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/*
* Copyright (c) 2003, 2012, 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
* @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.
*/
public class Expm1Tests {
private Expm1Tests(){}
static final double infinityD = Double.POSITIVE_INFINITY;
static final double NaNd = Double.NaN;
static int testExpm1() {
int failures = 0;
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(int i = 0; i < testCases.length; i++) {
failures += testExpm1CaseWithUlpDiff(testCases[i][0],
testCases[i][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);
failures += testExpm1Case(d, d);
failures += 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) {
failures += 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);
failures += testExpm1Case(d, infinityD);
}
// By monotonicity, once the limit is reached, the
// implemenation 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) {
failures += testExpm1CaseWithUlpDiff(d, -1.0, 1,
reachedLimit);
}
for(int i = 7; i <= Double.MAX_EXPONENT; i++) {
double d = -Math.scalb(2, i);
failures += 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] ) {
failures++;
System.err.println("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] ) {
failures++;
System.err.println("Monotonicity failure for StrictMath.expm1 on " +
pcNeighbors[j] + " and " +
pcNeighbors[j+1] + "\n\treturned " +
pcNeighborsStrictExpm1[j] + " and " +
pcNeighborsStrictExpm1[j+1] );
}
}
}
}
return failures;
}
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;
}
failures += Tests.testUlpDiffWithLowerBound("Math.expm1(double)",
input, mathOutput=Math.expm1(input),
expected, mathUlps, -1.0);
failures += 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;
}
public static void main(String argv[]) {
int failures = 0;
failures += testExpm1();
if (failures > 0) {
System.err.println("Testing expm1 incurred "
+ failures + " failures.");
throw new RuntimeException();
}
}
}
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