1 /*
2 * Copyright (c) 2003, 2015, 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 /lib/testlibrary/
27 * @build jdk.testlibrary.*
28 * @run main Log1pTests
29 * @bug 4851638 4939441 8078672
30 * @summary Tests for {Math, StrictMath}.log1p (use -Dseed=X to set PRNG seed)
31 * @author Joseph D. Darcy
32 * @key randomness
33 */
34
35 public class Log1pTests {
36 private Log1pTests(){}
37
38 static final double infinityD = Double.POSITIVE_INFINITY;
39 static final double NaNd = Double.NaN;
40
41 /**
42 * Formulation taken from HP-15C Advanced Functions Handbook, part
43 * number HP 0015-90011, p 181. This is accurate to a few ulps.
44 */
45 static double hp15cLogp(double x) {
46 double u = 1.0 + x;
47 return (u==1.0? x : StrictMath.log(u)*x/(u-1) );
48 }
49
50 /*
51 * The Taylor expansion of ln(1 + x) for -1 < x <= 1 is:
52 *
53 * x - x^2/2 + x^3/3 - ... -(-x^j)/j
54 *
55 * Therefore, for small values of x, log1p(x) ~= x. For large
56 * values of x, log1p(x) ~= log(x).
57 *
58 * Also x/(x+1) < ln(1+x) < x
59 */
60
61 static int testLog1p() {
62 int failures = 0;
63
64 double [][] testCases = {
65 {Double.NaN, NaNd},
66 {Double.longBitsToDouble(0x7FF0000000000001L), NaNd},
67 {Double.longBitsToDouble(0xFFF0000000000001L), NaNd},
68 {Double.longBitsToDouble(0x7FF8555555555555L), NaNd},
69 {Double.longBitsToDouble(0xFFF8555555555555L), NaNd},
70 {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd},
71 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd},
72 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd},
73 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd},
74 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd},
75 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd},
76 {Double.NEGATIVE_INFINITY, NaNd},
77 {-8.0, NaNd},
78 {-1.0, -infinityD},
79 {-0.0, -0.0},
80 {+0.0, +0.0},
81 {infinityD, infinityD},
82 };
83
84 // Test special cases
85 for(int i = 0; i < testCases.length; i++) {
86 failures += testLog1pCaseWithUlpDiff(testCases[i][0],
87 testCases[i][1], 0);
88 }
89
90 // For |x| < 2^-54 log1p(x) ~= x
91 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) {
92 double d = Math.scalb(2, i);
93 failures += testLog1pCase(d, d);
94 failures += testLog1pCase(-d, -d);
95 }
96
97 // For x > 2^53 log1p(x) ~= log(x)
98 for(int i = 53; i <= Double.MAX_EXPONENT; i++) {
99 double d = Math.scalb(2, i);
100 failures += testLog1pCaseWithUlpDiff(d, StrictMath.log(d), 2.001);
101 }
102
103 // Construct random values with exponents ranging from -53 to
104 // 52 and compare against HP-15C formula.
105 java.util.Random rand = RandomFactory.getRandom();
106 for(int i = 0; i < 1000; i++) {
107 double d = rand.nextDouble();
108
109 d = Math.scalb(d, -53 - Tests.ilogb(d));
110
111 for(int j = -53; j <= 52; j++) {
112 failures += testLog1pCaseWithUlpDiff(d, hp15cLogp(d), 5);
113
114 d *= 2.0; // increase exponent by 1
115 }
116 }
117
118 // Test for monotonicity failures near values y-1 where y ~=
119 // e^x. Test two numbers before and two numbers after each
120 // chosen value; i.e.
121 //
122 // pcNeighbors[] =
123 // {nextDown(nextDown(pc)),
124 // nextDown(pc),
125 // pc,
126 // nextUp(pc),
127 // nextUp(nextUp(pc))}
128 //
129 // and we test that log1p(pcNeighbors[i]) <= log1p(pcNeighbors[i+1])
130 {
131 double pcNeighbors[] = new double[5];
132 double pcNeighborsLog1p[] = new double[5];
133 double pcNeighborsStrictLog1p[] = new double[5];
134
135 for(int i = -36; i <= 36; i++) {
136 double pc = StrictMath.pow(Math.E, i) - 1;
137
138 pcNeighbors[2] = pc;
139 pcNeighbors[1] = Math.nextDown(pc);
140 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
141 pcNeighbors[3] = Math.nextUp(pc);
142 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
143
144 for(int j = 0; j < pcNeighbors.length; j++) {
145 pcNeighborsLog1p[j] = Math.log1p(pcNeighbors[j]);
146 pcNeighborsStrictLog1p[j] = StrictMath.log1p(pcNeighbors[j]);
147 }
148
149 for(int j = 0; j < pcNeighborsLog1p.length-1; j++) {
150 if(pcNeighborsLog1p[j] > pcNeighborsLog1p[j+1] ) {
151 failures++;
152 System.err.println("Monotonicity failure for Math.log1p on " +
153 pcNeighbors[j] + " and " +
154 pcNeighbors[j+1] + "\n\treturned " +
155 pcNeighborsLog1p[j] + " and " +
156 pcNeighborsLog1p[j+1] );
157 }
158
159 if(pcNeighborsStrictLog1p[j] > pcNeighborsStrictLog1p[j+1] ) {
160 failures++;
161 System.err.println("Monotonicity failure for StrictMath.log1p on " +
162 pcNeighbors[j] + " and " +
163 pcNeighbors[j+1] + "\n\treturned " +
164 pcNeighborsStrictLog1p[j] + " and " +
165 pcNeighborsStrictLog1p[j+1] );
166 }
167
168
169 }
170
171 }
172 }
173
174 return failures;
175 }
176
177 public static int testLog1pCase(double input,
178 double expected) {
179 return testLog1pCaseWithUlpDiff(input, expected, 1);
180 }
181
182 public static int testLog1pCaseWithUlpDiff(double input,
183 double expected,
184 double ulps) {
185 int failures = 0;
186 failures += Tests.testUlpDiff("Math.lop1p(double",
187 input, Math.log1p(input),
188 expected, ulps);
189 failures += Tests.testUlpDiff("StrictMath.log1p(double",
190 input, StrictMath.log1p(input),
191 expected, ulps);
192 return failures;
193 }
194
195 public static void main(String argv[]) {
196 int failures = 0;
197
198 failures += testLog1p();
199
200 if (failures > 0) {
201 System.err.println("Testing log1p incurred "
202 + failures + " failures.");
203 throw new RuntimeException();
204 }
205 }
206 }