--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/jdk/test/java/lang/Math/CubeRootTests.java Mon Jan 26 19:49:26 2009 -0800
@@ -0,0 +1,336 @@
+/*
+ * Copyright 2003 Sun Microsystems, Inc. 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 Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
+ * CA 95054 USA or visit www.sun.com if you need additional information or
+ * have any questions.
+ */
+
+/*
+ * @test
+ * @bug 4347132 4939441
+ * @summary Tests for {Math, StrictMath}.cbrt
+ * @author Joseph D. Darcy
+ */
+
+import sun.misc.FpUtils;
+import sun.misc.DoubleConsts;
+
+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 java.util.Random();
+
+ 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 <= DoubleConsts.MAX_EXPONENT/3; i++) {
+ failures += testCubeRootCase(FpUtils.scalb(1.0, 3*i),
+ FpUtils.scalb(1.0, i) );
+ }
+
+ // Test cbrt(2^(-3n)) = 2^-n.
+ for(int i = -1; i >= FpUtils.ilogb(Double.MIN_VALUE)/3; i--) {
+ failures += testCubeRootCase(FpUtils.scalb(1.0, 3*i),
+ FpUtils.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(FpUtils.scalb(1.0, 55)) &
+ DoubleConsts.EXP_BIT_MASK;
+ long exponentBits2=
+ Double.doubleToLongBits(FpUtils.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(FpUtils.isNaN(err)) {
+ failures++;
+ System.err.println("Encountered unexpected NaN value: d = " + d +
+ "\tcbrt(d) = " + y1);
+ } else {
+ if (err < 0.0) {
+ err_adjacent = StrictMath.pow(FpUtils.nextUp(y1), 3) - d;
+ }
+ else { // (err > 0.0)
+ err_adjacent = StrictMath.pow(FpUtils.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(FpUtils.isNaN(err)) {
+ failures++;
+ System.err.println("Encountered unexpected NaN value: d = " + d +
+ "\tcbrt(d) = " + y2);
+ } else {
+ if (err < 0.0) {
+ err_adjacent = StrictMath.pow(FpUtils.nextUp(y2), 3) - d;
+ }
+ else { // (err > 0.0)
+ err_adjacent = StrictMath.pow(FpUtils.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 <= DoubleConsts.MAX_EXPONENT/3; i++) {
+ double pc = FpUtils.scalb(1.0, 3*i);
+
+ pcNeighbors[2] = pc;
+ pcNeighbors[1] = FpUtils.nextDown(pc);
+ pcNeighbors[0] = FpUtils.nextDown(pcNeighbors[1]);
+ pcNeighbors[3] = FpUtils.nextUp(pc);
+ pcNeighbors[4] = FpUtils.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 >= FpUtils.ilogb(Double.MIN_VALUE)/3; i--) {
+ double pc = FpUtils.scalb(1.0, 3*i);
+
+ pcNeighbors[2] = pc;
+ pcNeighbors[1] = FpUtils.nextDown(pc);
+ pcNeighbors[0] = FpUtils.nextDown(pcNeighbors[1]);
+ pcNeighbors[3] = FpUtils.nextUp(pc);
+ pcNeighbors[4] = FpUtils.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();
+ }
+ }
+
+}