libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/18_laguerre/check_value.cc

   1 // 2007-02-04  Edward Smith-Rowland <3dw4rd@verizon.net>
   2 //
   3 // Copyright (C) 2007-2013 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
  22
  23 //  Compare against values generated by the GNU Scientific Library.
  24 //  The GSL can be found on the web: http://www.gnu.org/software/gsl/
  25
  26 #include <tr1/cmath>
  27 #if defined(__TEST_DEBUG)
  28 #include <iostream>
  29 #define VERIFY(A) \
  30 if (!(A)) \
  31   { \
  32     std::cout << "line " << __LINE__ \
  33       << "  max_abs_frac = " << max_abs_frac \
  34       << std::endl; \
  35   }
  36 #else
  37 #include <testsuite_hooks.h>
  38 #endif
  39 #include "../testcase.h"
  40
  41
  42 // Test data for n=0.
  43 testcase_laguerre<double> data001[] = {
  44   { 1.0000000000000000, 0, 0.0000000000000000 },
  45   { 1.0000000000000000, 0, 5.0000000000000000 },
  46   { 1.0000000000000000, 0, 10.000000000000000 },
  47   { 1.0000000000000000, 0, 15.000000000000000 },
  48   { 1.0000000000000000, 0, 20.000000000000000 },
  49   { 1.0000000000000000, 0, 25.000000000000000 },
  50   { 1.0000000000000000, 0, 30.000000000000000 },
  51   { 1.0000000000000000, 0, 35.000000000000000 },
  52   { 1.0000000000000000, 0, 40.000000000000000 },
  53   { 1.0000000000000000, 0, 45.000000000000000 },
  54   { 1.0000000000000000, 0, 50.000000000000000 },
  55   { 1.0000000000000000, 0, 55.000000000000000 },
  56   { 1.0000000000000000, 0, 60.000000000000000 },
  57   { 1.0000000000000000, 0, 65.000000000000000 },
  58   { 1.0000000000000000, 0, 70.000000000000000 },
  59   { 1.0000000000000000, 0, 75.000000000000000 },
  60   { 1.0000000000000000, 0, 80.000000000000000 },
  61   { 1.0000000000000000, 0, 85.000000000000000 },
  62   { 1.0000000000000000, 0, 90.000000000000000 },
  63   { 1.0000000000000000, 0, 95.000000000000000 },
  64   { 1.0000000000000000, 0, 100.00000000000000 },
  65 };
  66
  67 // Test function for n=0.
  68 template <typename Tp>
  69 void test001()
  70 {
  71   const Tp eps = std::numeric_limits<Tp>::epsilon();
  72   Tp max_abs_diff = -Tp(1);
  73   Tp max_abs_frac = -Tp(1);
  74   unsigned int num_datum = sizeof(data001)
  75                          / sizeof(testcase_laguerre<double>);
  76   for (unsigned int i = 0; i < num_datum; ++i)
  77     {
  78       const Tp f = std::tr1::laguerre(Tp(data001[i].n), Tp(data001[i].x));
  79       const Tp f0 = data001[i].f0;
  80       const Tp diff = f - f0;
  81       if (std::abs(diff) > max_abs_diff)
  82         max_abs_diff = std::abs(diff);
  83       if (std::abs(f0) > Tp(10) * eps
  84        && std::abs(f) > Tp(10) * eps)
  85         {
  86           const Tp frac = diff / f0;
  87           if (std::abs(frac) > max_abs_frac)
  88             max_abs_frac = std::abs(frac);
  89         }
  90     }
  91   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
  92 }
  93
  94 // Test data for n=1.
  95 testcase_laguerre<double> data002[] = {
  96   { 1.0000000000000000, 1, 0.0000000000000000 },
  97   { -4.0000000000000000, 1, 5.0000000000000000 },
  98   { -9.0000000000000000, 1, 10.000000000000000 },
  99   { -14.000000000000000, 1, 15.000000000000000 },
 100   { -19.000000000000000, 1, 20.000000000000000 },
 101   { -24.000000000000000, 1, 25.000000000000000 },
 102   { -29.000000000000000, 1, 30.000000000000000 },
 103   { -34.000000000000000, 1, 35.000000000000000 },
 104   { -39.000000000000000, 1, 40.000000000000000 },
 105   { -44.000000000000000, 1, 45.000000000000000 },
 106   { -49.000000000000000, 1, 50.000000000000000 },
 107   { -54.000000000000000, 1, 55.000000000000000 },
 108   { -59.000000000000000, 1, 60.000000000000000 },
 109   { -64.000000000000000, 1, 65.000000000000000 },
 110   { -69.000000000000000, 1, 70.000000000000000 },
 111   { -74.000000000000000, 1, 75.000000000000000 },
 112   { -79.000000000000000, 1, 80.000000000000000 },
 113   { -84.000000000000000, 1, 85.000000000000000 },
 114   { -89.000000000000000, 1, 90.000000000000000 },
 115   { -94.000000000000000, 1, 95.000000000000000 },
 116   { -99.000000000000000, 1, 100.00000000000000 },
 117 };
 118
 119 // Test function for n=1.
 120 template <typename Tp>
 121 void test002()
 122 {
 123   const Tp eps = std::numeric_limits<Tp>::epsilon();
 124   Tp max_abs_diff = -Tp(1);
 125   Tp max_abs_frac = -Tp(1);
 126   unsigned int num_datum = sizeof(data002)
 127                          / sizeof(testcase_laguerre<double>);
 128   for (unsigned int i = 0; i < num_datum; ++i)
 129     {
 130       const Tp f = std::tr1::laguerre(Tp(data002[i].n), Tp(data002[i].x));
 131       const Tp f0 = data002[i].f0;
 132       const Tp diff = f - f0;
 133       if (std::abs(diff) > max_abs_diff)
 134         max_abs_diff = std::abs(diff);
 135       if (std::abs(f0) > Tp(10) * eps
 136        && std::abs(f) > Tp(10) * eps)
 137         {
 138           const Tp frac = diff / f0;
 139           if (std::abs(frac) > max_abs_frac)
 140             max_abs_frac = std::abs(frac);
 141         }
 142     }
 143   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 144 }
 145
 146 // Test data for n=2.
 147 testcase_laguerre<double> data003[] = {
 148   { 1.0000000000000000, 2, 0.0000000000000000 },
 149   { 3.5000000000000000, 2, 5.0000000000000000 },
 150   { 31.000000000000000, 2, 10.000000000000000 },
 151   { 83.500000000000000, 2, 15.000000000000000 },
 152   { 161.00000000000000, 2, 20.000000000000000 },
 153   { 263.50000000000000, 2, 25.000000000000000 },
 154   { 391.00000000000000, 2, 30.000000000000000 },
 155   { 543.50000000000000, 2, 35.000000000000000 },
 156   { 721.00000000000000, 2, 40.000000000000000 },
 157   { 923.50000000000000, 2, 45.000000000000000 },
 158   { 1151.0000000000000, 2, 50.000000000000000 },
 159   { 1403.5000000000000, 2, 55.000000000000000 },
 160   { 1681.0000000000000, 2, 60.000000000000000 },
 161   { 1983.5000000000000, 2, 65.000000000000000 },
 162   { 2311.0000000000000, 2, 70.000000000000000 },
 163   { 2663.5000000000000, 2, 75.000000000000000 },
 164   { 3041.0000000000000, 2, 80.000000000000000 },
 165   { 3443.5000000000000, 2, 85.000000000000000 },
 166   { 3871.0000000000000, 2, 90.000000000000000 },
 167   { 4323.5000000000000, 2, 95.000000000000000 },
 168   { 4801.0000000000000, 2, 100.00000000000000 },
 169 };
 170
 171 // Test function for n=2.
 172 template <typename Tp>
 173 void test003()
 174 {
 175   const Tp eps = std::numeric_limits<Tp>::epsilon();
 176   Tp max_abs_diff = -Tp(1);
 177   Tp max_abs_frac = -Tp(1);
 178   unsigned int num_datum = sizeof(data003)
 179                          / sizeof(testcase_laguerre<double>);
 180   for (unsigned int i = 0; i < num_datum; ++i)
 181     {
 182       const Tp f = std::tr1::laguerre(Tp(data003[i].n), Tp(data003[i].x));
 183       const Tp f0 = data003[i].f0;
 184       const Tp diff = f - f0;
 185       if (std::abs(diff) > max_abs_diff)
 186         max_abs_diff = std::abs(diff);
 187       if (std::abs(f0) > Tp(10) * eps
 188        && std::abs(f) > Tp(10) * eps)
 189         {
 190           const Tp frac = diff / f0;
 191           if (std::abs(frac) > max_abs_frac)
 192             max_abs_frac = std::abs(frac);
 193         }
 194     }
 195   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 196 }
 197
 198 // Test data for n=5.
 199 testcase_laguerre<double> data004[] = {
 200   { 1.0000000000000000, 5, 0.0000000000000000 },
 201   { -3.1666666666666665, 5, 5.0000000000000000 },
 202   { 34.333333333333329, 5, 10.000000000000000 },
 203   { -355.25000000000000, 5, 15.000000000000000 },
 204   { -4765.6666666666670, 5, 20.000000000000000 },
 205   { -23040.666666666664, 5, 25.000000000000000 },
 206   { -74399.000000000000, 5, 30.000000000000000 },
 207   { -190559.41666666663, 5, 35.000000000000000 },
 208   { -418865.66666666663, 5, 40.000000000000000 },
 209   { -825411.50000000000, 5, 45.000000000000000 },
 210   { -1498165.6666666665, 5, 50.000000000000000 },
 211   { -2550096.9166666670, 5, 55.000000000000000 },
 212   { -4122299.0000000000, 5, 60.000000000000000 },
 213   { -6387115.6666666670, 5, 65.000000000000000 },
 214   { -9551265.6666666679, 5, 70.000000000000000 },
 215   { -13858967.750000000, 5, 75.000000000000000 },
 216   { -19595065.666666664, 5, 80.000000000000000 },
 217   { -27088153.166666668, 5, 85.000000000000000 },
 218   { -36713699.000000000, 5, 90.000000000000000 },
 219   { -48897171.916666657, 5, 95.000000000000000 },
 220   { -64117165.666666664, 5, 100.00000000000000 },
 221 };
 222
 223 // Test function for n=5.
 224 template <typename Tp>
 225 void test004()
 226 {
 227   const Tp eps = std::numeric_limits<Tp>::epsilon();
 228   Tp max_abs_diff = -Tp(1);
 229   Tp max_abs_frac = -Tp(1);
 230   unsigned int num_datum = sizeof(data004)
 231                          / sizeof(testcase_laguerre<double>);
 232   for (unsigned int i = 0; i < num_datum; ++i)
 233     {
 234       const Tp f = std::tr1::laguerre(Tp(data004[i].n), Tp(data004[i].x));
 235       const Tp f0 = data004[i].f0;
 236       const Tp diff = f - f0;
 237       if (std::abs(diff) > max_abs_diff)
 238         max_abs_diff = std::abs(diff);
 239       if (std::abs(f0) > Tp(10) * eps
 240        && std::abs(f) > Tp(10) * eps)
 241         {
 242           const Tp frac = diff / f0;
 243           if (std::abs(frac) > max_abs_frac)
 244             max_abs_frac = std::abs(frac);
 245         }
 246     }
 247   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 248 }
 249
 250 // Test data for n=10.
 251 testcase_laguerre<double> data005[] = {
 252   { 1.0000000000000000, 10, 0.0000000000000000 },
 253   { 1.7562761794532620, 10, 5.0000000000000000 },
 254   { 27.984126984126981, 10, 10.000000000000000 },
 255   { -237.51841517857147, 10, 15.000000000000000 },
 256   { 3227.8077601410932, 10, 20.000000000000000 },
 257   { -45786.199797453693, 10, 25.000000000000000 },
 258   { 15129.571428571489, 10, 30.000000000000000 },
 259   { 7764800.8179494590, 10, 35.000000000000000 },
 260   { 79724066.608465582, 10, 40.000000000000000 },
 261   { 469865425.65122765, 10, 45.000000000000000 },
 262   { 2037190065.3738980, 10, 50.000000000000000 },
 263   { 7187828002.9825764, 10, 55.000000000000000 },
 264   { 21804200401.000000, 10, 60.000000000000000 },
 265   { 58854343015.616211, 10, 65.000000000000000 },
 266   { 144688291819.51855, 10, 70.000000000000000 },
 267   { 329425241736.70038, 10, 75.000000000000000 },
 268   { 703324772760.08276, 10, 80.000000000000000 },
 269   { 1421627560118.6157, 10, 85.000000000000000 },
 270   { 2741055412243.8569, 10, 90.000000000000000 },
 271   { 5071986977681.8652, 10, 95.000000000000000 },
 272   { 9051283795429.5723, 10, 100.00000000000000 },
 273 };
 274
 275 // Test function for n=10.
 276 template <typename Tp>
 277 void test005()
 278 {
 279   const Tp eps = std::numeric_limits<Tp>::epsilon();
 280   Tp max_abs_diff = -Tp(1);
 281   Tp max_abs_frac = -Tp(1);
 282   unsigned int num_datum = sizeof(data005)
 283                          / sizeof(testcase_laguerre<double>);
 284   for (unsigned int i = 0; i < num_datum; ++i)
 285     {
 286       const Tp f = std::tr1::laguerre(Tp(data005[i].n), Tp(data005[i].x));
 287       const Tp f0 = data005[i].f0;
 288       const Tp diff = f - f0;
 289       if (std::abs(diff) > max_abs_diff)
 290         max_abs_diff = std::abs(diff);
 291       if (std::abs(f0) > Tp(10) * eps
 292        && std::abs(f) > Tp(10) * eps)
 293         {
 294           const Tp frac = diff / f0;
 295           if (std::abs(frac) > max_abs_frac)
 296             max_abs_frac = std::abs(frac);
 297         }
 298     }
 299   VERIFY(max_abs_frac < Tp(5.0000000000000039e-13));
 300 }
 301
 302 // Test data for n=20.
 303 testcase_laguerre<double> data006[] = {
 304   { 1.0000000000000000, 20, 0.0000000000000000 },
 305   { 2.0202257444769129, 20, 5.0000000000000000 },
 306   { -11.961333867812119, 20, 10.000000000000000 },
 307   { -50.151037960139455, 20, 15.000000000000000 },
 308   { 2829.4728613531738, 20, 20.000000000000000 },
 309   { -11583.947899113535, 20, 25.000000000000000 },
 310   { -18439.424502520938, 20, 30.000000000000000 },
 311   { -38838.223606979467, 20, 35.000000000000000 },
 312   { 24799805.877530701, 20, 40.000000000000000 },
 313   { -673953823.59913290, 20, 45.000000000000000 },
 314   { 7551960453.7672529, 20, 50.000000000000000 },
 315   { 31286508510.614754, 20, 55.000000000000000 },
 316   { -1379223608444.9155, 20, 60.000000000000000 },
 317   { -6692517968212.9727, 20, 65.000000000000000 },
 318   { 165423821874449.94, 20, 70.000000000000000 },
 319   { 3082390018008546.5, 20, 75.000000000000000 },
 320   { 29500368536981676., 20, 80.000000000000000 },
 321   { 2.0353526354974186e+17, 20, 85.000000000000000 },
 322   { 1.1292309514432899e+18, 20, 90.000000000000000 },
 323   { 5.3239262855563100e+18, 20, 95.000000000000000 },
 324   { 2.2061882785931735e+19, 20, 100.00000000000000 },
 325 };
 326
 327 // Test function for n=20.
 328 template <typename Tp>
 329 void test006()
 330 {
 331   const Tp eps = std::numeric_limits<Tp>::epsilon();
 332   Tp max_abs_diff = -Tp(1);
 333   Tp max_abs_frac = -Tp(1);
 334   unsigned int num_datum = sizeof(data006)
 335                          / sizeof(testcase_laguerre<double>);
 336   for (unsigned int i = 0; i < num_datum; ++i)
 337     {
 338       const Tp f = std::tr1::laguerre(Tp(data006[i].n), Tp(data006[i].x));
 339       const Tp f0 = data006[i].f0;
 340       const Tp diff = f - f0;
 341       if (std::abs(diff) > max_abs_diff)
 342         max_abs_diff = std::abs(diff);
 343       if (std::abs(f0) > Tp(10) * eps
 344        && std::abs(f) > Tp(10) * eps)
 345         {
 346           const Tp frac = diff / f0;
 347           if (std::abs(frac) > max_abs_frac)
 348             max_abs_frac = std::abs(frac);
 349         }
 350     }
 351   VERIFY(max_abs_frac < Tp(1.0000000000000008e-12));
 352 }
 353
 354 // Test data for n=50.
 355 testcase_laguerre<double> data007[] = {
 356   { 1.0000000000000000, 50, 0.0000000000000000 },
 357   { 1.4735258819430563, 50, 5.0000000000000000 },
 358   { 17.534183446338233, 50, 10.000000000000000 },
 359   { -195.62436619077388, 50, 15.000000000000000 },
 360   { 980.26961889790766, 50, 20.000000000000000 },
 361   { 24812.277673870871, 50, 25.000000000000000 },
 362   { 293000.50735962350, 50, 30.000000000000000 },
 363   { 2316195.5013375296, 50, 35.000000000000000 },
 364   { -14896937.968694847, 50, 40.000000000000000 },
 365   { -502066598.00813466, 50, 45.000000000000000 },
 366   { 2513677852.6916885, 50, 50.000000000000000 },
 367   { 45129675503.538948, 50, 55.000000000000000 },
 368   { -883876565337.99207, 50, 60.000000000000000 },
 369   { 9361319947203.8379, 50, 65.000000000000000 },
 370   { -80967880733583.219, 50, 70.000000000000000 },
 371   { 717391079438942.88, 50, 75.000000000000000 },
 372   { -8217471769564850.0, 50, 80.000000000000000 },
 373   { 1.2595276229009984e+17, 50, 85.000000000000000 },
 374   { -2.1140031308048906e+18, 50, 90.000000000000000 },
 375   { 3.2438187475835138e+19, 50, 95.000000000000000 },
 376   { -3.9710103487094673e+20, 50, 100.00000000000000 },
 377 };
 378
 379 // Test function for n=50.
 380 template <typename Tp>
 381 void test007()
 382 {
 383   const Tp eps = std::numeric_limits<Tp>::epsilon();
 384   Tp max_abs_diff = -Tp(1);
 385   Tp max_abs_frac = -Tp(1);
 386   unsigned int num_datum = sizeof(data007)
 387                          / sizeof(testcase_laguerre<double>);
 388   for (unsigned int i = 0; i < num_datum; ++i)
 389     {
 390       const Tp f = std::tr1::laguerre(Tp(data007[i].n), Tp(data007[i].x));
 391       const Tp f0 = data007[i].f0;
 392       const Tp diff = f - f0;
 393       if (std::abs(diff) > max_abs_diff)
 394         max_abs_diff = std::abs(diff);
 395       if (std::abs(f0) > Tp(10) * eps
 396        && std::abs(f) > Tp(10) * eps)
 397         {
 398           const Tp frac = diff / f0;
 399           if (std::abs(frac) > max_abs_frac)
 400             max_abs_frac = std::abs(frac);
 401         }
 402     }
 403   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 404 }
 405
 406 // Test data for n=100.
 407 testcase_laguerre<double> data008[] = {
 408   { 1.0000000000000000, 100, 0.0000000000000000 },
 409   { 1.4555271625328832, 100, 5.0000000000000000 },
 410   { 13.277662844303402, 100, 10.000000000000000 },
 411   { 91.737038454342013, 100, 15.000000000000000 },
 412   { 1854.0367283243393, 100, 20.000000000000000 },
 413   { -11281.698886837237, 100, 25.000000000000000 },
 414   { 170141.86987046539, 100, 30.000000000000000 },
 415   { -2950092.7025822792, 100, 35.000000000000000 },
 416   { -7272442.3156007063, 100, 40.000000000000000 },
 417   { 295697471.90876174, 100, 45.000000000000000 },
 418   { 4847420871.2690468, 100, 50.000000000000000 },
 419   { 59406998102.392273, 100, 55.000000000000000 },
 420   { 693492765740.29736, 100, 60.000000000000000 },
 421   { 6606192010150.3096, 100, 65.000000000000000 },
 422   { 17125518672239.707, 100, 70.000000000000000 },
 423   { -870493767065151.38, 100, 75.000000000000000 },
 424   { -13763178176383754., 100, 80.000000000000000 },
 425   { 30667078414479724., 100, 85.000000000000000 },
 426   { 2.1307220490380198e+18, 100, 90.000000000000000 },
 427   { -7.2706523009007862e+18, 100, 95.000000000000000 },
 428   { -2.6292260693068920e+20, 100, 100.00000000000000 },
 429 };
 430
 431 // Test function for n=100.
 432 template <typename Tp>
 433 void test008()
 434 {
 435   const Tp eps = std::numeric_limits<Tp>::epsilon();
 436   Tp max_abs_diff = -Tp(1);
 437   Tp max_abs_frac = -Tp(1);
 438   unsigned int num_datum = sizeof(data008)
 439                          / sizeof(testcase_laguerre<double>);
 440   for (unsigned int i = 0; i < num_datum; ++i)
 441     {
 442       const Tp f = std::tr1::laguerre(Tp(data008[i].n), Tp(data008[i].x));
 443       const Tp f0 = data008[i].f0;
 444       const Tp diff = f - f0;
 445       if (std::abs(diff) > max_abs_diff)
 446         max_abs_diff = std::abs(diff);
 447       if (std::abs(f0) > Tp(10) * eps
 448        && std::abs(f) > Tp(10) * eps)
 449         {
 450           const Tp frac = diff / f0;
 451           if (std::abs(frac) > max_abs_frac)
 452             max_abs_frac = std::abs(frac);
 453         }
 454     }
 455   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 456 }
 457
 458 int main(int, char**)
 459 {
 460   test001<double>();
 461   test002<double>();
 462   test003<double>();
 463   test004<double>();
 464   test005<double>();
 465   test006<double>();
 466   test007<double>();
 467   test008<double>();
 468   return 0;
 469 }