libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/11_cyl_neumann/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_neumann
  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_neumann<double> data001[] = {
  44   { -0.30851762524903376, 0.0000000000000000, 5.0000000000000000 },
  45   { 0.055671167283599395, 0.0000000000000000, 10.000000000000000 },
  46   { 0.20546429603891825, 0.0000000000000000, 15.000000000000000 },
  47   { 0.062640596809383955, 0.0000000000000000, 20.000000000000000 },
  48   { -0.12724943226800620, 0.0000000000000000, 25.000000000000000 },
  49   { -0.11729573168666411, 0.0000000000000000, 30.000000000000000 },
  50   { 0.045797987195155640, 0.0000000000000000, 35.000000000000000 },
  51   { 0.12593641705826095, 0.0000000000000000, 40.000000000000000 },
  52   { 0.027060469763313322, 0.0000000000000000, 45.000000000000000 },
  53   { -0.098064995470077104, 0.0000000000000000, 50.000000000000000 },
  54   { -0.077569178730412622, 0.0000000000000000, 55.000000000000000 },
  55   { 0.047358952209449412, 0.0000000000000000, 60.000000000000000 },
  56   { 0.097183557740181933, 0.0000000000000000, 65.000000000000000 },
  57   { 0.0093096664589410131, 0.0000000000000000, 70.000000000000000 },
  58   { -0.085369047647775642, 0.0000000000000000, 75.000000000000000 },
  59   { -0.055620339089769981, 0.0000000000000000, 80.000000000000000 },
  60   { 0.049567884951494258, 0.0000000000000000, 85.000000000000000 },
  61   { 0.079776475854877765, 0.0000000000000000, 90.000000000000000 },
  62   { -0.0028230995861232323, 0.0000000000000000, 95.000000000000000 },
  63   { -0.077244313365083112, 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_neumann<double>);
  75   for (unsigned int i = 0; i < num_datum; ++i)
  76     {
  77       const Tp f = std::tr1::cyl_neumann(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(1.0000000000000006e-10));
  91 }
  92
  93 // Test data for nu=0.33333333333333331.
  94 testcase_cyl_neumann<double> data002[] = {
  95   { -0.18192321129343830, 0.33333333333333331, 5.0000000000000000 },
  96   { 0.17020111788268769, 0.33333333333333331, 10.000000000000000 },
  97   { 0.18540507541540799, 0.33333333333333331, 15.000000000000000 },
  98   { -0.028777707635715091, 0.33333333333333331, 20.000000000000000 },
  99   { -0.15829741864944166, 0.33333333333333331, 25.000000000000000 },
 100   { -0.058645772316705216, 0.33333333333333331, 30.000000000000000 },
 101   { 0.10294930308870620, 0.33333333333333331, 35.000000000000000 },
 102   { 0.10547870367098920, 0.33333333333333331, 40.000000000000000 },
 103   { -0.034334228816010864, 0.33333333333333331, 45.000000000000000 },
 104   { -0.11283489933031278, 0.33333333333333331, 50.000000000000000 },
 105   { -0.030007358986895123, 0.33333333333333331, 55.000000000000000 },
 106   { 0.086699173295718093, 0.33333333333333331, 60.000000000000000 },
 107   { 0.074875579668878672, 0.33333333333333331, 65.000000000000000 },
 108   { -0.039323246374552645, 0.33333333333333331, 70.000000000000000 },
 109   { -0.091263539574475222, 0.33333333333333331, 75.000000000000000 },
 110   { -0.013358849535984282, 0.33333333333333331, 80.000000000000000 },
 111   { 0.078373575537830184, 0.33333333333333331, 85.000000000000000 },
 112   { 0.055812482883955974, 0.33333333333333331, 90.000000000000000 },
 113   { -0.043310380106990579, 0.33333333333333331, 95.000000000000000 },
 114   { -0.076900504962136587, 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_neumann<double>);
 126   for (unsigned int i = 0; i < num_datum; ++i)
 127     {
 128       const Tp f = std::tr1::cyl_neumann(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(2.5000000000000014e-11));
 142 }
 143
 144 // Test data for nu=0.50000000000000000.
 145 testcase_cyl_neumann<double> data003[] = {
 146   { -0.10121770918510843, 0.50000000000000000, 5.0000000000000000 },
 147   { 0.21170886633139813, 0.50000000000000000, 10.000000000000000 },
 148   { 0.15650551590730860, 0.50000000000000000, 15.000000000000000 },
 149   { -0.072806904785061841, 0.50000000000000000, 20.000000000000000 },
 150   { -0.15817308404205055, 0.50000000000000000, 25.000000000000000 },
 151   { -0.022470290598831121, 0.50000000000000000, 30.000000000000000 },
 152   { 0.12187835265849536, 0.50000000000000000, 35.000000000000000 },
 153   { 0.084138655676395432, 0.50000000000000000, 40.000000000000000 },
 154   { -0.062482641933003132, 0.50000000000000000, 45.000000000000000 },
 155   { -0.10888475635053953, 0.50000000000000000, 50.000000000000000 },
 156   { -0.0023805454010948804, 0.50000000000000000, 55.000000000000000 },
 157   { 0.098104683735037904, 0.50000000000000000, 60.000000000000000 },
 158   { 0.055663470218594434, 0.50000000000000000, 65.000000000000000 },
 159   { -0.060396767883824809, 0.50000000000000000, 70.000000000000000 },
 160   { -0.084922578922046868, 0.50000000000000000, 75.000000000000000 },
 161   { 0.0098472271924441215, 0.50000000000000000, 80.000000000000000 },
 162   { 0.085190643574343639, 0.50000000000000000, 85.000000000000000 },
 163   { 0.037684970437156261, 0.50000000000000000, 90.000000000000000 },
 164   { -0.059772904856097479, 0.50000000000000000, 95.000000000000000 },
 165   { -0.068803091468728053, 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_neumann<double>);
 177   for (unsigned int i = 0; i < num_datum; ++i)
 178     {
 179       const Tp f = std::tr1::cyl_neumann(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(5.0000000000000028e-11));
 193 }
 194
 195 // Test data for nu=0.66666666666666663.
 196 testcase_cyl_neumann<double> data004[] = {
 197   { -0.016050662643389616, 0.66666666666666663, 5.0000000000000000 },
 198   { 0.23937232657540730, 0.66666666666666663, 10.000000000000000 },
 199   { 0.11762106604241242, 0.66666666666666663, 15.000000000000000 },
 200   { -0.11182254014899563, 0.66666666666666663, 20.000000000000000 },
 201   { -0.14756582982938804, 0.66666666666666663, 25.000000000000000 },
 202   { 0.015078692908077665, 0.66666666666666663, 30.000000000000000 },
 203   { 0.13260911815705798, 0.66666666666666663, 35.000000000000000 },
 204   { 0.057217565989652795, 0.66666666666666663, 40.000000000000000 },
 205   { -0.086373755152382048, 0.66666666666666663, 45.000000000000000 },
 206   { -0.097624139208051630, 0.66666666666666663, 50.000000000000000 },
 207   { 0.025354902147023434, 0.66666666666666663, 55.000000000000000 },
 208   { 0.10288136476351209, 0.66666666666666663, 60.000000000000000 },
 209   { 0.032728379560128203, 0.66666666666666663, 65.000000000000000 },
 210   { -0.077363672735747777, 0.66666666666666663, 70.000000000000000 },
 211   { -0.072855870458293975, 0.66666666666666663, 75.000000000000000 },
 212   { 0.032358106046953494, 0.66666666666666663, 80.000000000000000 },
 213   { 0.086240651537394228, 0.66666666666666663, 85.000000000000000 },
 214   { 0.017029601697285159, 0.66666666666666663, 90.000000000000000 },
 215   { -0.072173520560584709, 0.66666666666666663, 95.000000000000000 },
 216   { -0.056057339204073985, 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_neumann<double>);
 228   for (unsigned int i = 0; i < num_datum; ++i)
 229     {
 230       const Tp f = std::tr1::cyl_neumann(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(2.5000000000000014e-11));
 244 }
 245
 246 // Test data for nu=1.0000000000000000.
 247 testcase_cyl_neumann<double> data005[] = {
 248   { 0.14786314339122689, 1.0000000000000000, 5.0000000000000000 },
 249   { 0.24901542420695388, 1.0000000000000000, 10.000000000000000 },
 250   { 0.021073628036873546, 1.0000000000000000, 15.000000000000000 },
 251   { -0.16551161436252118, 1.0000000000000000, 20.000000000000000 },
 252   { -0.098829964783237384, 1.0000000000000000, 25.000000000000000 },
 253   { 0.084425570661747149, 1.0000000000000000, 30.000000000000000 },
 254   { 0.12751273354559012, 1.0000000000000000, 35.000000000000000 },
 255   { -0.0057935058215496330, 1.0000000000000000, 40.000000000000000 },
 256   { -0.11552517964639945, 1.0000000000000000, 45.000000000000000 },
 257   { -0.056795668562014713, 1.0000000000000000, 50.000000000000000 },
 258   { 0.073846265432577940, 1.0000000000000000, 55.000000000000000 },
 259   { 0.091869609369866906, 1.0000000000000000, 60.000000000000000 },
 260   { -0.017940374275377303, 1.0000000000000000, 65.000000000000000 },
 261   { -0.094844652625716244, 1.0000000000000000, 70.000000000000000 },
 262   { -0.035213785160580456, 1.0000000000000000, 75.000000000000000 },
 263   { 0.069395913784588051, 1.0000000000000000, 80.000000000000000 },
 264   { 0.071233187582749782, 1.0000000000000000, 85.000000000000000 },
 265   { -0.026187238607768282, 1.0000000000000000, 90.000000000000000 },
 266   { -0.081827958724501229, 1.0000000000000000, 95.000000000000000 },
 267   { -0.020372312002759942, 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_neumann<double>);
 279   for (unsigned int i = 0; i < num_datum; ++i)
 280     {
 281       const Tp f = std::tr1::cyl_neumann(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(2.5000000000000014e-11));
 295 }
 296
 297 // Test data for nu=2.0000000000000000.
 298 testcase_cyl_neumann<double> data006[] = {
 299   { 0.36766288260552449, 2.0000000000000000, 5.0000000000000000 },
 300   { -0.0058680824422086154, 2.0000000000000000, 10.000000000000000 },
 301   { -0.20265447896733510, 2.0000000000000000, 15.000000000000000 },
 302   { -0.079191758245636068, 2.0000000000000000, 20.000000000000000 },
 303   { 0.11934303508534720, 2.0000000000000000, 25.000000000000000 },
 304   { 0.12292410306411393, 2.0000000000000000, 30.000000000000000 },
 305   { -0.038511545278264774, 2.0000000000000000, 35.000000000000000 },
 306   { -0.12622609234933843, 2.0000000000000000, 40.000000000000000 },
 307   { -0.032194922192042189, 2.0000000000000000, 45.000000000000000 },
 308   { 0.095793168727596509, 2.0000000000000000, 50.000000000000000 },
 309   { 0.080254497473415454, 2.0000000000000000, 55.000000000000000 },
 310   { -0.044296631897120513, 2.0000000000000000, 60.000000000000000 },
 311   { -0.097735569256347382, 2.0000000000000000, 65.000000000000000 },
 312   { -0.012019513676818619, 2.0000000000000000, 70.000000000000000 },
 313   { 0.084430013376826832, 2.0000000000000000, 75.000000000000000 },
 314   { 0.057355236934384685, 2.0000000000000000, 80.000000000000000 },
 315   { -0.047891809949547205, 2.0000000000000000, 85.000000000000000 },
 316   { -0.080358414490605948, 2.0000000000000000, 90.000000000000000 },
 317   { 0.0011004057182389959, 2.0000000000000000, 95.000000000000000 },
 318   { 0.076836867125027908, 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_neumann<double>);
 330   for (unsigned int i = 0; i < num_datum; ++i)
 331     {
 332       const Tp f = std::tr1::cyl_neumann(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(2.5000000000000017e-10));
 346 }
 347
 348 // Test data for nu=5.0000000000000000.
 349 testcase_cyl_neumann<double> data007[] = {
 350   { -0.45369482249110188, 5.0000000000000000, 5.0000000000000000 },
 351   { 0.13540304768936232, 5.0000000000000000, 10.000000000000000 },
 352   { 0.16717271575940021, 5.0000000000000000, 15.000000000000000 },
 353   { -0.10003576788953225, 5.0000000000000000, 20.000000000000000 },
 354   { -0.14705799311372267, 5.0000000000000000, 25.000000000000000 },
 355   { 0.031627359289264322, 5.0000000000000000, 30.000000000000000 },
 356   { 0.13554781474770031, 5.0000000000000000, 35.000000000000000 },
 357   { 0.031869448780850372, 5.0000000000000000, 40.000000000000000 },
 358   { -0.10426932700176872, 5.0000000000000000, 45.000000000000000 },
 359   { -0.078548413913081608, 5.0000000000000000, 50.000000000000000 },
 360   { 0.055257033062858382, 5.0000000000000000, 55.000000000000000 },
 361   { 0.099464632840450901, 5.0000000000000000, 60.000000000000000 },
 362   { 0.00023860469499600970, 5.0000000000000000, 65.000000000000000 },
 363   { -0.091861802216406066, 5.0000000000000000, 70.000000000000000 },
 364   { -0.048383671296970077, 5.0000000000000000, 75.000000000000000 },
 365   { 0.060293667104896330, 5.0000000000000000, 80.000000000000000 },
 366   { 0.077506166682734010, 5.0000000000000000, 85.000000000000000 },
 367   { -0.015338764062239803, 5.0000000000000000, 90.000000000000000 },
 368   { -0.081531504045514375, 5.0000000000000000, 95.000000000000000 },
 369   { -0.029480196281662041, 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_neumann<double>);
 381   for (unsigned int i = 0; i < num_datum; ++i)
 382     {
 383       const Tp f = std::tr1::cyl_neumann(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(2.5000000000000013e-09));
 397 }
 398
 399 // Test data for nu=10.000000000000000.
 400 testcase_cyl_neumann<double> data008[] = {
 401   { -25.129110095610098, 10.000000000000000, 5.0000000000000000 },
 402   { -0.35981415218340279, 10.000000000000000, 10.000000000000000 },
 403   { 0.21997141360195582, 10.000000000000000, 15.000000000000000 },
 404   { -0.043894653515658202, 10.000000000000000, 20.000000000000000 },
 405   { -0.14871839049980651, 10.000000000000000, 25.000000000000000 },
 406   { 0.075056702122397012, 10.000000000000000, 30.000000000000000 },
 407   { 0.12222473135000553, 10.000000000000000, 35.000000000000000 },
 408   { -0.046723877232677867, 10.000000000000000, 40.000000000000000 },
 409   { -0.11739339009322178, 10.000000000000000, 45.000000000000000 },
 410   { 0.0057238971820535740, 10.000000000000000, 50.000000000000000 },
 411   { 0.10733910125831635, 10.000000000000000, 55.000000000000000 },
 412   { 0.036290350559545506, 10.000000000000000, 60.000000000000000 },
 413   { -0.083239127691715639, 10.000000000000000, 65.000000000000000 },
 414   { -0.069639384138314872, 10.000000000000000, 70.000000000000000 },
 415   { 0.045798335061325038, 10.000000000000000, 75.000000000000000 },
 416   { 0.086269195064844428, 10.000000000000000, 80.000000000000000 },
 417   { -0.0018234674126248629, 10.000000000000000, 85.000000000000000 },
 418   { -0.082067762371231298, 10.000000000000000, 90.000000000000000 },
 419   { -0.038798074754578075, 10.000000000000000, 95.000000000000000 },
 420   { 0.058331574236414815, 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_neumann<double>);
 432   for (unsigned int i = 0; i < num_datum; ++i)
 433     {
 434       const Tp f = std::tr1::cyl_neumann(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(2.5000000000000017e-10));
 448 }
 449
 450 // Test data for nu=20.000000000000000.
 451 testcase_cyl_neumann<double> data009[] = {
 452   { -593396529.69143212, 20.000000000000000, 5.0000000000000000 },
 453   { -1597.4838482696264, 20.000000000000000, 10.000000000000000 },
 454   { -3.3087330924737630, 20.000000000000000, 15.000000000000000 },
 455   { -0.28548945860020319, 20.000000000000000, 20.000000000000000 },
 456   { 0.19804074776289243, 20.000000000000000, 25.000000000000000 },
 457   { -0.16848153948742675, 20.000000000000000, 30.000000000000000 },
 458   { 0.10102784152594022, 20.000000000000000, 35.000000000000000 },
 459   { 0.045161820565805928, 20.000000000000000, 40.000000000000000 },
 460   { -0.12556489308015448, 20.000000000000000, 45.000000000000000 },
 461   { 0.016442633948115841, 20.000000000000000, 50.000000000000000 },
 462   { 0.10853448778255187, 20.000000000000000, 55.000000000000000 },
 463   { -0.026721408520664677, 20.000000000000000, 60.000000000000000 },
 464   { -0.098780425256324203, 20.000000000000000, 65.000000000000000 },
 465   { 0.016201957786018205, 20.000000000000000, 70.000000000000000 },
 466   { 0.093591198265063735, 20.000000000000000, 75.000000000000000 },
 467   { 0.0040484400737295740, 20.000000000000000, 80.000000000000000 },
 468   { -0.086314929459920503, 20.000000000000000, 85.000000000000000 },
 469   { -0.028274110097231495, 20.000000000000000, 90.000000000000000 },
 470   { 0.072349520791638755, 20.000000000000000, 95.000000000000000 },
 471   { 0.051247973076188565, 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_neumann<double>);
 483   for (unsigned int i = 0; i < num_datum; ++i)
 484     {
 485       const Tp f = std::tr1::cyl_neumann(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(1.0000000000000006e-10));
 499 }
 500
 501 // Test data for nu=50.000000000000000.
 502 testcase_cyl_neumann<double> data010[] = {
 503   { -2.7888370175838943e+42, 50.000000000000000, 5.0000000000000000 },
 504   { -3.6410665018007421e+27, 50.000000000000000, 10.000000000000000 },
 505   { -1.0929732912175405e+19, 50.000000000000000, 15.000000000000000 },
 506   { -15606426801663.732, 50.000000000000000, 20.000000000000000 },
 507   { -753573251.44662631, 50.000000000000000, 25.000000000000000 },
 508   { -386759.32602734747, 50.000000000000000, 30.000000000000000 },
 509   { -1172.8690492895341, 50.000000000000000, 35.000000000000000 },
 510   { -15.615608873419953, 50.000000000000000, 40.000000000000000 },
 511   { -0.87058346204176951, 50.000000000000000, 45.000000000000000 },
 512   { -0.21031655464397736, 50.000000000000000, 50.000000000000000 },
 513   { 0.093048240412999375, 50.000000000000000, 55.000000000000000 },
 514   { 0.0086417699626745066, 50.000000000000000, 60.000000000000000 },
 515   { -0.025019788459221974, 50.000000000000000, 65.000000000000000 },
 516   { -0.0014815155191908913, 50.000000000000000, 70.000000000000000 },
 517   { 0.050335774732164155, 50.000000000000000, 75.000000000000000 },
 518   { -0.092924250967987204, 50.000000000000000, 80.000000000000000 },
 519   { 0.087332463030205670, 50.000000000000000, 85.000000000000000 },
 520   { -0.016164237701651891, 50.000000000000000, 90.000000000000000 },
 521   { -0.068897613820457920, 50.000000000000000, 95.000000000000000 },
 522   { 0.076505263944802962, 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_neumann<double>);
 534   for (unsigned int i = 0; i < num_datum; ++i)
 535     {
 536       const Tp f = std::tr1::cyl_neumann(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(2.5000000000000017e-10));
 550 }
 551
 552 // Test data for nu=100.00000000000000.
 553 testcase_cyl_neumann<double> data011[] = {
 554   { -5.0848639160196196e+115, 100.00000000000000, 5.0000000000000000 },
 555   { -4.8491482711800245e+85, 100.00000000000000, 10.000000000000000 },
 556   { -1.6375955323195320e+68, 100.00000000000000, 15.000000000000000 },
 557   { -8.2002648144679137e+55, 100.00000000000000, 20.000000000000000 },
 558   { -2.9712216432562373e+46, 100.00000000000000, 25.000000000000000 },
 559   { -7.2875284708240766e+38, 100.00000000000000, 30.000000000000000 },
 560   { -3.4251079902108953e+32, 100.00000000000000, 35.000000000000000 },
 561   { -1.4552439438101799e+27, 100.00000000000000, 40.000000000000000 },
 562   { -3.4506612476220073e+22, 100.00000000000000, 45.000000000000000 },
 563   { -3.2938001882025948e+18, 100.00000000000000, 50.000000000000000 },
 564   { -1005686182055527.4, 100.00000000000000, 55.000000000000000 },
 565   { -831892881402.11377, 100.00000000000000, 60.000000000000000 },
 566   { -1650863778.0598330, 100.00000000000000, 65.000000000000000 },
 567   { -7192614.1976097804, 100.00000000000000, 70.000000000000000 },
 568   { -64639.072261231602, 100.00000000000000, 75.000000000000000 },
 569   { -1152.5905185698464, 100.00000000000000, 80.000000000000000 },
 570   { -40.250761402102000, 100.00000000000000, 85.000000000000000 },
 571   { -2.8307771387185459, 100.00000000000000, 90.000000000000000 },
 572   { -0.45762200495904559, 100.00000000000000, 95.000000000000000 },
 573   { -0.16692141141757649, 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_neumann<double>);
 585   for (unsigned int i = 0; i < num_datum; ++i)
 586     {
 587       const Tp f = std::tr1::cyl_neumann(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(1.0000000000000006e-11));
 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 }