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* 2 along with this work; if not, write to the Free Software Foundation,
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/*
* @test
* @bug 4851638 4900189 4939441
* @summary Tests for {Math, StrictMath}.expm1
* @author Joseph D. Darcy
*/
/*
* The Taylor expansion of expxm1(x) = exp(x) -1 is
*
* 1 + x/1! + x^2/2! + x^3/3| + ... -1 =
*
* x + x^2/2! + x^3/3 + ...
*
* Therefore, for small values of x, expxm1 ~= x.
*
* For large values of x, expxm1(x) ~= exp(x)
*
* For large negative x, expxm1(x) ~= -1.
*/
package test.java.lang.Math;
import org.testng.annotations.Test;
import org.testng.Assert;
public class Expm1Tests {
private Expm1Tests() {
}
static final double infinityD = Double.POSITIVE_INFINITY;
static final double NaNd = Double.NaN;
@Test
public void testExpm1() {
double[][] testCases = {
{Double.NaN, 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},
{infinityD, infinityD},
{-infinityD, -1.0},
{-0.0, -0.0},
{+0.0, +0.0},
};
// Test special cases
for (double[] testCase : testCases) {
testExpm1CaseWithUlpDiff(testCase[0], testCase[1], 0, null);
}
// For |x| < 2^-54 expm1(x) ~= x
for (int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) {
double d = Math.scalb(2, i);
testExpm1Case(d, d);
testExpm1Case(-d, -d);
}
// For values of y where exp(y) > 2^54, expm1(x) ~= exp(x).
// The least such y is ln(2^54) ~= 37.42994775023705; exp(x)
// overflows for x > ~= 709.8
// Use a 2-ulp error threshold to account for errors in the
// exp implementation; the increments of d in the loop will be
// exact.
for (double d = 37.5; d <= 709.5; d += 1.0) {
testExpm1CaseWithUlpDiff(d, StrictMath.exp(d), 2, null);
}
// For x > 710, expm1(x) should be infinity
for (int i = 10; i <= Double.MAX_EXPONENT; i++) {
double d = Math.scalb(2, i);
testExpm1Case(d, infinityD);
}
// By monotonicity, once the limit is reached, the
// implementation should return the limit for all smaller
// values.
boolean[] reachedLimit = {false, false};
// Once exp(y) < 0.5 * ulp(1), expm1(y) ~= -1.0;
// The greatest such y is ln(2^-53) ~= -36.7368005696771.
for (double d = -36.75; d >= -127.75; d -= 1.0) {
testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit);
}
for (int i = 7; i <= Double.MAX_EXPONENT; i++) {
double d = -Math.scalb(2, i);
testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit);
}
// Test for monotonicity failures near multiples of log(2).
// Test two numbers before and two numbers after each chosen
// value; i.e.
//
// pcNeighbors[] =
// {nextDown(nextDown(pc)),
// nextDown(pc),
// pc,
// nextUp(pc),
// nextUp(nextUp(pc))}
//
// and we test that expm1(pcNeighbors[i]) <= expm1(pcNeighbors[i+1])
{
double[] pcNeighbors = new double[5];
double[] pcNeighborsExpm1 = new double[5];
double[] pcNeighborsStrictExpm1 = new double[5];
for (int i = -50; i <= 50; i++) {
double pc = StrictMath.log(2) * 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++) {
pcNeighborsExpm1[j] = Math.expm1(pcNeighbors[j]);
pcNeighborsStrictExpm1[j] = StrictMath.expm1(pcNeighbors[j]);
}
for (int j = 0; j < pcNeighborsExpm1.length - 1; j++) {
if (pcNeighborsExpm1[j] > pcNeighborsExpm1[j + 1]) {
Assert.fail("Monotonicity failure for Math.expm1 on " +
pcNeighbors[j] + " and " +
pcNeighbors[j + 1] + "\n\treturned " +
pcNeighborsExpm1[j] + " and " +
pcNeighborsExpm1[j + 1]);
}
if (pcNeighborsStrictExpm1[j] > pcNeighborsStrictExpm1[j + 1]) {
Assert.fail("Monotonicity failure for StrictMath.expm1 on " +
pcNeighbors[j] + " and " +
pcNeighbors[j + 1] + "\n\treturned " +
pcNeighborsStrictExpm1[j] + " and " +
pcNeighborsStrictExpm1[j + 1]);
}
}
}
}
}
public static int testExpm1Case(double input,
double expected) {
return testExpm1CaseWithUlpDiff(input, expected, 1, null);
}
public static int testExpm1CaseWithUlpDiff(double input,
double expected,
double ulps,
boolean[] reachedLimit) {
int failures = 0;
double mathUlps = ulps, strictUlps = ulps;
double mathOutput;
double strictOutput;
if (reachedLimit != null) {
if (reachedLimit[0]) {
mathUlps = 0;
}
if (reachedLimit[1]) {
strictUlps = 0;
}
}
Tests.testUlpDiffWithLowerBound("Math.expm1(double)",
input, mathOutput = Math.expm1(input),
expected, mathUlps, -1.0);
Tests.testUlpDiffWithLowerBound("StrictMath.expm1(double)",
input, strictOutput = StrictMath.expm1(input),
expected, strictUlps, -1.0);
if (reachedLimit != null) {
reachedLimit[0] |= (mathOutput == -1.0);
reachedLimit[1] |= (strictOutput == -1.0);
}
return failures;
}
}