Log1pTests.java revision 4601:6b6b6ee2afd9
1/* 2 * Copyright (c) 2003, 2011 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 4939441 27 * @summary Tests for {Math, StrictMath}.log1p 28 * @author Joseph D. Darcy 29 */ 30 31import sun.misc.DoubleConsts; 32import sun.misc.FpUtils; 33 34public class Log1pTests { 35 private Log1pTests(){} 36 37 static final double infinityD = Double.POSITIVE_INFINITY; 38 static final double NaNd = Double.NaN; 39 40 /** 41 * Formulation taken from HP-15C Advanced Functions Handbook, part 42 * number HP 0015-90011, p 181. This is accurate to a few ulps. 43 */ 44 static double hp15cLogp(double x) { 45 double u = 1.0 + x; 46 return (u==1.0? x : StrictMath.log(u)*x/(u-1) ); 47 } 48 49 /* 50 * The Taylor expansion of ln(1 + x) for -1 < x <= 1 is: 51 * 52 * x - x^2/2 + x^3/3 - ... -(-x^j)/j 53 * 54 * Therefore, for small values of x, log1p(x) ~= x. For large 55 * values of x, log1p(x) ~= log(x). 56 * 57 * Also x/(x+1) < ln(1+x) < x 58 */ 59 60 static int testLog1p() { 61 int failures = 0; 62 63 double [][] testCases = { 64 {Double.NaN, NaNd}, 65 {Double.longBitsToDouble(0x7FF0000000000001L), NaNd}, 66 {Double.longBitsToDouble(0xFFF0000000000001L), NaNd}, 67 {Double.longBitsToDouble(0x7FF8555555555555L), NaNd}, 68 {Double.longBitsToDouble(0xFFF8555555555555L), NaNd}, 69 {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd}, 70 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd}, 71 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, 72 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, 73 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, 74 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, 75 {Double.NEGATIVE_INFINITY, NaNd}, 76 {-8.0, NaNd}, 77 {-1.0, -infinityD}, 78 {-0.0, -0.0}, 79 {+0.0, +0.0}, 80 {infinityD, infinityD}, 81 }; 82 83 // Test special cases 84 for(int i = 0; i < testCases.length; i++) { 85 failures += testLog1pCaseWithUlpDiff(testCases[i][0], 86 testCases[i][1], 0); 87 } 88 89 // For |x| < 2^-54 log1p(x) ~= x 90 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) { 91 double d = Math.scalb(2, i); 92 failures += testLog1pCase(d, d); 93 failures += testLog1pCase(-d, -d); 94 } 95 96 // For x > 2^53 log1p(x) ~= log(x) 97 for(int i = 53; i <= DoubleConsts.MAX_EXPONENT; i++) { 98 double d = Math.scalb(2, i); 99 failures += testLog1pCaseWithUlpDiff(d, StrictMath.log(d), 2.001); 100 } 101 102 // Construct random values with exponents ranging from -53 to 103 // 52 and compare against HP-15C formula. 104 java.util.Random rand = new java.util.Random(); 105 for(int i = 0; i < 1000; i++) { 106 double d = rand.nextDouble(); 107 108 d = Math.scalb(d, -53 - FpUtils.ilogb(d)); 109 110 for(int j = -53; j <= 52; j++) { 111 failures += testLog1pCaseWithUlpDiff(d, hp15cLogp(d), 5); 112 113 d *= 2.0; // increase exponent by 1 114 } 115 } 116 117 // Test for monotonicity failures near values y-1 where y ~= 118 // e^x. Test two numbers before and two numbers after each 119 // chosen value; i.e. 120 // 121 // pcNeighbors[] = 122 // {nextDown(nextDown(pc)), 123 // nextDown(pc), 124 // pc, 125 // nextUp(pc), 126 // nextUp(nextUp(pc))} 127 // 128 // and we test that log1p(pcNeighbors[i]) <= log1p(pcNeighbors[i+1]) 129 { 130 double pcNeighbors[] = new double[5]; 131 double pcNeighborsLog1p[] = new double[5]; 132 double pcNeighborsStrictLog1p[] = new double[5]; 133 134 for(int i = -36; i <= 36; i++) { 135 double pc = StrictMath.pow(Math.E, i) - 1; 136 137 pcNeighbors[2] = pc; 138 pcNeighbors[1] = Math.nextDown(pc); 139 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]); 140 pcNeighbors[3] = Math.nextUp(pc); 141 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]); 142 143 for(int j = 0; j < pcNeighbors.length; j++) { 144 pcNeighborsLog1p[j] = Math.log1p(pcNeighbors[j]); 145 pcNeighborsStrictLog1p[j] = StrictMath.log1p(pcNeighbors[j]); 146 } 147 148 for(int j = 0; j < pcNeighborsLog1p.length-1; j++) { 149 if(pcNeighborsLog1p[j] > pcNeighborsLog1p[j+1] ) { 150 failures++; 151 System.err.println("Monotonicity failure for Math.log1p on " + 152 pcNeighbors[j] + " and " + 153 pcNeighbors[j+1] + "\n\treturned " + 154 pcNeighborsLog1p[j] + " and " + 155 pcNeighborsLog1p[j+1] ); 156 } 157 158 if(pcNeighborsStrictLog1p[j] > pcNeighborsStrictLog1p[j+1] ) { 159 failures++; 160 System.err.println("Monotonicity failure for StrictMath.log1p on " + 161 pcNeighbors[j] + " and " + 162 pcNeighbors[j+1] + "\n\treturned " + 163 pcNeighborsStrictLog1p[j] + " and " + 164 pcNeighborsStrictLog1p[j+1] ); 165 } 166 167 168 } 169 170 } 171 } 172 173 return failures; 174 } 175 176 public static int testLog1pCase(double input, 177 double expected) { 178 return testLog1pCaseWithUlpDiff(input, expected, 1); 179 } 180 181 public static int testLog1pCaseWithUlpDiff(double input, 182 double expected, 183 double ulps) { 184 int failures = 0; 185 failures += Tests.testUlpDiff("Math.lop1p(double", 186 input, Math.log1p(input), 187 expected, ulps); 188 failures += Tests.testUlpDiff("StrictMath.log1p(double", 189 input, StrictMath.log1p(input), 190 expected, ulps); 191 return failures; 192 } 193 194 public static void main(String argv[]) { 195 int failures = 0; 196 197 failures += testLog1p(); 198 199 if (failures > 0) { 200 System.err.println("Testing log1p incurred " 201 + failures + " failures."); 202 throw new RuntimeException(); 203 } 204 } 205} 206