/* * Copyright (c) 2003, 2017, 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 * @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]); } } } } } }