libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/10_cyl_bessel_k/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 //  cyl_bessel_k
  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 nu=0.0000000000000000.
  43 testcase_cyl_bessel_k<double> data001[] = {
  44   { 0.0036910983340425947, 0.0000000000000000, 5.0000000000000000 },
  45   { 1.7780062316167650e-05, 0.0000000000000000, 10.000000000000000 },
  46   { 9.8195364823964333e-08, 0.0000000000000000, 15.000000000000000 },
  47   { 5.7412378153365238e-10, 0.0000000000000000, 20.000000000000000 },
  48   { 3.4641615622131151e-12, 0.0000000000000000, 25.000000000000000 },
  49   { 2.1324774964630566e-14, 0.0000000000000000, 30.000000000000000 },
  50   { 1.3310351491429464e-16, 0.0000000000000000, 35.000000000000000 },
  51   { 8.3928611000995700e-19, 0.0000000000000000, 40.000000000000000 },
  52   { 5.3334561226187255e-21, 0.0000000000000000, 45.000000000000000 },
  53   { 3.4101677497894956e-23, 0.0000000000000000, 50.000000000000000 },
  54   { 2.1913102183534147e-25, 0.0000000000000000, 55.000000000000000 },
  55   { 1.4138978405591074e-27, 0.0000000000000000, 60.000000000000000 },
  56   { 9.1544673210030045e-30, 0.0000000000000000, 65.000000000000000 },
  57   { 5.9446613372925013e-32, 0.0000000000000000, 70.000000000000000 },
  58   { 3.8701170455869113e-34, 0.0000000000000000, 75.000000000000000 },
  59   { 2.5251198425054723e-36, 0.0000000000000000, 80.000000000000000 },
  60   { 1.6507623579783908e-38, 0.0000000000000000, 85.000000000000000 },
  61   { 1.0810242556984256e-40, 0.0000000000000000, 90.000000000000000 },
  62   { 7.0901249699001278e-43, 0.0000000000000000, 95.000000000000000 },
  63   { 4.6566282291759032e-45, 0.0000000000000000, 100.00000000000000 },
  64 };
  65
  66 // Test function for nu=0.0000000000000000.
  67 template <typename Tp>
  68 void test001()
  69 {
  70   const Tp eps = std::numeric_limits<Tp>::epsilon();
  71   Tp max_abs_diff = -Tp(1);
  72   Tp max_abs_frac = -Tp(1);
  73   unsigned int num_datum = sizeof(data001)
  74                          / sizeof(testcase_cyl_bessel_k<double>);
  75   for (unsigned int i = 0; i < num_datum; ++i)
  76     {
  77       const Tp f = std::tr1::cyl_bessel_k(Tp(data001[i].nu), Tp(data001[i].x));
  78       const Tp f0 = data001[i].f0;
  79       const Tp diff = f - f0;
  80       if (std::abs(diff) > max_abs_diff)
  81         max_abs_diff = std::abs(diff);
  82       if (std::abs(f0) > Tp(10) * eps
  83        && std::abs(f) > Tp(10) * eps)
  84         {
  85           const Tp frac = diff / f0;
  86           if (std::abs(frac) > max_abs_frac)
  87             max_abs_frac = std::abs(frac);
  88         }
  89     }
  90   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
  91 }
  92
  93 // Test data for nu=0.33333333333333331.
  94 testcase_cyl_bessel_k<double> data002[] = {
  95   { 0.0037288750960535887, 0.33333333333333331, 5.0000000000000000 },
  96   { 1.7874608271055339e-05, 0.33333333333333331, 10.000000000000000 },
  97   { 9.8548341568798317e-08, 0.33333333333333331, 15.000000000000000 },
  98   { 5.7568278247790865e-10, 0.33333333333333331, 20.000000000000000 },
  99   { 3.4717201424907059e-12, 0.33333333333333331, 25.000000000000000 },
 100   { 2.1363664736611189e-14, 0.33333333333333331, 30.000000000000000 },
 101   { 1.3331202314165813e-16, 0.33333333333333331, 35.000000000000000 },
 102   { 8.4043837769480934e-19, 0.33333333333333331, 40.000000000000000 },
 103   { 5.3399731261024948e-21, 0.33333333333333331, 45.000000000000000 },
 104   { 3.4139217813583632e-23, 0.33333333333333331, 50.000000000000000 },
 105   { 2.1935050179185627e-25, 0.33333333333333331, 55.000000000000000 },
 106   { 1.4151968805623662e-27, 0.33333333333333331, 60.000000000000000 },
 107   { 9.1622357217019043e-30, 0.33333333333333331, 65.000000000000000 },
 108   { 5.9493479703461315e-32, 0.33333333333333331, 70.000000000000000 },
 109   { 3.8729660011055947e-34, 0.33333333333333331, 75.000000000000000 },
 110   { 2.5268631828013877e-36, 0.33333333333333331, 80.000000000000000 },
 111   { 1.6518353676138867e-38, 0.33333333333333331, 85.000000000000000 },
 112   { 1.0816880942511496e-40, 0.33333333333333331, 90.000000000000000 },
 113   { 7.0942508599231512e-43, 0.33333333333333331, 95.000000000000000 },
 114   { 4.6592031570213454e-45, 0.33333333333333331, 100.00000000000000 },
 115 };
 116
 117 // Test function for nu=0.33333333333333331.
 118 template <typename Tp>
 119 void test002()
 120 {
 121   const Tp eps = std::numeric_limits<Tp>::epsilon();
 122   Tp max_abs_diff = -Tp(1);
 123   Tp max_abs_frac = -Tp(1);
 124   unsigned int num_datum = sizeof(data002)
 125                          / sizeof(testcase_cyl_bessel_k<double>);
 126   for (unsigned int i = 0; i < num_datum; ++i)
 127     {
 128       const Tp f = std::tr1::cyl_bessel_k(Tp(data002[i].nu), Tp(data002[i].x));
 129       const Tp f0 = data002[i].f0;
 130       const Tp diff = f - f0;
 131       if (std::abs(diff) > max_abs_diff)
 132         max_abs_diff = std::abs(diff);
 133       if (std::abs(f0) > Tp(10) * eps
 134        && std::abs(f) > Tp(10) * eps)
 135         {
 136           const Tp frac = diff / f0;
 137           if (std::abs(frac) > max_abs_frac)
 138             max_abs_frac = std::abs(frac);
 139         }
 140     }
 141   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 142 }
 143
 144 // Test data for nu=0.50000000000000000.
 145 testcase_cyl_bessel_k<double> data003[] = {
 146   { 0.0037766133746428825, 0.50000000000000000, 5.0000000000000000 },
 147   { 1.7993478093705181e-05, 0.50000000000000000, 10.000000000000000 },
 148   { 9.8991312032877236e-08, 0.50000000000000000, 15.000000000000000 },
 149   { 5.7763739747074450e-10, 0.50000000000000000, 20.000000000000000 },
 150   { 3.4811912768406949e-12, 0.50000000000000000, 25.000000000000000 },
 151   { 2.1412375659560111e-14, 0.50000000000000000, 30.000000000000000 },
 152   { 1.3357311366035824e-16, 0.50000000000000000, 35.000000000000000 },
 153   { 8.4188091949489049e-19, 0.50000000000000000, 40.000000000000000 },
 154   { 5.3481305002517408e-21, 0.50000000000000000, 45.000000000000000 },
 155   { 3.4186200954570754e-23, 0.50000000000000000, 50.000000000000000 },
 156   { 2.1962515908772453e-25, 0.50000000000000000, 55.000000000000000 },
 157   { 1.4168223500353693e-27, 0.50000000000000000, 60.000000000000000 },
 158   { 9.1719554473256892e-30, 0.50000000000000000, 65.000000000000000 },
 159   { 5.9552114337788932e-32, 0.50000000000000000, 70.000000000000000 },
 160   { 3.8765301321409432e-34, 0.50000000000000000, 75.000000000000000 },
 161   { 2.5290440439442910e-36, 0.50000000000000000, 80.000000000000000 },
 162   { 1.6531776067605980e-38, 0.50000000000000000, 85.000000000000000 },
 163   { 1.0825184636529955e-40, 0.50000000000000000, 90.000000000000000 },
 164   { 7.0994115873258822e-43, 0.50000000000000000, 95.000000000000000 },
 165   { 4.6624238126346715e-45, 0.50000000000000000, 100.00000000000000 },
 166 };
 167
 168 // Test function for nu=0.50000000000000000.
 169 template <typename Tp>
 170 void test003()
 171 {
 172   const Tp eps = std::numeric_limits<Tp>::epsilon();
 173   Tp max_abs_diff = -Tp(1);
 174   Tp max_abs_frac = -Tp(1);
 175   unsigned int num_datum = sizeof(data003)
 176                          / sizeof(testcase_cyl_bessel_k<double>);
 177   for (unsigned int i = 0; i < num_datum; ++i)
 178     {
 179       const Tp f = std::tr1::cyl_bessel_k(Tp(data003[i].nu), Tp(data003[i].x));
 180       const Tp f0 = data003[i].f0;
 181       const Tp diff = f - f0;
 182       if (std::abs(diff) > max_abs_diff)
 183         max_abs_diff = std::abs(diff);
 184       if (std::abs(f0) > Tp(10) * eps
 185        && std::abs(f) > Tp(10) * eps)
 186         {
 187           const Tp frac = diff / f0;
 188           if (std::abs(frac) > max_abs_frac)
 189             max_abs_frac = std::abs(frac);
 190         }
 191     }
 192   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 193 }
 194
 195 // Test data for nu=0.66666666666666663.
 196 testcase_cyl_bessel_k<double> data004[] = {
 197   { 0.0038444246344968226, 0.66666666666666663, 5.0000000000000000 },
 198   { 1.8161187569530204e-05, 0.66666666666666663, 10.000000000000000 },
 199   { 9.9614751542305571e-08, 0.66666666666666663, 15.000000000000000 },
 200   { 5.8038484271925811e-10, 0.66666666666666663, 20.000000000000000 },
 201   { 3.4944937498488603e-12, 0.66666666666666663, 25.000000000000000 },
 202   { 2.1480755645577720e-14, 0.66666666666666663, 30.000000000000000 },
 203   { 1.3393949190152161e-16, 0.66666666666666663, 35.000000000000000 },
 204   { 8.4390460553642992e-19, 0.66666666666666663, 40.000000000000000 },
 205   { 5.3595716143622089e-21, 0.66666666666666663, 45.000000000000000 },
 206   { 3.4252085301433749e-23, 0.66666666666666663, 50.000000000000000 },
 207   { 2.2001025377982308e-25, 0.66666666666666663, 55.000000000000000 },
 208   { 1.4191011274172078e-27, 0.66666666666666663, 60.000000000000000 },
 209   { 9.1855803020269763e-30, 0.66666666666666663, 65.000000000000000 },
 210   { 5.9634299472578764e-32, 0.66666666666666663, 70.000000000000000 },
 211   { 3.8815254026478500e-34, 0.66666666666666663, 75.000000000000000 },
 212   { 2.5321003991943851e-36, 0.66666666666666663, 80.000000000000000 },
 213   { 1.6550585670593067e-38, 0.66666666666666663, 85.000000000000000 },
 214   { 1.0836820479428609e-40, 0.66666666666666663, 90.000000000000000 },
 215   { 7.1066428916285356e-43, 0.66666666666666663, 95.000000000000000 },
 216   { 4.6669364587280465e-45, 0.66666666666666663, 100.00000000000000 },
 217 };
 218
 219 // Test function for nu=0.66666666666666663.
 220 template <typename Tp>
 221 void test004()
 222 {
 223   const Tp eps = std::numeric_limits<Tp>::epsilon();
 224   Tp max_abs_diff = -Tp(1);
 225   Tp max_abs_frac = -Tp(1);
 226   unsigned int num_datum = sizeof(data004)
 227                          / sizeof(testcase_cyl_bessel_k<double>);
 228   for (unsigned int i = 0; i < num_datum; ++i)
 229     {
 230       const Tp f = std::tr1::cyl_bessel_k(Tp(data004[i].nu), Tp(data004[i].x));
 231       const Tp f0 = data004[i].f0;
 232       const Tp diff = f - f0;
 233       if (std::abs(diff) > max_abs_diff)
 234         max_abs_diff = std::abs(diff);
 235       if (std::abs(f0) > Tp(10) * eps
 236        && std::abs(f) > Tp(10) * eps)
 237         {
 238           const Tp frac = diff / f0;
 239           if (std::abs(frac) > max_abs_frac)
 240             max_abs_frac = std::abs(frac);
 241         }
 242     }
 243   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 244 }
 245
 246 // Test data for nu=1.0000000000000000.
 247 testcase_cyl_bessel_k<double> data005[] = {
 248   { 0.0040446134454521655, 1.0000000000000000, 5.0000000000000000 },
 249   { 1.8648773453825582e-05, 1.0000000000000000, 10.000000000000000 },
 250   { 1.0141729369762091e-07, 1.0000000000000000, 15.000000000000000 },
 251   { 5.8830579695570384e-10, 1.0000000000000000, 20.000000000000000 },
 252   { 3.5327780731999345e-12, 1.0000000000000000, 25.000000000000000 },
 253   { 2.1677320018915498e-14, 1.0000000000000000, 30.000000000000000 },
 254   { 1.3499178340011053e-16, 1.0000000000000000, 35.000000000000000 },
 255   { 8.4971319548610435e-19, 1.0000000000000000, 40.000000000000000 },
 256   { 5.3923945937225050e-21, 1.0000000000000000, 45.000000000000000 },
 257   { 3.4441022267175555e-23, 1.0000000000000000, 50.000000000000000 },
 258   { 2.2111422716117463e-25, 1.0000000000000000, 55.000000000000000 },
 259   { 1.4256320265171041e-27, 1.0000000000000000, 60.000000000000000 },
 260   { 9.2246195278906156e-30, 1.0000000000000000, 65.000000000000000 },
 261   { 5.9869736739138550e-32, 1.0000000000000000, 70.000000000000000 },
 262   { 3.8958329467421912e-34, 1.0000000000000000, 75.000000000000000 },
 263   { 2.5408531275211708e-36, 1.0000000000000000, 80.000000000000000 },
 264   { 1.6604444948567571e-38, 1.0000000000000000, 85.000000000000000 },
 265   { 1.0870134457498335e-40, 1.0000000000000000, 90.000000000000000 },
 266   { 7.1273442329907240e-43, 1.0000000000000000, 95.000000000000000 },
 267   { 4.6798537356369101e-45, 1.0000000000000000, 100.00000000000000 },
 268 };
 269
 270 // Test function for nu=1.0000000000000000.
 271 template <typename Tp>
 272 void test005()
 273 {
 274   const Tp eps = std::numeric_limits<Tp>::epsilon();
 275   Tp max_abs_diff = -Tp(1);
 276   Tp max_abs_frac = -Tp(1);
 277   unsigned int num_datum = sizeof(data005)
 278                          / sizeof(testcase_cyl_bessel_k<double>);
 279   for (unsigned int i = 0; i < num_datum; ++i)
 280     {
 281       const Tp f = std::tr1::cyl_bessel_k(Tp(data005[i].nu), Tp(data005[i].x));
 282       const Tp f0 = data005[i].f0;
 283       const Tp diff = f - f0;
 284       if (std::abs(diff) > max_abs_diff)
 285         max_abs_diff = std::abs(diff);
 286       if (std::abs(f0) > Tp(10) * eps
 287        && std::abs(f) > Tp(10) * eps)
 288         {
 289           const Tp frac = diff / f0;
 290           if (std::abs(frac) > max_abs_frac)
 291             max_abs_frac = std::abs(frac);
 292         }
 293     }
 294   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 295 }
 296
 297 // Test data for nu=2.0000000000000000.
 298 testcase_cyl_bessel_k<double> data006[] = {
 299   { 0.0053089437122234608, 2.0000000000000000, 5.0000000000000000 },
 300   { 2.1509817006932767e-05, 2.0000000000000000, 10.000000000000000 },
 301   { 1.1171767065031378e-07, 2.0000000000000000, 15.000000000000000 },
 302   { 6.3295436122922281e-10, 2.0000000000000000, 20.000000000000000 },
 303   { 3.7467838080691102e-12, 2.0000000000000000, 25.000000000000000 },
 304   { 2.2769929632558265e-14, 2.0000000000000000, 30.000000000000000 },
 305   { 1.4081733110858665e-16, 2.0000000000000000, 35.000000000000000 },
 306   { 8.8177176978426223e-19, 2.0000000000000000, 40.000000000000000 },
 307   { 5.5731181045619477e-21, 2.0000000000000000, 45.000000000000000 },
 308   { 3.5479318388581979e-23, 2.0000000000000000, 50.000000000000000 },
 309   { 2.2717153918665688e-25, 2.0000000000000000, 55.000000000000000 },
 310   { 1.4614189081096777e-27, 2.0000000000000000, 60.000000000000000 },
 311   { 9.4383017680150234e-30, 2.0000000000000000, 65.000000000000000 },
 312   { 6.1157177279757537e-32, 2.0000000000000000, 70.000000000000000 },
 313   { 3.9740059241667034e-34, 2.0000000000000000, 75.000000000000000 },
 314   { 2.5886411706935015e-36, 2.0000000000000000, 80.000000000000000 },
 315   { 1.6898316402103145e-38, 2.0000000000000000, 85.000000000000000 },
 316   { 1.1051801100484218e-40, 2.0000000000000000, 90.000000000000000 },
 317   { 7.2401743221736176e-43, 2.0000000000000000, 95.000000000000000 },
 318   { 4.7502253038886413e-45, 2.0000000000000000, 100.00000000000000 },
 319 };
 320
 321 // Test function for nu=2.0000000000000000.
 322 template <typename Tp>
 323 void test006()
 324 {
 325   const Tp eps = std::numeric_limits<Tp>::epsilon();
 326   Tp max_abs_diff = -Tp(1);
 327   Tp max_abs_frac = -Tp(1);
 328   unsigned int num_datum = sizeof(data006)
 329                          / sizeof(testcase_cyl_bessel_k<double>);
 330   for (unsigned int i = 0; i < num_datum; ++i)
 331     {
 332       const Tp f = std::tr1::cyl_bessel_k(Tp(data006[i].nu), Tp(data006[i].x));
 333       const Tp f0 = data006[i].f0;
 334       const Tp diff = f - f0;
 335       if (std::abs(diff) > max_abs_diff)
 336         max_abs_diff = std::abs(diff);
 337       if (std::abs(f0) > Tp(10) * eps
 338        && std::abs(f) > Tp(10) * eps)
 339         {
 340           const Tp frac = diff / f0;
 341           if (std::abs(frac) > max_abs_frac)
 342             max_abs_frac = std::abs(frac);
 343         }
 344     }
 345   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 346 }
 347
 348 // Test data for nu=5.0000000000000000.
 349 testcase_cyl_bessel_k<double> data007[] = {
 350   { 0.032706273712031865, 5.0000000000000000, 5.0000000000000000 },
 351   { 5.7541849985312275e-05, 5.0000000000000000, 10.000000000000000 },
 352   { 2.1878261369258224e-07, 5.0000000000000000, 15.000000000000000 },
 353   { 1.0538660139974233e-09, 5.0000000000000000, 20.000000000000000 },
 354   { 5.6485921365284157e-12, 5.0000000000000000, 25.000000000000000 },
 355   { 3.2103335105890266e-14, 5.0000000000000000, 30.000000000000000 },
 356   { 1.8919208406439644e-16, 5.0000000000000000, 35.000000000000000 },
 357   { 1.1423814375953188e-18, 5.0000000000000000, 40.000000000000000 },
 358   { 7.0181216822204116e-21, 5.0000000000000000, 45.000000000000000 },
 359   { 4.3671822541009859e-23, 5.0000000000000000, 50.000000000000000 },
 360   { 2.7444967640357869e-25, 5.0000000000000000, 55.000000000000000 },
 361   { 1.7382232741886986e-27, 5.0000000000000000, 60.000000000000000 },
 362   { 1.1078474298959669e-29, 5.0000000000000000, 65.000000000000000 },
 363   { 7.0974537081794416e-32, 5.0000000000000000, 70.000000000000000 },
 364   { 4.5667269500061064e-34, 5.0000000000000000, 75.000000000000000 },
 365   { 2.9491764420206150e-36, 5.0000000000000000, 80.000000000000000 },
 366   { 1.9105685973117463e-38, 5.0000000000000000, 85.000000000000000 },
 367   { 1.2411034311592645e-40, 5.0000000000000000, 90.000000000000000 },
 368   { 8.0814211331379146e-43, 5.0000000000000000, 95.000000000000000 },
 369   { 5.2732561132929509e-45, 5.0000000000000000, 100.00000000000000 },
 370 };
 371
 372 // Test function for nu=5.0000000000000000.
 373 template <typename Tp>
 374 void test007()
 375 {
 376   const Tp eps = std::numeric_limits<Tp>::epsilon();
 377   Tp max_abs_diff = -Tp(1);
 378   Tp max_abs_frac = -Tp(1);
 379   unsigned int num_datum = sizeof(data007)
 380                          / sizeof(testcase_cyl_bessel_k<double>);
 381   for (unsigned int i = 0; i < num_datum; ++i)
 382     {
 383       const Tp f = std::tr1::cyl_bessel_k(Tp(data007[i].nu), Tp(data007[i].x));
 384       const Tp f0 = data007[i].f0;
 385       const Tp diff = f - f0;
 386       if (std::abs(diff) > max_abs_diff)
 387         max_abs_diff = std::abs(diff);
 388       if (std::abs(f0) > Tp(10) * eps
 389        && std::abs(f) > Tp(10) * eps)
 390         {
 391           const Tp frac = diff / f0;
 392           if (std::abs(frac) > max_abs_frac)
 393             max_abs_frac = std::abs(frac);
 394         }
 395     }
 396   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 397 }
 398
 399 // Test data for nu=10.000000000000000.
 400 testcase_cyl_bessel_k<double> data008[] = {
 401   { 9.7585628291778121, 10.000000000000000, 5.0000000000000000 },
 402   { 0.0016142553003906700, 10.000000000000000, 10.000000000000000 },
 403   { 2.2605303776606440e-06, 10.000000000000000, 15.000000000000000 },
 404   { 6.3162145283215787e-09, 10.000000000000000, 20.000000000000000 },
 405   { 2.4076769602801230e-11, 10.000000000000000, 25.000000000000000 },
 406   { 1.0842816942222975e-13, 10.000000000000000, 30.000000000000000 },
 407   { 5.3976770429777191e-16, 10.000000000000000, 35.000000000000000 },
 408   { 2.8680293113671932e-18, 10.000000000000000, 40.000000000000000 },
 409   { 1.5939871900169603e-20, 10.000000000000000, 45.000000000000000 },
 410   { 9.1509882099879962e-23, 10.000000000000000, 50.000000000000000 },
 411   { 5.3823846249592858e-25, 10.000000000000000, 55.000000000000000 },
 412   { 3.2253408700563144e-27, 10.000000000000000, 60.000000000000000 },
 413   { 1.9613367530075138e-29, 10.000000000000000, 65.000000000000000 },
 414   { 1.2068471495933484e-31, 10.000000000000000, 70.000000000000000 },
 415   { 7.4979152649449644e-34, 10.000000000000000, 75.000000000000000 },
 416   { 4.6957285830490538e-36, 10.000000000000000, 80.000000000000000 },
 417   { 2.9606323347034084e-38, 10.000000000000000, 85.000000000000000 },
 418   { 1.8773542561131613e-40, 10.000000000000000, 90.000000000000000 },
 419   { 1.1962899527846350e-42, 10.000000000000000, 95.000000000000000 },
 420   { 7.6554279773881018e-45, 10.000000000000000, 100.00000000000000 },
 421 };
 422
 423 // Test function for nu=10.000000000000000.
 424 template <typename Tp>
 425 void test008()
 426 {
 427   const Tp eps = std::numeric_limits<Tp>::epsilon();
 428   Tp max_abs_diff = -Tp(1);
 429   Tp max_abs_frac = -Tp(1);
 430   unsigned int num_datum = sizeof(data008)
 431                          / sizeof(testcase_cyl_bessel_k<double>);
 432   for (unsigned int i = 0; i < num_datum; ++i)
 433     {
 434       const Tp f = std::tr1::cyl_bessel_k(Tp(data008[i].nu), Tp(data008[i].x));
 435       const Tp f0 = data008[i].f0;
 436       const Tp diff = f - f0;
 437       if (std::abs(diff) > max_abs_diff)
 438         max_abs_diff = std::abs(diff);
 439       if (std::abs(f0) > Tp(10) * eps
 440        && std::abs(f) > Tp(10) * eps)
 441         {
 442           const Tp frac = diff / f0;
 443           if (std::abs(frac) > max_abs_frac)
 444             max_abs_frac = std::abs(frac);
 445         }
 446     }
 447   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 448 }
 449
 450 // Test data for nu=20.000000000000000.
 451 testcase_cyl_bessel_k<double> data009[] = {
 452   { 482700052.06214869, 20.000000000000000, 5.0000000000000000 },
 453   { 178.74427820770549, 20.000000000000000, 10.000000000000000 },
 454   { 0.012141257729731146, 20.000000000000000, 15.000000000000000 },
 455   { 5.5431116361258155e-06, 20.000000000000000, 20.000000000000000 },
 456   { 6.3744029330352105e-09, 20.000000000000000, 25.000000000000000 },
 457   { 1.2304516475442478e-11, 20.000000000000000, 30.000000000000000 },
 458   { 3.2673136479809012e-14, 20.000000000000000, 35.000000000000000 },
 459   { 1.0703023799997383e-16, 20.000000000000000, 40.000000000000000 },
 460   { 4.0549953175660486e-19, 20.000000000000000, 45.000000000000000 },
 461   { 1.7061483797220352e-21, 20.000000000000000, 50.000000000000000 },
 462   { 7.7617008115659413e-24, 20.000000000000000, 55.000000000000000 },
 463   { 3.7482954006874725e-26, 20.000000000000000, 60.000000000000000 },
 464   { 1.8966880763956578e-28, 20.000000000000000, 65.000000000000000 },
 465   { 9.9615763479998882e-31, 20.000000000000000, 70.000000000000000 },
 466   { 5.3921623063091066e-33, 20.000000000000000, 75.000000000000000 },
 467   { 2.9920407657642272e-35, 20.000000000000000, 80.000000000000000 },
 468   { 1.6948662723618263e-37, 20.000000000000000, 85.000000000000000 },
 469   { 9.7689149642963025e-40, 20.000000000000000, 90.000000000000000 },
 470   { 5.7143603019220823e-42, 20.000000000000000, 95.000000000000000 },
 471   { 3.3852054148901700e-44, 20.000000000000000, 100.00000000000000 },
 472 };
 473
 474 // Test function for nu=20.000000000000000.
 475 template <typename Tp>
 476 void test009()
 477 {
 478   const Tp eps = std::numeric_limits<Tp>::epsilon();
 479   Tp max_abs_diff = -Tp(1);
 480   Tp max_abs_frac = -Tp(1);
 481   unsigned int num_datum = sizeof(data009)
 482                          / sizeof(testcase_cyl_bessel_k<double>);
 483   for (unsigned int i = 0; i < num_datum; ++i)
 484     {
 485       const Tp f = std::tr1::cyl_bessel_k(Tp(data009[i].nu), Tp(data009[i].x));
 486       const Tp f0 = data009[i].f0;
 487       const Tp diff = f - f0;
 488       if (std::abs(diff) > max_abs_diff)
 489         max_abs_diff = std::abs(diff);
 490       if (std::abs(f0) > Tp(10) * eps
 491        && std::abs(f) > Tp(10) * eps)
 492         {
 493           const Tp frac = diff / f0;
 494           if (std::abs(frac) > max_abs_frac)
 495             max_abs_frac = std::abs(frac);
 496         }
 497     }
 498   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 499 }
 500
 501 // Test data for nu=50.000000000000000.
 502 testcase_cyl_bessel_k<double> data010[] = {
 503   { 3.3943222434301628e+42, 50.000000000000000, 5.0000000000000000 },
 504   { 2.0613737753892579e+27, 50.000000000000000, 10.000000000000000 },
 505   { 1.7267736974519191e+18, 50.000000000000000, 15.000000000000000 },
 506   { 411711209122.01794, 50.000000000000000, 20.000000000000000 },
 507   { 1972478.7419813862, 50.000000000000000, 25.000000000000000 },
 508   { 58.770686258007267, 50.000000000000000, 30.000000000000000 },
 509   { 0.0058659391182535195, 50.000000000000000, 35.000000000000000 },
 510   { 1.3634854128794103e-06, 50.000000000000000, 40.000000000000000 },
 511   { 5.8652396362160840e-10, 50.000000000000000, 45.000000000000000 },
 512   { 4.0060134766400903e-13, 50.000000000000000, 50.000000000000000 },
 513   { 3.9062324485711016e-16, 50.000000000000000, 55.000000000000000 },
 514   { 5.0389298085176520e-19, 50.000000000000000, 60.000000000000000 },
 515   { 8.1305344250110396e-22, 50.000000000000000, 65.000000000000000 },
 516   { 1.5732816234949002e-24, 50.000000000000000, 70.000000000000000 },
 517   { 3.5349854993874397e-27, 50.000000000000000, 75.000000000000000 },
 518   { 8.9940101003189485e-30, 50.000000000000000, 80.000000000000000 },
 519   { 2.5403205503080723e-32, 50.000000000000000, 85.000000000000000 },
 520   { 7.8397596486715711e-35, 50.000000000000000, 90.000000000000000 },
 521   { 2.6098900651329550e-37, 50.000000000000000, 95.000000000000000 },
 522   { 9.2745226536133274e-40, 50.000000000000000, 100.00000000000000 },
 523 };
 524
 525 // Test function for nu=50.000000000000000.
 526 template <typename Tp>
 527 void test010()
 528 {
 529   const Tp eps = std::numeric_limits<Tp>::epsilon();
 530   Tp max_abs_diff = -Tp(1);
 531   Tp max_abs_frac = -Tp(1);
 532   unsigned int num_datum = sizeof(data010)
 533                          / sizeof(testcase_cyl_bessel_k<double>);
 534   for (unsigned int i = 0; i < num_datum; ++i)
 535     {
 536       const Tp f = std::tr1::cyl_bessel_k(Tp(data010[i].nu), Tp(data010[i].x));
 537       const Tp f0 = data010[i].f0;
 538       const Tp diff = f - f0;
 539       if (std::abs(diff) > max_abs_diff)
 540         max_abs_diff = std::abs(diff);
 541       if (std::abs(f0) > Tp(10) * eps
 542        && std::abs(f) > Tp(10) * eps)
 543         {
 544           const Tp frac = diff / f0;
 545           if (std::abs(frac) > max_abs_frac)
 546             max_abs_frac = std::abs(frac);
 547         }
 548     }
 549   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 550 }
 551
 552 // Test data for nu=100.00000000000000.
 553 testcase_cyl_bessel_k<double> data011[] = {
 554   { 7.0398601930616797e+115, 100.00000000000000, 5.0000000000000000 },
 555   { 4.5966740842695286e+85, 100.00000000000000, 10.000000000000000 },
 556   { 8.2565552242653898e+67, 100.00000000000000, 15.000000000000000 },
 557   { 1.7081356456876038e+55, 100.00000000000000, 20.000000000000000 },
 558   { 1.9858028128780595e+45, 100.00000000000000, 25.000000000000000 },
 559   { 1.2131584253026677e+37, 100.00000000000000, 30.000000000000000 },
 560   { 1.1016916354696684e+30, 100.00000000000000, 35.000000000000000 },
 561   { 7.0074023297775712e+23, 100.00000000000000, 40.000000000000000 },
 562   { 1.9236643958470909e+18, 100.00000000000000, 45.000000000000000 },
 563   { 16394035276269.254, 100.00000000000000, 50.000000000000000 },
 564   { 343254952.89495456, 100.00000000000000, 55.000000000000000 },
 565   { 14870.012754946305, 100.00000000000000, 60.000000000000000 },
 566   { 1.1708099078572209, 100.00000000000000, 65.000000000000000 },
 567   { 0.00015161193930722305, 100.00000000000000, 70.000000000000000 },
 568   { 2.9850234381623436e-08, 100.00000000000000, 75.000000000000000 },
 569   { 8.3928710724649065e-12, 100.00000000000000, 80.000000000000000 },
 570   { 3.2033435630927728e-15, 100.00000000000000, 85.000000000000000 },
 571   { 1.5922281431788077e-18, 100.00000000000000, 90.000000000000000 },
 572   { 9.9589454577674300e-22, 100.00000000000000, 95.000000000000000 },
 573   { 7.6171296304940858e-25, 100.00000000000000, 100.00000000000000 },
 574 };
 575
 576 // Test function for nu=100.00000000000000.
 577 template <typename Tp>
 578 void test011()
 579 {
 580   const Tp eps = std::numeric_limits<Tp>::epsilon();
 581   Tp max_abs_diff = -Tp(1);
 582   Tp max_abs_frac = -Tp(1);
 583   unsigned int num_datum = sizeof(data011)
 584                          / sizeof(testcase_cyl_bessel_k<double>);
 585   for (unsigned int i = 0; i < num_datum; ++i)
 586     {
 587       const Tp f = std::tr1::cyl_bessel_k(Tp(data011[i].nu), Tp(data011[i].x));
 588       const Tp f0 = data011[i].f0;
 589       const Tp diff = f - f0;
 590       if (std::abs(diff) > max_abs_diff)
 591         max_abs_diff = std::abs(diff);
 592       if (std::abs(f0) > Tp(10) * eps
 593        && std::abs(f) > Tp(10) * eps)
 594         {
 595           const Tp frac = diff / f0;
 596           if (std::abs(frac) > max_abs_frac)
 597             max_abs_frac = std::abs(frac);
 598         }
 599     }
 600   VERIFY(max_abs_frac < Tp(5.0000000000000039e-13));
 601 }
 602
 603 int main(int, char**)
 604 {
 605   test001<double>();
 606   test002<double>();
 607   test003<double>();
 608   test004<double>();
 609   test005<double>();
 610   test006<double>();
 611   test007<double>();
 612   test008<double>();
 613   test009<double>();
 614   test010<double>();
 615   test011<double>();
 616   return 0;
 617 }