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