libstdc++-v3/testsuite/special_functions/12_ellint_2/check_value.cc

   1 // { dg-do run { target c++11 } }
   2 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
   3 //
   4 // Copyright (C) 2016 Free Software Foundation, Inc.
   5 //
   6 // This file is part of the GNU ISO C++ Library.  This library is free
   7 // software; you can redistribute it and/or modify it under the
   8 // terms of the GNU General Public License as published by the
   9 // Free Software Foundation; either version 3, or (at your option)
  10 // any later version.
  11 //
  12 // This library is distributed in the hope that it will be useful,
  13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 // GNU General Public License for more details.
  16 //
  17 // You should have received a copy of the GNU General Public License along
  18 // with this library; see the file COPYING3.  If not see
  19 // <http://www.gnu.org/licenses/>.
  20
  21 //  ellint_2
  22 //  Compare against values generated by the GNU Scientific Library.
  23 //  The GSL can be found on the web: http://www.gnu.org/software/gsl/
  24 #include <limits>
  25 #include <cmath>
  26 #if defined(__TEST_DEBUG)
  27 #  include <iostream>
  28 #  define VERIFY(A) \
  29   if (!(A)) \
  30     { \
  31       std::cout << "line " << __LINE__ \
  32         << "  max_abs_frac = " << max_abs_frac \
  33         << std::endl; \
  34     }
  35 #else
  36 #  include <testsuite_hooks.h>
  37 #endif
  38 #include <specfun_testcase.h>
  39
  40
  41 // Test data for k=-0.90000000000000002.
  42 // max(|f - f_GSL|): 6.6613381477509392e-16
  43 // max(|f - f_GSL| / |f_GSL|): 6.6116483711056737e-16
  44 const testcase_ellint_2<double>
  45 data001[10] =
  46 {
  47   { 0.0000000000000000, -0.90000000000000002, 0.0000000000000000 },
  48   { 0.17381690606167960, -0.90000000000000002, 0.17453292519943295 },
  49   { 0.34337919186972055, -0.90000000000000002, 0.34906585039886590 },
  50   { 0.50464268659856326, -0.90000000000000002, 0.52359877559829882 },
  51   { 0.65400003842368570, -0.90000000000000002, 0.69813170079773179 },
  52   { 0.78854928419904646, -0.90000000000000002, 0.87266462599716477 },
  53   { 0.90645698626315396, -0.90000000000000002, 1.0471975511965976 },
  54   { 1.0075154899135925, -0.90000000000000002, 1.2217304763960306 },
  55   { 1.0940135583194068, -0.90000000000000002, 1.3962634015954636 },
  56   { 1.1716970527816140, -0.90000000000000002, 1.5707963267948966 },
  57 };
  58 const double toler001 = 2.5000000000000020e-13;
  59
  60 // Test data for k=-0.80000000000000004.
  61 // max(|f - f_GSL|): 4.4408920985006262e-16
  62 // max(|f - f_GSL| / |f_GSL|): 3.4793687438660849e-16
  63 const testcase_ellint_2<double>
  64 data002[10] =
  65 {
  66   { 0.0000000000000000, -0.80000000000000004, 0.0000000000000000 },
  67   { 0.17396762274534805, -0.80000000000000004, 0.17453292519943295 },
  68   { 0.34458685226969316, -0.80000000000000004, 0.34906585039886590 },
  69   { 0.50872923654502433, -0.80000000000000004, 0.52359877559829882 },
  70   { 0.66372016539176215, -0.80000000000000004, 0.69813170079773179 },
  71   { 0.80760344410167406, -0.80000000000000004, 0.87266462599716477 },
  72   { 0.93945480372495049, -0.80000000000000004, 1.0471975511965976 },
  73   { 1.0597473310395036, -0.80000000000000004, 1.2217304763960306 },
  74   { 1.1706981862452361, -0.80000000000000004, 1.3962634015954636 },
  75   { 1.2763499431699064, -0.80000000000000004, 1.5707963267948966 },
  76 };
  77 const double toler002 = 2.5000000000000020e-13;
  78
  79 // Test data for k=-0.69999999999999996.
  80 // max(|f - f_GSL|): 3.3306690738754696e-16
  81 // max(|f - f_GSL| / |f_GSL|): 4.0435005012914979e-16
  82 const testcase_ellint_2<double>
  83 data003[10] =
  84 {
  85   { 0.0000000000000000, -0.69999999999999996, 0.0000000000000000 },
  86   { 0.17410041242702542, -0.69999999999999996, 0.17453292519943295 },
  87   { 0.34564605085764760, -0.69999999999999996, 0.34906585039886590 },
  88   { 0.51228495693314646, -0.69999999999999996, 0.52359877559829882 },
  89   { 0.67207654098799530, -0.69999999999999996, 0.69813170079773179 },
  90   { 0.82370932631556515, -0.69999999999999996, 0.87266462599716477 },
  91   { 0.96672313309452795, -0.69999999999999996, 1.0471975511965976 },
  92   { 1.1017090644949503, -0.69999999999999996, 1.2217304763960306 },
  93   { 1.2304180097292914, -0.69999999999999996, 1.3962634015954636 },
  94   { 1.3556611355719554, -0.69999999999999996, 1.5707963267948966 },
  95 };
  96 const double toler003 = 2.5000000000000020e-13;
  97
  98 // Test data for k=-0.59999999999999998.
  99 // max(|f - f_GSL|): 4.4408920985006262e-16
 100 // max(|f - f_GSL| / |f_GSL|): 3.9101039108874066e-16
 101 const testcase_ellint_2<double>
 102 data004[10] =
 103 {
 104   { 0.0000000000000000, -0.59999999999999998, 0.0000000000000000 },
 105   { 0.17421534919599127, -0.59999999999999998, 0.17453292519943295 },
 106   { 0.34655927787174101, -0.59999999999999998, 0.34906585039886590 },
 107   { 0.51533034538432143, -0.59999999999999998, 0.52359877559829882 },
 108   { 0.67916550597453018, -0.59999999999999998, 0.69813170079773179 },
 109   { 0.83720218180349870, -0.59999999999999998, 0.87266462599716477 },
 110   { 0.98922159354937755, -0.59999999999999998, 1.0471975511965976 },
 111   { 1.1357478470419360, -0.59999999999999998, 1.2217304763960306 },
 112   { 1.2780617372844056, -0.59999999999999998, 1.3962634015954636 },
 113   { 1.4180833944487241, -0.59999999999999998, 1.5707963267948966 },
 114 };
 115 const double toler004 = 2.5000000000000020e-13;
 116
 117 // Test data for k=-0.50000000000000000.
 118 // max(|f - f_GSL|): 2.2204460492503131e-16
 119 // max(|f - f_GSL| / |f_GSL|): 3.2412420886495652e-16
 120 const testcase_ellint_2<double>
 121 data005[10] =
 122 {
 123   { 0.0000000000000000, -0.50000000000000000, 0.0000000000000000 },
 124   { 0.17431249677315910, -0.50000000000000000, 0.17453292519943295 },
 125   { 0.34732862537770803, -0.50000000000000000, 0.34906585039886590 },
 126   { 0.51788193485993794, -0.50000000000000000, 0.52359877559829882 },
 127   { 0.68506022954164536, -0.50000000000000000, 0.69813170079773179 },
 128   { 0.84831662803347196, -0.50000000000000000, 0.87266462599716477 },
 129   { 1.0075555551444717, -0.50000000000000000, 1.0471975511965976 },
 130   { 1.1631768599287300, -0.50000000000000000, 1.2217304763960306 },
 131   { 1.3160584048772543, -0.50000000000000000, 1.3962634015954636 },
 132   { 1.4674622093394274, -0.50000000000000000, 1.5707963267948966 },
 133 };
 134 const double toler005 = 2.5000000000000020e-13;
 135
 136 // Test data for k=-0.40000000000000002.
 137 // max(|f - f_GSL|): 6.6613381477509392e-16
 138 // max(|f - f_GSL| / |f_GSL|): 5.6222658248988364e-16
 139 const testcase_ellint_2<double>
 140 data006[10] =
 141 {
 142   { 0.0000000000000000, -0.40000000000000002, 0.0000000000000000 },
 143   { 0.17439190872481267, -0.40000000000000002, 0.17453292519943295 },
 144   { 0.34795581767099210, -0.40000000000000002, 0.34906585039886590 },
 145   { 0.51995290683804463, -0.40000000000000002, 0.52359877559829882 },
 146   { 0.68981638464431538, -0.40000000000000002, 0.69813170079773179 },
 147   { 0.85722088859936041, -0.40000000000000002, 0.87266462599716477 },
 148   { 1.0221301327876993, -0.40000000000000002, 1.0471975511965976 },
 149   { 1.1848138019818371, -0.40000000000000002, 1.2217304763960306 },
 150   { 1.3458259266501533, -0.40000000000000002, 1.3962634015954636 },
 151   { 1.5059416123600402, -0.40000000000000002, 1.5707963267948966 },
 152 };
 153 const double toler006 = 2.5000000000000020e-13;
 154
 155 // Test data for k=-0.30000000000000004.
 156 // max(|f - f_GSL|): 8.8817841970012523e-16
 157 // max(|f - f_GSL| / |f_GSL|): 6.3860540218057383e-16
 158 const testcase_ellint_2<double>
 159 data007[10] =
 160 {
 161   { 0.0000000000000000, -0.30000000000000004, 0.0000000000000000 },
 162   { 0.17445362864048913, -0.30000000000000004, 0.17453292519943295 },
 163   { 0.34844223535713464, -0.30000000000000004, 0.34906585039886590 },
 164   { 0.52155353877411770, -0.30000000000000004, 0.52359877559829882 },
 165   { 0.69347584418369879, -0.30000000000000004, 0.69813170079773179 },
 166   { 0.86403609928237668, -0.30000000000000004, 0.87266462599716477 },
 167   { 1.0332234514065408, -0.30000000000000004, 1.0471975511965976 },
 168   { 1.2011943182068923, -0.30000000000000004, 1.2217304763960306 },
 169   { 1.3682566113689623, -0.30000000000000004, 1.3962634015954636 },
 170   { 1.5348334649232491, -0.30000000000000004, 1.5707963267948966 },
 171 };
 172 const double toler007 = 2.5000000000000020e-13;
 173
 174 // Test data for k=-0.19999999999999996.
 175 // max(|f - f_GSL|): 4.4408920985006262e-16
 176 // max(|f - f_GSL| / |f_GSL|): 4.2658819988515356e-16
 177 const testcase_ellint_2<double>
 178 data008[10] =
 179 {
 180   { 0.0000000000000000, -0.19999999999999996, 0.0000000000000000 },
 181   { 0.17449769027652812, -0.19999999999999996, 0.17453292519943295 },
 182   { 0.34878893400762095, -0.19999999999999996, 0.34906585039886590 },
 183   { 0.52269152856057410, -0.19999999999999996, 0.52359877559829882 },
 184   { 0.69606913360157563, -0.19999999999999996, 0.69813170079773179 },
 185   { 0.86884782374863356, -0.19999999999999996, 0.87266462599716477 },
 186   { 1.0410255369689567, -0.19999999999999996, 1.0471975511965976 },
 187   { 1.2126730391631360, -0.19999999999999996, 1.2217304763960306 },
 188   { 1.3839259540325153, -0.19999999999999996, 1.3962634015954636 },
 189   { 1.5549685462425291, -0.19999999999999996, 1.5707963267948966 },
 190 };
 191 const double toler008 = 2.5000000000000020e-13;
 192
 193 // Test data for k=-0.099999999999999978.
 194 // max(|f - f_GSL|): 4.4408920985006262e-16
 195 // max(|f - f_GSL| / |f_GSL|): 3.1875595485348029e-16
 196 const testcase_ellint_2<double>
 197 data009[10] =
 198 {
 199   { 0.0000000000000000, -0.099999999999999978, 0.0000000000000000 },
 200   { 0.17452411766649939, -0.099999999999999978, 0.17453292519943295 },
 201   { 0.34899665805442404, -0.099999999999999978, 0.34906585039886590 },
 202   { 0.52337222400508776, -0.099999999999999978, 0.52359877559829882 },
 203   { 0.69761705217284864, -0.099999999999999978, 0.69813170079773179 },
 204   { 0.87171309273007491, -0.099999999999999978, 0.87266462599716477 },
 205   { 1.0456602197056326, -0.099999999999999978, 1.0471975511965976 },
 206   { 1.2194762899272025, -0.099999999999999978, 1.2217304763960306 },
 207   { 1.3931950229892744, -0.099999999999999978, 1.3962634015954636 },
 208   { 1.5668619420216685, -0.099999999999999978, 1.5707963267948966 },
 209 };
 210 const double toler009 = 2.5000000000000020e-13;
 211
 212 // Test data for k=0.0000000000000000.
 213 // max(|f - f_GSL|): 2.2204460492503131e-16
 214 // max(|f - f_GSL| / |f_GSL|): 2.1203697876423452e-16
 215 const testcase_ellint_2<double>
 216 data010[10] =
 217 {
 218   { 0.0000000000000000, 0.0000000000000000, 0.0000000000000000 },
 219   { 0.17453292519943292, 0.0000000000000000, 0.17453292519943295 },
 220   { 0.34906585039886584, 0.0000000000000000, 0.34906585039886590 },
 221   { 0.52359877559829870, 0.0000000000000000, 0.52359877559829882 },
 222   { 0.69813170079773168, 0.0000000000000000, 0.69813170079773179 },
 223   { 0.87266462599716477, 0.0000000000000000, 0.87266462599716477 },
 224   { 1.0471975511965974, 0.0000000000000000, 1.0471975511965976 },
 225   { 1.2217304763960304, 0.0000000000000000, 1.2217304763960306 },
 226   { 1.3962634015954631, 0.0000000000000000, 1.3962634015954636 },
 227   { 1.5707963267948966, 0.0000000000000000, 1.5707963267948966 },
 228 };
 229 const double toler010 = 2.5000000000000020e-13;
 230
 231 // Test data for k=0.10000000000000009.
 232 // max(|f - f_GSL|): 4.4408920985006262e-16
 233 // max(|f - f_GSL| / |f_GSL|): 3.1875595485348029e-16
 234 const testcase_ellint_2<double>
 235 data011[10] =
 236 {
 237   { 0.0000000000000000, 0.10000000000000009, 0.0000000000000000 },
 238   { 0.17452411766649939, 0.10000000000000009, 0.17453292519943295 },
 239   { 0.34899665805442404, 0.10000000000000009, 0.34906585039886590 },
 240   { 0.52337222400508776, 0.10000000000000009, 0.52359877559829882 },
 241   { 0.69761705217284864, 0.10000000000000009, 0.69813170079773179 },
 242   { 0.87171309273007491, 0.10000000000000009, 0.87266462599716477 },
 243   { 1.0456602197056326, 0.10000000000000009, 1.0471975511965976 },
 244   { 1.2194762899272025, 0.10000000000000009, 1.2217304763960306 },
 245   { 1.3931950229892744, 0.10000000000000009, 1.3962634015954636 },
 246   { 1.5668619420216685, 0.10000000000000009, 1.5707963267948966 },
 247 };
 248 const double toler011 = 2.5000000000000020e-13;
 249
 250 // Test data for k=0.19999999999999996.
 251 // max(|f - f_GSL|): 4.4408920985006262e-16
 252 // max(|f - f_GSL| / |f_GSL|): 4.2658819988515356e-16
 253 const testcase_ellint_2<double>
 254 data012[10] =
 255 {
 256   { 0.0000000000000000, 0.19999999999999996, 0.0000000000000000 },
 257   { 0.17449769027652812, 0.19999999999999996, 0.17453292519943295 },
 258   { 0.34878893400762095, 0.19999999999999996, 0.34906585039886590 },
 259   { 0.52269152856057410, 0.19999999999999996, 0.52359877559829882 },
 260   { 0.69606913360157563, 0.19999999999999996, 0.69813170079773179 },
 261   { 0.86884782374863356, 0.19999999999999996, 0.87266462599716477 },
 262   { 1.0410255369689567, 0.19999999999999996, 1.0471975511965976 },
 263   { 1.2126730391631360, 0.19999999999999996, 1.2217304763960306 },
 264   { 1.3839259540325153, 0.19999999999999996, 1.3962634015954636 },
 265   { 1.5549685462425291, 0.19999999999999996, 1.5707963267948966 },
 266 };
 267 const double toler012 = 2.5000000000000020e-13;
 268
 269 // Test data for k=0.30000000000000004.
 270 // max(|f - f_GSL|): 8.8817841970012523e-16
 271 // max(|f - f_GSL| / |f_GSL|): 6.3860540218057383e-16
 272 const testcase_ellint_2<double>
 273 data013[10] =
 274 {
 275   { 0.0000000000000000, 0.30000000000000004, 0.0000000000000000 },
 276   { 0.17445362864048913, 0.30000000000000004, 0.17453292519943295 },
 277   { 0.34844223535713464, 0.30000000000000004, 0.34906585039886590 },
 278   { 0.52155353877411770, 0.30000000000000004, 0.52359877559829882 },
 279   { 0.69347584418369879, 0.30000000000000004, 0.69813170079773179 },
 280   { 0.86403609928237668, 0.30000000000000004, 0.87266462599716477 },
 281   { 1.0332234514065408, 0.30000000000000004, 1.0471975511965976 },
 282   { 1.2011943182068923, 0.30000000000000004, 1.2217304763960306 },
 283   { 1.3682566113689623, 0.30000000000000004, 1.3962634015954636 },
 284   { 1.5348334649232491, 0.30000000000000004, 1.5707963267948966 },
 285 };
 286 const double toler013 = 2.5000000000000020e-13;
 287
 288 // Test data for k=0.39999999999999991.
 289 // max(|f - f_GSL|): 8.8817841970012523e-16
 290 // max(|f - f_GSL| / |f_GSL|): 5.8978277272530773e-16
 291 const testcase_ellint_2<double>
 292 data014[10] =
 293 {
 294   { 0.0000000000000000, 0.39999999999999991, 0.0000000000000000 },
 295   { 0.17439190872481267, 0.39999999999999991, 0.17453292519943295 },
 296   { 0.34795581767099210, 0.39999999999999991, 0.34906585039886590 },
 297   { 0.51995290683804463, 0.39999999999999991, 0.52359877559829882 },
 298   { 0.68981638464431538, 0.39999999999999991, 0.69813170079773179 },
 299   { 0.85722088859936041, 0.39999999999999991, 0.87266462599716477 },
 300   { 1.0221301327876993, 0.39999999999999991, 1.0471975511965976 },
 301   { 1.1848138019818373, 0.39999999999999991, 1.2217304763960306 },
 302   { 1.3458259266501533, 0.39999999999999991, 1.3962634015954636 },
 303   { 1.5059416123600404, 0.39999999999999991, 1.5707963267948966 },
 304 };
 305 const double toler014 = 2.5000000000000020e-13;
 306
 307 // Test data for k=0.50000000000000000.
 308 // max(|f - f_GSL|): 2.2204460492503131e-16
 309 // max(|f - f_GSL| / |f_GSL|): 3.2412420886495652e-16
 310 const testcase_ellint_2<double>
 311 data015[10] =
 312 {
 313   { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000 },
 314   { 0.17431249677315910, 0.50000000000000000, 0.17453292519943295 },
 315   { 0.34732862537770803, 0.50000000000000000, 0.34906585039886590 },
 316   { 0.51788193485993794, 0.50000000000000000, 0.52359877559829882 },
 317   { 0.68506022954164536, 0.50000000000000000, 0.69813170079773179 },
 318   { 0.84831662803347196, 0.50000000000000000, 0.87266462599716477 },
 319   { 1.0075555551444717, 0.50000000000000000, 1.0471975511965976 },
 320   { 1.1631768599287300, 0.50000000000000000, 1.2217304763960306 },
 321   { 1.3160584048772543, 0.50000000000000000, 1.3962634015954636 },
 322   { 1.4674622093394274, 0.50000000000000000, 1.5707963267948966 },
 323 };
 324 const double toler015 = 2.5000000000000020e-13;
 325
 326 // Test data for k=0.60000000000000009.
 327 // max(|f - f_GSL|): 4.4408920985006262e-16
 328 // max(|f - f_GSL| / |f_GSL|): 3.9101039108874066e-16
 329 const testcase_ellint_2<double>
 330 data016[10] =
 331 {
 332   { 0.0000000000000000, 0.60000000000000009, 0.0000000000000000 },
 333   { 0.17421534919599127, 0.60000000000000009, 0.17453292519943295 },
 334   { 0.34655927787174101, 0.60000000000000009, 0.34906585039886590 },
 335   { 0.51533034538432143, 0.60000000000000009, 0.52359877559829882 },
 336   { 0.67916550597453018, 0.60000000000000009, 0.69813170079773179 },
 337   { 0.83720218180349870, 0.60000000000000009, 0.87266462599716477 },
 338   { 0.98922159354937744, 0.60000000000000009, 1.0471975511965976 },
 339   { 1.1357478470419360, 0.60000000000000009, 1.2217304763960306 },
 340   { 1.2780617372844056, 0.60000000000000009, 1.3962634015954636 },
 341   { 1.4180833944487241, 0.60000000000000009, 1.5707963267948966 },
 342 };
 343 const double toler016 = 2.5000000000000020e-13;
 344
 345 // Test data for k=0.69999999999999996.
 346 // max(|f - f_GSL|): 3.3306690738754696e-16
 347 // max(|f - f_GSL| / |f_GSL|): 4.0435005012914979e-16
 348 const testcase_ellint_2<double>
 349 data017[10] =
 350 {
 351   { 0.0000000000000000, 0.69999999999999996, 0.0000000000000000 },
 352   { 0.17410041242702542, 0.69999999999999996, 0.17453292519943295 },
 353   { 0.34564605085764760, 0.69999999999999996, 0.34906585039886590 },
 354   { 0.51228495693314646, 0.69999999999999996, 0.52359877559829882 },
 355   { 0.67207654098799530, 0.69999999999999996, 0.69813170079773179 },
 356   { 0.82370932631556515, 0.69999999999999996, 0.87266462599716477 },
 357   { 0.96672313309452795, 0.69999999999999996, 1.0471975511965976 },
 358   { 1.1017090644949503, 0.69999999999999996, 1.2217304763960306 },
 359   { 1.2304180097292914, 0.69999999999999996, 1.3962634015954636 },
 360   { 1.3556611355719554, 0.69999999999999996, 1.5707963267948966 },
 361 };
 362 const double toler017 = 2.5000000000000020e-13;
 363
 364 // Test data for k=0.80000000000000004.
 365 // max(|f - f_GSL|): 4.4408920985006262e-16
 366 // max(|f - f_GSL| / |f_GSL|): 3.4793687438660849e-16
 367 const testcase_ellint_2<double>
 368 data018[10] =
 369 {
 370   { 0.0000000000000000, 0.80000000000000004, 0.0000000000000000 },
 371   { 0.17396762274534805, 0.80000000000000004, 0.17453292519943295 },
 372   { 0.34458685226969316, 0.80000000000000004, 0.34906585039886590 },
 373   { 0.50872923654502433, 0.80000000000000004, 0.52359877559829882 },
 374   { 0.66372016539176215, 0.80000000000000004, 0.69813170079773179 },
 375   { 0.80760344410167406, 0.80000000000000004, 0.87266462599716477 },
 376   { 0.93945480372495049, 0.80000000000000004, 1.0471975511965976 },
 377   { 1.0597473310395036, 0.80000000000000004, 1.2217304763960306 },
 378   { 1.1706981862452361, 0.80000000000000004, 1.3962634015954636 },
 379   { 1.2763499431699064, 0.80000000000000004, 1.5707963267948966 },
 380 };
 381 const double toler018 = 2.5000000000000020e-13;
 382
 383 // Test data for k=0.89999999999999991.
 384 // max(|f - f_GSL|): 4.4408920985006262e-16
 385 // max(|f - f_GSL| / |f_GSL|): 3.7901367831880493e-16
 386 const testcase_ellint_2<double>
 387 data019[10] =
 388 {
 389   { 0.0000000000000000, 0.89999999999999991, 0.0000000000000000 },
 390   { 0.17381690606167960, 0.89999999999999991, 0.17453292519943295 },
 391   { 0.34337919186972055, 0.89999999999999991, 0.34906585039886590 },
 392   { 0.50464268659856326, 0.89999999999999991, 0.52359877559829882 },
 393   { 0.65400003842368570, 0.89999999999999991, 0.69813170079773179 },
 394   { 0.78854928419904657, 0.89999999999999991, 0.87266462599716477 },
 395   { 0.90645698626315407, 0.89999999999999991, 1.0471975511965976 },
 396   { 1.0075154899135930, 0.89999999999999991, 1.2217304763960306 },
 397   { 1.0940135583194071, 0.89999999999999991, 1.3962634015954636 },
 398   { 1.1716970527816144, 0.89999999999999991, 1.5707963267948966 },
 399 };
 400 const double toler019 = 2.5000000000000020e-13;
 401
 402 template<typename Tp, unsigned int Num>
 403   void
 404   test(const testcase_ellint_2<Tp> (&data)[Num], Tp toler)
 405   {
 406     const Tp eps = std::numeric_limits<Tp>::epsilon();
 407     Tp max_abs_diff = -Tp(1);
 408     Tp max_abs_frac = -Tp(1);
 409     unsigned int num_datum = Num;
 410     for (unsigned int i = 0; i < num_datum; ++i)
 411       {
 412         const Tp f = std::ellint_2(data[i].k, data[i].phi);
 413         const Tp f0 = data[i].f0;
 414         const Tp diff = f - f0;
 415         if (std::abs(diff) > max_abs_diff)
 416           max_abs_diff = std::abs(diff);
 417         if (std::abs(f0) > Tp(10) * eps
 418          && std::abs(f) > Tp(10) * eps)
 419           {
 420             const Tp frac = diff / f0;
 421             if (std::abs(frac) > max_abs_frac)
 422               max_abs_frac = std::abs(frac);
 423           }
 424       }
 425     VERIFY(max_abs_frac < toler);
 426   }
 427
 428 int
 429 main()
 430 {
 431   test(data001, toler001);
 432   test(data002, toler002);
 433   test(data003, toler003);
 434   test(data004, toler004);
 435   test(data005, toler005);
 436   test(data006, toler006);
 437   test(data007, toler007);
 438   test(data008, toler008);
 439   test(data009, toler009);
 440   test(data010, toler010);
 441   test(data011, toler011);
 442   test(data012, toler012);
 443   test(data013, toler013);
 444   test(data014, toler014);
 445   test(data015, toler015);
 446   test(data016, toler016);
 447   test(data017, toler017);
 448   test(data018, toler018);
 449   test(data019, toler019);
 450   return 0;
 451 }