| /* | |
| * Copyright (c) 2003, 2023, 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 | |
| * @build Tests | |
| * @run main CubeRootTests | |
| * @bug 4347132 4939441 8078672 | |
| * @summary Tests for {Math, StrictMath}.cbrt (use -Dseed=X to set PRNG seed) | |
| * @key randomness | |
| */ | |
| import jdk.test.lib.RandomFactory; | |
| import static java.lang.Double.longBitsToDouble; | |
| 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(); | |
| private static int testCubeRootCase(double input, double expected) { | |
| int failures=0; | |
| failures+=Tests.test("Math.cbrt", input, Math::cbrt, expected); | |
| failures+=Tests.test("Math.cbrt", -input, Math::cbrt, -expected); | |
| failures+=Tests.test("StrictMath.cbrt", input, StrictMath::cbrt, expected); | |
| failures+=Tests.test("StrictMath.cbrt", -input, StrictMath::cbrt, -expected); | |
| return failures; | |
| } | |
| private static int testCubeRoot() { | |
| int failures = 0; | |
| for(double nan : Tests.NaNs) { | |
| failures += testCubeRootCase(nan, NaNd); | |
| } | |
| double [][] testCases = { | |
| {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(); | |
| } | |
| } | |
| } |