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
|
// (C) Copyright John Maddock 2006.
// 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/concepts/real_concept.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/binomial.hpp>
#include <boost/math/tools/test.hpp>
#include "functor.hpp"
#include <boost/array.hpp>
#include "handle_test_result.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the function binomial_coefficient<T>.
// The accuracy tests
// use values generated with NTL::RR at 1000-bit precision
// and our generic versions of these function.
//
// 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
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*large.*", // test data group
".*", 100, 20); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*large.*", // test data group
".*", 200, 100); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*", // test data group
".*", 100, 30); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
".*", // test type(s)
".*", // test data group
".*", 2, 1); // test function
//
// Finish off by printing out the compiler/stdlib/platform names,
// we do this to make it easier to mark up expected error rates.
//
std::cout << "Tests run with " << BOOST_COMPILER << ", "
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
template <class T>
T binomial_wrapper(T n, T k)
{
return boost::math::binomial_coefficient<T>(
boost::math::tools::real_cast<unsigned>(n),
boost::math::tools::real_cast<unsigned>(k));
}
template <class T>
void test_binomial(T, const char* type_name)
{
using namespace std;
typedef T (*func_t)(T, T);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
func_t f = &binomial_wrapper<T>;
#else
func_t f = &binomial_wrapper;
#endif
#include "binomial_data.ipp"
boost::math::tools::test_result<T> result = boost::math::tools::test(
binomial_data,
bind_func(f, 0, 1),
extract_result(2));
std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"
"Test results for small arguments and type " << type_name << std::endl << std::endl;
std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
handle_test_result(result, binomial_data[result.worst()], result.worst(), type_name, "binomial_coefficient", "Binomials: small arguments");
std::cout << std::endl;
#include "binomial_large_data.ipp"
result = boost::math::tools::test(
binomial_large_data,
bind_func(f, 0, 1),
extract_result(2));
std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n"
"Test results for large arguments and type " << type_name << std::endl << std::endl;
std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
handle_test_result(result, binomial_large_data[result.worst()], result.worst(), type_name, "binomial_coefficient", "Binomials: large arguments");
std::cout << std::endl;
}
template <class T>
void test_spots(T, const char* name)
{
T tolerance = boost::math::tools::epsilon<T>() * 50 * 100; // 50 eps as a percentage
if(!std::numeric_limits<T>::is_specialized)
tolerance *= 10; // beta function not so accurate without lanczos support
std::cout << "Testing spot checks for type " << name << " with tolerance " << tolerance << "%\n";
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 0), static_cast<T>(1));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 1), static_cast<T>(20));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 2), static_cast<T>(190));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 3), static_cast<T>(1140));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 20), static_cast<T>(1));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 19), static_cast<T>(20));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 18), static_cast<T>(190));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 17), static_cast<T>(1140));
BOOST_CHECK_EQUAL(boost::math::binomial_coefficient<T>(20, 10), static_cast<T>(184756L));
BOOST_CHECK_CLOSE(boost::math::binomial_coefficient<T>(100, 5), static_cast<T>(7.528752e7L), tolerance);
BOOST_CHECK_CLOSE(boost::math::binomial_coefficient<T>(100, 81), static_cast<T>(1.323415729392122674e20L), tolerance);
BOOST_CHECK_CLOSE(boost::math::binomial_coefficient<T>(300, 3), static_cast<T>(4.45510e6L), tolerance);
BOOST_CHECK_CLOSE(boost::math::binomial_coefficient<T>(300, 7), static_cast<T>(4.043855956140000e13L), tolerance);
BOOST_CHECK_CLOSE(boost::math::binomial_coefficient<T>(300, 290), static_cast<T>(1.3983202332417017700000000e18L), tolerance);
BOOST_CHECK_CLOSE(boost::math::binomial_coefficient<T>(300, 275), static_cast<T>(1.953265141442868389822364184842211512000000e36L), tolerance);
}
int test_main(int, char* [])
{
expected_results();
BOOST_MATH_CONTROL_FP;
test_spots(1.0F, "float");
test_spots(1.0, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_spots(1.0L, "long double");
test_spots(boost::math::concepts::real_concept(), "real_concept");
#endif
test_binomial(1.0F, "float");
test_binomial(1.0, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_binomial(1.0L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
test_binomial(boost::math::concepts::real_concept(), "real_concept");
#endif
#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;
}
|
