSquares();
        failures += almostFourRoundingDown();
        failures += almostFourRoundingUp();
        failures += nearTen();
        failures += nearOne();
        failures += halfWay();

        if (failures > 0 ) {
            throw new RuntimeException("Incurred " + failures + " failures" +
                                       " testing BigDecimal.sqrt().");
        }
    }

    private static int negativeTests() {
        int failures = 0;

        for (long i = -10; i < 0; i++) {
            for (int j = -5; j < 5; j++) {
                try {
                    BigDecimal input = BigDecimal.valueOf(i, j);
                    BigDecimal result = input.sqrt(MathContext.DECIMAL64);
                    System.err.println("Unexpected sqrt of negative: (" +
                                       input + ").sqrt() = " + result );
                    failures += 1;
                } catch (ArithmeticException e) {
                    ; // Expected
                }
            }
        }

        return failures;
    }

    private static int zeroTests() {
        int failures = 0;

        for (int i = -100; i < 100; i++) {
            BigDecimal expected = BigDecimal.valueOf(0L, i/2);
            // These results are independent of rounding mode
            failures += compare(BigDecimal.valueOf(0L, i).sqrt(MathContext.UNLIMITED),
                                expected, true, "zeros");

            failures += compare(BigDecimal.valueOf(0L, i).sqrt(MathContext.DECIMAL64),
                                expected, true, "zeros");
        }

        return failures;
    }

    /**
     * Probe inputs with one digit of precision, 1 ... 9 and those
     * values scaled by 10^-1, 0.1, ... 0.9.
     */
    private static int oneDigitTests() {
        int failures = 0;

        List<BigDecimal> oneToNine =
            List.of(ONE,        TWO,        valueOf(3),
                    valueOf(4), valueOf(5), valueOf(6),
                    valueOf(7), valueOf(8), valueOf(9));

        List<RoundingMode> modes =
            List.of(RoundingMode.UP,      RoundingMode.DOWN,
                    RoundingMode.CEILING, RoundingMode.FLOOR,
                    RoundingMode.HALF_UP, RoundingMode.HALF_DOWN, RoundingMode.HALF_EVEN);

        for (int i = 1; i < 20; i++) {
            for (RoundingMode rm : modes) {
                for (BigDecimal bd  : oneToNine) {
                    MathContext mc = new MathContext(i, rm);

                    failures += compareSqrtImplementations(bd, mc);
                    bd = bd.multiply(ONE_TENTH);
                    failures += compareSqrtImplementations(bd, mc);
                }
            }
        }

        return failures;
    }

    /**
     * Probe inputs with two digits of precision, (10 ... 99) and
     * those values scaled by 10^-1 (1, ... 9.9) and scaled by 10^-2
     * (0.1 ... 0.99).
     */
    private static int twoDigitTests() {
        int failures = 0;

        List<RoundingMode> modes =
            List.of(RoundingMode.UP,      RoundingMode.DOWN,
                    RoundingMode.CEILING, RoundingMode.FLOOR,
                    RoundingMode.HALF_UP, RoundingMode.HALF_DOWN, RoundingMode.HALF_EVEN);

        for (int i = 10; i < 100; i++) {
            BigDecimal bd0 = BigDecimal.valueOf(i);
            BigDecimal bd1 = bd0.multiply(ONE_TENTH);
            BigDecimal bd2 = bd1.multiply(ONE_TENTH);

            for (BigDecimal bd : List.of(bd0, bd1, bd2)) {
                for (int precision = 1; i < 20; i++) {
                    for (RoundingMode rm : modes) {
                        MathContext mc = new MathContext(precision, rm);
                        failures += compareSqrtImplementations(bd, mc);
                    }
                }
            }
        }

        return failures;
    }

    private static int compareSqrtImplementations(BigDecimal bd, MathContext mc) {
        return equalNumerically(BigSquareRoot.sqrt(bd, mc),
                                bd.sqrt(mc), "sqrt(" + bd + ") under " + mc);
    }

    /**
     * sqrt(10^2N) is 10^N
     * Both numerical value and representation should be verified
     */
    private static int evenPowersOfTenTests() {
        int failures = 0;
        MathContext oneDigitExactly = new MathContext(1, RoundingMode.UNNECESSARY);

        for (int scale = -100; scale <= 100; scale++) {
            BigDecimal testValue               = BigDecimal.valueOf(1, 2*scale);
            BigDecimal expectedNumericalResult = BigDecimal.valueOf(1,   scale);

            BigDecimal result;

            failures += equalNumerically(expectedNumericalResult,
                                         result = testValue.sqrt(MathContext.DECIMAL64),
                                         "Even powers of 10, DECIMAL64");

            // Can round to one digit of precision exactly
            failures += equalNumerically(expectedNumericalResult,
                                         result = testValue.sqrt(oneDigitExactly),
                                         "even powers of 10, 1 digit");

            if (result.precision() > 1) {
                failures += 1;
                System.err.println("Excess precision for " + result);
            }

            // If rounding to more than one digit, do precision / scale checking...
        }

        return failures;
    }

    private static int squareRootTwoTests() {
        int failures = 0;

        // Square root of 2 truncated to 65 digits
        BigDecimal highPrecisionRoot2 =
            new BigDecimal("1.41421356237309504880168872420969807856967187537694807317667973799");

        RoundingMode[] modes = {
            RoundingMode.UP,       RoundingMode.DOWN,
            RoundingMode.CEILING, RoundingMode.FLOOR,
            RoundingMode.HALF_UP, RoundingMode.HALF_DOWN, RoundingMode.HALF_EVEN
        };

        // For each interesting rounding mode, for precisions 1 to, say,
        // 63 numerically compare TWO.sqrt(mc) to
        // highPrecisionRoot2.round(mc) and the alternative internal high-precision
        // implementation of square root.
        for (RoundingMode mode : modes) {
            for (int precision = 1; precision < 63; precision++) {
                MathContext mc = new MathContext(precision, mode);
                BigDecimal expected = highPrecisionRoot2.round(mc);
                BigDecimal computed = TWO.sqrt(mc);
                BigDecimal altComputed = BigSquareRoot.sqrt(TWO, mc);

                failures += equalNumerically(expected, computed, "sqrt(2)");
                failures += equalNumerically(computed, altComputed, "computed & altComputed");
            }
        }

        return failures;
    }

    private static int lowPrecisionPerfectSquares() {
        int failures = 0;

        // For 5^2 through 9^2, if the input is rounded to one digit
        // first before the root is computed, the wrong answer will
        // result. Verify results and scale for different rounding
        // modes and precisions.
        long[][] squaresWithOneDigitRoot = {{ 4, 2},
                                            { 9, 3},
                                            {25, 5},
                                            {36, 6},
                                            {49, 7},
                                            {64, 8},
                                            {81, 9}};

        for (long[] squareAndRoot : squaresWithOneDigitRoot) {
            BigDecimal square     = new BigDecimal(squareAndRoot[0]);
            BigDecimal expected   = new BigDecimal(squareAndRoot[1]);

            for (int scale = 0; scale <= 4; scale++) {
                BigDecimal scaledSquare = square.setScale(scale, RoundingMode.UNNECESSARY);
                int expectedScale = scale/2;
                for (int precision = 0; precision <= 5; precision++) {
                    for (RoundingMode rm : RoundingMode.values()) {
                        MathContext mc = new MathContext(precision, rm);
                        BigDecimal computedRoot = scaledSquare.sqrt(mc);
                        failures += equalNumerically(expected, computedRoot, "simple squares");
                        int computedScale = computedRoot.scale();
                        if (precision >=  expectedScale + 1 &&
                            computedScale != expectedScale) {
                            System.err.printf("%s\tprecision=%d\trm=%s%n",
                                              computedRoot.toString(), precision, rm);
                            failures++;
                            System.err.printf("\t%s does not have expected scale of %d%n.",
                                              computedRoot, expectedScale);
                        }
                    }
                }
            }
        }

        return failures;
    }

    /**
     * Test around 3.9999 that the sqrt doesn't improperly round-up to
     * a numerical value of 2.
     */
    private static int almostFourRoundingDown() {
        int failures = 0;
        BigDecimal nearFour = new BigDecimal("3.999999999999999999999999999999");

        // Sqrt is 1.9999...

        for (int i = 1; i < 64; i++) {
            MathContext mc = new MathContext(i, RoundingMode.FLOOR);
            BigDecimal result = nearFour.sqrt(mc);
            BigDecimal expected = BigSquareRoot.sqrt(nearFour, mc);
            failures += equalNumerically(expected, result, "near four rounding down");
            failures += (result.compareTo(TWO) < 0) ? 0  : 1 ;
        }

        return failures;
    }

    /**
     * Test around 4.000...1 that the sqrt doesn't improperly
     * round-down to a numerical value of 2.
     */
    private static int almostFourRoundingUp() {
        int failures = 0;
        BigDecimal nearFour = new BigDecimal("4.000000000000000000000000000001");

        // Sqrt is 2.0000....<non-zero digits>

        for (int i = 1; i < 64; i++) {
            MathContext mc = new MathContext(i, RoundingMode.CEILING);
            BigDecimal result = nearFour.sqrt(mc);
            BigDecimal expected = BigSquareRoot.sqrt(nearFour, mc);
            failures += equalNumerically(expected, result, "near four rounding up");
            failures += (result.compareTo(TWO) > 0) ? 0  : 1 ;
        }

        return failures;
    }

    private static int nearTen() {
        int failures = 0;

         BigDecimal near10 = new BigDecimal("9.99999999999999999999");

         BigDecimal near10sq = near10.multiply(near10);

         BigDecimal near10sq_ulp = near10sq.add(near10sq.ulp());

        for (int i = 10; i < 23; i++) {
            MathContext mc = new MathContext(i, RoundingMode.HALF_EVEN);

            failures += equalNumerically(BigSquareRoot.sqrt(near10sq_ulp, mc),
                                         near10sq_ulp.sqrt(mc),
                                         "near 10 rounding half even");
        }

        return failures;
    }

    /*
     * Probe for rounding failures near a power of ten, 1 = 10^0,
     * where an ulp has a different size above and below the value.
     */
    private static int nearOne() {
        int failures = 0;

         BigDecimal near1 = new BigDecimal(".999999999999999999999");
         BigDecimal near1sq = near1.multiply(near1);
         BigDecimal near1sq_ulp = near1sq.add(near1sq.ulp());

         for (int i = 10; i < 23; i++) {
             for (RoundingMode rm : List.of(RoundingMode.HALF_EVEN,
                                            RoundingMode.UP,
                                            RoundingMode.DOWN )) {
                 MathContext mc = new MathContext(i, rm);
                 failures += equalNumerically(BigSquareRoot.sqrt(near1sq_ulp, mc),
                                              near1sq_ulp.sqrt(mc),
                                              mc.toString());
             }
         }

         return failures;
    }

    private static int halfWay() {
        int failures = 0;

        /*
         * Use enough digits that the exact result cannot be computed
         * from the sqrt of a double.
         */
        BigDecimal[] halfWayCases = {
            // Odd next digit, truncate on HALF_EVEN
            new BigDecimal("123456789123456789.5"),

             // Even next digit, round up on HALF_EVEN
            new BigDecimal("123456789123456788.5"),
        };

        for (BigDecimal halfWayCase : halfWayCases) {
            // Round result to next-to-last place
            int precision = halfWayCase.precision() - 1;
            BigDecimal square = halfWayCase.multiply(halfWayCase);

            for (RoundingMode rm : List.of(RoundingMode.HALF_EVEN,
                                           RoundingMode.HALF_UP,
                                           RoundingMode.HALF_DOWN)) {
                MathContext mc = new MathContext(precision, rm);

                System.out.println("\nRounding mode " + rm);
                System.out.println("\t" + halfWayCase.round(mc) + "\t" + halfWayCase);
                System.out.println("\t" + BigSquareRoot.sqrt(square, mc));

                failures += equalNumerically(/*square.sqrt(mc),*/
                                             BigSquareRoot.sqrt(square, mc),
                                             halfWayCase.round(mc),
                                             "Rounding halway " + rm);
            }
        }

        return failures;
    }

    private static int compare(BigDecimal a, BigDecimal b, boolean expected, String prefix) {
        boolean result = a.equals(b);
        int failed = (result==expected) ? 0 : 1;
        if (failed == 1) {
            System.err.println("Testing " + prefix +
                               "(" + a + ").compareTo(" + b + ") => " + result +
                               "\n\tExpected " + expected);
        }
        return failed;
    }

    private static int equalNumerically(BigDecimal a, BigDecimal b,
                                        String prefix) {
        return compareNumerically(a, b, 0, prefix);
    }

    private static int compareNumerically(BigDecimal a, BigDecimal b,
                                          int expected, String prefix) {
        int result = a.compareTo(b);
        int failed = (result==expected) ? 0 : 1;
        if (failed == 1) {
            System.err.println("Testing " + prefix +
                               "(" + a + ").compareTo(" + b + ") => " + result +
                               "\n\tExpected " + expected);
        }
        return failed;
    }

    /**
     * Alternative implementation of BigDecimal square root which uses
     * higher-precision for a simpler set of termination conditions
     * for the Newton iteration.
     */
    private static class BigSquareRoot {

        /**
         * The value 0.5, with a scale of 1.
         */
        private static final BigDecimal ONE_HALF = valueOf(5L, 1);

        public static boolean isPowerOfTen(BigDecimal bd) {
            return BigInteger.ONE.equals(bd.unscaledValue());
        }

        public static BigDecimal square(BigDecimal bd) {
            return bd.multiply(bd);
        }

        public static BigDecimal sqrt(BigDecimal bd, MathContext mc) {
            int signum = bd.signum();
            if (signum == 1) {
                /*
                 * The following code draws on the algorithm presented in
                 * "Properly Rounded Variable Precision Square Root," Hull and
                 * Abrham, ACM Transactions on Mathematical Software, Vol 11,
                 * No. 3, September 1985, Pages 229-237.
                 *
                 * The BigDecimal computational model differs from the one
                 * presented in the paper in several ways: first BigDecimal
                 * numbers aren't necessarily normalized, second many more
                 * rounding modes are supported, including UNNECESSARY, and
                 * exact results can be requested.
                 *
                 * The main steps of the algorithm below are as follows,
                 * first argument reduce the value to the numerical range
                 * [1, 10) using the following relations:
                 *
                 * x = y * 10 ^ exp
                 * sqrt(x) = sqrt(y) * 10^(exp / 2) if exp is even
                 * sqrt(x) = sqrt(y/10) * 10 ^((exp+1)/2) is exp is odd
                 *
                 * Then use Newton's iteration on the reduced value to compute
                 * the numerical digits of the desired result.
                 *
                 * Finally, scale back to the desired exponent range and
                 * perform any adjustment to get the preferred scale in the
                 * representation.
                 */

                // The code below favors relative simplicity over checking
                // for special cases that could run faster.

                int preferredScale = bd.scale()/2;
                BigDecimal zeroWithFinalPreferredScale =
                    BigDecimal.valueOf(0L, preferredScale);

                // First phase of numerical normalization, strip trailing
                // zeros and check for even powers of 10.
                BigDecimal stripped = bd.stripTrailingZeros();
                int strippedScale = stripped.scale();

                // Numerically sqrt(10^2N) = 10^N
                if (isPowerOfTen(stripped) &&
                    strippedScale % 2 == 0) {
                    BigDecimal result = BigDecimal.valueOf(1L, strippedScale/2);
                    if (result.scale() != preferredScale) {
                        // Adjust to requested precision and preferred
                        // scale as appropriate.
                        result = result.add(zeroWithFinalPreferredScale, mc);
                    }
                    return result;
                }

                // After stripTrailingZeros, the representation is normalized as
                //
                // unscaledValue * 10^(-scale)
                //
                // where unscaledValue is an integer with the mimimum
                // precision for the cohort of the numerical value. To
                // allow binary floating-point hardware to be used to get
                // approximately a 15 digit approximation to the square
                // root, it is helpful to instead normalize this so that
                // the significand portion is to right of the decimal
                // point by roughly (scale() - precision() + 1).

                // Now the precision / scale adjustment
                int scaleAdjust = 0;
                int scale = stripped.scale() - stripped.precision() + 1;
                if (scale % 2 == 0) {
                    scaleAdjust = scale;
                } else {
                    scaleAdjust = scale - 1;
                }

                BigDecimal working = stripped.scaleByPowerOfTen(scaleAdjust);

                assert  // Verify 0.1 <= working < 10
                    ONE_TENTH.compareTo(working) <= 0 && working.compareTo(TEN) < 0;

                // Use good ole' Math.sqrt to get the initial guess for
                // the Newton iteration, good to at least 15 decimal
                // digits. This approach does incur the cost of a
                //
                // BigDecimal -> double -> BigDecimal
                //
                // conversion cycle, but it avoids the need for several
                // Newton iterations in BigDecimal arithmetic to get the
                // working answer to 15 digits of precision. If many fewer
                // than 15 digits were needed, it might be faster to do
                // the loop entirely in BigDecimal arithmetic.
                //
                // (A double value might have as much many as 17 decimal
                // digits of precision; it depends on the relative density
                // of binary and decimal numbers at different regions of
                // the number line.)
                //
                // (It would be possible to check for certain special
                // cases to avoid doing any Newton iterations. For
                // example, if the BigDecimal -> double conversion was
                // known to be exact and the rounding mode had a
                // low-enough precision, the post-Newton rounding logic
                // could be applied directly.)

                BigDecimal guess = new BigDecimal(Math.sqrt(working.doubleValue()));
                int guessPrecision = 15;
                int originalPrecision = mc.getPrecision();
                int targetPrecision;

                // If an exact value is requested, it must only need
                // about half of the input digits to represent since
                // multiplying an N digit number by itself yield a (2N
                // - 1) digit or 2N digit result.
                if (originalPrecision == 0) {
                    targetPrecision = stripped.precision()/2 + 1;
                } else {
                    targetPrecision = originalPrecision;
                }

                // When setting the precision to use inside the Newton
                // iteration loop, take care to avoid the case where the
                // precision of the input exceeds the requested precision
                // and rounding the input value too soon.
                BigDecimal approx = guess;
                int workingPrecision = working.precision();
                // Use "2p + 2" property to guarantee enough
                // intermediate precision so that a double-rounding
                // error does not occur when rounded to the final
                // destination precision.
                int loopPrecision =
                    Math.max(2 * Math.max(targetPrecision, workingPrecision) + 2,
                             34); // Force at least two Netwon
                                  // iterations on the Math.sqrt
                                  // result.
                do {
                    MathContext mcTmp = new MathContext(loopPrecision, RoundingMode.HALF_EVEN);
                    // approx = 0.5 * (approx + fraction / approx)
                    approx = ONE_HALF.multiply(approx.add(working.divide(approx, mcTmp), mcTmp));
                    guessPrecision *= 2;
                } while (guessPrecision < loopPrecision);

                BigDecimal result;
                RoundingMode targetRm = mc.getRoundingMode();
                if (targetRm == RoundingMode.UNNECESSARY || originalPrecision == 0) {
                    RoundingMode tmpRm =
                        (targetRm == RoundingMode.UNNECESSARY) ? RoundingMode.DOWN : targetRm;
                    MathContext mcTmp = new MathContext(targetPrecision, tmpRm);
                    result = approx.scaleByPowerOfTen(-scaleAdjust/2).round(mcTmp);

                    // If result*result != this numerically, the square
                    // root isn't exact
                    if (bd.subtract(square(result)).compareTo(ZERO) != 0) {
                        throw new ArithmeticException("Computed square root not exact.");
                    }
                } else {
                    result = approx.scaleByPowerOfTen(-scaleAdjust/2).round(mc);
                }

                assert squareRootResultAssertions(bd, result, mc);
                if (result.scale() != preferredScale) {
                    // The preferred scale of an add is
                    // max(addend.scale(), augend.scale()). Therefore, if
                    // the scale of the result is first minimized using
                    // stripTrailingZeros(), adding a zero of the
                    // preferred scale rounding the correct precision will
                    // perform the proper scale vs precision tradeoffs.
                    result = result.stripTrailingZeros().
                        add(zeroWithFinalPreferredScale,
                            new MathContext(originalPrecision, RoundingMode.UNNECESSARY));
                }
                return result;
            } else {
                switch (signum) {
                case -1:
                    throw new ArithmeticException("Attempted square root " +
                                                  "of negative BigDecimal");
                case 0:
                    return valueOf(0L, bd.scale()/2);

                default:
                    throw new AssertionError("Bad value from signum");
                }
            }
        }

        /**
         * For nonzero values, check numerical correctness properties of
         * the computed result for the chosen rounding mode.
         *
         * For the directed roundings, for DOWN and FLOOR, result^2 must
         * be {@code <=} the input and (result+ulp)^2 must be {@code >} the
         * input. Conversely, for UP and CEIL, result^2 must be {@code >=} the
         * input and (result-ulp)^2 must be {@code <} the input.
         */
        private static boolean squareRootResultAssertions(BigDecimal input, BigDecimal result, MathContext mc) {
            if (result.signum() == 0) {
                return squareRootZeroResultAssertions(input, result, mc);
            } else {
                RoundingMode rm = mc.getRoundingMode();
                BigDecimal ulp = result.ulp();
                BigDecimal neighborUp   = result.add(ulp);
                // Make neighbor down accurate even for powers of ten
                if (isPowerOfTen(result)) {
                    ulp = ulp.divide(TEN);
                }
                BigDecimal neighborDown = result.subtract(ulp);

                // Both the starting value and result should be nonzero and positive.
                if (result.signum() != 1 ||
                    input.signum() != 1) {
                    return false;
                }

                switch (rm) {
                case DOWN:
                case FLOOR:
                    assert
                        square(result).compareTo(input)    <= 0 &&
                        square(neighborUp).compareTo(input) > 0:
                    "Square of result out for bounds rounding " + rm;
                    return true;

                case UP:
                case CEILING:
                    assert
                        square(result).compareTo(input) >= 0 :
                    "Square of result too small rounding " + rm;

                    assert
                        square(neighborDown).compareTo(input) < 0 :
                    "Square of down neighbor too large rounding " + rm + "\n" +
                        "\t input: " + input + "\t neighborDown: " +  neighborDown +"\t sqrt: " + result +
                        "\t" + mc;
                    return true;

                case HALF_DOWN:
                case HALF_EVEN:
                case HALF_UP:
                    BigDecimal err = square(result).subtract(input).abs();
                    BigDecimal errUp = square(neighborUp).subtract(input);
                    BigDecimal errDown =  input.subtract(square(neighborDown));
                    // All error values should be positive so don't need to
                    // compare absolute values.

                    int err_comp_errUp = err.compareTo(errUp);
                    int err_comp_errDown = err.compareTo(errDown);

                    assert
                        errUp.signum()   == 1 &&
                        errDown.signum() == 1 :
                    "Errors of neighbors squared don't have correct signs";

                    // At least one of these must be true, but not both
//                     assert
//                         err_comp_errUp   <= 0 : "Upper neighbor is closer than result: " + rm +
//                         "\t" + input + "\t result" + result;
//                     assert
//                         err_comp_errDown <= 0 : "Lower neighbor is closer than result: " + rm +
//                         "\t" + input + "\t result " + result + "\t lower neighbor: " + neighborDown;

                    assert
                        ((err_comp_errUp   == 0 ) ? err_comp_errDown < 0 : true) &&
                        ((err_comp_errDown == 0 ) ? err_comp_errUp   < 0 : true) :
                            "Incorrect error relationships";
                        // && could check for digit conditions for ties too
                        return true;

                default: // Definition of UNNECESSARY already verified.
                    return true;
                }
            }
        }

        private static boolean squareRootZeroResultAssertions(BigDecimal input,
                                                              BigDecimal result,
                                                              MathContext mc) {
            return input.compareTo(ZERO) == 0;
        }
    }
}

quality86%

¤ Dauer der Verarbeitung: 0.18 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.