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
45public 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}
229