1 // (C) Copyright John Maddock 2006.
2 // Use, modification and distribution are subject to the
3 // Boost Software License, Version 1.0. (See accompanying file
4 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
5
6 #include <pch_light.hpp>
7 #include "test_legendre.hpp"
8
9 //
10 // DESCRIPTION:
11 // ~~~~~~~~~~~~
12 //
13 // This file tests the legendre polynomials.
14 // There are two sets of tests, spot
15 // tests which compare our results with selected values computed
16 // using the online special function calculator at
17 // functions.wolfram.com, while the bulk of the accuracy tests
18 // use values generated with NTL::RR at 1000-bit precision
19 // and our generic versions of these functions.
20 //
21 // Note that when this file is first run on a new platform many of
22 // these tests will fail: the default accuracy is 1 epsilon which
23 // is too tight for most platforms. In this situation you will
24 // need to cast a human eye over the error rates reported and make
25 // a judgement as to whether they are acceptable. Either way please
26 // report the results to the Boost mailing list. Acceptable rates of
27 // error are marked up below as a series of regular expressions that
28 // identify the compiler/stdlib/platform/data-type/test-data/test-function
29 // along with the maximum expected peek and RMS mean errors for that
30 // test.
31 //
32
expected_results()33 void expected_results()
34 {
35 //
36 // Define the max and mean errors expected for
37 // various compilers and platforms.
38 //
39 const char* largest_type;
40 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
41 if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
42 {
43 largest_type = "(long\\s+)?double";
44 }
45 else
46 {
47 largest_type = "long double";
48 }
49 #else
50 largest_type = "(long\\s+)?double";
51 #endif
52 //
53 // Linux:
54 //
55 if((std::numeric_limits<long double>::digits <= 64)
56 && (std::numeric_limits<long double>::digits != std::numeric_limits<double>::digits))
57 {
58 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
59 add_expected_result(
60 ".*", // compiler
61 ".*", // stdlib
62 ".*", // platform
63 "double", // test type(s)
64 ".*", // test data group
65 ".*", 10, 5); // test function
66 #endif
67 }
68 if(std::numeric_limits<long double>::digits == 64)
69 {
70 add_expected_result(
71 ".*", // compiler
72 ".*", // stdlib
73 ".*", // platform
74 largest_type, // test type(s)
75 "Legendre Polynomials.*Large.*", // test data group
76 "legendre_p", 1000, 200); // test function
77 add_expected_result(
78 "Intel.*", // compiler
79 ".*", // stdlib
80 ".*", // platform
81 largest_type, // test type(s)
82 "Legendre Polynomials.*Large.*", // test data group
83 "legendre_q", 10000, 1000); // test function
84 add_expected_result(
85 ".*", // compiler
86 ".*", // stdlib
87 ".*", // platform
88 largest_type, // test type(s)
89 "Legendre Polynomials.*Large.*", // test data group
90 "legendre_q", 7000, 1000); // test function
91 add_expected_result(
92 ".*", // compiler
93 ".*", // stdlib
94 ".*", // platform
95 "real_concept", // test type(s)
96 "Legendre Polynomials.*Large.*", // test data group
97 "legendre_p", 1000, 200); // test function
98 add_expected_result(
99 ".*", // compiler
100 ".*", // stdlib
101 ".*", // platform
102 "real_concept", // test type(s)
103 "Legendre Polynomials.*Large.*", // test data group
104 "legendre_q", 7000, 1000); // test function
105 }
106 //
107 // Catch all cases come last:
108 //
109 add_expected_result(
110 ".*", // compiler
111 ".*", // stdlib
112 ".*", // platform
113 largest_type, // test type(s)
114 "Legendre Polynomials.*Large.*", // test data group
115 "legendre_p", 500, 200); // test function
116 add_expected_result(
117 ".*", // compiler
118 ".*", // stdlib
119 ".*", // platform
120 largest_type, // test type(s)
121 "Legendre Polynomials.*Large.*", // test data group
122 "legendre_q", 5400, 500); // test function
123 add_expected_result(
124 ".*", // compiler
125 ".*", // stdlib
126 ".*", // platform
127 largest_type, // test type(s)
128 "Legendre Polynomials.*", // test data group
129 "legendre_p", 300, 80); // test function
130 add_expected_result(
131 ".*", // compiler
132 ".*", // stdlib
133 ".*", // platform
134 largest_type, // test type(s)
135 "Legendre Polynomials.*", // test data group
136 "legendre_q", 100, 50); // test function
137 add_expected_result(
138 "Intel.*", // compiler
139 ".*", // stdlib
140 ".*", // platform
141 largest_type, // test type(s)
142 "Associated Legendre Polynomials.*", // test data group
143 ".*", 300, 20); // test function
144 add_expected_result(
145 ".*", // compiler
146 ".*", // stdlib
147 ".*", // platform
148 largest_type, // test type(s)
149 "Associated Legendre Polynomials.*", // test data group
150 ".*", 200, 20); // test function
151
152 add_expected_result(
153 ".*", // compiler
154 ".*", // stdlib
155 ".*", // platform
156 "real_concept", // test type(s)
157 "Legendre Polynomials.*Large.*", // test data group
158 "legendre_p", 500, 200); // test function
159 add_expected_result(
160 ".*", // compiler
161 ".*", // stdlib
162 ".*", // platform
163 "real_concept", // test type(s)
164 "Legendre Polynomials.*Large.*", // test data group
165 "legendre_q", 5400, 500); // test function
166 add_expected_result(
167 ".*", // compiler
168 ".*", // stdlib
169 ".*", // platform
170 "real_concept", // test type(s)
171 "Legendre Polynomials.*", // test data group
172 "legendre_p", 300, 80); // test function
173 add_expected_result(
174 ".*", // compiler
175 ".*", // stdlib
176 ".*", // platform
177 "real_concept", // test type(s)
178 "Legendre Polynomials.*", // test data group
179 "legendre_q", 100, 50); // test function
180 add_expected_result(
181 ".*", // compiler
182 ".*", // stdlib
183 ".*", // platform
184 "real_concept", // test type(s)
185 "Associated Legendre Polynomials.*", // test data group
186 ".*", 200, 20); // test function
187 //
188 // Finish off by printing out the compiler/stdlib/platform names,
189 // we do this to make it easier to mark up expected error rates.
190 //
191 std::cout << "Tests run with " << BOOST_COMPILER << ", "
192 << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
193 }
194
195
BOOST_AUTO_TEST_CASE(test_main)196 BOOST_AUTO_TEST_CASE( test_main )
197 {
198 BOOST_MATH_CONTROL_FP;
199 test_spots(0.0F, "float");
200 test_spots(0.0, "double");
201 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
202 test_spots(0.0L, "long double");
203 test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
204 #endif
205
206 expected_results();
207
208 test_legendre_p(0.1F, "float");
209 test_legendre_p(0.1, "double");
210 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
211 test_legendre_p(0.1L, "long double");
212 #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
213 test_legendre_p(boost::math::concepts::real_concept(0.1), "real_concept");
214 #endif
215 #else
216 std::cout << "<note>The long double tests have been disabled on this platform "
217 "either because the long double overloads of the usual math functions are "
218 "not available at all, or because they are too inaccurate for these tests "
219 "to pass.</note>" << std::endl;
220 #endif
221
222 test_legendre_p_prime<float>();
223 test_legendre_p_prime<double>();
224 test_legendre_p_prime<long double>();
225
226 int ulp_distance = test_legendre_p_zeros_double_ulp(1, 100);
227 BOOST_CHECK(ulp_distance <= 2);
228 test_legendre_p_zeros<float>();
229 test_legendre_p_zeros<double>();
230 test_legendre_p_zeros<long double>();
231 }
232