```   1 /*
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
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11  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
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13  * accompanied this code).
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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  *
20  * CA 95054 USA or visit www.sun.com if you need additional information or
21  * have any 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},
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]);
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
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 " +
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 }
```