```   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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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).
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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  * or visit www.oracle.com if you need additional information or have any
21  * questions.
22  */
23
24 /*
25  * @test
26  * @bug 4851638 4939441
27  * @summary Tests for {Math, StrictMath}.log1p
28  * @author Joseph D. Darcy
29  */
30
31 public class Log1pTests {
32     private Log1pTests(){}
33
34     static final double infinityD = Double.POSITIVE_INFINITY;
35     static final double NaNd = Double.NaN;
36
37     /**
38      * Formulation taken from HP-15C Advanced Functions Handbook, part
39      * number HP 0015-90011, p 181.  This is accurate to a few ulps.
40      */
41     static double hp15cLogp(double x) {
42         double u = 1.0 + x;
43         return (u==1.0? x : StrictMath.log(u)*x/(u-1) );
44     }
45
46     /*
47      * The Taylor expansion of ln(1 + x) for -1 < x <= 1 is:
48      *
49      * x - x^2/2 + x^3/3 - ... -(-x^j)/j
50      *
51      * Therefore, for small values of x, log1p(x) ~= x.  For large
52      * values of x, log1p(x) ~= log(x).
53      *
54      * Also x/(x+1) < ln(1+x) < x
55      */
56
57     static int testLog1p() {
58         int failures = 0;
59
60         double [][] testCases = {
61             {Double.NaN,                NaNd},
62             {Double.longBitsToDouble(0x7FF0000000000001L),      NaNd},
63             {Double.longBitsToDouble(0xFFF0000000000001L),      NaNd},
64             {Double.longBitsToDouble(0x7FF8555555555555L),      NaNd},
65             {Double.longBitsToDouble(0xFFF8555555555555L),      NaNd},
66             {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL),      NaNd},
67             {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL),      NaNd},
70             {Double.longBitsToDouble(0x7FFCafeBabe00000L),      NaNd},
71             {Double.longBitsToDouble(0xFFFCafeBabe00000L),      NaNd},
72             {Double.NEGATIVE_INFINITY,  NaNd},
73             {-8.0,                      NaNd},
74             {-1.0,                      -infinityD},
75             {-0.0,                      -0.0},
76             {+0.0,                      +0.0},
77             {infinityD,                 infinityD},
78         };
79
80         // Test special cases
81         for(int i = 0; i < testCases.length; i++) {
82             failures += testLog1pCaseWithUlpDiff(testCases[i][0],
83                                                  testCases[i][1], 0);
84         }
85
86         // For |x| < 2^-54 log1p(x) ~= x
87         for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) {
88             double d = Math.scalb(2, i);
89             failures += testLog1pCase(d, d);
90             failures += testLog1pCase(-d, -d);
91         }
92
93         // For x > 2^53 log1p(x) ~= log(x)
94         for(int i = 53; i <= Double.MAX_EXPONENT; i++) {
95             double d = Math.scalb(2, i);
96             failures += testLog1pCaseWithUlpDiff(d, StrictMath.log(d), 2.001);
97         }
98
99         // Construct random values with exponents ranging from -53 to
100         // 52 and compare against HP-15C formula.
101         java.util.Random rand = new java.util.Random();
102         for(int i = 0; i < 1000; i++) {
103             double d = rand.nextDouble();
104
105             d = Math.scalb(d, -53 - Tests.ilogb(d));
106
107             for(int j = -53; j <= 52; j++) {
108                 failures += testLog1pCaseWithUlpDiff(d, hp15cLogp(d), 5);
109
110                 d *= 2.0; // increase exponent by 1
111             }
112         }
113
114         // Test for monotonicity failures near values y-1 where y ~=
115         // e^x.  Test two numbers before and two numbers after each
116         // chosen value; i.e.
117         //
118         // pcNeighbors[] =
119         // {nextDown(nextDown(pc)),
120         // nextDown(pc),
121         // pc,
122         // nextUp(pc),
123         // nextUp(nextUp(pc))}
124         //
125         // and we test that log1p(pcNeighbors[i]) <= log1p(pcNeighbors[i+1])
126         {
127             double pcNeighbors[] = new double[5];
128             double pcNeighborsLog1p[] = new double[5];
129             double pcNeighborsStrictLog1p[] = new double[5];
130
131             for(int i = -36; i <= 36; i++) {
132                 double pc = StrictMath.pow(Math.E, i) - 1;
133
134                 pcNeighbors[2] = pc;
135                 pcNeighbors[1] = Math.nextDown(pc);
136                 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
137                 pcNeighbors[3] = Math.nextUp(pc);
138                 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
139
140                 for(int j = 0; j < pcNeighbors.length; j++) {
141                     pcNeighborsLog1p[j]       =       Math.log1p(pcNeighbors[j]);
143                 }
144
145                 for(int j = 0; j < pcNeighborsLog1p.length-1; j++) {
146                     if(pcNeighborsLog1p[j] >  pcNeighborsLog1p[j+1] ) {
147                         failures++;
148                         System.err.println("Monotonicity failure for Math.log1p on " +
149                                           pcNeighbors[j] + " and "  +
150                                           pcNeighbors[j+1] + "\n\treturned " +
151                                           pcNeighborsLog1p[j] + " and " +
152                                           pcNeighborsLog1p[j+1] );
153                     }
154
156                         failures++;
157                         System.err.println("Monotonicity failure for StrictMath.log1p on " +
158                                           pcNeighbors[j] + " and "  +
159                                           pcNeighbors[j+1] + "\n\treturned " +
160                                           pcNeighborsStrictLog1p[j] + " and " +
162                     }
163
164
165                 }
166
167             }
168         }
169
170         return failures;
171     }
172
173     public static int testLog1pCase(double input,
174                                     double expected) {
175         return testLog1pCaseWithUlpDiff(input, expected, 1);
176     }
177
178     public static int testLog1pCaseWithUlpDiff(double input,
179                                                double expected,
180                                                double ulps) {
181         int failures = 0;
182         failures += Tests.testUlpDiff("Math.lop1p(double",
183                                       input, Math.log1p(input),
184                                       expected, ulps);
185         failures += Tests.testUlpDiff("StrictMath.log1p(double",
186                                       input, StrictMath.log1p(input),
187                                       expected, ulps);
188         return failures;
189     }
190
191     public static void main(String argv[]) {
192         int failures = 0;
193
194         failures += testLog1p();
195
196         if (failures > 0) {
197             System.err.println("Testing log1p incurred "
198                                + failures + " failures.");
199             throw new RuntimeException();
200         }
201     }
202 }
```