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__" }
   3 //
   4 // Copyright (C) 2016-2017 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 <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
  41 // Test data for l=0.
  42 // max(|f - f_GSL|): 0.0000000000000000
  43 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
  44 const testcase_legendre<double>
  45 data001[21] =
  46 {
  47   { 1.0000000000000000, 0, -1.0000000000000000 },
  48   { 1.0000000000000000, 0, -0.90000000000000002 },
  49   { 1.0000000000000000, 0, -0.80000000000000004 },
  50   { 1.0000000000000000, 0, -0.69999999999999996 },
  51   { 1.0000000000000000, 0, -0.59999999999999998 },
  52   { 1.0000000000000000, 0, -0.50000000000000000 },
  53   { 1.0000000000000000, 0, -0.40000000000000002 },
  54   { 1.0000000000000000, 0, -0.30000000000000004 },
  55   { 1.0000000000000000, 0, -0.19999999999999996 },
  56   { 1.0000000000000000, 0, -0.099999999999999978 },
  57   { 1.0000000000000000, 0, 0.0000000000000000 },
  58   { 1.0000000000000000, 0, 0.10000000000000009 },
  59   { 1.0000000000000000, 0, 0.19999999999999996 },
  60   { 1.0000000000000000, 0, 0.30000000000000004 },
  61   { 1.0000000000000000, 0, 0.39999999999999991 },
  62   { 1.0000000000000000, 0, 0.50000000000000000 },
  63   { 1.0000000000000000, 0, 0.60000000000000009 },
  64   { 1.0000000000000000, 0, 0.69999999999999996 },
  65   { 1.0000000000000000, 0, 0.80000000000000004 },
  66   { 1.0000000000000000, 0, 0.89999999999999991 },
  67   { 1.0000000000000000, 0, 1.0000000000000000 },
  68 };
  69 const double toler001 = 2.5000000000000020e-13;
  70
  71 // Test data for l=1.
  72 // max(|f - f_GSL|): 0.0000000000000000
  73 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
  74 const testcase_legendre<double>
  75 data002[21] =
  76 {
  77   { -1.0000000000000000, 1, -1.0000000000000000 },
  78   { -0.90000000000000002, 1, -0.90000000000000002 },
  79   { -0.80000000000000004, 1, -0.80000000000000004 },
  80   { -0.69999999999999996, 1, -0.69999999999999996 },
  81   { -0.59999999999999998, 1, -0.59999999999999998 },
  82   { -0.50000000000000000, 1, -0.50000000000000000 },
  83   { -0.40000000000000002, 1, -0.40000000000000002 },
  84   { -0.30000000000000004, 1, -0.30000000000000004 },
  85   { -0.19999999999999996, 1, -0.19999999999999996 },
  86   { -0.099999999999999978, 1, -0.099999999999999978 },
  87   { 0.0000000000000000, 1, 0.0000000000000000 },
  88   { 0.10000000000000009, 1, 0.10000000000000009 },
  89   { 0.19999999999999996, 1, 0.19999999999999996 },
  90   { 0.30000000000000004, 1, 0.30000000000000004 },
  91   { 0.39999999999999991, 1, 0.39999999999999991 },
  92   { 0.50000000000000000, 1, 0.50000000000000000 },
  93   { 0.60000000000000009, 1, 0.60000000000000009 },
  94   { 0.69999999999999996, 1, 0.69999999999999996 },
  95   { 0.80000000000000004, 1, 0.80000000000000004 },
  96   { 0.89999999999999991, 1, 0.89999999999999991 },
  97   { 1.0000000000000000, 1, 1.0000000000000000 },
  98 };
  99 const double toler002 = 2.5000000000000020e-13;
 100
 101 // Test data for l=2.
 102 // max(|f - f_GSL|): 1.1102230246251565e-16
 103 // max(|f - f_GSL| / |f_GSL|): 1.3877787807814482e-15
 104 const testcase_legendre<double>
 105 data003[21] =
 106 {
 107   { 1.0000000000000000, 2, -1.0000000000000000 },
 108   { 0.71500000000000008, 2, -0.90000000000000002 },
 109   { 0.46000000000000019, 2, -0.80000000000000004 },
 110   { 0.23499999999999988, 2, -0.69999999999999996 },
 111   { 0.039999999999999925, 2, -0.59999999999999998 },
 112   { -0.12500000000000000, 2, -0.50000000000000000 },
 113   { -0.25999999999999995, 2, -0.40000000000000002 },
 114   { -0.36499999999999999, 2, -0.30000000000000004 },
 115   { -0.44000000000000006, 2, -0.19999999999999996 },
 116   { -0.48499999999999999, 2, -0.099999999999999978 },
 117   { -0.50000000000000000, 2, 0.0000000000000000 },
 118   { -0.48499999999999999, 2, 0.10000000000000009 },
 119   { -0.44000000000000006, 2, 0.19999999999999996 },
 120   { -0.36499999999999999, 2, 0.30000000000000004 },
 121   { -0.26000000000000012, 2, 0.39999999999999991 },
 122   { -0.12500000000000000, 2, 0.50000000000000000 },
 123   { 0.040000000000000147, 2, 0.60000000000000009 },
 124   { 0.23499999999999988, 2, 0.69999999999999996 },
 125   { 0.46000000000000019, 2, 0.80000000000000004 },
 126   { 0.71499999999999986, 2, 0.89999999999999991 },
 127   { 1.0000000000000000, 2, 1.0000000000000000 },
 128 };
 129 const double toler003 = 2.5000000000000020e-13;
 130
 131 // Test data for l=5.
 132 // max(|f - f_GSL|): 2.0122792321330962e-16
 133 // max(|f - f_GSL| / |f_GSL|): 4.8911475274404243e-15
 134 const testcase_legendre<double>
 135 data004[21] =
 136 {
 137   { -1.0000000000000000, 5, -1.0000000000000000 },
 138   { 0.041141250000000087, 5, -0.90000000000000002 },
 139   { 0.39951999999999993, 5, -0.80000000000000004 },
 140   { 0.36519874999999991, 5, -0.69999999999999996 },
 141   { 0.15263999999999994, 5, -0.59999999999999998 },
 142   { -0.089843750000000000, 5, -0.50000000000000000 },
 143   { -0.27063999999999994, 5, -0.40000000000000002 },
 144   { -0.34538625000000001, 5, -0.30000000000000004 },
 145   { -0.30751999999999996, 5, -0.19999999999999996 },
 146   { -0.17882874999999995, 5, -0.099999999999999978 },
 147   { 0.0000000000000000, 5, 0.0000000000000000 },
 148   { 0.17882875000000015, 5, 0.10000000000000009 },
 149   { 0.30751999999999996, 5, 0.19999999999999996 },
 150   { 0.34538625000000001, 5, 0.30000000000000004 },
 151   { 0.27064000000000010, 5, 0.39999999999999991 },
 152   { 0.089843750000000000, 5, 0.50000000000000000 },
 153   { -0.15264000000000016, 5, 0.60000000000000009 },
 154   { -0.36519874999999991, 5, 0.69999999999999996 },
 155   { -0.39951999999999993, 5, 0.80000000000000004 },
 156   { -0.041141250000000261, 5, 0.89999999999999991 },
 157   { 1.0000000000000000, 5, 1.0000000000000000 },
 158 };
 159 const double toler004 = 2.5000000000000020e-13;
 160
 161 // Test data for l=10.
 162 // max(|f - f_GSL|): 2.7755575615628914e-16
 163 // max(|f - f_GSL| / |f_GSL|): 1.0547610802636413e-15
 164 const testcase_legendre<double>
 165 data005[21] =
 166 {
 167   { 1.0000000000000000, 10, -1.0000000000000000 },
 168   { -0.26314561785585960, 10, -0.90000000000000002 },
 169   { 0.30052979560000004, 10, -0.80000000000000004 },
 170   { 0.085805795531640333, 10, -0.69999999999999996 },
 171   { -0.24366274560000001, 10, -0.59999999999999998 },
 172   { -0.18822860717773438, 10, -0.50000000000000000 },
 173   { 0.096839064399999925, 10, -0.40000000000000002 },
 174   { 0.25147634951601561, 10, -0.30000000000000004 },
 175   { 0.12907202559999983, 10, -0.19999999999999996 },
 176   { -0.12212499738710943, 10, -0.099999999999999978 },
 177   { -0.24609375000000000, 10, 0.0000000000000000 },
 178   { -0.12212499738710922, 10, 0.10000000000000009 },
 179   { 0.12907202559999983, 10, 0.19999999999999996 },
 180   { 0.25147634951601561, 10, 0.30000000000000004 },
 181   { 0.096839064400000258, 10, 0.39999999999999991 },
 182   { -0.18822860717773438, 10, 0.50000000000000000 },
 183   { -0.24366274559999984, 10, 0.60000000000000009 },
 184   { 0.085805795531640333, 10, 0.69999999999999996 },
 185   { 0.30052979560000004, 10, 0.80000000000000004 },
 186   { -0.26314561785585899, 10, 0.89999999999999991 },
 187   { 1.0000000000000000, 10, 1.0000000000000000 },
 188 };
 189 const double toler005 = 2.5000000000000020e-13;
 190
 191 // Test data for l=20.
 192 // max(|f - f_GSL|): 3.3306690738754696e-16
 193 // max(|f - f_GSL| / |f_GSL|): 2.2307336678138069e-15
 194 const testcase_legendre<double>
 195 data006[21] =
 196 {
 197   { 1.0000000000000000, 20, -1.0000000000000000 },
 198   { -0.14930823530984835, 20, -0.90000000000000002 },
 199   { 0.22420460541741347, 20, -0.80000000000000004 },
 200   { -0.20457394463834172, 20, -0.69999999999999996 },
 201   { 0.15916752910098109, 20, -0.59999999999999998 },
 202   { -0.048358381067373557, 20, -0.50000000000000000 },
 203   { -0.10159261558628156, 20, -0.40000000000000002 },
 204   { 0.18028715947998042, 20, -0.30000000000000004 },
 205   { -0.098042194344594796, 20, -0.19999999999999996 },
 206   { -0.082077130944527663, 20, -0.099999999999999978 },
 207   { 0.17619705200195312, 20, 0.0000000000000000 },
 208   { -0.082077130944528023, 20, 0.10000000000000009 },
 209   { -0.098042194344594796, 20, 0.19999999999999996 },
 210   { 0.18028715947998042, 20, 0.30000000000000004 },
 211   { -0.10159261558628112, 20, 0.39999999999999991 },
 212   { -0.048358381067373557, 20, 0.50000000000000000 },
 213   { 0.15916752910098075, 20, 0.60000000000000009 },
 214   { -0.20457394463834172, 20, 0.69999999999999996 },
 215   { 0.22420460541741347, 20, 0.80000000000000004 },
 216   { -0.14930823530984924, 20, 0.89999999999999991 },
 217   { 1.0000000000000000, 20, 1.0000000000000000 },
 218 };
 219 const double toler006 = 2.5000000000000020e-13;
 220
 221 // Test data for l=50.
 222 // max(|f - f_GSL|): 3.6082248300317588e-16
 223 // max(|f - f_GSL| / |f_GSL|): 2.1700196856209138e-15
 224 const testcase_legendre<double>
 225 data007[21] =
 226 {
 227   { 1.0000000000000000, 50, -1.0000000000000000 },
 228   { -0.17003765994383671, 50, -0.90000000000000002 },
 229   { 0.13879737345093113, 50, -0.80000000000000004 },
 230   { -0.014572731645892852, 50, -0.69999999999999996 },
 231   { -0.058860798844002096, 50, -0.59999999999999998 },
 232   { -0.031059099239609811, 50, -0.50000000000000000 },
 233   { 0.041569033381825375, 50, -0.40000000000000002 },
 234   { 0.10911051574714797, 50, -0.30000000000000004 },
 235   { 0.083432272204197494, 50, -0.19999999999999996 },
 236   { -0.038205812661313600, 50, -0.099999999999999978 },
 237   { -0.11227517265921705, 50, 0.0000000000000000 },
 238   { -0.038205812661314155, 50, 0.10000000000000009 },
 239   { 0.083432272204197494, 50, 0.19999999999999996 },
 240   { 0.10911051574714797, 50, 0.30000000000000004 },
 241   { 0.041569033381824674, 50, 0.39999999999999991 },
 242   { -0.031059099239609811, 50, 0.50000000000000000 },
 243   { -0.058860798844001430, 50, 0.60000000000000009 },
 244   { -0.014572731645892852, 50, 0.69999999999999996 },
 245   { 0.13879737345093113, 50, 0.80000000000000004 },
 246   { -0.17003765994383657, 50, 0.89999999999999991 },
 247   { 1.0000000000000000, 50, 1.0000000000000000 },
 248 };
 249 const double toler007 = 2.5000000000000020e-13;
 250
 251 // Test data for l=100.
 252 // max(|f - f_GSL|): 3.4694469519536142e-16
 253 // max(|f - f_GSL| / |f_GSL|): 6.8214063779431592e-15
 254 const testcase_legendre<double>
 255 data008[21] =
 256 {
 257   { 1.0000000000000000, 100, -1.0000000000000000 },
 258   { 0.10226582055871893, 100, -0.90000000000000002 },
 259   { 0.050861167913584228, 100, -0.80000000000000004 },
 260   { -0.077132507199778641, 100, -0.69999999999999996 },
 261   { -0.023747023905133141, 100, -0.59999999999999998 },
 262   { -0.060518025961861198, 100, -0.50000000000000000 },
 263   { -0.072258202125684470, 100, -0.40000000000000002 },
 264   { 0.057127392202801566, 100, -0.30000000000000004 },
 265   { 0.014681835355659706, 100, -0.19999999999999996 },
 266   { -0.063895098434750205, 100, -0.099999999999999978 },
 267   { 0.079589237387178727, 100, 0.0000000000000000 },
 268   { -0.063895098434749761, 100, 0.10000000000000009 },
 269   { 0.014681835355659706, 100, 0.19999999999999996 },
 270   { 0.057127392202801566, 100, 0.30000000000000004 },
 271   { -0.072258202125685025, 100, 0.39999999999999991 },
 272   { -0.060518025961861198, 100, 0.50000000000000000 },
 273   { -0.023747023905134217, 100, 0.60000000000000009 },
 274   { -0.077132507199778641, 100, 0.69999999999999996 },
 275   { 0.050861167913584228, 100, 0.80000000000000004 },
 276   { 0.10226582055871711, 100, 0.89999999999999991 },
 277   { 1.0000000000000000, 100, 1.0000000000000000 },
 278 };
 279 const double toler008 = 5.0000000000000039e-13;
 280
 281 template<typename Tp, unsigned int Num>
 282   void
 283   test(const testcase_legendre<Tp> (&data)[Num], Tp toler)
 284   {
 285     const Tp eps = std::numeric_limits<Tp>::epsilon();
 286     Tp max_abs_diff = -Tp(1);
 287     Tp max_abs_frac = -Tp(1);
 288     unsigned int num_datum = Num;
 289     for (unsigned int i = 0; i < num_datum; ++i)
 290       {
 291         const Tp f = std::legendre(data[i].l, data[i].x);
 292         const Tp f0 = data[i].f0;
 293         const Tp diff = f - f0;
 294         if (std::abs(diff) > max_abs_diff)
 295           max_abs_diff = std::abs(diff);
 296         if (std::abs(f0) > Tp(10) * eps
 297          && std::abs(f) > Tp(10) * eps)
 298           {
 299             const Tp frac = diff / f0;
 300             if (std::abs(frac) > max_abs_frac)
 301               max_abs_frac = std::abs(frac);
 302           }
 303       }
 304     VERIFY(max_abs_frac < toler);
 305   }
 306
 307 int
 308 main()
 309 {
 310   test(data001, toler001);
 311   test(data002, toler002);
 312   test(data003, toler003);
 313   test(data004, toler004);
 314   test(data005, toler005);
 315   test(data006, toler006);
 316   test(data007, toler007);
 317   test(data008, toler008);
 318   return 0;
 319 }