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[/] [openrisc/] [trunk/] [gnu-src/] [gcc-4.5.1/] [libstdc++-v3/] [testsuite/] [tr1/] [5_numerical_facilities/] [special_functions/] [19_legendre/] [check_value.cc] - Blame information for rev 424

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Line No. Rev Author Line
1 424 jeremybenn
// 2007-02-04  Edward Smith-Rowland <3dw4rd@verizon.net>
2
//
3
// Copyright (C) 2007, 2009 Free Software Foundation, Inc.
4
//
5
// This file is part of the GNU ISO C++ Library.  This library is free
6
// software; you can redistribute it and/or modify it under the
7
// terms of the GNU General Public License as published by the
8
// Free Software Foundation; either version 3, or (at your option)
9
// any later version.
10
//
11
// This library is distributed in the hope that it will be useful,
12
// but WITHOUT ANY WARRANTY; without even the implied warranty of
13
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
14
// GNU General Public License for more details.
15
//
16
// You should have received a copy of the GNU General Public License along
17
// with this library; see the file COPYING3.  If not see
18
// <http://www.gnu.org/licenses/>.
19
 
20
//  legendre
21
 
22
 
23
//  Compare against values generated by the GNU Scientific Library.
24
//  The GSL can be found on the web: http://www.gnu.org/software/gsl/
25
 
26
#include <tr1/cmath>
27
#if defined(__TEST_DEBUG)
28
#include <iostream>
29
#define VERIFY(A) \
30
if (!(A)) \
31
  { \
32
    std::cout << "line " << __LINE__ \
33
      << "  max_abs_frac = " << max_abs_frac \
34
      << std::endl; \
35
  }
36
#else
37
#include <testsuite_hooks.h>
38
#endif
39
#include "../testcase.h"
40
 
41
 
42
// Test data for l=0.
43
testcase_legendre<double> data001[] = {
44
  { 1.0000000000000000, 0, -1.0000000000000000 },
45
  { 1.0000000000000000, 0, -0.90000000000000002 },
46
  { 1.0000000000000000, 0, -0.80000000000000004 },
47
  { 1.0000000000000000, 0, -0.69999999999999996 },
48
  { 1.0000000000000000, 0, -0.59999999999999998 },
49
  { 1.0000000000000000, 0, -0.50000000000000000 },
50
  { 1.0000000000000000, 0, -0.40000000000000002 },
51
  { 1.0000000000000000, 0, -0.30000000000000004 },
52
  { 1.0000000000000000, 0, -0.19999999999999996 },
53
  { 1.0000000000000000, 0, -0.099999999999999978 },
54
  { 1.0000000000000000, 0, 0.0000000000000000 },
55
  { 1.0000000000000000, 0, 0.10000000000000009 },
56
  { 1.0000000000000000, 0, 0.19999999999999996 },
57
  { 1.0000000000000000, 0, 0.30000000000000004 },
58
  { 1.0000000000000000, 0, 0.39999999999999991 },
59
  { 1.0000000000000000, 0, 0.50000000000000000 },
60
  { 1.0000000000000000, 0, 0.60000000000000009 },
61
  { 1.0000000000000000, 0, 0.69999999999999996 },
62
  { 1.0000000000000000, 0, 0.80000000000000004 },
63
  { 1.0000000000000000, 0, 0.89999999999999991 },
64
  { 1.0000000000000000, 0, 1.0000000000000000 },
65
};
66
 
67
// Test function for l=0.
68
template <typename Tp>
69
void test001()
70
{
71
  const Tp eps = std::numeric_limits<Tp>::epsilon();
72
  Tp max_abs_diff = -Tp(1);
73
  Tp max_abs_frac = -Tp(1);
74
  unsigned int num_datum = sizeof(data001)
75
                         / sizeof(testcase_legendre<double>);
76
  for (unsigned int i = 0; i < num_datum; ++i)
77
    {
78
      const Tp f = std::tr1::legendre(Tp(data001[i].l), Tp(data001[i].x));
79
      const Tp f0 = data001[i].f0;
80
      const Tp diff = f - f0;
81
      if (std::abs(diff) > max_abs_diff)
82
        max_abs_diff = std::abs(diff);
83
      if (std::abs(f0) > Tp(10) * eps
84
       && std::abs(f) > Tp(10) * eps)
85
        {
86
          const Tp frac = diff / f0;
87
          if (std::abs(frac) > max_abs_frac)
88
            max_abs_frac = std::abs(frac);
89
        }
90
    }
91
  VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
92
}
93
 
94
// Test data for l=1.
95
testcase_legendre<double> data002[] = {
96
  { -1.0000000000000000, 1, -1.0000000000000000 },
97
  { -0.90000000000000002, 1, -0.90000000000000002 },
98
  { -0.80000000000000004, 1, -0.80000000000000004 },
99
  { -0.69999999999999996, 1, -0.69999999999999996 },
100
  { -0.59999999999999998, 1, -0.59999999999999998 },
101
  { -0.50000000000000000, 1, -0.50000000000000000 },
102
  { -0.40000000000000002, 1, -0.40000000000000002 },
103
  { -0.30000000000000004, 1, -0.30000000000000004 },
104
  { -0.19999999999999996, 1, -0.19999999999999996 },
105
  { -0.099999999999999978, 1, -0.099999999999999978 },
106
  { 0.0000000000000000, 1, 0.0000000000000000 },
107
  { 0.10000000000000009, 1, 0.10000000000000009 },
108
  { 0.19999999999999996, 1, 0.19999999999999996 },
109
  { 0.30000000000000004, 1, 0.30000000000000004 },
110
  { 0.39999999999999991, 1, 0.39999999999999991 },
111
  { 0.50000000000000000, 1, 0.50000000000000000 },
112
  { 0.60000000000000009, 1, 0.60000000000000009 },
113
  { 0.69999999999999996, 1, 0.69999999999999996 },
114
  { 0.80000000000000004, 1, 0.80000000000000004 },
115
  { 0.89999999999999991, 1, 0.89999999999999991 },
116
  { 1.0000000000000000, 1, 1.0000000000000000 },
117
};
118
 
119
// Test function for l=1.
120
template <typename Tp>
121
void test002()
122
{
123
  const Tp eps = std::numeric_limits<Tp>::epsilon();
124
  Tp max_abs_diff = -Tp(1);
125
  Tp max_abs_frac = -Tp(1);
126
  unsigned int num_datum = sizeof(data002)
127
                         / sizeof(testcase_legendre<double>);
128
  for (unsigned int i = 0; i < num_datum; ++i)
129
    {
130
      const Tp f = std::tr1::legendre(Tp(data002[i].l), Tp(data002[i].x));
131
      const Tp f0 = data002[i].f0;
132
      const Tp diff = f - f0;
133
      if (std::abs(diff) > max_abs_diff)
134
        max_abs_diff = std::abs(diff);
135
      if (std::abs(f0) > Tp(10) * eps
136
       && std::abs(f) > Tp(10) * eps)
137
        {
138
          const Tp frac = diff / f0;
139
          if (std::abs(frac) > max_abs_frac)
140
            max_abs_frac = std::abs(frac);
141
        }
142
    }
143
  VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
144
}
145
 
146
// Test data for l=2.
147
testcase_legendre<double> data003[] = {
148
  { 1.0000000000000000, 2, -1.0000000000000000 },
149
  { 0.71500000000000008, 2, -0.90000000000000002 },
150
  { 0.46000000000000019, 2, -0.80000000000000004 },
151
  { 0.23499999999999988, 2, -0.69999999999999996 },
152
  { 0.039999999999999925, 2, -0.59999999999999998 },
153
  { -0.12500000000000000, 2, -0.50000000000000000 },
154
  { -0.25999999999999995, 2, -0.40000000000000002 },
155
  { -0.36499999999999999, 2, -0.30000000000000004 },
156
  { -0.44000000000000006, 2, -0.19999999999999996 },
157
  { -0.48499999999999999, 2, -0.099999999999999978 },
158
  { -0.50000000000000000, 2, 0.0000000000000000 },
159
  { -0.48499999999999999, 2, 0.10000000000000009 },
160
  { -0.44000000000000006, 2, 0.19999999999999996 },
161
  { -0.36499999999999999, 2, 0.30000000000000004 },
162
  { -0.26000000000000012, 2, 0.39999999999999991 },
163
  { -0.12500000000000000, 2, 0.50000000000000000 },
164
  { 0.040000000000000147, 2, 0.60000000000000009 },
165
  { 0.23499999999999988, 2, 0.69999999999999996 },
166
  { 0.46000000000000019, 2, 0.80000000000000004 },
167
  { 0.71499999999999986, 2, 0.89999999999999991 },
168
  { 1.0000000000000000, 2, 1.0000000000000000 },
169
};
170
 
171
// Test function for l=2.
172
template <typename Tp>
173
void test003()
174
{
175
  const Tp eps = std::numeric_limits<Tp>::epsilon();
176
  Tp max_abs_diff = -Tp(1);
177
  Tp max_abs_frac = -Tp(1);
178
  unsigned int num_datum = sizeof(data003)
179
                         / sizeof(testcase_legendre<double>);
180
  for (unsigned int i = 0; i < num_datum; ++i)
181
    {
182
      const Tp f = std::tr1::legendre(Tp(data003[i].l), Tp(data003[i].x));
183
      const Tp f0 = data003[i].f0;
184
      const Tp diff = f - f0;
185
      if (std::abs(diff) > max_abs_diff)
186
        max_abs_diff = std::abs(diff);
187
      if (std::abs(f0) > Tp(10) * eps
188
       && std::abs(f) > Tp(10) * eps)
189
        {
190
          const Tp frac = diff / f0;
191
          if (std::abs(frac) > max_abs_frac)
192
            max_abs_frac = std::abs(frac);
193
        }
194
    }
195
  VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
196
}
197
 
198
// Test data for l=5.
199
testcase_legendre<double> data004[] = {
200
  { -1.0000000000000000, 5, -1.0000000000000000 },
201
  { 0.041141249999999997, 5, -0.90000000000000002 },
202
  { 0.39951999999999993, 5, -0.80000000000000004 },
203
  { 0.36519874999999991, 5, -0.69999999999999996 },
204
  { 0.15263999999999994, 5, -0.59999999999999998 },
205
  { -0.089843750000000000, 5, -0.50000000000000000 },
206
  { -0.27063999999999988, 5, -0.40000000000000002 },
207
  { -0.34538624999999995, 5, -0.30000000000000004 },
208
  { -0.30751999999999996, 5, -0.19999999999999996 },
209
  { -0.17882874999999995, 5, -0.099999999999999978 },
210
  { 0.0000000000000000, 5, 0.0000000000000000 },
211
  { 0.17882875000000015, 5, 0.10000000000000009 },
212
  { 0.30751999999999996, 5, 0.19999999999999996 },
213
  { 0.34538624999999995, 5, 0.30000000000000004 },
214
  { 0.27064000000000010, 5, 0.39999999999999991 },
215
  { 0.089843750000000000, 5, 0.50000000000000000 },
216
  { -0.15264000000000022, 5, 0.60000000000000009 },
217
  { -0.36519874999999991, 5, 0.69999999999999996 },
218
  { -0.39951999999999993, 5, 0.80000000000000004 },
219
  { -0.041141250000000407, 5, 0.89999999999999991 },
220
  { 1.0000000000000000, 5, 1.0000000000000000 },
221
};
222
 
223
// Test function for l=5.
224
template <typename Tp>
225
void test004()
226
{
227
  const Tp eps = std::numeric_limits<Tp>::epsilon();
228
  Tp max_abs_diff = -Tp(1);
229
  Tp max_abs_frac = -Tp(1);
230
  unsigned int num_datum = sizeof(data004)
231
                         / sizeof(testcase_legendre<double>);
232
  for (unsigned int i = 0; i < num_datum; ++i)
233
    {
234
      const Tp f = std::tr1::legendre(Tp(data004[i].l), Tp(data004[i].x));
235
      const Tp f0 = data004[i].f0;
236
      const Tp diff = f - f0;
237
      if (std::abs(diff) > max_abs_diff)
238
        max_abs_diff = std::abs(diff);
239
      if (std::abs(f0) > Tp(10) * eps
240
       && std::abs(f) > Tp(10) * eps)
241
        {
242
          const Tp frac = diff / f0;
243
          if (std::abs(frac) > max_abs_frac)
244
            max_abs_frac = std::abs(frac);
245
        }
246
    }
247
  VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
248
}
249
 
250
// Test data for l=10.
251
testcase_legendre<double> data005[] = {
252
  { 1.0000000000000000, 10, -1.0000000000000000 },
253
  { -0.26314561785585977, 10, -0.90000000000000002 },
254
  { 0.30052979559999998, 10, -0.80000000000000004 },
255
  { 0.085805795531640333, 10, -0.69999999999999996 },
256
  { -0.24366274560000006, 10, -0.59999999999999998 },
257
  { -0.18822860717773438, 10, -0.50000000000000000 },
258
  { 0.096839064399999869, 10, -0.40000000000000002 },
259
  { 0.25147634951601561, 10, -0.30000000000000004 },
260
  { 0.12907202559999989, 10, -0.19999999999999996 },
261
  { -0.12212499738710947, 10, -0.099999999999999978 },
262
  { -0.24609375000000000, 10, 0.0000000000000000 },
263
  { -0.12212499738710922, 10, 0.10000000000000009 },
264
  { 0.12907202559999989, 10, 0.19999999999999996 },
265
  { 0.25147634951601561, 10, 0.30000000000000004 },
266
  { 0.096839064400000258, 10, 0.39999999999999991 },
267
  { -0.18822860717773438, 10, 0.50000000000000000 },
268
  { -0.24366274559999987, 10, 0.60000000000000009 },
269
  { 0.085805795531640333, 10, 0.69999999999999996 },
270
  { 0.30052979559999998, 10, 0.80000000000000004 },
271
  { -0.26314561785585888, 10, 0.89999999999999991 },
272
  { 1.0000000000000000, 10, 1.0000000000000000 },
273
};
274
 
275
// Test function for l=10.
276
template <typename Tp>
277
void test005()
278
{
279
  const Tp eps = std::numeric_limits<Tp>::epsilon();
280
  Tp max_abs_diff = -Tp(1);
281
  Tp max_abs_frac = -Tp(1);
282
  unsigned int num_datum = sizeof(data005)
283
                         / sizeof(testcase_legendre<double>);
284
  for (unsigned int i = 0; i < num_datum; ++i)
285
    {
286
      const Tp f = std::tr1::legendre(Tp(data005[i].l), Tp(data005[i].x));
287
      const Tp f0 = data005[i].f0;
288
      const Tp diff = f - f0;
289
      if (std::abs(diff) > max_abs_diff)
290
        max_abs_diff = std::abs(diff);
291
      if (std::abs(f0) > Tp(10) * eps
292
       && std::abs(f) > Tp(10) * eps)
293
        {
294
          const Tp frac = diff / f0;
295
          if (std::abs(frac) > max_abs_frac)
296
            max_abs_frac = std::abs(frac);
297
        }
298
    }
299
  VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
300
}
301
 
302
// Test data for l=20.
303
testcase_legendre<double> data006[] = {
304
  { 1.0000000000000000, 20, -1.0000000000000000 },
305
  { -0.14930823530984821, 20, -0.90000000000000002 },
306
  { 0.22420460541741344, 20, -0.80000000000000004 },
307
  { -0.20457394463834172, 20, -0.69999999999999996 },
308
  { 0.15916752910098114, 20, -0.59999999999999998 },
309
  { -0.048358381067373557, 20, -0.50000000000000000 },
310
  { -0.10159261558628156, 20, -0.40000000000000002 },
311
  { 0.18028715947998047, 20, -0.30000000000000004 },
312
  { -0.098042194344594741, 20, -0.19999999999999996 },
313
  { -0.082077130944527649, 20, -0.099999999999999978 },
314
  { 0.17619705200195312, 20, 0.0000000000000000 },
315
  { -0.082077130944528037, 20, 0.10000000000000009 },
316
  { -0.098042194344594741, 20, 0.19999999999999996 },
317
  { 0.18028715947998047, 20, 0.30000000000000004 },
318
  { -0.10159261558628112, 20, 0.39999999999999991 },
319
  { -0.048358381067373557, 20, 0.50000000000000000 },
320
  { 0.15916752910098084, 20, 0.60000000000000009 },
321
  { -0.20457394463834172, 20, 0.69999999999999996 },
322
  { 0.22420460541741344, 20, 0.80000000000000004 },
323
  { -0.14930823530984949, 20, 0.89999999999999991 },
324
  { 1.0000000000000000, 20, 1.0000000000000000 },
325
};
326
 
327
// Test function for l=20.
328
template <typename Tp>
329
void test006()
330
{
331
  const Tp eps = std::numeric_limits<Tp>::epsilon();
332
  Tp max_abs_diff = -Tp(1);
333
  Tp max_abs_frac = -Tp(1);
334
  unsigned int num_datum = sizeof(data006)
335
                         / sizeof(testcase_legendre<double>);
336
  for (unsigned int i = 0; i < num_datum; ++i)
337
    {
338
      const Tp f = std::tr1::legendre(Tp(data006[i].l), Tp(data006[i].x));
339
      const Tp f0 = data006[i].f0;
340
      const Tp diff = f - f0;
341
      if (std::abs(diff) > max_abs_diff)
342
        max_abs_diff = std::abs(diff);
343
      if (std::abs(f0) > Tp(10) * eps
344
       && std::abs(f) > Tp(10) * eps)
345
        {
346
          const Tp frac = diff / f0;
347
          if (std::abs(frac) > max_abs_frac)
348
            max_abs_frac = std::abs(frac);
349
        }
350
    }
351
  VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
352
}
353
 
354
// Test data for l=50.
355
testcase_legendre<double> data007[] = {
356
  { 1.0000000000000000, 50, -1.0000000000000000 },
357
  { -0.17003765994383685, 50, -0.90000000000000002 },
358
  { 0.13879737345093118, 50, -0.80000000000000004 },
359
  { -0.014572731645892805, 50, -0.69999999999999996 },
360
  { -0.058860798844002173, 50, -0.59999999999999998 },
361
  { -0.031059099239609828, 50, -0.50000000000000000 },
362
  { 0.041569033381825368, 50, -0.40000000000000002 },
363
  { 0.10911051574714808, 50, -0.30000000000000004 },
364
  { 0.083432272204197466, 50, -0.19999999999999996 },
365
  { -0.038205812661313579, 50, -0.099999999999999978 },
366
  { -0.11227517265921705, 50, 0.0000000000000000 },
367
  { -0.038205812661314169, 50, 0.10000000000000009 },
368
  { 0.083432272204197466, 50, 0.19999999999999996 },
369
  { 0.10911051574714808, 50, 0.30000000000000004 },
370
  { 0.041569033381824647, 50, 0.39999999999999991 },
371
  { -0.031059099239609828, 50, 0.50000000000000000 },
372
  { -0.058860798844001430, 50, 0.60000000000000009 },
373
  { -0.014572731645892805, 50, 0.69999999999999996 },
374
  { 0.13879737345093118, 50, 0.80000000000000004 },
375
  { -0.17003765994383663, 50, 0.89999999999999991 },
376
  { 1.0000000000000000, 50, 1.0000000000000000 },
377
};
378
 
379
// Test function for l=50.
380
template <typename Tp>
381
void test007()
382
{
383
  const Tp eps = std::numeric_limits<Tp>::epsilon();
384
  Tp max_abs_diff = -Tp(1);
385
  Tp max_abs_frac = -Tp(1);
386
  unsigned int num_datum = sizeof(data007)
387
                         / sizeof(testcase_legendre<double>);
388
  for (unsigned int i = 0; i < num_datum; ++i)
389
    {
390
      const Tp f = std::tr1::legendre(Tp(data007[i].l), Tp(data007[i].x));
391
      const Tp f0 = data007[i].f0;
392
      const Tp diff = f - f0;
393
      if (std::abs(diff) > max_abs_diff)
394
        max_abs_diff = std::abs(diff);
395
      if (std::abs(f0) > Tp(10) * eps
396
       && std::abs(f) > Tp(10) * eps)
397
        {
398
          const Tp frac = diff / f0;
399
          if (std::abs(frac) > max_abs_frac)
400
            max_abs_frac = std::abs(frac);
401
        }
402
    }
403
  VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
404
}
405
 
406
// Test data for l=100.
407
testcase_legendre<double> data008[] = {
408
  { 1.0000000000000000, 100, -1.0000000000000000 },
409
  { 0.10226582055871908, 100, -0.90000000000000002 },
410
  { 0.050861167913584124, 100, -0.80000000000000004 },
411
  { -0.077132507199778780, 100, -0.69999999999999996 },
412
  { -0.023747023905133110, 100, -0.59999999999999998 },
413
  { -0.060518025961861198, 100, -0.50000000000000000 },
414
  { -0.072258202125684429, 100, -0.40000000000000002 },
415
  { 0.057127392202801719, 100, -0.30000000000000004 },
416
  { 0.014681835355659636, 100, -0.19999999999999996 },
417
  { -0.063895098434750303, 100, -0.099999999999999978 },
418
  { 0.079589237387178727, 100, 0.0000000000000000 },
419
  { -0.063895098434749775, 100, 0.10000000000000009 },
420
  { 0.014681835355659636, 100, 0.19999999999999996 },
421
  { 0.057127392202801719, 100, 0.30000000000000004 },
422
  { -0.072258202125685012, 100, 0.39999999999999991 },
423
  { -0.060518025961861198, 100, 0.50000000000000000 },
424
  { -0.023747023905134217, 100, 0.60000000000000009 },
425
  { -0.077132507199778780, 100, 0.69999999999999996 },
426
  { 0.050861167913584124, 100, 0.80000000000000004 },
427
  { 0.10226582055871723, 100, 0.89999999999999991 },
428
  { 1.0000000000000000, 100, 1.0000000000000000 },
429
};
430
 
431
// Test function for l=100.
432
template <typename Tp>
433
void test008()
434
{
435
  const Tp eps = std::numeric_limits<Tp>::epsilon();
436
  Tp max_abs_diff = -Tp(1);
437
  Tp max_abs_frac = -Tp(1);
438
  unsigned int num_datum = sizeof(data008)
439
                         / sizeof(testcase_legendre<double>);
440
  for (unsigned int i = 0; i < num_datum; ++i)
441
    {
442
      const Tp f = std::tr1::legendre(Tp(data008[i].l), Tp(data008[i].x));
443
      const Tp f0 = data008[i].f0;
444
      const Tp diff = f - f0;
445
      if (std::abs(diff) > max_abs_diff)
446
        max_abs_diff = std::abs(diff);
447
      if (std::abs(f0) > Tp(10) * eps
448
       && std::abs(f) > Tp(10) * eps)
449
        {
450
          const Tp frac = diff / f0;
451
          if (std::abs(frac) > max_abs_frac)
452
            max_abs_frac = std::abs(frac);
453
        }
454
    }
455
  VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
456
}
457
 
458
int main(int, char**)
459
{
460
  test001<double>();
461
  test002<double>();
462
  test003<double>();
463
  test004<double>();
464
  test005<double>();
465
  test006<double>();
466
  test007<double>();
467
  test008<double>();
468
  return 0;
469
}

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