1 /*
2 * Copyright (c) 2003, 2012, 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 4900189 4939441
27 * @summary Tests for {Math, StrictMath}.expm1
28 * @author Joseph D. Darcy
29 */
30
31 import sun.misc.DoubleConsts;
32
33 /*
34 * The Taylor expansion of expxm1(x) = exp(x) -1 is
35 *
36 * 1 + x/1! + x^2/2! + x^3/3| + ... -1 =
37 *
38 * x + x^2/2! + x^3/3 + ...
39 *
40 * Therefore, for small values of x, expxm1 ~= x.
41 *
42 * For large values of x, expxm1(x) ~= exp(x)
43 *
44 * For large negative x, expxm1(x) ~= -1.
45 */
46
47 public class Expm1Tests {
48
49 private Expm1Tests(){}
50
51 static final double infinityD = Double.POSITIVE_INFINITY;
52 static final double NaNd = Double.NaN;
53
54 static int testExpm1() {
55 int failures = 0;
56
57 double [][] testCases = {
58 {Double.NaN, NaNd},
59 {Double.longBitsToDouble(0x7FF0000000000001L), NaNd},
60 {Double.longBitsToDouble(0xFFF0000000000001L), NaNd},
61 {Double.longBitsToDouble(0x7FF8555555555555L), NaNd},
62 {Double.longBitsToDouble(0xFFF8555555555555L), NaNd},
63 {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd},
64 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd},
65 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd},
66 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd},
67 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd},
68 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd},
69 {infinityD, infinityD},
70 {-infinityD, -1.0},
71 {-0.0, -0.0},
72 {+0.0, +0.0},
73 };
74
75 // Test special cases
76 for(int i = 0; i < testCases.length; i++) {
77 failures += testExpm1CaseWithUlpDiff(testCases[i][0],
78 testCases[i][1], 0, null);
79 }
80
81
82 // For |x| < 2^-54 expm1(x) ~= x
83 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) {
84 double d = Math.scalb(2, i);
85 failures += testExpm1Case(d, d);
86 failures += testExpm1Case(-d, -d);
87 }
88
89
90 // For values of y where exp(y) > 2^54, expm1(x) ~= exp(x).
91 // The least such y is ln(2^54) ~= 37.42994775023705; exp(x)
92 // overflows for x > ~= 709.8
93
94 // Use a 2-ulp error threshold to account for errors in the
95 // exp implementation; the increments of d in the loop will be
96 // exact.
97 for(double d = 37.5; d <= 709.5; d += 1.0) {
98 failures += testExpm1CaseWithUlpDiff(d, StrictMath.exp(d), 2, null);
99 }
100
101 // For x > 710, expm1(x) should be infinity
102 for(int i = 10; i <= DoubleConsts.MAX_EXPONENT; i++) {
103 double d = Math.scalb(2, i);
104 failures += testExpm1Case(d, infinityD);
105 }
106
107 // By monotonicity, once the limit is reached, the
108 // implemenation should return the limit for all smaller
109 // values.
110 boolean reachedLimit [] = {false, false};
111
112 // Once exp(y) < 0.5 * ulp(1), expm1(y) ~= -1.0;
113 // The greatest such y is ln(2^-53) ~= -36.7368005696771.
114 for(double d = -36.75; d >= -127.75; d -= 1.0) {
115 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1,
116 reachedLimit);
117 }
118
119 for(int i = 7; i <= DoubleConsts.MAX_EXPONENT; i++) {
120 double d = -Math.scalb(2, i);
121 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit);
122 }
123
124 // Test for monotonicity failures near multiples of log(2).
125 // Test two numbers before and two numbers after each chosen
126 // value; i.e.
127 //
128 // pcNeighbors[] =
129 // {nextDown(nextDown(pc)),
130 // nextDown(pc),
131 // pc,
132 // nextUp(pc),
133 // nextUp(nextUp(pc))}
134 //
135 // and we test that expm1(pcNeighbors[i]) <= expm1(pcNeighbors[i+1])
136 {
137 double pcNeighbors[] = new double[5];
138 double pcNeighborsExpm1[] = new double[5];
139 double pcNeighborsStrictExpm1[] = new double[5];
140
141 for(int i = -50; i <= 50; i++) {
142 double pc = StrictMath.log(2)*i;
143
144 pcNeighbors[2] = pc;
145 pcNeighbors[1] = Math.nextDown(pc);
146 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
147 pcNeighbors[3] = Math.nextUp(pc);
148 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
149
150 for(int j = 0; j < pcNeighbors.length; j++) {
151 pcNeighborsExpm1[j] = Math.expm1(pcNeighbors[j]);
152 pcNeighborsStrictExpm1[j] = StrictMath.expm1(pcNeighbors[j]);
153 }
154
155 for(int j = 0; j < pcNeighborsExpm1.length-1; j++) {
156 if(pcNeighborsExpm1[j] > pcNeighborsExpm1[j+1] ) {
157 failures++;
158 System.err.println("Monotonicity failure for Math.expm1 on " +
159 pcNeighbors[j] + " and " +
160 pcNeighbors[j+1] + "\n\treturned " +
161 pcNeighborsExpm1[j] + " and " +
162 pcNeighborsExpm1[j+1] );
163 }
164
165 if(pcNeighborsStrictExpm1[j] > pcNeighborsStrictExpm1[j+1] ) {
166 failures++;
167 System.err.println("Monotonicity failure for StrictMath.expm1 on " +
168 pcNeighbors[j] + " and " +
169 pcNeighbors[j+1] + "\n\treturned " +
170 pcNeighborsStrictExpm1[j] + " and " +
171 pcNeighborsStrictExpm1[j+1] );
172 }
173
174
175 }
176
177 }
178 }
179
180 return failures;
181 }
182
183 public static int testExpm1Case(double input,
184 double expected) {
185 return testExpm1CaseWithUlpDiff(input, expected, 1, null);
186 }
187
188 public static int testExpm1CaseWithUlpDiff(double input,
189 double expected,
190 double ulps,
191 boolean [] reachedLimit) {
192 int failures = 0;
193 double mathUlps = ulps, strictUlps = ulps;
194 double mathOutput;
195 double strictOutput;
196
197 if (reachedLimit != null) {
198 if (reachedLimit[0])
199 mathUlps = 0;
200
201 if (reachedLimit[1])
202 strictUlps = 0;
203 }
204
205 failures += Tests.testUlpDiffWithLowerBound("Math.expm1(double)",
206 input, mathOutput=Math.expm1(input),
207 expected, mathUlps, -1.0);
208 failures += Tests.testUlpDiffWithLowerBound("StrictMath.expm1(double)",
209 input, strictOutput=StrictMath.expm1(input),
210 expected, strictUlps, -1.0);
211 if (reachedLimit != null) {
212 reachedLimit[0] |= (mathOutput == -1.0);
213 reachedLimit[1] |= (strictOutput == -1.0);
214 }
215
216 return failures;
217 }
218
219 public static void main(String argv[]) {
220 int failures = 0;
221
222 failures += testExpm1();
223
224 if (failures > 0) {
225 System.err.println("Testing expm1 incurred "
226 + failures + " failures.");
227 throw new RuntimeException();
228 }
229 }
230 }