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git.ipfire.org Git - thirdparty/gcc.git/blob - libstdc++-v3/testsuite/special_functions/17_legendre/check_value.cc
1 // { dg-do run { target c++11 } }
2 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
4 // Copyright (C) 2016-2022 Free Software Foundation, Inc.
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
9 // Free Software Foundation; either version 3, or (at your option)
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.
17 // You should have received a copy of the GNU General Public License along
18 // with this library; see the file COPYING3. If not see
19 // <http://www.gnu.org/licenses/>.
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/
26 #if defined(__TEST_DEBUG)
31 std::cout << "line " << __LINE__ \
32 << " max_abs_frac = " << max_abs_frac \
36 # include <testsuite_hooks.h>
38 #include <specfun_testcase.h>
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>
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 },
71 const double toler001
= 2.5000000000000020e-13;
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>
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 },
104 const double toler002
= 2.5000000000000020e-13;
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>
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 },
137 const double toler003
= 2.5000000000000020e-13;
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>
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 },
170 const double toler004
= 2.5000000000000020e-13;
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>
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 },
203 const double toler005
= 2.5000000000000020e-13;
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>
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 },
236 const double toler006
= 2.5000000000000020e-13;
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>
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 },
269 const double toler007
= 2.5000000000000020e-13;
271 // Test data for l=100.
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>
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 },
302 const double toler008
= 5.0000000000000039e-13;
304 template<typename Ret
, unsigned int Num
>
306 test(const testcase_legendre
<Ret
> (&data
)[Num
], Ret toler
)
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
)
315 const Ret f
= std::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
)
323 const Ret frac
= diff
/ f0
;
324 if (std::abs(frac
) > max_abs_frac
)
325 max_abs_frac
= std::abs(frac
);
328 VERIFY(max_abs_frac
< toler
);
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
);