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b4688136 ESR |
1 | // { dg-do run { target c++11 } } |
2 | // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" } | |
7c62b943 | 3 | // |
a5544970 | 4 | // Copyright (C) 2016-2019 Free Software Foundation, Inc. |
7c62b943 BK |
5 | // |
6 | // This file is part of the GNU ISO C++ Library. This library is free | |
7 | // software; you can redistribute it and/or modify it under the | |
8 | // terms of the GNU General Public License as published by the | |
748086b7 | 9 | // Free Software Foundation; either version 3, or (at your option) |
7c62b943 BK |
10 | // any later version. |
11 | // | |
12 | // This library is distributed in the hope that it will be useful, | |
13 | // but WITHOUT ANY WARRANTY; without even the implied warranty of | |
14 | // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
15 | // GNU General Public License for more details. | |
16 | // | |
17 | // You should have received a copy of the GNU General Public License along | |
748086b7 JJ |
18 | // with this library; see the file COPYING3. If not see |
19 | // <http://www.gnu.org/licenses/>. | |
7c62b943 BK |
20 | |
21 | // legendre | |
7c62b943 BK |
22 | // Compare against values generated by the GNU Scientific Library. |
23 | // The GSL can be found on the web: http://www.gnu.org/software/gsl/ | |
b4688136 | 24 | #include <limits> |
7c62b943 BK |
25 | #include <tr1/cmath> |
26 | #if defined(__TEST_DEBUG) | |
b4688136 ESR |
27 | # include <iostream> |
28 | # define VERIFY(A) \ | |
29 | if (!(A)) \ | |
30 | { \ | |
31 | std::cout << "line " << __LINE__ \ | |
32 | << " max_abs_frac = " << max_abs_frac \ | |
33 | << std::endl; \ | |
34 | } | |
7c62b943 | 35 | #else |
b4688136 | 36 | # include <testsuite_hooks.h> |
7c62b943 | 37 | #endif |
b4688136 | 38 | #include <specfun_testcase.h> |
7c62b943 BK |
39 | |
40 | // Test data for l=0. | |
b4688136 ESR |
41 | // max(|f - f_GSL|): 0.0000000000000000 at index 0 |
42 | // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000 | |
43 | // mean(f - f_GSL): 0.0000000000000000 | |
44 | // variance(f - f_GSL): 0.0000000000000000 | |
45 | // stddev(f - f_GSL): 0.0000000000000000 | |
46 | const testcase_legendre<double> | |
47 | data001[21] = | |
7c62b943 | 48 | { |
b4688136 ESR |
49 | { 1.0000000000000000, 0, -1.0000000000000000, 0.0 }, |
50 | { 1.0000000000000000, 0, -0.90000000000000002, 0.0 }, | |
51 | { 1.0000000000000000, 0, -0.80000000000000004, 0.0 }, | |
52 | { 1.0000000000000000, 0, -0.69999999999999996, 0.0 }, | |
53 | { 1.0000000000000000, 0, -0.59999999999999998, 0.0 }, | |
54 | { 1.0000000000000000, 0, -0.50000000000000000, 0.0 }, | |
55 | { 1.0000000000000000, 0, -0.39999999999999991, 0.0 }, | |
56 | { 1.0000000000000000, 0, -0.29999999999999993, 0.0 }, | |
57 | { 1.0000000000000000, 0, -0.19999999999999996, 0.0 }, | |
58 | { 1.0000000000000000, 0, -0.099999999999999978, 0.0 }, | |
59 | { 1.0000000000000000, 0, 0.0000000000000000, 0.0 }, | |
60 | { 1.0000000000000000, 0, 0.10000000000000009, 0.0 }, | |
61 | { 1.0000000000000000, 0, 0.20000000000000018, 0.0 }, | |
62 | { 1.0000000000000000, 0, 0.30000000000000004, 0.0 }, | |
63 | { 1.0000000000000000, 0, 0.40000000000000013, 0.0 }, | |
64 | { 1.0000000000000000, 0, 0.50000000000000000, 0.0 }, | |
65 | { 1.0000000000000000, 0, 0.60000000000000009, 0.0 }, | |
66 | { 1.0000000000000000, 0, 0.70000000000000018, 0.0 }, | |
67 | { 1.0000000000000000, 0, 0.80000000000000004, 0.0 }, | |
68 | { 1.0000000000000000, 0, 0.90000000000000013, 0.0 }, | |
69 | { 1.0000000000000000, 0, 1.0000000000000000, 0.0 }, | |
7c62b943 | 70 | }; |
b4688136 | 71 | const double toler001 = 2.5000000000000020e-13; |
7c62b943 | 72 | |
b4688136 ESR |
73 | // Test data for l=1. |
74 | // max(|f - f_GSL|): 0.0000000000000000 at index 0 | |
75 | // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000 | |
76 | // mean(f - f_GSL): 0.0000000000000000 | |
77 | // variance(f - f_GSL): 0.0000000000000000 | |
78 | // stddev(f - f_GSL): 0.0000000000000000 | |
79 | const testcase_legendre<double> | |
80 | data002[21] = | |
7c62b943 | 81 | { |
b4688136 ESR |
82 | { -1.0000000000000000, 1, -1.0000000000000000, 0.0 }, |
83 | { -0.90000000000000002, 1, -0.90000000000000002, 0.0 }, | |
84 | { -0.80000000000000004, 1, -0.80000000000000004, 0.0 }, | |
85 | { -0.69999999999999996, 1, -0.69999999999999996, 0.0 }, | |
86 | { -0.59999999999999998, 1, -0.59999999999999998, 0.0 }, | |
87 | { -0.50000000000000000, 1, -0.50000000000000000, 0.0 }, | |
88 | { -0.39999999999999991, 1, -0.39999999999999991, 0.0 }, | |
89 | { -0.29999999999999993, 1, -0.29999999999999993, 0.0 }, | |
90 | { -0.19999999999999996, 1, -0.19999999999999996, 0.0 }, | |
91 | { -0.099999999999999978, 1, -0.099999999999999978, 0.0 }, | |
92 | { 0.0000000000000000, 1, 0.0000000000000000, 0.0 }, | |
93 | { 0.10000000000000009, 1, 0.10000000000000009, 0.0 }, | |
94 | { 0.20000000000000018, 1, 0.20000000000000018, 0.0 }, | |
95 | { 0.30000000000000004, 1, 0.30000000000000004, 0.0 }, | |
96 | { 0.40000000000000013, 1, 0.40000000000000013, 0.0 }, | |
97 | { 0.50000000000000000, 1, 0.50000000000000000, 0.0 }, | |
98 | { 0.60000000000000009, 1, 0.60000000000000009, 0.0 }, | |
99 | { 0.70000000000000018, 1, 0.70000000000000018, 0.0 }, | |
100 | { 0.80000000000000004, 1, 0.80000000000000004, 0.0 }, | |
101 | { 0.90000000000000013, 1, 0.90000000000000013, 0.0 }, | |
102 | { 1.0000000000000000, 1, 1.0000000000000000, 0.0 }, | |
7c62b943 | 103 | }; |
b4688136 | 104 | const double toler002 = 2.5000000000000020e-13; |
7c62b943 | 105 | |
b4688136 ESR |
106 | // Test data for l=2. |
107 | // max(|f - f_GSL|): 1.1102230246251565e-16 at index 17 | |
108 | // max(|f - f_GSL| / |f_GSL|): 1.3877787807814482e-15 | |
109 | // mean(f - f_GSL): 1.8503717077085941e-17 | |
110 | // variance(f - f_GSL): 1.7975346147614202e-35 | |
111 | // stddev(f - f_GSL): 4.2397342071896678e-18 | |
112 | const testcase_legendre<double> | |
113 | data003[21] = | |
7c62b943 | 114 | { |
b4688136 ESR |
115 | { 1.0000000000000000, 2, -1.0000000000000000, 0.0 }, |
116 | { 0.71500000000000008, 2, -0.90000000000000002, 0.0 }, | |
117 | { 0.46000000000000019, 2, -0.80000000000000004, 0.0 }, | |
118 | { 0.23499999999999988, 2, -0.69999999999999996, 0.0 }, | |
119 | { 0.039999999999999925, 2, -0.59999999999999998, 0.0 }, | |
120 | { -0.12500000000000000, 2, -0.50000000000000000, 0.0 }, | |
121 | { -0.26000000000000012, 2, -0.39999999999999991, 0.0 }, | |
122 | { -0.36500000000000005, 2, -0.29999999999999993, 0.0 }, | |
123 | { -0.44000000000000006, 2, -0.19999999999999996, 0.0 }, | |
124 | { -0.48499999999999999, 2, -0.099999999999999978, 0.0 }, | |
125 | { -0.50000000000000000, 2, 0.0000000000000000, 0.0 }, | |
126 | { -0.48499999999999999, 2, 0.10000000000000009, 0.0 }, | |
127 | { -0.43999999999999989, 2, 0.20000000000000018, 0.0 }, | |
128 | { -0.36499999999999999, 2, 0.30000000000000004, 0.0 }, | |
129 | { -0.25999999999999984, 2, 0.40000000000000013, 0.0 }, | |
130 | { -0.12500000000000000, 2, 0.50000000000000000, 0.0 }, | |
131 | { 0.040000000000000147, 2, 0.60000000000000009, 0.0 }, | |
132 | { 0.23500000000000032, 2, 0.70000000000000018, 0.0 }, | |
133 | { 0.46000000000000019, 2, 0.80000000000000004, 0.0 }, | |
134 | { 0.71500000000000030, 2, 0.90000000000000013, 0.0 }, | |
135 | { 1.0000000000000000, 2, 1.0000000000000000, 0.0 }, | |
7c62b943 | 136 | }; |
b4688136 | 137 | const double toler003 = 2.5000000000000020e-13; |
7c62b943 | 138 | |
b4688136 ESR |
139 | // Test data for l=5. |
140 | // max(|f - f_GSL|): 2.0122792321330962e-16 at index 19 | |
141 | // max(|f - f_GSL| / |f_GSL|): 4.8911475274405560e-15 | |
142 | // mean(f - f_GSL): -2.3129646346357427e-18 | |
143 | // variance(f - f_GSL): 2.8086478355647191e-37 | |
144 | // stddev(f - f_GSL): 5.2996677589870847e-19 | |
145 | const testcase_legendre<double> | |
146 | data004[21] = | |
7c62b943 | 147 | { |
b4688136 ESR |
148 | { -1.0000000000000000, 5, -1.0000000000000000, 0.0 }, |
149 | { 0.041141250000000087, 5, -0.90000000000000002, 0.0 }, | |
150 | { 0.39951999999999993, 5, -0.80000000000000004, 0.0 }, | |
151 | { 0.36519874999999991, 5, -0.69999999999999996, 0.0 }, | |
152 | { 0.15263999999999994, 5, -0.59999999999999998, 0.0 }, | |
153 | { -0.089843750000000000, 5, -0.50000000000000000, 0.0 }, | |
154 | { -0.27064000000000010, 5, -0.39999999999999991, 0.0 }, | |
155 | { -0.34538624999999995, 5, -0.29999999999999993, 0.0 }, | |
156 | { -0.30751999999999996, 5, -0.19999999999999996, 0.0 }, | |
157 | { -0.17882874999999995, 5, -0.099999999999999978, 0.0 }, | |
158 | { 0.0000000000000000, 5, 0.0000000000000000, 0.0 }, | |
159 | { 0.17882875000000015, 5, 0.10000000000000009, 0.0 }, | |
160 | { 0.30752000000000013, 5, 0.20000000000000018, 0.0 }, | |
161 | { 0.34538625000000001, 5, 0.30000000000000004, 0.0 }, | |
162 | { 0.27063999999999988, 5, 0.40000000000000013, 0.0 }, | |
163 | { 0.089843750000000000, 5, 0.50000000000000000, 0.0 }, | |
164 | { -0.15264000000000016, 5, 0.60000000000000009, 0.0 }, | |
165 | { -0.36519875000000024, 5, 0.70000000000000018, 0.0 }, | |
166 | { -0.39951999999999993, 5, 0.80000000000000004, 0.0 }, | |
167 | { -0.041141249999999151, 5, 0.90000000000000013, 0.0 }, | |
168 | { 1.0000000000000000, 5, 1.0000000000000000, 0.0 }, | |
7c62b943 | 169 | }; |
b4688136 | 170 | const double toler004 = 2.5000000000000020e-13; |
7c62b943 | 171 | |
b4688136 ESR |
172 | // Test data for l=10. |
173 | // max(|f - f_GSL|): 3.8857805861880479e-16 at index 19 | |
174 | // max(|f - f_GSL| / |f_GSL|): 1.4766655123690915e-15 | |
175 | // mean(f - f_GSL): -2.5112187461759493e-17 | |
176 | // variance(f - f_GSL): 3.3107652853513909e-35 | |
177 | // stddev(f - f_GSL): 5.7539249954716919e-18 | |
178 | const testcase_legendre<double> | |
179 | data005[21] = | |
7c62b943 | 180 | { |
b4688136 ESR |
181 | { 1.0000000000000000, 10, -1.0000000000000000, 0.0 }, |
182 | { -0.26314561785585960, 10, -0.90000000000000002, 0.0 }, | |
183 | { 0.30052979560000004, 10, -0.80000000000000004, 0.0 }, | |
184 | { 0.085805795531640333, 10, -0.69999999999999996, 0.0 }, | |
185 | { -0.24366274560000001, 10, -0.59999999999999998, 0.0 }, | |
186 | { -0.18822860717773438, 10, -0.50000000000000000, 0.0 }, | |
187 | { 0.096839064400000258, 10, -0.39999999999999991, 0.0 }, | |
188 | { 0.25147634951601561, 10, -0.29999999999999993, 0.0 }, | |
189 | { 0.12907202559999983, 10, -0.19999999999999996, 0.0 }, | |
190 | { -0.12212499738710943, 10, -0.099999999999999978, 0.0 }, | |
191 | { -0.24609375000000000, 10, 0.0000000000000000, 0.0 }, | |
192 | { -0.12212499738710922, 10, 0.10000000000000009, 0.0 }, | |
193 | { 0.12907202560000042, 10, 0.20000000000000018, 0.0 }, | |
194 | { 0.25147634951601561, 10, 0.30000000000000004, 0.0 }, | |
195 | { 0.096839064399999633, 10, 0.40000000000000013, 0.0 }, | |
196 | { -0.18822860717773438, 10, 0.50000000000000000, 0.0 }, | |
197 | { -0.24366274559999984, 10, 0.60000000000000009, 0.0 }, | |
198 | { 0.085805795531641277, 10, 0.70000000000000018, 0.0 }, | |
199 | { 0.30052979560000004, 10, 0.80000000000000004, 0.0 }, | |
200 | { -0.26314561785586010, 10, 0.90000000000000013, 0.0 }, | |
201 | { 1.0000000000000000, 10, 1.0000000000000000, 0.0 }, | |
7c62b943 | 202 | }; |
b4688136 | 203 | const double toler005 = 2.5000000000000020e-13; |
7c62b943 | 204 | |
b4688136 ESR |
205 | // Test data for l=20. |
206 | // max(|f - f_GSL|): 3.6082248300317588e-16 at index 19 | |
207 | // max(|f - f_GSL| / |f_GSL|): 2.4166281401316513e-15 | |
208 | // mean(f - f_GSL): 0.0000000000000000 | |
209 | // variance(f - f_GSL): 4.9424644697959907e-65 | |
210 | // stddev(f - f_GSL): 7.0302663319365015e-33 | |
211 | const testcase_legendre<double> | |
212 | data006[21] = | |
7c62b943 | 213 | { |
b4688136 ESR |
214 | { 1.0000000000000000, 20, -1.0000000000000000, 0.0 }, |
215 | { -0.14930823530984835, 20, -0.90000000000000002, 0.0 }, | |
216 | { 0.22420460541741347, 20, -0.80000000000000004, 0.0 }, | |
217 | { -0.20457394463834172, 20, -0.69999999999999996, 0.0 }, | |
218 | { 0.15916752910098109, 20, -0.59999999999999998, 0.0 }, | |
219 | { -0.048358381067373557, 20, -0.50000000000000000, 0.0 }, | |
220 | { -0.10159261558628112, 20, -0.39999999999999991, 0.0 }, | |
221 | { 0.18028715947998047, 20, -0.29999999999999993, 0.0 }, | |
222 | { -0.098042194344594796, 20, -0.19999999999999996, 0.0 }, | |
223 | { -0.082077130944527663, 20, -0.099999999999999978, 0.0 }, | |
224 | { 0.17619705200195312, 20, 0.0000000000000000, 0.0 }, | |
225 | { -0.082077130944528023, 20, 0.10000000000000009, 0.0 }, | |
226 | { -0.098042194344594089, 20, 0.20000000000000018, 0.0 }, | |
227 | { 0.18028715947998042, 20, 0.30000000000000004, 0.0 }, | |
228 | { -0.10159261558628192, 20, 0.40000000000000013, 0.0 }, | |
229 | { -0.048358381067373557, 20, 0.50000000000000000, 0.0 }, | |
230 | { 0.15916752910098075, 20, 0.60000000000000009, 0.0 }, | |
231 | { -0.20457394463834136, 20, 0.70000000000000018, 0.0 }, | |
232 | { 0.22420460541741347, 20, 0.80000000000000004, 0.0 }, | |
233 | { -0.14930823530984758, 20, 0.90000000000000013, 0.0 }, | |
234 | { 1.0000000000000000, 20, 1.0000000000000000, 0.0 }, | |
7c62b943 | 235 | }; |
b4688136 | 236 | const double toler006 = 2.5000000000000020e-13; |
7c62b943 | 237 | |
b4688136 ESR |
238 | // Test data for l=50. |
239 | // max(|f - f_GSL|): 1.6653345369377348e-16 at index 2 | |
240 | // max(|f - f_GSL| / |f_GSL|): 1.6665460706897444e-15 | |
241 | // mean(f - f_GSL): -8.0953762212251003e-18 | |
242 | // variance(f - f_GSL): 3.4405935985667807e-36 | |
243 | // stddev(f - f_GSL): 1.8548837156454796e-18 | |
244 | const testcase_legendre<double> | |
245 | data007[21] = | |
7c62b943 | 246 | { |
b4688136 ESR |
247 | { 1.0000000000000000, 50, -1.0000000000000000, 0.0 }, |
248 | { -0.17003765994383671, 50, -0.90000000000000002, 0.0 }, | |
249 | { 0.13879737345093113, 50, -0.80000000000000004, 0.0 }, | |
250 | { -0.014572731645892852, 50, -0.69999999999999996, 0.0 }, | |
251 | { -0.058860798844002096, 50, -0.59999999999999998, 0.0 }, | |
252 | { -0.031059099239609811, 50, -0.50000000000000000, 0.0 }, | |
253 | { 0.041569033381824674, 50, -0.39999999999999991, 0.0 }, | |
254 | { 0.10911051574714790, 50, -0.29999999999999993, 0.0 }, | |
255 | { 0.083432272204197494, 50, -0.19999999999999996, 0.0 }, | |
256 | { -0.038205812661313600, 50, -0.099999999999999978, 0.0 }, | |
257 | { -0.11227517265921705, 50, 0.0000000000000000, 0.0 }, | |
258 | { -0.038205812661314155, 50, 0.10000000000000009, 0.0 }, | |
259 | { 0.083432272204196564, 50, 0.20000000000000018, 0.0 }, | |
260 | { 0.10911051574714797, 50, 0.30000000000000004, 0.0 }, | |
261 | { 0.041569033381826007, 50, 0.40000000000000013, 0.0 }, | |
262 | { -0.031059099239609811, 50, 0.50000000000000000, 0.0 }, | |
263 | { -0.058860798844001430, 50, 0.60000000000000009, 0.0 }, | |
264 | { -0.014572731645890737, 50, 0.70000000000000018, 0.0 }, | |
265 | { 0.13879737345093113, 50, 0.80000000000000004, 0.0 }, | |
266 | { -0.17003765994383679, 50, 0.90000000000000013, 0.0 }, | |
267 | { 1.0000000000000000, 50, 1.0000000000000000, 0.0 }, | |
268 | }; | |
269 | const double toler007 = 2.5000000000000020e-13; | |
7c62b943 BK |
270 | |
271 | // Test data for l=100. | |
b4688136 ESR |
272 | // max(|f - f_GSL|): 3.4694469519536142e-16 at index 2 |
273 | // max(|f - f_GSL| / |f_GSL|): 6.8214063779431592e-15 | |
274 | // mean(f - f_GSL): -4.1385545784018113e-17 | |
275 | // variance(f - f_GSL): 8.9920078491655612e-35 | |
276 | // stddev(f - f_GSL): 9.4826198116161765e-18 | |
277 | const testcase_legendre<double> | |
278 | data008[21] = | |
279 | { | |
280 | { 1.0000000000000000, 100, -1.0000000000000000, 0.0 }, | |
281 | { 0.10226582055871893, 100, -0.90000000000000002, 0.0 }, | |
282 | { 0.050861167913584228, 100, -0.80000000000000004, 0.0 }, | |
283 | { -0.077132507199778641, 100, -0.69999999999999996, 0.0 }, | |
284 | { -0.023747023905133141, 100, -0.59999999999999998, 0.0 }, | |
285 | { -0.060518025961861198, 100, -0.50000000000000000, 0.0 }, | |
286 | { -0.072258202125685025, 100, -0.39999999999999991, 0.0 }, | |
287 | { 0.057127392202801046, 100, -0.29999999999999993, 0.0 }, | |
288 | { 0.014681835355659706, 100, -0.19999999999999996, 0.0 }, | |
289 | { -0.063895098434750205, 100, -0.099999999999999978, 0.0 }, | |
290 | { 0.079589237387178727, 100, 0.0000000000000000, 0.0 }, | |
291 | { -0.063895098434749761, 100, 0.10000000000000009, 0.0 }, | |
292 | { 0.014681835355657875, 100, 0.20000000000000018, 0.0 }, | |
293 | { 0.057127392202801566, 100, 0.30000000000000004, 0.0 }, | |
294 | { -0.072258202125684082, 100, 0.40000000000000013, 0.0 }, | |
295 | { -0.060518025961861198, 100, 0.50000000000000000, 0.0 }, | |
296 | { -0.023747023905134217, 100, 0.60000000000000009, 0.0 }, | |
297 | { -0.077132507199780501, 100, 0.70000000000000018, 0.0 }, | |
298 | { 0.050861167913584228, 100, 0.80000000000000004, 0.0 }, | |
299 | { 0.10226582055872063, 100, 0.90000000000000013, 0.0 }, | |
300 | { 1.0000000000000000, 100, 1.0000000000000000, 0.0 }, | |
7c62b943 | 301 | }; |
b4688136 | 302 | const double toler008 = 5.0000000000000039e-13; |
7c62b943 | 303 | |
b4688136 ESR |
304 | template<typename Ret, unsigned int Num> |
305 | void | |
306 | test(const testcase_legendre<Ret> (&data)[Num], Ret toler) | |
307 | { | |
308 | bool test __attribute__((unused)) = true; | |
309 | const Ret eps = std::numeric_limits<Ret>::epsilon(); | |
310 | Ret max_abs_diff = -Ret(1); | |
311 | Ret max_abs_frac = -Ret(1); | |
312 | unsigned int num_datum = Num; | |
313 | for (unsigned int i = 0; i < num_datum; ++i) | |
314 | { | |
315 | const Ret f = std::tr1::legendre(data[i].l, data[i].x); | |
316 | const Ret f0 = data[i].f0; | |
317 | const Ret diff = f - f0; | |
318 | if (std::abs(diff) > max_abs_diff) | |
319 | max_abs_diff = std::abs(diff); | |
320 | if (std::abs(f0) > Ret(10) * eps | |
321 | && std::abs(f) > Ret(10) * eps) | |
322 | { | |
323 | const Ret frac = diff / f0; | |
324 | if (std::abs(frac) > max_abs_frac) | |
325 | max_abs_frac = std::abs(frac); | |
326 | } | |
327 | } | |
328 | VERIFY(max_abs_frac < toler); | |
329 | } | |
7c62b943 | 330 | |
b4688136 ESR |
331 | int |
332 | main() | |
7c62b943 | 333 | { |
b4688136 ESR |
334 | test(data001, toler001); |
335 | test(data002, toler002); | |
336 | test(data003, toler003); | |
337 | test(data004, toler004); | |
338 | test(data005, toler005); | |
339 | test(data006, toler006); | |
340 | test(data007, toler007); | |
341 | test(data008, toler008); | |
7c62b943 BK |
342 | return 0; |
343 | } |