1 /* 2 * Copyright (c) 2003, 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 import sun.misc.DoubleConsts; 32 import sun.misc.FpUtils; 33 34 /* 35 * The Taylor expansion of expxm1(x) = exp(x) -1 is 36 * 37 * 1 + x/1! + x^2/2! + x^3/3| + ... -1 = 38 * 39 * x + x^2/2! + x^3/3 + ... 40 * 41 * Therefore, for small values of x, expxm1 ~= x. 42 * 43 * For large values of x, expxm1(x) ~= exp(x) 44 * 45 * For large negative x, expxm1(x) ~= -1. 46 */ 47 48 public class Expm1Tests { 49 50 private Expm1Tests(){} 51 52 static final double infinityD = Double.POSITIVE_INFINITY; 53 static final double NaNd = Double.NaN; 54 55 static int testExpm1() { 56 int failures = 0; 57 58 double [][] testCases = { 59 {Double.NaN, NaNd}, 60 {Double.longBitsToDouble(0x7FF0000000000001L), NaNd}, 61 {Double.longBitsToDouble(0xFFF0000000000001L), NaNd}, 62 {Double.longBitsToDouble(0x7FF8555555555555L), NaNd}, 63 {Double.longBitsToDouble(0xFFF8555555555555L), NaNd}, 64 {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd}, 65 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd}, 66 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, 67 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, 68 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, 69 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, 70 {infinityD, infinityD}, 71 {-infinityD, -1.0}, 72 {-0.0, -0.0}, 73 {+0.0, +0.0}, 74 }; 75 76 // Test special cases 77 for(int i = 0; i < testCases.length; i++) { 78 failures += testExpm1CaseWithUlpDiff(testCases[i][0], 79 testCases[i][1], 0, null); 80 } 81 82 83 // For |x| < 2^-54 expm1(x) ~= x 84 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) { 85 double d = Math.scalb(2, i); 86 failures += testExpm1Case(d, d); 87 failures += testExpm1Case(-d, -d); 88 } 89 90 91 // For values of y where exp(y) > 2^54, expm1(x) ~= exp(x). 92 // The least such y is ln(2^54) ~= 37.42994775023705; exp(x) 93 // overflows for x > ~= 709.8 94 95 // Use a 2-ulp error threshold to account for errors in the 96 // exp implementation; the increments of d in the loop will be 97 // exact. 98 for(double d = 37.5; d <= 709.5; d += 1.0) { 99 failures += testExpm1CaseWithUlpDiff(d, StrictMath.exp(d), 2, null); 100 } 101 102 // For x > 710, expm1(x) should be infinity 103 for(int i = 10; i <= DoubleConsts.MAX_EXPONENT; i++) { 104 double d = Math.scalb(2, i); 105 failures += testExpm1Case(d, infinityD); 106 } 107 108 // By monotonicity, once the limit is reached, the 109 // implemenation should return the limit for all smaller 110 // values. 111 boolean reachedLimit [] = {false, false}; 112 113 // Once exp(y) < 0.5 * ulp(1), expm1(y) ~= -1.0; 114 // The greatest such y is ln(2^-53) ~= -36.7368005696771. 115 for(double d = -36.75; d >= -127.75; d -= 1.0) { 116 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, 117 reachedLimit); 118 } 119 120 for(int i = 7; i <= DoubleConsts.MAX_EXPONENT; i++) { 121 double d = -Math.scalb(2, i); 122 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit); 123 } 124 125 // Test for monotonicity failures near multiples of log(2). 126 // Test two numbers before and two numbers after each chosen 127 // value; i.e. 128 // 129 // pcNeighbors[] = 130 // {nextDown(nextDown(pc)), 131 // nextDown(pc), 132 // pc, 133 // nextUp(pc), 134 // nextUp(nextUp(pc))} 135 // 136 // and we test that expm1(pcNeighbors[i]) <= expm1(pcNeighbors[i+1]) 137 { 138 double pcNeighbors[] = new double[5]; 139 double pcNeighborsExpm1[] = new double[5]; 140 double pcNeighborsStrictExpm1[] = new double[5]; 141 142 for(int i = -50; i <= 50; i++) { 143 double pc = StrictMath.log(2)*i; 144 145 pcNeighbors[2] = pc; 146 pcNeighbors[1] = FpUtils.nextDown(pc); 147 pcNeighbors[0] = FpUtils.nextDown(pcNeighbors[1]); 148 pcNeighbors[3] = Math.nextUp(pc); 149 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]); 150 151 for(int j = 0; j < pcNeighbors.length; j++) { 152 pcNeighborsExpm1[j] = Math.expm1(pcNeighbors[j]); 153 pcNeighborsStrictExpm1[j] = StrictMath.expm1(pcNeighbors[j]); 154 } 155 156 for(int j = 0; j < pcNeighborsExpm1.length-1; j++) { 157 if(pcNeighborsExpm1[j] > pcNeighborsExpm1[j+1] ) { 158 failures++; 159 System.err.println("Monotonicity failure for Math.expm1 on " + 160 pcNeighbors[j] + " and " + 161 pcNeighbors[j+1] + "\n\treturned " + 162 pcNeighborsExpm1[j] + " and " + 163 pcNeighborsExpm1[j+1] ); 164 } 165 166 if(pcNeighborsStrictExpm1[j] > pcNeighborsStrictExpm1[j+1] ) { 167 failures++; 168 System.err.println("Monotonicity failure for StrictMath.expm1 on " + 169 pcNeighbors[j] + " and " + 170 pcNeighbors[j+1] + "\n\treturned " + 171 pcNeighborsStrictExpm1[j] + " and " + 172 pcNeighborsStrictExpm1[j+1] ); 173 } 174 175 176 } 177 178 } 179 } 180 181 return failures; 182 } 183 184 public static int testExpm1Case(double input, 185 double expected) { 186 return testExpm1CaseWithUlpDiff(input, expected, 1, null); 187 } 188 189 public static int testExpm1CaseWithUlpDiff(double input, 190 double expected, 191 double ulps, 192 boolean [] reachedLimit) { 193 int failures = 0; 194 double mathUlps = ulps, strictUlps = ulps; 195 double mathOutput; 196 double strictOutput; 197 198 if (reachedLimit != null) { 199 if (reachedLimit[0]) 200 mathUlps = 0; 201 202 if (reachedLimit[1]) 203 strictUlps = 0; 204 } 205 206 failures += Tests.testUlpDiffWithLowerBound("Math.expm1(double)", 207 input, mathOutput=Math.expm1(input), 208 expected, mathUlps, -1.0); 209 failures += Tests.testUlpDiffWithLowerBound("StrictMath.expm1(double)", 210 input, strictOutput=StrictMath.expm1(input), 211 expected, strictUlps, -1.0); 212 if (reachedLimit != null) { 213 reachedLimit[0] |= (mathOutput == -1.0); 214 reachedLimit[1] |= (strictOutput == -1.0); 215 } 216 217 return failures; 218 } 219 220 public static void main(String argv[]) { 221 int failures = 0; 222 223 failures += testExpm1(); 224 225 if (failures > 0) { 226 System.err.println("Testing expm1 incurred " 227 + failures + " failures."); 228 throw new RuntimeException(); 229 } 230 } 231 }