libstdc++-v3/testsuite/special_functions/16_laguerre/check_value.cc

   1 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
   2 //
   3 // Copyright (C) 2016 Free Software Foundation, Inc.
   4 //
   5 // This file is part of the GNU ISO C++ Library.  This library is free
   6 // software; you can redistribute it and/or modify it under the
   7 // terms of the GNU General Public License as published by the
   8 // Free Software Foundation; either version 3, or (at your option)
   9 // any later version.
  10 //
  11 // This library is distributed in the hope that it will be useful,
  12 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14 // GNU General Public License for more details.
  15 //
  16 // You should have received a copy of the GNU General Public License along
  17 // with this library; see the file COPYING3.  If not see
  18 // <http://www.gnu.org/licenses/>.
  19
  20 //  laguerre
  21 //  Compare against values generated by the GNU Scientific Library.
  22 //  The GSL can be found on the web: http://www.gnu.org/software/gsl/
  23 #include <limits>
  24 #include <cmath>
  25 #if defined(__TEST_DEBUG)
  26 #  include <iostream>
  27 #  define VERIFY(A) \
  28   if (!(A)) \
  29     { \
  30       std::cout << "line " << __LINE__ \
  31         << "  max_abs_frac = " << max_abs_frac \
  32         << std::endl; \
  33     }
  34 #else
  35 #  include <testsuite_hooks.h>
  36 #endif
  37 #include <specfun_testcase.h>
  38
  39
  40 // Test data for n=0.
  41 // max(|f - f_GSL|): 0.0000000000000000
  42 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
  43 const testcase_laguerre<double>
  44 data001[21] =
  45 {
  46   { 1.0000000000000000, 0, 0.0000000000000000 },
  47   { 1.0000000000000000, 0, 5.0000000000000000 },
  48   { 1.0000000000000000, 0, 10.000000000000000 },
  49   { 1.0000000000000000, 0, 15.000000000000000 },
  50   { 1.0000000000000000, 0, 20.000000000000000 },
  51   { 1.0000000000000000, 0, 25.000000000000000 },
  52   { 1.0000000000000000, 0, 30.000000000000000 },
  53   { 1.0000000000000000, 0, 35.000000000000000 },
  54   { 1.0000000000000000, 0, 40.000000000000000 },
  55   { 1.0000000000000000, 0, 45.000000000000000 },
  56   { 1.0000000000000000, 0, 50.000000000000000 },
  57   { 1.0000000000000000, 0, 55.000000000000000 },
  58   { 1.0000000000000000, 0, 60.000000000000000 },
  59   { 1.0000000000000000, 0, 65.000000000000000 },
  60   { 1.0000000000000000, 0, 70.000000000000000 },
  61   { 1.0000000000000000, 0, 75.000000000000000 },
  62   { 1.0000000000000000, 0, 80.000000000000000 },
  63   { 1.0000000000000000, 0, 85.000000000000000 },
  64   { 1.0000000000000000, 0, 90.000000000000000 },
  65   { 1.0000000000000000, 0, 95.000000000000000 },
  66   { 1.0000000000000000, 0, 100.00000000000000 },
  67 };
  68 const double toler001 = 2.5000000000000020e-13;
  69
  70 // Test data for n=1.
  71 // max(|f - f_GSL|): 0.0000000000000000
  72 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
  73 const testcase_laguerre<double>
  74 data002[21] =
  75 {
  76   { 1.0000000000000000, 1, 0.0000000000000000 },
  77   { -4.0000000000000000, 1, 5.0000000000000000 },
  78   { -9.0000000000000000, 1, 10.000000000000000 },
  79   { -14.000000000000000, 1, 15.000000000000000 },
  80   { -19.000000000000000, 1, 20.000000000000000 },
  81   { -24.000000000000000, 1, 25.000000000000000 },
  82   { -29.000000000000000, 1, 30.000000000000000 },
  83   { -34.000000000000000, 1, 35.000000000000000 },
  84   { -39.000000000000000, 1, 40.000000000000000 },
  85   { -44.000000000000000, 1, 45.000000000000000 },
  86   { -49.000000000000000, 1, 50.000000000000000 },
  87   { -54.000000000000000, 1, 55.000000000000000 },
  88   { -59.000000000000000, 1, 60.000000000000000 },
  89   { -64.000000000000000, 1, 65.000000000000000 },
  90   { -69.000000000000000, 1, 70.000000000000000 },
  91   { -74.000000000000000, 1, 75.000000000000000 },
  92   { -79.000000000000000, 1, 80.000000000000000 },
  93   { -84.000000000000000, 1, 85.000000000000000 },
  94   { -89.000000000000000, 1, 90.000000000000000 },
  95   { -94.000000000000000, 1, 95.000000000000000 },
  96   { -99.000000000000000, 1, 100.00000000000000 },
  97 };
  98 const double toler002 = 2.5000000000000020e-13;
  99
 100 // Test data for n=2.
 101 // max(|f - f_GSL|): 0.0000000000000000
 102 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 103 const testcase_laguerre<double>
 104 data003[21] =
 105 {
 106   { 1.0000000000000000, 2, 0.0000000000000000 },
 107   { 3.5000000000000000, 2, 5.0000000000000000 },
 108   { 31.000000000000000, 2, 10.000000000000000 },
 109   { 83.500000000000000, 2, 15.000000000000000 },
 110   { 161.00000000000000, 2, 20.000000000000000 },
 111   { 263.50000000000000, 2, 25.000000000000000 },
 112   { 391.00000000000000, 2, 30.000000000000000 },
 113   { 543.50000000000000, 2, 35.000000000000000 },
 114   { 721.00000000000000, 2, 40.000000000000000 },
 115   { 923.50000000000000, 2, 45.000000000000000 },
 116   { 1151.0000000000000, 2, 50.000000000000000 },
 117   { 1403.5000000000000, 2, 55.000000000000000 },
 118   { 1681.0000000000000, 2, 60.000000000000000 },
 119   { 1983.5000000000000, 2, 65.000000000000000 },
 120   { 2311.0000000000000, 2, 70.000000000000000 },
 121   { 2663.5000000000000, 2, 75.000000000000000 },
 122   { 3041.0000000000000, 2, 80.000000000000000 },
 123   { 3443.5000000000000, 2, 85.000000000000000 },
 124   { 3871.0000000000000, 2, 90.000000000000000 },
 125   { 4323.5000000000000, 2, 95.000000000000000 },
 126   { 4801.0000000000000, 2, 100.00000000000000 },
 127 };
 128 const double toler003 = 2.5000000000000020e-13;
 129
 130 // Test data for n=5.
 131 // max(|f - f_GSL|): 7.4505805969238281e-09
 132 // max(|f - f_GSL| / |f_GSL|): 1.9501553136894460e-16
 133 const testcase_laguerre<double>
 134 data004[21] =
 135 {
 136   { 1.0000000000000000, 5, 0.0000000000000000 },
 137   { -3.1666666666666665, 5, 5.0000000000000000 },
 138   { 34.333333333333329, 5, 10.000000000000000 },
 139   { -355.25000000000000, 5, 15.000000000000000 },
 140   { -4765.6666666666670, 5, 20.000000000000000 },
 141   { -23040.666666666664, 5, 25.000000000000000 },
 142   { -74399.000000000000, 5, 30.000000000000000 },
 143   { -190559.41666666663, 5, 35.000000000000000 },
 144   { -418865.66666666663, 5, 40.000000000000000 },
 145   { -825411.50000000000, 5, 45.000000000000000 },
 146   { -1498165.6666666665, 5, 50.000000000000000 },
 147   { -2550096.9166666670, 5, 55.000000000000000 },
 148   { -4122299.0000000000, 5, 60.000000000000000 },
 149   { -6387115.6666666670, 5, 65.000000000000000 },
 150   { -9551265.6666666679, 5, 70.000000000000000 },
 151   { -13858967.750000000, 5, 75.000000000000000 },
 152   { -19595065.666666664, 5, 80.000000000000000 },
 153   { -27088153.166666668, 5, 85.000000000000000 },
 154   { -36713699.000000000, 5, 90.000000000000000 },
 155   { -48897171.916666657, 5, 95.000000000000000 },
 156   { -64117165.666666664, 5, 100.00000000000000 },
 157 };
 158 const double toler004 = 2.5000000000000020e-13;
 159
 160 // Test data for n=10.
 161 // max(|f - f_GSL|): 0.0029296875000000000
 162 // max(|f - f_GSL| / |f_GSL|): 6.1315986390500118e-15
 163 const testcase_laguerre<double>
 164 data005[21] =
 165 {
 166   { 1.0000000000000000, 10, 0.0000000000000000 },
 167   { 1.7562761794532631, 10, 5.0000000000000000 },
 168   { 27.984126984126977, 10, 10.000000000000000 },
 169   { -237.51841517857147, 10, 15.000000000000000 },
 170   { 3227.8077601410932, 10, 20.000000000000000 },
 171   { -45786.199797453693, 10, 25.000000000000000 },
 172   { 15129.571428571455, 10, 30.000000000000000 },
 173   { 7764800.8179494590, 10, 35.000000000000000 },
 174   { 79724066.608465582, 10, 40.000000000000000 },
 175   { 469865425.65122765, 10, 45.000000000000000 },
 176   { 2037190065.3738980, 10, 50.000000000000000 },
 177   { 7187828002.9825764, 10, 55.000000000000000 },
 178   { 21804200401.000000, 10, 60.000000000000000 },
 179   { 58854343015.616211, 10, 65.000000000000000 },
 180   { 144688291819.51855, 10, 70.000000000000000 },
 181   { 329425241736.70038, 10, 75.000000000000000 },
 182   { 703324772760.08276, 10, 80.000000000000000 },
 183   { 1421627560118.6157, 10, 85.000000000000000 },
 184   { 2741055412243.8569, 10, 90.000000000000000 },
 185   { 5071986977681.8652, 10, 95.000000000000000 },
 186   { 9051283795429.5723, 10, 100.00000000000000 },
 187 };
 188 const double toler005 = 5.0000000000000039e-13;
 189
 190 // Test data for n=20.
 191 // max(|f - f_GSL|): 2048.0000000000000
 192 // max(|f - f_GSL| / |f_GSL|): 7.1189246999774008e-15
 193 const testcase_laguerre<double>
 194 data006[21] =
 195 {
 196   { 1.0000000000000000, 20, 0.0000000000000000 },
 197   { 2.0202257444769134, 20, 5.0000000000000000 },
 198   { -11.961333867812119, 20, 10.000000000000000 },
 199   { -50.151037960139455, 20, 15.000000000000000 },
 200   { 2829.4728613531743, 20, 20.000000000000000 },
 201   { -11583.947899113540, 20, 25.000000000000000 },
 202   { -18439.424502520938, 20, 30.000000000000000 },
 203   { -38838.223606979285, 20, 35.000000000000000 },
 204   { 24799805.877530713, 20, 40.000000000000000 },
 205   { -673953823.59913278, 20, 45.000000000000000 },
 206   { 7551960453.7672548, 20, 50.000000000000000 },
 207   { 31286508510.614746, 20, 55.000000000000000 },
 208   { -1379223608444.9155, 20, 60.000000000000000 },
 209   { -6692517968212.9717, 20, 65.000000000000000 },
 210   { 165423821874449.94, 20, 70.000000000000000 },
 211   { 3082390018008546.5, 20, 75.000000000000000 },
 212   { 29500368536981676., 20, 80.000000000000000 },
 213   { 2.0353526354974186e+17, 20, 85.000000000000000 },
 214   { 1.1292309514432901e+18, 20, 90.000000000000000 },
 215   { 5.3239262855563100e+18, 20, 95.000000000000000 },
 216   { 2.2061882785931735e+19, 20, 100.00000000000000 },
 217 };
 218 const double toler006 = 5.0000000000000039e-13;
 219
 220 // Test data for n=50.
 221 // max(|f - f_GSL|): 196608.00000000000
 222 // max(|f - f_GSL| / |f_GSL|): 4.2910775919271532e-15
 223 const testcase_laguerre<double>
 224 data007[21] =
 225 {
 226   { 1.0000000000000000, 50, 0.0000000000000000 },
 227   { 1.4735258819430543, 50, 5.0000000000000000 },
 228   { 17.534183446338233, 50, 10.000000000000000 },
 229   { -195.62436619077380, 50, 15.000000000000000 },
 230   { 980.26961889791028, 50, 20.000000000000000 },
 231   { 24812.277673870878, 50, 25.000000000000000 },
 232   { 293000.50735962362, 50, 30.000000000000000 },
 233   { 2316195.5013375278, 50, 35.000000000000000 },
 234   { -14896937.968694873, 50, 40.000000000000000 },
 235   { -502066598.00813466, 50, 45.000000000000000 },
 236   { 2513677852.6916871, 50, 50.000000000000000 },
 237   { 45129675503.538910, 50, 55.000000000000000 },
 238   { -883876565337.99219, 50, 60.000000000000000 },
 239   { 9361319947203.8418, 50, 65.000000000000000 },
 240   { -80967880733583.234, 50, 70.000000000000000 },
 241   { 717391079438942.62, 50, 75.000000000000000 },
 242   { -8217471769564841.0, 50, 80.000000000000000 },
 243   { 1.2595276229009978e+17, 50, 85.000000000000000 },
 244   { -2.1140031308048891e+18, 50, 90.000000000000000 },
 245   { 3.2438187475835134e+19, 50, 95.000000000000000 },
 246   { -3.9710103487094692e+20, 50, 100.00000000000000 },
 247 };
 248 const double toler007 = 2.5000000000000020e-13;
 249
 250 // Test data for n=100.
 251 // max(|f - f_GSL|): 98304.000000000000
 252 // max(|f - f_GSL| / |f_GSL|): 3.8776197831393928e-15
 253 const testcase_laguerre<double>
 254 data008[21] =
 255 {
 256   { 1.0000000000000000, 100, 0.0000000000000000 },
 257   { 1.4555271625328801, 100, 5.0000000000000000 },
 258   { 13.277662844303450, 100, 10.000000000000000 },
 259   { 91.737038454342454, 100, 15.000000000000000 },
 260   { 1854.0367283243388, 100, 20.000000000000000 },
 261   { -11281.698886837261, 100, 25.000000000000000 },
 262   { 170141.86987046551, 100, 30.000000000000000 },
 263   { -2950092.7025822806, 100, 35.000000000000000 },
 264   { -7272442.3156006960, 100, 40.000000000000000 },
 265   { 295697471.90876162, 100, 45.000000000000000 },
 266   { 4847420871.2690506, 100, 50.000000000000000 },
 267   { 59406998102.392288, 100, 55.000000000000000 },
 268   { 693492765740.29688, 100, 60.000000000000000 },
 269   { 6606192010150.3154, 100, 65.000000000000000 },
 270   { 17125518672239.770, 100, 70.000000000000000 },
 271   { -870493767065150.12, 100, 75.000000000000000 },
 272   { -13763178176383768., 100, 80.000000000000000 },
 273   { 30667078414479584., 100, 85.000000000000000 },
 274   { 2.1307220490380173e+18, 100, 90.000000000000000 },
 275   { -7.2706523009007821e+18, 100, 95.000000000000000 },
 276   { -2.6292260693068916e+20, 100, 100.00000000000000 },
 277 };
 278 const double toler008 = 2.5000000000000020e-13;
 279
 280 template<typename Tp, unsigned int Num>
 281   void
 282   test(const testcase_laguerre<Tp> (&data)[Num], Tp toler)
 283   {
 284     bool test __attribute__((unused)) = true;
 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::laguerre(data[i].n, 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 }