1 /* 2 * Copyright (c) 2003, 2012, Oracle and/or its affiliates. All rights reserved. 3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. 4 * 5 * This code is free software; you can redistribute it and/or modify it 6 * under the terms of the GNU General Public License version 2 only, as 7 * published by the Free Software Foundation. 8 * 9 * This code is distributed in the hope that it will be useful, but WITHOUT 10 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 11 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 12 * version 2 for more details (a copy is included in the LICENSE file that 13 * accompanied this code). 14 * 15 * You should have received a copy of the GNU General Public License version 16 * 2 along with this work; if not, write to the Free Software Foundation, 17 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. 18 * 19 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA 20 * or visit www.oracle.com if you need additional information or have any 21 * questions. 22 */ 23 24 /* 25 * @test 26 * @bug 4851638 4900189 4939441 27 * @summary Tests for {Math, StrictMath}.expm1 28 * @author Joseph D. Darcy 29 */ 30 31 /* 32 * The Taylor expansion of expxm1(x) = exp(x) -1 is 33 * 34 * 1 + x/1! + x^2/2! + x^3/3| + ... -1 = 35 * 36 * x + x^2/2! + x^3/3 + ... 37 * 38 * Therefore, for small values of x, expxm1 ~= x. 39 * 40 * For large values of x, expxm1(x) ~= exp(x) 41 * 42 * For large negative x, expxm1(x) ~= -1. 43 */ 44 package test.java.lang.Math; 45 46 import org.testng.annotations.Test; 47 import org.testng.Assert; 48 49 public class Expm1Tests { 50 Expm1Tests()51 private Expm1Tests() { 52 } 53 54 static final double infinityD = Double.POSITIVE_INFINITY; 55 static final double NaNd = Double.NaN; 56 57 @Test testExpm1()58 public void testExpm1() { 59 double[][] testCases = { 60 {Double.NaN, NaNd}, 61 {Double.longBitsToDouble(0x7FF0000000000001L), NaNd}, 62 {Double.longBitsToDouble(0xFFF0000000000001L), NaNd}, 63 {Double.longBitsToDouble(0x7FF8555555555555L), NaNd}, 64 {Double.longBitsToDouble(0xFFF8555555555555L), NaNd}, 65 {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd}, 66 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd}, 67 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, 68 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, 69 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, 70 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, 71 {infinityD, infinityD}, 72 {-infinityD, -1.0}, 73 {-0.0, -0.0}, 74 {+0.0, +0.0}, 75 }; 76 77 // Test special cases 78 for (double[] testCase : testCases) { 79 testExpm1CaseWithUlpDiff(testCase[0], testCase[1], 0, null); 80 } 81 82 // For |x| < 2^-54 expm1(x) ~= x 83 for (int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) { 84 double d = Math.scalb(2, i); 85 testExpm1Case(d, d); 86 testExpm1Case(-d, -d); 87 } 88 89 // For values of y where exp(y) > 2^54, expm1(x) ~= exp(x). 90 // The least such y is ln(2^54) ~= 37.42994775023705; exp(x) 91 // overflows for x > ~= 709.8 92 93 // Use a 2-ulp error threshold to account for errors in the 94 // exp implementation; the increments of d in the loop will be 95 // exact. 96 for (double d = 37.5; d <= 709.5; d += 1.0) { 97 testExpm1CaseWithUlpDiff(d, StrictMath.exp(d), 2, null); 98 } 99 100 // For x > 710, expm1(x) should be infinity 101 for (int i = 10; i <= Double.MAX_EXPONENT; i++) { 102 double d = Math.scalb(2, i); 103 testExpm1Case(d, infinityD); 104 } 105 106 // By monotonicity, once the limit is reached, the 107 // implementation should return the limit for all smaller 108 // values. 109 boolean[] reachedLimit = {false, false}; 110 111 // Once exp(y) < 0.5 * ulp(1), expm1(y) ~= -1.0; 112 // The greatest such y is ln(2^-53) ~= -36.7368005696771. 113 for (double d = -36.75; d >= -127.75; d -= 1.0) { 114 testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit); 115 } 116 117 for (int i = 7; i <= Double.MAX_EXPONENT; i++) { 118 double d = -Math.scalb(2, i); 119 testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit); 120 } 121 122 // Test for monotonicity failures near multiples of log(2). 123 // Test two numbers before and two numbers after each chosen 124 // value; i.e. 125 // 126 // pcNeighbors[] = 127 // {nextDown(nextDown(pc)), 128 // nextDown(pc), 129 // pc, 130 // nextUp(pc), 131 // nextUp(nextUp(pc))} 132 // 133 // and we test that expm1(pcNeighbors[i]) <= expm1(pcNeighbors[i+1]) 134 { 135 double[] pcNeighbors = new double[5]; 136 double[] pcNeighborsExpm1 = new double[5]; 137 double[] pcNeighborsStrictExpm1 = new double[5]; 138 139 for (int i = -50; i <= 50; i++) { 140 double pc = StrictMath.log(2) * i; 141 142 pcNeighbors[2] = pc; 143 pcNeighbors[1] = Math.nextDown(pc); 144 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]); 145 pcNeighbors[3] = Math.nextUp(pc); 146 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]); 147 148 for (int j = 0; j < pcNeighbors.length; j++) { 149 pcNeighborsExpm1[j] = Math.expm1(pcNeighbors[j]); 150 pcNeighborsStrictExpm1[j] = StrictMath.expm1(pcNeighbors[j]); 151 } 152 153 for (int j = 0; j < pcNeighborsExpm1.length - 1; j++) { 154 if (pcNeighborsExpm1[j] > pcNeighborsExpm1[j + 1]) { 155 Assert.fail("Monotonicity failure for Math.expm1 on " + 156 pcNeighbors[j] + " and " + 157 pcNeighbors[j + 1] + "\n\treturned " + 158 pcNeighborsExpm1[j] + " and " + 159 pcNeighborsExpm1[j + 1]); 160 } 161 162 if (pcNeighborsStrictExpm1[j] > pcNeighborsStrictExpm1[j + 1]) { 163 Assert.fail("Monotonicity failure for StrictMath.expm1 on " + 164 pcNeighbors[j] + " and " + 165 pcNeighbors[j + 1] + "\n\treturned " + 166 pcNeighborsStrictExpm1[j] + " and " + 167 pcNeighborsStrictExpm1[j + 1]); 168 } 169 170 171 } 172 173 } 174 } 175 } 176 testExpm1Case(double input, double expected)177 public static int testExpm1Case(double input, 178 double expected) { 179 return testExpm1CaseWithUlpDiff(input, expected, 1, null); 180 } 181 testExpm1CaseWithUlpDiff(double input, double expected, double ulps, boolean[] reachedLimit)182 public static int testExpm1CaseWithUlpDiff(double input, 183 double expected, 184 double ulps, 185 boolean[] reachedLimit) { 186 int failures = 0; 187 double mathUlps = ulps, strictUlps = ulps; 188 double mathOutput; 189 double strictOutput; 190 191 if (reachedLimit != null) { 192 if (reachedLimit[0]) { 193 mathUlps = 0; 194 } 195 196 if (reachedLimit[1]) { 197 strictUlps = 0; 198 } 199 } 200 201 Tests.testUlpDiffWithLowerBound("Math.expm1(double)", 202 input, mathOutput = Math.expm1(input), 203 expected, mathUlps, -1.0); 204 Tests.testUlpDiffWithLowerBound("StrictMath.expm1(double)", 205 input, strictOutput = StrictMath.expm1(input), 206 expected, strictUlps, -1.0); 207 if (reachedLimit != null) { 208 reachedLimit[0] |= (mathOutput == -1.0); 209 reachedLimit[1] |= (strictOutput == -1.0); 210 } 211 212 return failures; 213 } 214 } 215