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 4900189 4939441
27 * @summary Tests for {Math, StrictMath}.expm1
28 * @author Joseph D. Darcy
29 */
30
31 import sun.misc.DoubleConsts;
32 import sun.misc.FpUtils;
33
34 /*
35 * The Taylor expansion of expxm1(x) = exp(x) -1 is
36 *
37 * 1 + x/1! + x^2/2! + x^3/3| + ... -1 =
38 *
39 * x + x^2/2! + x^3/3 + ...
40 *
41 * Therefore, for small values of x, expxm1 ~= x.
42 *
43 * For large values of x, expxm1(x) ~= exp(x)
44 *
45 * For large negative x, expxm1(x) ~= -1.
46 */
47
48 public class Expm1Tests {
49
50 private Expm1Tests(){}
51
52 static final double infinityD = Double.POSITIVE_INFINITY;
53 static final double NaNd = Double.NaN;
54
55 static int testExpm1() {
56 int failures = 0;
57
58 double [][] testCases = {
59 {Double.NaN, NaNd},
60 {Double.longBitsToDouble(0x7FF0000000000001L), NaNd},
61 {Double.longBitsToDouble(0xFFF0000000000001L), NaNd},
62 {Double.longBitsToDouble(0x7FF8555555555555L), NaNd},
63 {Double.longBitsToDouble(0xFFF8555555555555L), NaNd},
64 {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd},
65 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd},
66 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd},
67 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd},
68 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd},
69 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd},
70 {infinityD, infinityD},
71 {-infinityD, -1.0},
72 {-0.0, -0.0},
73 {+0.0, +0.0},
74 };
75
76 // Test special cases
77 for(int i = 0; i < testCases.length; i++) {
78 failures += testExpm1CaseWithUlpDiff(testCases[i][0],
79 testCases[i][1], 0, null);
80 }
81
82
83 // For |x| < 2^-54 expm1(x) ~= x
84 for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) {
85 double d = FpUtils.scalb(2, i);
86 failures += testExpm1Case(d, d);
87 failures += testExpm1Case(-d, -d);
88 }
89
90
91 // For values of y where exp(y) > 2^54, expm1(x) ~= exp(x).
92 // The least such y is ln(2^54) ~= 37.42994775023705; exp(x)
93 // overflows for x > ~= 709.8
94
95 // Use a 2-ulp error threshold to account for errors in the
96 // exp implementation; the increments of d in the loop will be
97 // exact.
98 for(double d = 37.5; d <= 709.5; d += 1.0) {
99 failures += testExpm1CaseWithUlpDiff(d, StrictMath.exp(d), 2, null);
100 }
101
102 // For x > 710, expm1(x) should be infinity
103 for(int i = 10; i <= DoubleConsts.MAX_EXPONENT; i++) {
104 double d = FpUtils.scalb(2, i);
105 failures += testExpm1Case(d, infinityD);
106 }
107
108 // By monotonicity, once the limit is reached, the
109 // implemenation should return the limit for all smaller
110 // values.
111 boolean reachedLimit [] = {false, false};
112
113 // Once exp(y) < 0.5 * ulp(1), expm1(y) ~= -1.0;
114 // The greatest such y is ln(2^-53) ~= -36.7368005696771.
115 for(double d = -36.75; d >= -127.75; d -= 1.0) {
116 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1,
117 reachedLimit);
118 }
119
120 for(int i = 7; i <= DoubleConsts.MAX_EXPONENT; i++) {
121 double d = -FpUtils.scalb(2, i);
122 failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit);
123 }
124
125 // Test for monotonicity failures near multiples of log(2).
126 // Test two numbers before and two numbers after each chosen
127 // value; i.e.
128 //
129 // pcNeighbors[] =
130 // {nextDown(nextDown(pc)),
131 // nextDown(pc),
132 // pc,
133 // nextUp(pc),
134 // nextUp(nextUp(pc))}
135 //
136 // and we test that expm1(pcNeighbors[i]) <= expm1(pcNeighbors[i+1])
137 {
138 double pcNeighbors[] = new double[5];
139 double pcNeighborsExpm1[] = new double[5];
140 double pcNeighborsStrictExpm1[] = new double[5];
141
142 for(int i = -50; i <= 50; i++) {
143 double pc = StrictMath.log(2)*i;
144
145 pcNeighbors[2] = pc;
146 pcNeighbors[1] = FpUtils.nextDown(pc);
147 pcNeighbors[0] = FpUtils.nextDown(pcNeighbors[1]);
148 pcNeighbors[3] = FpUtils.nextUp(pc);
149 pcNeighbors[4] = FpUtils.nextUp(pcNeighbors[3]);
150
151 for(int j = 0; j < pcNeighbors.length; j++) {
152 pcNeighborsExpm1[j] = Math.expm1(pcNeighbors[j]);
153 pcNeighborsStrictExpm1[j] = StrictMath.expm1(pcNeighbors[j]);
154 }
155
156 for(int j = 0; j < pcNeighborsExpm1.length-1; j++) {
157 if(pcNeighborsExpm1[j] > pcNeighborsExpm1[j+1] ) {
158 failures++;
159 System.err.println("Monotonicity failure for Math.expm1 on " +
160 pcNeighbors[j] + " and " +
161 pcNeighbors[j+1] + "\n\treturned " +
162 pcNeighborsExpm1[j] + " and " +
163 pcNeighborsExpm1[j+1] );
164 }
165
166 if(pcNeighborsStrictExpm1[j] > pcNeighborsStrictExpm1[j+1] ) {
167 failures++;
168 System.err.println("Monotonicity failure for StrictMath.expm1 on " +
169 pcNeighbors[j] + " and " +
170 pcNeighbors[j+1] + "\n\treturned " +
171 pcNeighborsStrictExpm1[j] + " and " +
172 pcNeighborsStrictExpm1[j+1] );
173 }
174
175
176 }
177
178 }
179 }
180
181 return failures;
182 }
183
184 public static int testExpm1Case(double input,
185 double expected) {
186 return testExpm1CaseWithUlpDiff(input, expected, 1, null);
187 }
188
189 public static int testExpm1CaseWithUlpDiff(double input,
190 double expected,
191 double ulps,
192 boolean [] reachedLimit) {
193 int failures = 0;
194 double mathUlps = ulps, strictUlps = ulps;
195 double mathOutput;
196 double strictOutput;
197
198 if (reachedLimit != null) {
199 if (reachedLimit[0])
200 mathUlps = 0;
201
202 if (reachedLimit[1])
203 strictUlps = 0;
204 }
205
206 failures += Tests.testUlpDiffWithLowerBound("Math.expm1(double)",
207 input, mathOutput=Math.expm1(input),
208 expected, mathUlps, -1.0);
209 failures += Tests.testUlpDiffWithLowerBound("StrictMath.expm1(double)",
210 input, strictOutput=StrictMath.expm1(input),
211 expected, strictUlps, -1.0);
212 if (reachedLimit != null) {
213 reachedLimit[0] |= (mathOutput == -1.0);
214 reachedLimit[1] |= (strictOutput == -1.0);
215 }
216
217 return failures;
218 }
219
220 public static void main(String argv[]) {
221 int failures = 0;
222
223 failures += testExpm1();
224
225 if (failures > 0) {
226 System.err.println("Testing expm1 incurred "
227 + failures + " failures.");
228 throw new RuntimeException();
229 }
230 }
231 }