libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/19_legendre/check_value.cc

   1 // { dg-do run { target c++11 } }
   2 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
   3 //
   4 // Copyright (C) 2016-2022 Free Software Foundation, Inc.
   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
   9 // Free Software Foundation; either version 3, or (at your option)
  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
  18 // with this library; see the file COPYING3.  If not see
  19 // <http://www.gnu.org/licenses/>.
  20
  21 //  legendre
  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/
  24 #include <limits>
  25 #include <tr1/cmath>
  26 #if defined(__TEST_DEBUG)
  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     }
  35 #else
  36 #  include <testsuite_hooks.h>
  37 #endif
  38 #include <specfun_testcase.h>
  39
  40 // Test data for l=0.
  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] =
  48 {
  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 },
  70 };
  71 const double toler001 = 2.5000000000000020e-13;
  72
  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] =
  81 {
  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 },
 103 };
 104 const double toler002 = 2.5000000000000020e-13;
 105
 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] =
 114 {
 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 },
 136 };
 137 const double toler003 = 2.5000000000000020e-13;
 138
 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] =
 147 {
 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 },
 169 };
 170 const double toler004 = 2.5000000000000020e-13;
 171
 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] =
 180 {
 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 },
 202 };
 203 const double toler005 = 2.5000000000000020e-13;
 204
 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] =
 213 {
 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 },
 235 };
 236 const double toler006 = 2.5000000000000020e-13;
 237
 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] =
 246 {
 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;
 270
 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>
 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 },
 301 };
 302 const double toler008 = 5.0000000000000039e-13;
 303
 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   }
 330
 331 int
 332 main()
 333 {
 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);
 342   return 0;
 343 }