1 /* 2 * Copyright (c) 2003, 2014, 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 31 import sun.misc.DoubleConsts; 32 33 public class Log1pTests { 34 private Log1pTests(){} 35 36 static final double infinityD = Double.POSITIVE_INFINITY; 37 static final double NaNd = Double.NaN; 38 39 /** 40 * Formulation taken from HP-15C Advanced Functions Handbook, part 41 * number HP 0015-90011, p 181. This is accurate to a few ulps. 42 */ 43 static double hp15cLogp(double x) { 44 double u = 1.0 + x; 45 return (u==1.0? x : StrictMath.log(u)*x/(u-1) ); 46 } 47 48 /* 49 * The Taylor expansion of ln(1 + x) for -1 < x <= 1 is: 50 * 51 * x - x^2/2 + x^3/3 - ... -(-x^j)/j 52 * 53 * Therefore, for small values of x, log1p(x) ~= x. For large 54 * values of x, log1p(x) ~= log(x). 55 * 56 * Also x/(x+1) < ln(1+x) < x 57 */ 58 59 static int testLog1p() { 60 int failures = 0; 61 62 double [][] testCases = { 63 {Double.NaN, NaNd}, 64 {Double.longBitsToDouble(0x7FF0000000000001L), NaNd}, 65 {Double.longBitsToDouble(0xFFF0000000000001L), NaNd}, 66 {Double.longBitsToDouble(0x7FF8555555555555L), NaNd}, 67 {Double.longBitsToDouble(0xFFF8555555555555L), NaNd}, 68 {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd}, 69 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd}, 70 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, 71 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, 72 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, 73 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, 74 {Double.NEGATIVE_INFINITY, NaNd}, 75 {-8.0, NaNd}, 76 {-1.0, -infinityD}, 77 {-0.0, -0.0}, 78 {+0.0, +0.0}, 79 {infinityD, infinityD}, 80 }; 81 82 // Test special cases 83 for(int i = 0; i < testCases.length; i++) { 84 failures += testLog1pCaseWithUlpDiff(testCases[i][0], 85 testCases[i][1], 0); 86 } 87 88 // For |x| < 2^-54 log1p(x) ~= x 89 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) { 90 double d = Math.scalb(2, i); 91 failures += testLog1pCase(d, d); 92 failures += testLog1pCase(-d, -d); 93 } 94 95 // For x > 2^53 log1p(x) ~= log(x) 96 for(int i = 53; i <= DoubleConsts.MAX_EXPONENT; i++) { 97 double d = Math.scalb(2, i); 98 failures += testLog1pCaseWithUlpDiff(d, StrictMath.log(d), 2.001); 99 } 100 101 // Construct random values with exponents ranging from -53 to 102 // 52 and compare against HP-15C formula. 103 java.util.Random rand = new java.util.Random(); 104 for(int i = 0; i < 1000; i++) { 105 double d = rand.nextDouble(); 106 107 d = Math.scalb(d, -53 - Tests.ilogb(d)); 108 109 for(int j = -53; j <= 52; j++) { 110 failures += testLog1pCaseWithUlpDiff(d, hp15cLogp(d), 5); 111 112 d *= 2.0; // increase exponent by 1 113 } 114 } 115 116 // Test for monotonicity failures near values y-1 where y ~= 117 // e^x. Test two numbers before and two numbers after each 118 // chosen value; i.e. 119 // 120 // pcNeighbors[] = 121 // {nextDown(nextDown(pc)), 122 // nextDown(pc), 123 // pc, 124 // nextUp(pc), 125 // nextUp(nextUp(pc))} 126 // 127 // and we test that log1p(pcNeighbors[i]) <= log1p(pcNeighbors[i+1]) 128 { 129 double pcNeighbors[] = new double[5]; 130 double pcNeighborsLog1p[] = new double[5]; 131 double pcNeighborsStrictLog1p[] = new double[5]; 132 133 for(int i = -36; i <= 36; i++) { 134 double pc = StrictMath.pow(Math.E, i) - 1; 135 136 pcNeighbors[2] = pc; 137 pcNeighbors[1] = Math.nextDown(pc); 138 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]); 139 pcNeighbors[3] = Math.nextUp(pc); 140 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]); 141 142 for(int j = 0; j < pcNeighbors.length; j++) { 143 pcNeighborsLog1p[j] = Math.log1p(pcNeighbors[j]); 144 pcNeighborsStrictLog1p[j] = StrictMath.log1p(pcNeighbors[j]); 145 } 146 147 for(int j = 0; j < pcNeighborsLog1p.length-1; j++) { 148 if(pcNeighborsLog1p[j] > pcNeighborsLog1p[j+1] ) { 149 failures++; 150 System.err.println("Monotonicity failure for Math.log1p on " + 151 pcNeighbors[j] + " and " + 152 pcNeighbors[j+1] + "\n\treturned " + 153 pcNeighborsLog1p[j] + " and " + 154 pcNeighborsLog1p[j+1] ); 155 } 156 157 if(pcNeighborsStrictLog1p[j] > pcNeighborsStrictLog1p[j+1] ) { 158 failures++; 159 System.err.println("Monotonicity failure for StrictMath.log1p on " + 160 pcNeighbors[j] + " and " + 161 pcNeighbors[j+1] + "\n\treturned " + 162 pcNeighborsStrictLog1p[j] + " and " + 163 pcNeighborsStrictLog1p[j+1] ); 164 } 165 166 167 } 168 169 } 170 } 171 172 return failures; 173 } 174 175 public static int testLog1pCase(double input, 176 double expected) { 177 return testLog1pCaseWithUlpDiff(input, expected, 1); 178 } 179 180 public static int testLog1pCaseWithUlpDiff(double input, 181 double expected, 182 double ulps) { 183 int failures = 0; 184 failures += Tests.testUlpDiff("Math.lop1p(double", 185 input, Math.log1p(input), 186 expected, ulps); 187 failures += Tests.testUlpDiff("StrictMath.log1p(double", 188 input, StrictMath.log1p(input), 189 expected, ulps); 190 return failures; 191 } 192 193 public static void main(String argv[]) { 194 int failures = 0; 195 196 failures += testLog1p(); 197 198 if (failures > 0) { 199 System.err.println("Testing log1p incurred " 200 + failures + " failures."); 201 throw new RuntimeException(); 202 } 203 } 204 }