1 /*
2 * Copyright (c) 2003, 2017, 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 * @library /test/lib
27 * @run main Log1pTests
28 * @bug 4851638 4939441 8078672
29 * @summary Tests for {Math, StrictMath}.log1p (use -Dseed=X to set PRNG seed)
30 * @author Joseph D. Darcy
31 * @key randomness
32 */
33
34 import jdk.test.lib.RandomFactory;
35
36 public class Log1pTests {
37 private Log1pTests(){}
38
39 static final double infinityD = Double.POSITIVE_INFINITY;
40 static final double NaNd = Double.NaN;
41
42 /**
43 * Formulation taken from HP-15C Advanced Functions Handbook, part
44 * number HP 0015-90011, p 181. This is accurate to a few ulps.
45 */
46 static double hp15cLogp(double x) {
47 double u = 1.0 + x;
48 return (u==1.0? x : StrictMath.log(u)*x/(u-1) );
49 }
50
51 /*
52 * The Taylor expansion of ln(1 + x) for -1 < x <= 1 is:
53 *
54 * x - x^2/2 + x^3/3 - ... -(-x^j)/j
55 *
56 * Therefore, for small values of x, log1p(x) ~= x. For large
57 * values of x, log1p(x) ~= log(x).
58 *
59 * Also x/(x+1) < ln(1+x) < x
60 */
61
62 static int testLog1p() {
63 int failures = 0;
64
65 double [][] testCases = {
66 {Double.NaN, NaNd},
67 {Double.longBitsToDouble(0x7FF0000000000001L), NaNd},
68 {Double.longBitsToDouble(0xFFF0000000000001L), NaNd},
69 {Double.longBitsToDouble(0x7FF8555555555555L), NaNd},
70 {Double.longBitsToDouble(0xFFF8555555555555L), NaNd},
71 {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd},
72 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd},
73 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd},
74 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd},
75 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd},
76 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd},
77 {Double.NEGATIVE_INFINITY, NaNd},
78 {-8.0, NaNd},
79 {-1.0, -infinityD},
80 {-0.0, -0.0},
81 {+0.0, +0.0},
82 {infinityD, infinityD},
83 };
84
85 // Test special cases
86 for(int i = 0; i < testCases.length; i++) {
87 failures += testLog1pCaseWithUlpDiff(testCases[i][0],
88 testCases[i][1], 0);
89 }
90
91 // For |x| < 2^-54 log1p(x) ~= x
92 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) {
93 double d = Math.scalb(2, i);
94 failures += testLog1pCase(d, d);
95 failures += testLog1pCase(-d, -d);
96 }
97
98 // For x > 2^53 log1p(x) ~= log(x)
99 for(int i = 53; i <= Double.MAX_EXPONENT; i++) {
100 double d = Math.scalb(2, i);
101 failures += testLog1pCaseWithUlpDiff(d, StrictMath.log(d), 2.001);
102 }
103
104 // Construct random values with exponents ranging from -53 to
105 // 52 and compare against HP-15C formula.
106 java.util.Random rand = RandomFactory.getRandom();
107 for(int i = 0; i < 1000; i++) {
108 double d = rand.nextDouble();
109
110 d = Math.scalb(d, -53 - Tests.ilogb(d));
111
112 for(int j = -53; j <= 52; j++) {
113 failures += testLog1pCaseWithUlpDiff(d, hp15cLogp(d), 5);
114
115 d *= 2.0; // increase exponent by 1
116 }
117 }
118
119 // Test for monotonicity failures near values y-1 where y ~=
120 // e^x. Test two numbers before and two numbers after each
121 // chosen value; i.e.
122 //
123 // pcNeighbors[] =
124 // {nextDown(nextDown(pc)),
125 // nextDown(pc),
126 // pc,
127 // nextUp(pc),
128 // nextUp(nextUp(pc))}
129 //
130 // and we test that log1p(pcNeighbors[i]) <= log1p(pcNeighbors[i+1])
131 {
132 double pcNeighbors[] = new double[5];
133 double pcNeighborsLog1p[] = new double[5];
134 double pcNeighborsStrictLog1p[] = new double[5];
135
136 for(int i = -36; i <= 36; i++) {
137 double pc = StrictMath.pow(Math.E, i) - 1;
138
139 pcNeighbors[2] = pc;
140 pcNeighbors[1] = Math.nextDown(pc);
141 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
142 pcNeighbors[3] = Math.nextUp(pc);
143 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
144
145 for(int j = 0; j < pcNeighbors.length; j++) {
146 pcNeighborsLog1p[j] = Math.log1p(pcNeighbors[j]);
147 pcNeighborsStrictLog1p[j] = StrictMath.log1p(pcNeighbors[j]);
148 }
149
150 for(int j = 0; j < pcNeighborsLog1p.length-1; j++) {
151 if(pcNeighborsLog1p[j] > pcNeighborsLog1p[j+1] ) {
152 failures++;
153 System.err.println("Monotonicity failure for Math.log1p on " +
154 pcNeighbors[j] + " and " +
155 pcNeighbors[j+1] + "\n\treturned " +
156 pcNeighborsLog1p[j] + " and " +
157 pcNeighborsLog1p[j+1] );
158 }
159
160 if(pcNeighborsStrictLog1p[j] > pcNeighborsStrictLog1p[j+1] ) {
161 failures++;
162 System.err.println("Monotonicity failure for StrictMath.log1p on " +
163 pcNeighbors[j] + " and " +
164 pcNeighbors[j+1] + "\n\treturned " +
165 pcNeighborsStrictLog1p[j] + " and " +
166 pcNeighborsStrictLog1p[j+1] );
167 }
168
169
170 }
171
172 }
173 }
174
175 return failures;
176 }
177
178 public static int testLog1pCase(double input,
179 double expected) {
180 return testLog1pCaseWithUlpDiff(input, expected, 1);
181 }
182
183 public static int testLog1pCaseWithUlpDiff(double input,
184 double expected,
185 double ulps) {
186 int failures = 0;
187 failures += Tests.testUlpDiff("Math.lop1p(double",
188 input, Math.log1p(input),
189 expected, ulps);
190 failures += Tests.testUlpDiff("StrictMath.log1p(double",
191 input, StrictMath.log1p(input),
192 expected, ulps);
193 return failures;
194 }
195
196 public static void main(String argv[]) {
197 int failures = 0;
198
199 failures += testLog1p();
200
201 if (failures > 0) {
202 System.err.println("Testing log1p incurred "
203 + failures + " failures.");
204 throw new RuntimeException();
205 }
206 }
207 }