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