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 45 public class Expm1Tests { 46 Expm1Tests()47 private Expm1Tests(){} 48 49 static final double infinityD = Double.POSITIVE_INFINITY; 50 static final double NaNd = Double.NaN; 51 testExpm1()52 static int testExpm1() { 53 int failures = 0; 54 55 double [][] testCases = { 56 {Double.NaN, NaNd}, 57 {Double.longBitsToDouble(0x7FF0000000000001L), NaNd}, 58 {Double.longBitsToDouble(0xFFF0000000000001L), NaNd}, 59 {Double.longBitsToDouble(0x7FF8555555555555L), NaNd}, 60 {Double.longBitsToDouble(0xFFF8555555555555L), NaNd}, 61 {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd}, 62 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd}, 63 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, 64 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, 65 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, 66 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, 67 {infinityD, infinityD}, 68 {-infinityD, -1.0}, 69 {-0.0, -0.0}, 70 {+0.0, +0.0}, 71 }; 72 73 // Test special cases 74 for(int i = 0; i < testCases.length; i++) { 75 failures += testExpm1CaseWithUlpDiff(testCases[i][0], 76 testCases[i][1], 0, null); 77 } 78 79 80 // For |x| < 2^-54 expm1(x) ~= x 81 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) { 82 double d = Math.scalb(2, i); 83 failures += testExpm1Case(d, d); 84 failures += testExpm1Case(-d, -d); 85 } 86 87 88 // For values of y where exp(y) > 2^54, expm1(x) ~= exp(x). 89 // The least such y is ln(2^54) ~= 37.42994775023705; exp(x) 90 // overflows for x > ~= 709.8 91 92 // Use a 2-ulp error threshold to account for errors in the 93 // exp implementation; the increments of d in the loop will be 94 // exact. 95 for(double d = 37.5; d <= 709.5; d += 1.0) { 96 failures += testExpm1CaseWithUlpDiff(d, StrictMath.exp(d), 2, null); 97 } 98 99 // For x > 710, expm1(x) should be infinity 100 for(int i = 10; i <= Double.MAX_EXPONENT; i++) { 101 double d = Math.scalb(2, i); 102 failures += testExpm1Case(d, infinityD); 103 } 104 105 // By monotonicity, once the limit is reached, the 106 // implemenation should return the limit for all smaller 107 // values. 108 boolean reachedLimit [] = {false, false}; 109 110 // Once exp(y) < 0.5 * ulp(1), expm1(y) ~= -1.0; 111 // The greatest such y is ln(2^-53) ~= -36.7368005696771. 112 for(double d = -36.75; d >= -127.75; d -= 1.0) { 113 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, 114 reachedLimit); 115 } 116 117 for(int i = 7; i <= Double.MAX_EXPONENT; i++) { 118 double d = -Math.scalb(2, i); 119 failures += 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 failures++; 156 System.err.println("Monotonicity failure for Math.expm1 on " + 157 pcNeighbors[j] + " and " + 158 pcNeighbors[j+1] + "\n\treturned " + 159 pcNeighborsExpm1[j] + " and " + 160 pcNeighborsExpm1[j+1] ); 161 } 162 163 if(pcNeighborsStrictExpm1[j] > pcNeighborsStrictExpm1[j+1] ) { 164 failures++; 165 System.err.println("Monotonicity failure for StrictMath.expm1 on " + 166 pcNeighbors[j] + " and " + 167 pcNeighbors[j+1] + "\n\treturned " + 168 pcNeighborsStrictExpm1[j] + " and " + 169 pcNeighborsStrictExpm1[j+1] ); 170 } 171 172 173 } 174 175 } 176 } 177 178 return failures; 179 } 180 testExpm1Case(double input, double expected)181 public static int testExpm1Case(double input, 182 double expected) { 183 return testExpm1CaseWithUlpDiff(input, expected, 1, null); 184 } 185 testExpm1CaseWithUlpDiff(double input, double expected, double ulps, boolean [] reachedLimit)186 public static int testExpm1CaseWithUlpDiff(double input, 187 double expected, 188 double ulps, 189 boolean [] reachedLimit) { 190 int failures = 0; 191 double mathUlps = ulps, strictUlps = ulps; 192 double mathOutput; 193 double strictOutput; 194 195 if (reachedLimit != null) { 196 if (reachedLimit[0]) 197 mathUlps = 0; 198 199 if (reachedLimit[1]) 200 strictUlps = 0; 201 } 202 203 failures += Tests.testUlpDiffWithLowerBound("Math.expm1(double)", 204 input, mathOutput=Math.expm1(input), 205 expected, mathUlps, -1.0); 206 failures += Tests.testUlpDiffWithLowerBound("StrictMath.expm1(double)", 207 input, strictOutput=StrictMath.expm1(input), 208 expected, strictUlps, -1.0); 209 if (reachedLimit != null) { 210 reachedLimit[0] |= (mathOutput == -1.0); 211 reachedLimit[1] |= (strictOutput == -1.0); 212 } 213 214 return failures; 215 } 216 main(String argv[])217 public static void main(String argv[]) { 218 int failures = 0; 219 220 failures += testExpm1(); 221 222 if (failures > 0) { 223 System.err.println("Testing expm1 incurred " 224 + failures + " failures."); 225 throw new RuntimeException(); 226 } 227 } 228 } 229