329 lines
13 KiB
Java
329 lines
13 KiB
Java
/*
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* Copyright (c) 2003, 2023, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*/
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/*
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* @test
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* @library /test/lib
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* @build jdk.test.lib.RandomFactory
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* @build Tests
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* @run main CubeRootTests
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* @bug 4347132 4939441 8078672
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* @summary Tests for {Math, StrictMath}.cbrt (use -Dseed=X to set PRNG seed)
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* @key randomness
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*/
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import jdk.test.lib.RandomFactory;
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import static java.lang.Double.longBitsToDouble;
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public class CubeRootTests {
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private CubeRootTests(){}
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static final double infinityD = Double.POSITIVE_INFINITY;
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static final double NaNd = Double.NaN;
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// Initialize shared random number generator
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static java.util.Random rand = RandomFactory.getRandom();
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private static int testCubeRootCase(double input, double expected) {
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int failures=0;
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failures+=Tests.test("Math.cbrt", input, Math::cbrt, expected);
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failures+=Tests.test("Math.cbrt", -input, Math::cbrt, -expected);
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failures+=Tests.test("StrictMath.cbrt", input, StrictMath::cbrt, expected);
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failures+=Tests.test("StrictMath.cbrt", -input, StrictMath::cbrt, -expected);
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return failures;
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}
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private static int testCubeRoot() {
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int failures = 0;
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for(double nan : Tests.NaNs) {
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failures += testCubeRootCase(nan, NaNd);
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}
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double [][] testCases = {
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{Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY},
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{Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY},
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{+0.0, +0.0},
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{-0.0, -0.0},
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{+1.0, +1.0},
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{-1.0, -1.0},
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{+8.0, +2.0},
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{-8.0, -2.0}
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};
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for(int i = 0; i < testCases.length; i++) {
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failures += testCubeRootCase(testCases[i][0],
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testCases[i][1]);
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}
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// Test integer perfect cubes less than 2^53.
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for(int i = 0; i <= 208063; i++) {
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double d = i;
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failures += testCubeRootCase(d*d*d, (double)i);
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}
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// Test cbrt(2^(3n)) = 2^n.
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for(int i = 18; i <= Double.MAX_EXPONENT/3; i++) {
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failures += testCubeRootCase(Math.scalb(1.0, 3*i),
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Math.scalb(1.0, i) );
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}
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// Test cbrt(2^(-3n)) = 2^-n.
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for(int i = -1; i >= DoubleConsts.MIN_SUB_EXPONENT/3; i--) {
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failures += testCubeRootCase(Math.scalb(1.0, 3*i),
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Math.scalb(1.0, i) );
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}
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// Test random perfect cubes. Create double values with
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// modest exponents but only have at most the 17 most
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// significant bits in the significand set; 17*3 = 51, which
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// is less than the number of bits in a double's significand.
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long exponentBits1 =
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Double.doubleToLongBits(Math.scalb(1.0, 55)) &
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DoubleConsts.EXP_BIT_MASK;
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long exponentBits2=
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Double.doubleToLongBits(Math.scalb(1.0, -55)) &
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DoubleConsts.EXP_BIT_MASK;
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for(int i = 0; i < 100; i++) {
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// Take 16 bits since the 17th bit is implicit in the
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// exponent
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double input1 =
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Double.longBitsToDouble(exponentBits1 |
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// Significand bits
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((long) (rand.nextInt() & 0xFFFF))<<
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(DoubleConsts.SIGNIFICAND_WIDTH-1-16));
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failures += testCubeRootCase(input1*input1*input1, input1);
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double input2 =
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Double.longBitsToDouble(exponentBits2 |
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// Significand bits
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((long) (rand.nextInt() & 0xFFFF))<<
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(DoubleConsts.SIGNIFICAND_WIDTH-1-16));
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failures += testCubeRootCase(input2*input2*input2, input2);
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}
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// Directly test quality of implementation properties of cbrt
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// for values that aren't perfect cubes. Verify returned
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// result meets the 1 ulp test. That is, we want to verify
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// that for positive x > 1,
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// y = cbrt(x),
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//
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// if (err1=x - y^3 ) < 0, abs((y_pp^3 -x )) < err1
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// if (err1=x - y^3 ) > 0, abs((y_mm^3 -x )) < err1
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//
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// where y_mm and y_pp are the next smaller and next larger
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// floating-point value to y. In other words, if y^3 is too
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// big, making y larger does not improve the result; likewise,
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// if y^3 is too small, making y smaller does not improve the
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// result.
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//
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// ...-----|--?--|--?--|-----... Where is the true result?
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// y_mm y y_pp
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//
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// The returned value y should be one of the floating-point
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// values braketing the true result. However, given y, a
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// priori we don't know if the true result falls in [y_mm, y]
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// or [y, y_pp]. The above test looks at the error in x-y^3
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// to determine which region the true result is in; e.g. if
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// y^3 is smaller than x, the true result should be in [y,
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// y_pp]. Therefore, it would be an error for y_mm to be a
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// closer approximation to x^(1/3). In this case, it is
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// permissible, although not ideal, for y_pp^3 to be a closer
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// approximation to x^(1/3) than y^3.
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//
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// We will use pow(y,3) to compute y^3. Although pow is not
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// correctly rounded, StrictMath.pow should have at most 1 ulp
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// error. For y > 1, pow(y_mm,3) and pow(y_pp,3) will differ
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// from pow(y,3) by more than one ulp so the comparision of
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// errors should still be valid.
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for(int i = 0; i < 1000; i++) {
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double d = 1.0 + rand.nextDouble();
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double err, err_adjacent;
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double y1 = Math.cbrt(d);
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double y2 = StrictMath.cbrt(d);
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err = d - StrictMath.pow(y1, 3);
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if (err != 0.0) {
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if(Double.isNaN(err)) {
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failures++;
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System.err.println("Encountered unexpected NaN value: d = " + d +
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"\tcbrt(d) = " + y1);
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} else {
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if (err < 0.0) {
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err_adjacent = StrictMath.pow(Math.nextUp(y1), 3) - d;
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}
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else { // (err > 0.0)
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err_adjacent = StrictMath.pow(Math.nextAfter(y1,0.0), 3) - d;
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}
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if (Math.abs(err) > Math.abs(err_adjacent)) {
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failures++;
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System.err.println("For Math.cbrt(" + d + "), returned result " +
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y1 + "is not as good as adjacent value.");
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}
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}
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}
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err = d - StrictMath.pow(y2, 3);
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if (err != 0.0) {
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if(Double.isNaN(err)) {
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failures++;
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System.err.println("Encountered unexpected NaN value: d = " + d +
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"\tcbrt(d) = " + y2);
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} else {
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if (err < 0.0) {
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err_adjacent = StrictMath.pow(Math.nextUp(y2), 3) - d;
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}
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else { // (err > 0.0)
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err_adjacent = StrictMath.pow(Math.nextAfter(y2,0.0), 3) - d;
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}
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if (Math.abs(err) > Math.abs(err_adjacent)) {
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failures++;
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System.err.println("For StrictMath.cbrt(" + d + "), returned result " +
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y2 + "is not as good as adjacent value.");
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}
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}
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}
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}
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// Test monotonicity properites near perfect cubes; test two
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// numbers before and two numbers after; i.e. for
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//
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// pcNeighbors[] =
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// {nextDown(nextDown(pc)),
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// nextDown(pc),
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// pc,
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// nextUp(pc),
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// nextUp(nextUp(pc))}
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//
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// test that cbrt(pcNeighbors[i]) <= cbrt(pcNeighbors[i+1])
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{
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double pcNeighbors[] = new double[5];
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double pcNeighborsCbrt[] = new double[5];
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double pcNeighborsStrictCbrt[] = new double[5];
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// Test near cbrt(2^(3n)) = 2^n.
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for(int i = 18; i <= Double.MAX_EXPONENT/3; i++) {
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double pc = Math.scalb(1.0, 3*i);
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pcNeighbors[2] = pc;
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pcNeighbors[1] = Math.nextDown(pc);
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pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
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pcNeighbors[3] = Math.nextUp(pc);
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pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
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for(int j = 0; j < pcNeighbors.length; j++) {
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pcNeighborsCbrt[j] = Math.cbrt(pcNeighbors[j]);
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pcNeighborsStrictCbrt[j] = StrictMath.cbrt(pcNeighbors[j]);
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}
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for(int j = 0; j < pcNeighborsCbrt.length-1; j++) {
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if(pcNeighborsCbrt[j] > pcNeighborsCbrt[j+1] ) {
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failures++;
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System.err.println("Monotonicity failure for Math.cbrt on " +
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pcNeighbors[j] + " and " +
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pcNeighbors[j+1] + "\n\treturned " +
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pcNeighborsCbrt[j] + " and " +
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pcNeighborsCbrt[j+1] );
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}
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if(pcNeighborsStrictCbrt[j] > pcNeighborsStrictCbrt[j+1] ) {
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failures++;
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System.err.println("Monotonicity failure for StrictMath.cbrt on " +
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pcNeighbors[j] + " and " +
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pcNeighbors[j+1] + "\n\treturned " +
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pcNeighborsStrictCbrt[j] + " and " +
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pcNeighborsStrictCbrt[j+1] );
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}
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}
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}
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// Test near cbrt(2^(-3n)) = 2^-n.
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for(int i = -1; i >= DoubleConsts.MIN_SUB_EXPONENT/3; i--) {
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double pc = Math.scalb(1.0, 3*i);
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pcNeighbors[2] = pc;
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pcNeighbors[1] = Math.nextDown(pc);
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pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
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pcNeighbors[3] = Math.nextUp(pc);
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pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
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for(int j = 0; j < pcNeighbors.length; j++) {
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pcNeighborsCbrt[j] = Math.cbrt(pcNeighbors[j]);
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pcNeighborsStrictCbrt[j] = StrictMath.cbrt(pcNeighbors[j]);
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}
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for(int j = 0; j < pcNeighborsCbrt.length-1; j++) {
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if(pcNeighborsCbrt[j] > pcNeighborsCbrt[j+1] ) {
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failures++;
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System.err.println("Monotonicity failure for Math.cbrt on " +
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pcNeighbors[j] + " and " +
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pcNeighbors[j+1] + "\n\treturned " +
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pcNeighborsCbrt[j] + " and " +
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pcNeighborsCbrt[j+1] );
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}
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if(pcNeighborsStrictCbrt[j] > pcNeighborsStrictCbrt[j+1] ) {
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failures++;
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System.err.println("Monotonicity failure for StrictMath.cbrt on " +
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pcNeighbors[j] + " and " +
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pcNeighbors[j+1] + "\n\treturned " +
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pcNeighborsStrictCbrt[j] + " and " +
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pcNeighborsStrictCbrt[j+1] );
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}
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}
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}
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}
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return failures;
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}
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public static void main(String... argv) {
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int failures = 0;
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failures += testCubeRoot();
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if (failures > 0) {
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System.err.println("Testing cbrt incurred "
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+ failures + " failures.");
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throw new RuntimeException();
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}
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}
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}
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