1 /*
2 * Copyright (c) 2003, 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 import sun.misc.FpUtils;
33
34 public 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] = FpUtils.nextDown(pc);
139 pcNeighbors[0] = FpUtils.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 }