1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
|
// (C) Copyright John Maddock 2007.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#include <pch.hpp>
#include <boost/math/concepts/real_concept.hpp>
#include <boost/math/special_functions/expint.hpp>
#include <boost/math/special_functions/trunc.hpp>
#include <boost/test/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/tools/stats.hpp>
#include <boost/math/tools/test.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/array.hpp>
#include "functor.hpp"
#include "handle_test_result.hpp"
#include "test_expint_hooks.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the expint functions. There are two sets of tests:
// 1) Sanity checks: comparison to test values created with the
// online calculator at functions.wolfram.com
// 2) Accuracy tests use values generated with NTL::RR at
// 1000-bit precision and our generic versions of these functions.
//
// Note that when this file is first run on a new platform many of
// these tests will fail: the default accuracy is 1 epsilon which
// is too tight for most platforms. In this situation you will
// need to cast a human eye over the error rates reported and make
// a judgement as to whether they are acceptable. Either way please
// report the results to the Boost mailing list. Acceptable rates of
// error are marked up below as a series of regular expressions that
// identify the compiler/stdlib/platform/data-type/test-data/test-function
// along with the maximum expected peek and RMS mean errors for that
// test.
//
void expected_results()
{
//
// Define the max and mean errors expected for
// various compilers and platforms.
//
const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
{
largest_type = "(long\\s+)?double";
}
else
{
largest_type = "long double";
}
#else
largest_type = "(long\\s+)?double";
#endif
//
// On MacOS X erfc has much higher error levels than
// expected: given that the implementation is basically
// just a rational function evaluation combined with
// exponentiation, we conclude that exp and pow are less
// accurate on this platform, especially when the result
// is outside the range of a double.
//
add_expected_result(
".*", // compiler
".*", // stdlib
"Mac OS", // platform
"float|double|long double", // test type(s)
".*E1.*", // test data group
".*", 30, 10); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"Mac OS", // platform
"float|double|long double", // test type(s)
".*Ei.*", // test data group
".*", 300, 200); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"Mac OS", // platform
".*", // test type(s)
".*", // test data group
".*", 40, 15); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"float|double|long double", // test type(s)
".*E1.*", // test data group
".*", 2, 1); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"float|double|long double", // test type(s)
".*Ei.*", // test data group
".*", 6, 3); // test function
if(std::numeric_limits<long double>::digits > 100)
{
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*Ei.*", // test data group
".*", 150, 50); // test function
}
add_expected_result(
"Sun.*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*Ei.*", // test data group
".*", 150, 50); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*Ei.*", // test data group
".*", 50, 20); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
".*", // test type(s)
".*", // test data group
".*", 25, 5); // test function
std::cout << "Tests run with " << BOOST_COMPILER << ", "
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
template <class T>
T expint_wrapper(T n, T z)
{
return boost::math::expint(
boost::math::itrunc(n), z);
}
#ifdef TEST_OTHER
template <class T>
T other_expint_wrapper(T n, T z)
{
return other::expint(
boost::math::itrunc(n), z);
}
#endif
template <class T>
void do_test_expint(const T& data, const char* type_name, const char* test_name)
{
//
// test En(T) against data:
//
using namespace std;
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
std::cout << test_name << " with type " << type_name << std::endl;
typedef value_type (*pg)(value_type, value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = expint_wrapper<value_type>;
#else
pg funcp = expint_wrapper;
#endif
boost::math::tools::test_result<value_type> result;
//
// test expint against data:
//
result = boost::math::tools::test(
data,
bind_func(funcp, 0, 1),
extract_result(2));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::expint", test_name);
#ifdef TEST_OTHER
if(boost::is_floating_point<value_type>::value && other::expint(2u, 2.0))
{
funcp = other_expint_wrapper;
//
// test expint against data:
//
result = boost::math::tools::test(
data,
bind_func(funcp, 0, 1),
extract_result(2));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "other::expint", test_name);
}
#endif
std::cout << std::endl;
}
template <class T>
void do_test_expint_Ei(const T& data, const char* type_name, const char* test_name)
{
//
// test Ei(T) against data:
//
using namespace std;
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
std::cout << test_name << " with type " << type_name << std::endl;
typedef value_type (*pg)(value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::expint<value_type>;
#else
pg funcp = boost::math::expint;
#endif
boost::math::tools::test_result<value_type> result;
//
// test expint against data:
//
result = boost::math::tools::test(
data,
bind_func(funcp, 0),
extract_result(1));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::expint", test_name);
#ifdef TEST_OTHER
if(boost::is_floating_point<value_type>::value && other::expint(2.0))
{
funcp = other::expint;
//
// test expint against data:
//
result = boost::math::tools::test(
data,
bind_func(funcp, 0),
extract_result(1));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "other::expint", test_name);
}
#endif
}
template <class T>
void test_expint(T, const char* name)
{
//
// The actual test data is rather verbose, so it's in a separate file
//
#include "expint_data.ipp"
do_test_expint(expint_data, name, "Exponential Integral En");
#include "expint_small_data.ipp"
do_test_expint(expint_small_data, name, "Exponential Integral En: small z values");
#include "expint_1_data.ipp"
do_test_expint(expint_1_data, name, "Exponential Integral E1");
#include "expinti_data.ipp"
do_test_expint_Ei(expinti_data, name, "Exponential Integral Ei");
if(boost::math::tools::log_max_value<T>() > 100)
{
#include "expinti_data_double.ipp"
do_test_expint_Ei(expinti_data_double, name, "Exponential Integral Ei: double exponent range");
}
#if defined(LDBL_MAX_10_EXP) && (LDBL_MAX_10_EXP > 2000)
if(boost::math::tools::log_max_value<T>() > 1000)
{
#include "expinti_data_long.ipp"
do_test_expint_Ei(expinti_data_long, name, "Exponential Integral Ei: long exponent range");
}
#endif
}
template <class T>
void test_spots(T, const char* t)
{
std::cout << "Testing basic sanity checks for type " << t << std::endl;
//
// Basic sanity checks, tolerance is 100 epsilon
// expressed as a percentage:
//
T tolerance = boost::math::tools::epsilon<T>() * 100 *
(boost::is_floating_point<T>::value ? 500 : 500);
//
// En:
//
BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast<T>(1)/1024), static_cast<T>(1023.0004881223430781283448725609773366468629307172L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast<T>(0.125F)), static_cast<T>(7.0599752206767632229191371458324058897760385999252L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast<T>(0.5F)), static_cast<T>(1.2130613194252668472075990699823609068838362709744L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast<T>(1.5F)), static_cast<T>(0.14875344009895321928885364717600834756144775290739L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast<T>(4.5F)), static_cast<T>(0.0024686658973871792213651409526512283936753927790603L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast<T>(50.0F)), static_cast<T>(3.8574996959278355660346856330540251495056653024605e-24L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast<T>(1)/1024), static_cast<T>(6.3552324648310718026144555193580322129376300855378L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast<T>(0.125F)), static_cast<T>(1.6234256405841687914563069246244088736331060573721L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast<T>(0.5F)), static_cast<T>(0.55977359477616081174679593931508523522684689031635L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast<T>(1.5F)), static_cast<T>(0.10001958240663265190190933991166697826173000614035L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast<T>(4.5F)), static_cast<T>(0.0020734007547146144328855938695797884889319725701443L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast<T>(50.0F)), static_cast<T>(3.7832640295504590186989678540212857803028931862511e-24L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast<T>(1)/1024), static_cast<T>(0.99281763247803906867747111039220635198625517639812L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast<T>(0.125F)), static_cast<T>(0.67956869751157430393285377765099962701786656781914L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast<T>(0.5F)), static_cast<T>(0.32664386232455301773040156533363783582849469032901L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast<T>(1.5F)), static_cast<T>(0.073100786538480851080416460896512053949576620150553L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast<T>(4.5F)), static_cast<T>(0.0017786931420265415481579618738214795713453909401220L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast<T>(50.0F)), static_cast<T>(3.7117833188688273667858889516369684601386058104706e-24L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast<T>(1)/1024), static_cast<T>(0.24967471743034509414923673526350536071348482068601L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast<T>(0.125F)), static_cast<T>(0.21195078838966585733668853784460504343264488743527L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast<T>(0.5F)), static_cast<T>(0.13097731169586484777931864012654136046214618229236L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast<T>(1.5F)), static_cast<T>(0.038529924425495155395971538166055731456940831714065L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast<T>(4.5F)), static_cast<T>(0.0012311157382296328534406162790653865883418172939975L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast<T>(50.0F)), static_cast<T>(3.5124400631332394056901125740903320085753990490695e-24L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast<T>(1)/1024), static_cast<T>(0.047570244582119027573000641518739337055625638422014L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast<T>(0.125F)), static_cast<T>(0.041762730174712898120606793100375713866392079558609L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast<T>(0.5F)), static_cast<T>(0.028178840877963713109230354192609362941651630844684L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast<T>(1.5F)), static_cast<T>(0.0098864453561701486668317763826728620676449196215016L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast<T>(4.5F)), static_cast<T>(0.00043257793497205419001613830279995985617548506505159L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast<T>(50.0F)), static_cast<T>(2.6900194251201629500599598206345018300567305625080e-24L), tolerance);
//
// Ei:
//
BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(1)/1024), static_cast<T>(-6.35327933972759151358547423727042905862963067106751711596065L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(0.125)), static_cast<T>(-1.37320852494298333781545045921206470808223543321810480716122L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(0.5)), static_cast<T>(0.454219904863173579920523812662802365281405554352642045162818L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(1)), static_cast<T>(1.89511781635593675546652093433163426901706058173270759164623L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(50.5)), static_cast<T>(1.72763195602911805201155668940185673806099654090456049881069e20L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(-1)/1024), static_cast<T>(-6.35523246483107180261445551935803221293763008553775821607264L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(-0.125)), static_cast<T>(-1.62342564058416879145630692462440887363310605737209536579267L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(-0.5)), static_cast<T>(-0.559773594776160811746795939315085235226846890316353515248293L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(-1)), static_cast<T>(-0.219383934395520273677163775460121649031047293406908207577979L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::expint(static_cast<T>(-50.5)), static_cast<T>(-2.27237132932219350440719707268817831250090574830769670186618e-24L), tolerance);
}
int test_main(int, char* [])
{
expected_results();
BOOST_MATH_CONTROL_FP;
boost::math::expint(114.7);
test_spots(0.0f, "float");
test_spots(0.0, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_spots(0.0L, "long double");
test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
#else
std::cout << "<note>The long double tests have been disabled on this platform "
"either because the long double overloads of the usual math functions are "
"not available at all, or because they are too inaccurate for these tests "
"to pass.</note>" << std::cout;
#endif
test_expint(0.1F, "float");
test_expint(0.1, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_expint(0.1L, "long double");
test_expint(boost::math::concepts::real_concept(0.1), "real_concept");
#else
std::cout << "<note>The long double tests have been disabled on this platform "
"either because the long double overloads of the usual math functions are "
"not available at all, or because they are too inaccurate for these tests "
"to pass.</note>" << std::cout;
#endif
return 0;
}
|
