Java example source code file (CubeRootTests.java)
The CubeRootTests.java Java example source code/*
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* This code is free software; you can redistribute it and/or modify it
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* 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
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*/
/*
* @test
* @bug 4347132 4939441
* @summary Tests for {Math, StrictMath}.cbrt
* @author Joseph D. Darcy
*/
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(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 <= DoubleConsts.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();
}
}
}
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