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
|
// Copyright John Maddock 2006.
// Copyright Paul A. Bristow 2007, 2009
// Copyright Matt Borland 2024.
// 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 <boost/math/tools/config.hpp>
#include <boost/math/concepts/real_concept.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/math/special_functions/math_fwd.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 "table_type.hpp"
#ifndef SC_
#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
#endif
#ifdef BOOST_MATH_NO_EXCEPTIONS
# undef BOOST_CHECK_THROW
# define BOOST_CHECK_THROW(x, y)
#endif
template <class Real, class T>
void do_test_erf(const T& data, const char* type_name, const char* test_name)
{
typedef Real value_type;
typedef value_type (*pg)(value_type);
#ifdef ERF_FUNCTION_TO_TEST
pg funcp = ERF_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::erf<value_type>;
#else
pg funcp = boost::math::erf;
#endif
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test erf against data:
//
#if !(defined(ERROR_REPORTING_MODE) && !defined(ERF_FUNCTION_TO_TEST))
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(funcp, 0),
extract_result<Real>(1));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "erf", test_name);
#endif
//
// test erfc against data:
//
#ifdef ERFC_FUNCTION_TO_TEST
funcp = ERFC_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
funcp = boost::math::erfc<value_type>;
#else
funcp = boost::math::erfc;
#endif
#if !(defined(ERROR_REPORTING_MODE) && !defined(ERFC_FUNCTION_TO_TEST))
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(funcp, 0),
extract_result<Real>(2));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "erfc", test_name);
std::cout << std::endl;
#endif
}
template <class Real, class T>
void do_test_erf_inv(const T& data, const char* type_name, const char* test_name)
{
#if !(defined(ERROR_REPORTING_MODE) && !defined(ERF_INV_FUNCTION_TO_TEST))
typedef Real value_type;
typedef value_type (*pg)(value_type);
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test erf_inv against data:
//
#ifdef ERF_INV_FUNCTION_TO_TEST
pg funcp = ERF_INV_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::erf_inv<value_type>;
#else
pg funcp = boost::math::erf_inv;
#endif
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(funcp, 0),
extract_result<Real>(1));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "erf_inv", test_name);
std::cout << std::endl;
#endif
}
template <class Real, class T>
void do_test_erfc_inv(const T& data, const char* type_name, const char* test_name)
{
#if !(defined(ERROR_REPORTING_MODE) && !defined(ERFC_INV_FUNCTION_TO_TEST))
typedef Real value_type;
typedef value_type (*pg)(value_type);
boost::math::tools::test_result<value_type> result;
std::cout << "Testing " << test_name << " with type " << type_name
<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
//
// test erfc_inv against data:
//
#ifdef ERFC_INV_FUNCTION_TO_TEST
pg funcp = ERFC_INV_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
pg funcp = boost::math::erfc_inv<value_type>;
#else
pg funcp = boost::math::erfc_inv;
#endif
result = boost::math::tools::test_hetero<Real>(
data,
bind_func<Real>(funcp, 0),
extract_result<Real>(1));
handle_test_result(result, data[result.worst()], result.worst(), type_name, "erfc_inv", test_name);
std::cout << std::endl;
#endif
}
template <class T>
void test_erf(T, const char* name)
{
//
// The actual test data is rather verbose, so it's in a separate file
//
// The contents are as follows, each row of data contains
// three items, input value a, input value b and erf(a, b):
//
# include "erf_small_data.ipp"
do_test_erf<T>(erf_small_data, name, "Erf Function: Small Values");
# include "erf_data.ipp"
do_test_erf<T>(erf_data, name, "Erf Function: Medium Values");
# include "erf_large_data.ipp"
do_test_erf<T>(erf_large_data, name, "Erf Function: Large Values");
# include "erf_inv_data.ipp"
do_test_erf_inv<T>(erf_inv_data, name, "Inverse Erf Function");
# include "erfc_inv_data.ipp"
do_test_erfc_inv<T>(erfc_inv_data, name, "Inverse Erfc Function");
# include "erfc_inv_big_data.ipp"
if(std::numeric_limits<T>::min_exponent <= -4500)
{
do_test_erfc_inv<T>(erfc_inv_big_data, name, "Inverse Erfc Function: extreme values");
}
BOOST_IF_CONSTEXPR(std::numeric_limits<T>::has_quiet_NaN)
{
BOOST_CHECK_THROW(boost::math::erf(std::numeric_limits<T>::quiet_NaN()), std::domain_error);
BOOST_CHECK_THROW(boost::math::erfc(std::numeric_limits<T>::quiet_NaN()), std::domain_error);
}
BOOST_CHECK_THROW(boost::math::erfc_inv(T(-0.5)), std::domain_error);
BOOST_CHECK_THROW(boost::math::erfc_inv(T(2.1)), std::domain_error);
BOOST_CHECK_THROW(boost::math::erf_inv(T(-1.1)), std::domain_error);
BOOST_CHECK_THROW(boost::math::erf_inv(T(1.1)), std::domain_error);
BOOST_IF_CONSTEXPR(std::numeric_limits<T>::has_infinity)
{
BOOST_CHECK_EQUAL(boost::math::erfc_inv(T(0)), std::numeric_limits<T>::infinity());
BOOST_CHECK_EQUAL(boost::math::erfc_inv(T(2)), -std::numeric_limits<T>::infinity());
BOOST_CHECK_EQUAL(boost::math::erf_inv(T(1)), std::numeric_limits<T>::infinity());
BOOST_CHECK_EQUAL(boost::math::erf_inv(T(-1)), -std::numeric_limits<T>::infinity());
BOOST_CHECK_EQUAL(boost::math::erf_inv(T(0)), T(0));
BOOST_CHECK_EQUAL(boost::math::erf(std::numeric_limits<T>::infinity()), T(1));
BOOST_CHECK_EQUAL(boost::math::erf(-std::numeric_limits<T>::infinity()), T(-1));
BOOST_CHECK_EQUAL(boost::math::erfc(std::numeric_limits<T>::infinity()), T(0));
BOOST_CHECK_EQUAL(boost::math::erfc(-std::numeric_limits<T>::infinity()), T(2));
}
BOOST_CHECK_EQUAL(boost::math::erf(boost::math::tools::max_value<T>()), T(1));
BOOST_CHECK_EQUAL(boost::math::erf(-boost::math::tools::max_value<T>()), T(-1));
BOOST_CHECK_EQUAL(boost::math::erfc(boost::math::tools::max_value<T>()), T(0));
BOOST_CHECK_EQUAL(boost::math::erfc(-boost::math::tools::max_value<T>()), T(2));
}
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 10 epsilon expressed as a percentage:
//
T tolerance = boost::math::tools::epsilon<T>() * 1000;
BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(0.125)), static_cast<T>(0.85968379519866618260697055347837660181302041685015L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(0.5)), static_cast<T>(0.47950012218695346231725334610803547126354842424204L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(1)), static_cast<T>(0.15729920705028513065877936491739074070393300203370L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(5)), static_cast<T>(1.5374597944280348501883434853833788901180503147234e-12L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(-0.125)), static_cast<T>(1.1403162048013338173930294465216233981869795831498L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(-0.5)), static_cast<T>(1.5204998778130465376827466538919645287364515757580L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(0)), static_cast<T>(1), tolerance);
BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(0.125)), static_cast<T>(0.14031620480133381739302944652162339818697958314985L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(0.5)), static_cast<T>(0.52049987781304653768274665389196452873645157575796L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(1)), static_cast<T>(0.84270079294971486934122063508260925929606699796630L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(5)), static_cast<T>(0.9999999999984625402055719651498116565146166211099L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(-0.125)), static_cast<T>(-0.14031620480133381739302944652162339818697958314985L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(-0.5)), static_cast<T>(-0.52049987781304653768274665389196452873645157575796L), tolerance);
BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(0)), static_cast<T>(0), tolerance);
tolerance = boost::math::tools::epsilon<T>() * 100 * 200; // 200 eps %.
#if defined(__CYGWIN__)
// some platforms long double is only reliably accurate to double precision:
if(sizeof(T) == sizeof(long double))
tolerance = boost::math::tools::epsilon<double>() * 100 * 200; // 200 eps %.
#endif
for(T i = -0.95f; i < 1; i += 0.125f)
{
T inv = boost::math::erf_inv(i);
T b = boost::math::erf(inv);
BOOST_CHECK_CLOSE(b, i, tolerance);
}
for(T j = 0.125f; j < 2; j += 0.125f)
{
T inv = boost::math::erfc_inv(j);
T b = boost::math::erfc(inv);
BOOST_CHECK_CLOSE(b, j, tolerance);
}
}
|
