| /* |
| * Copyright (c) 2003, 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 |
| */ |
| |
| import sun.misc.DoubleConsts; |
| import sun.misc.FpUtils; |
| |
| /* |
| * 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 = FpUtils.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 <= DoubleConsts.MAX_EXPONENT; i++) { |
| double d = FpUtils.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 <= DoubleConsts.MAX_EXPONENT; i++) { |
| double d = -FpUtils.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] = 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++) { |
| 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(); |
| } |
| } |
| } |
