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) 2016-2025 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 // Test data for k=-0.90000000000000002.
  41 // max(|f - f_Boost|): 6.6613381477509392e-16 at index 7
  42 // max(|f - f_Boost| / |f_Boost|): 6.6116483711056727e-16
  43 // mean(f - f_Boost): -8.6042284408449634e-17
  44 // variance(f - f_Boost): 4.1543973284335233e-32
  45 // stddev(f - f_Boost): 2.0382338748125847e-16
  46 const testcase_ellint_2<double>
  47 data001[10] =
  48 {
  49   { 0.0000000000000000, -0.90000000000000002, 0.0000000000000000, 0.0 },
  50   { 0.17381690606167963, -0.90000000000000002, 0.17453292519943295, 0.0 },
  51   { 0.34337919186972055, -0.90000000000000002, 0.34906585039886590, 0.0 },
  52   { 0.50464268659856337, -0.90000000000000002, 0.52359877559829882, 0.0 },
  53   { 0.65400003842368593, -0.90000000000000002, 0.69813170079773179, 0.0 },
  54   { 0.78854928419904635, -0.90000000000000002, 0.87266462599716477, 0.0 },
  55   { 0.90645698626315396, -0.90000000000000002, 1.0471975511965976, 0.0 },
  56   { 1.0075154899135927, -0.90000000000000002, 1.2217304763960306, 0.0 },
  57   { 1.0940135583194071, -0.90000000000000002, 1.3962634015954636, 0.0 },
  58   { 1.1716970527816142, -0.90000000000000002, 1.5707963267948966, 0.0 },
  59 };
  60 const double toler001 = 2.5000000000000020e-13;
  61
  62 // Test data for k=-0.80000000000000004.
  63 // max(|f - f_Boost|): 1.3322676295501878e-15 at index 9
  64 // max(|f - f_Boost| / |f_Boost|): 1.0438106231598255e-15
  65 // mean(f - f_Boost): 1.8318679906315082e-16
  66 // variance(f - f_Boost): 1.6301071049293564e-31
  67 // stddev(f - f_Boost): 4.0374584888632060e-16
  68 const testcase_ellint_2<double>
  69 data002[10] =
  70 {
  71   { 0.0000000000000000, -0.80000000000000004, 0.0000000000000000, 0.0 },
  72   { 0.17396762274534805, -0.80000000000000004, 0.17453292519943295, 0.0 },
  73   { 0.34458685226969321, -0.80000000000000004, 0.34906585039886590, 0.0 },
  74   { 0.50872923654502433, -0.80000000000000004, 0.52359877559829882, 0.0 },
  75   { 0.66372016539176226, -0.80000000000000004, 0.69813170079773179, 0.0 },
  76   { 0.80760344410167406, -0.80000000000000004, 0.87266462599716477, 0.0 },
  77   { 0.93945480372495072, -0.80000000000000004, 1.0471975511965976, 0.0 },
  78   { 1.0597473310395040, -0.80000000000000004, 1.2217304763960306, 0.0 },
  79   { 1.1706981862452359, -0.80000000000000004, 1.3962634015954636, 0.0 },
  80   { 1.2763499431699064, -0.80000000000000004, 1.5707963267948966, 0.0 },
  81 };
  82 const double toler002 = 2.5000000000000020e-13;
  83
  84 // Test data for k=-0.69999999999999996.
  85 // max(|f - f_Boost|): 6.6613381477509392e-16 at index 8
  86 // max(|f - f_Boost| / |f_Boost|): 5.4138821888802831e-16
  87 // mean(f - f_Boost): 1.9428902930940238e-17
  88 // variance(f - f_Boost): 2.6524572947662036e-32
  89 // stddev(f - f_Boost): 1.6286366368119696e-16
  90 const testcase_ellint_2<double>
  91 data003[10] =
  92 {
  93   { 0.0000000000000000, -0.69999999999999996, 0.0000000000000000, 0.0 },
  94   { 0.17410041242702540, -0.69999999999999996, 0.17453292519943295, 0.0 },
  95   { 0.34564605085764760, -0.69999999999999996, 0.34906585039886590, 0.0 },
  96   { 0.51228495693314657, -0.69999999999999996, 0.52359877559829882, 0.0 },
  97   { 0.67207654098799530, -0.69999999999999996, 0.69813170079773179, 0.0 },
  98   { 0.82370932631556493, -0.69999999999999996, 0.87266462599716477, 0.0 },
  99   { 0.96672313309452806, -0.69999999999999996, 1.0471975511965976, 0.0 },
 100   { 1.1017090644949501, -0.69999999999999996, 1.2217304763960306, 0.0 },
 101   { 1.2304180097292916, -0.69999999999999996, 1.3962634015954636, 0.0 },
 102   { 1.3556611355719554, -0.69999999999999996, 1.5707963267948966, 0.0 },
 103 };
 104 const double toler003 = 2.5000000000000020e-13;
 105
 106 // Test data for k=-0.59999999999999998.
 107 // max(|f - f_Boost|): 2.2204460492503131e-16 at index 7
 108 // max(|f - f_Boost| / |f_Boost|): 1.9550519554437030e-16
 109 // mean(f - f_Boost): 1.9428902930940238e-17
 110 // variance(f - f_Boost): 4.6602749271592373e-35
 111 // stddev(f - f_Boost): 6.8266206333435850e-18
 112 const testcase_ellint_2<double>
 113 data004[10] =
 114 {
 115   { 0.0000000000000000, -0.59999999999999998, 0.0000000000000000, 0.0 },
 116   { 0.17421534919599127, -0.59999999999999998, 0.17453292519943295, 0.0 },
 117   { 0.34655927787174096, -0.59999999999999998, 0.34906585039886590, 0.0 },
 118   { 0.51533034538432143, -0.59999999999999998, 0.52359877559829882, 0.0 },
 119   { 0.67916550597453018, -0.59999999999999998, 0.69813170079773179, 0.0 },
 120   { 0.83720218180349881, -0.59999999999999998, 0.87266462599716477, 0.0 },
 121   { 0.98922159354937755, -0.59999999999999998, 1.0471975511965976, 0.0 },
 122   { 1.1357478470419362, -0.59999999999999998, 1.2217304763960306, 0.0 },
 123   { 1.2780617372844061, -0.59999999999999998, 1.3962634015954636, 0.0 },
 124   { 1.4180833944487241, -0.59999999999999998, 1.5707963267948966, 0.0 },
 125 };
 126 const double toler004 = 2.5000000000000020e-13;
 127
 128 // Test data for k=-0.50000000000000000.
 129 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 7
 130 // max(|f - f_Boost| / |f_Boost|): 3.8178992821201131e-16
 131 // mean(f - f_Boost): -4.9960036108132046e-17
 132 // variance(f - f_Boost): 3.0133908324921077e-32
 133 // stddev(f - f_Boost): 1.7359121039073689e-16
 134 const testcase_ellint_2<double>
 135 data005[10] =
 136 {
 137   { 0.0000000000000000, -0.50000000000000000, 0.0000000000000000, 0.0 },
 138   { 0.17431249677315908, -0.50000000000000000, 0.17453292519943295, 0.0 },
 139   { 0.34732862537770803, -0.50000000000000000, 0.34906585039886590, 0.0 },
 140   { 0.51788193485993794, -0.50000000000000000, 0.52359877559829882, 0.0 },
 141   { 0.68506022954164547, -0.50000000000000000, 0.69813170079773179, 0.0 },
 142   { 0.84831662803347208, -0.50000000000000000, 0.87266462599716477, 0.0 },
 143   { 1.0075555551444719, -0.50000000000000000, 1.0471975511965976, 0.0 },
 144   { 1.1631768599287302, -0.50000000000000000, 1.2217304763960306, 0.0 },
 145   { 1.3160584048772548, -0.50000000000000000, 1.3962634015954636, 0.0 },
 146   { 1.4674622093394272, -0.50000000000000000, 1.5707963267948966, 0.0 },
 147 };
 148 const double toler005 = 2.5000000000000020e-13;
 149
 150 // Test data for k=-0.39999999999999991.
 151 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 9
 152 // max(|f - f_Boost| / |f_Boost|): 2.9489138636265387e-16
 153 // mean(f - f_Boost): 8.6042284408449634e-17
 154 // variance(f - f_Boost): 1.5826864298542218e-32
 155 // stddev(f - f_Boost): 1.2580486595733180e-16
 156 const testcase_ellint_2<double>
 157 data006[10] =
 158 {
 159   { 0.0000000000000000, -0.39999999999999991, 0.0000000000000000, 0.0 },
 160   { 0.17439190872481267, -0.39999999999999991, 0.17453292519943295, 0.0 },
 161   { 0.34795581767099210, -0.39999999999999991, 0.34906585039886590, 0.0 },
 162   { 0.51995290683804463, -0.39999999999999991, 0.52359877559829882, 0.0 },
 163   { 0.68981638464431527, -0.39999999999999991, 0.69813170079773179, 0.0 },
 164   { 0.85722088859936030, -0.39999999999999991, 0.87266462599716477, 0.0 },
 165   { 1.0221301327876993, -0.39999999999999991, 1.0471975511965976, 0.0 },
 166   { 1.1848138019818375, -0.39999999999999991, 1.2217304763960306, 0.0 },
 167   { 1.3458259266501533, -0.39999999999999991, 1.3962634015954636, 0.0 },
 168   { 1.5059416123600404, -0.39999999999999991, 1.5707963267948966, 0.0 },
 169 };
 170 const double toler006 = 2.5000000000000020e-13;
 171
 172 // Test data for k=-0.29999999999999993.
 173 // max(|f - f_Boost|): 6.6613381477509392e-16 at index 9
 174 // max(|f - f_Boost| / |f_Boost|): 4.3401048387253188e-16
 175 // mean(f - f_Boost): 7.2164496600635178e-17
 176 // variance(f - f_Boost): 4.3555500115139682e-32
 177 // stddev(f - f_Boost): 2.0869954507650391e-16
 178 const testcase_ellint_2<double>
 179 data007[10] =
 180 {
 181   { 0.0000000000000000, -0.29999999999999993, 0.0000000000000000, 0.0 },
 182   { 0.17445362864048913, -0.29999999999999993, 0.17453292519943295, 0.0 },
 183   { 0.34844223535713470, -0.29999999999999993, 0.34906585039886590, 0.0 },
 184   { 0.52155353877411759, -0.29999999999999993, 0.52359877559829882, 0.0 },
 185   { 0.69347584418369890, -0.29999999999999993, 0.69813170079773179, 0.0 },
 186   { 0.86403609928237657, -0.29999999999999993, 0.87266462599716477, 0.0 },
 187   { 1.0332234514065408, -0.29999999999999993, 1.0471975511965976, 0.0 },
 188   { 1.2011943182068923, -0.29999999999999993, 1.2217304763960306, 0.0 },
 189   { 1.3682566113689625, -0.29999999999999993, 1.3962634015954636, 0.0 },
 190   { 1.5348334649232489, -0.29999999999999993, 1.5707963267948966, 0.0 },
 191 };
 192 const double toler007 = 2.5000000000000020e-13;
 193
 194 // Test data for k=-0.19999999999999996.
 195 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 6
 196 // max(|f - f_Boost| / |f_Boost|): 4.2658819988515356e-16
 197 // mean(f - f_Boost): -5.2735593669694933e-17
 198 // variance(f - f_Boost): 3.0473442641042680e-32
 199 // stddev(f - f_Boost): 1.7456644190978597e-16
 200 const testcase_ellint_2<double>
 201 data008[10] =
 202 {
 203   { 0.0000000000000000, -0.19999999999999996, 0.0000000000000000, 0.0 },
 204   { 0.17449769027652809, -0.19999999999999996, 0.17453292519943295, 0.0 },
 205   { 0.34878893400762090, -0.19999999999999996, 0.34906585039886590, 0.0 },
 206   { 0.52269152856057410, -0.19999999999999996, 0.52359877559829882, 0.0 },
 207   { 0.69606913360157574, -0.19999999999999996, 0.69813170079773179, 0.0 },
 208   { 0.86884782374863379, -0.19999999999999996, 0.87266462599716477, 0.0 },
 209   { 1.0410255369689567, -0.19999999999999996, 1.0471975511965976, 0.0 },
 210   { 1.2126730391631364, -0.19999999999999996, 1.2217304763960306, 0.0 },
 211   { 1.3839259540325151, -0.19999999999999996, 1.3962634015954636, 0.0 },
 212   { 1.5549685462425293, -0.19999999999999996, 1.5707963267948966, 0.0 },
 213 };
 214 const double toler008 = 2.5000000000000020e-13;
 215
 216 // Test data for k=-0.099999999999999978.
 217 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 8
 218 // max(|f - f_Boost| / |f_Boost|): 3.1875595485348024e-16
 219 // mean(f - f_Boost): -4.7184478546569152e-17
 220 // variance(f - f_Boost): 2.7486111305082032e-34
 221 // stddev(f - f_Boost): 1.6578935823834422e-17
 222 const testcase_ellint_2<double>
 223 data009[10] =
 224 {
 225   { 0.0000000000000000, -0.099999999999999978, 0.0000000000000000, 0.0 },
 226   { 0.17452411766649942, -0.099999999999999978, 0.17453292519943295, 0.0 },
 227   { 0.34899665805442409, -0.099999999999999978, 0.34906585039886590, 0.0 },
 228   { 0.52337222400508787, -0.099999999999999978, 0.52359877559829882, 0.0 },
 229   { 0.69761705217284864, -0.099999999999999978, 0.69813170079773179, 0.0 },
 230   { 0.87171309273007491, -0.099999999999999978, 0.87266462599716477, 0.0 },
 231   { 1.0456602197056326, -0.099999999999999978, 1.0471975511965976, 0.0 },
 232   { 1.2194762899272027, -0.099999999999999978, 1.2217304763960306, 0.0 },
 233   { 1.3931950229892747, -0.099999999999999978, 1.3962634015954636, 0.0 },
 234   { 1.5668619420216683, -0.099999999999999978, 1.5707963267948966, 0.0 },
 235 };
 236 const double toler009 = 2.5000000000000020e-13;
 237
 238 // Test data for k=0.0000000000000000.
 239 // max(|f - f_Boost|): 2.2204460492503131e-16 at index 7
 240 // max(|f - f_Boost| / |f_Boost|): 2.1203697876423447e-16
 241 // mean(f - f_Boost): -1.9428902930940238e-17
 242 // variance(f - f_Boost): 4.6602749271592373e-35
 243 // stddev(f - f_Boost): 6.8266206333435850e-18
 244 const testcase_ellint_2<double>
 245 data010[10] =
 246 {
 247   { 0.0000000000000000, 0.0000000000000000, 0.0000000000000000, 0.0 },
 248   { 0.17453292519943295, 0.0000000000000000, 0.17453292519943295, 0.0 },
 249   { 0.34906585039886590, 0.0000000000000000, 0.34906585039886590, 0.0 },
 250   { 0.52359877559829882, 0.0000000000000000, 0.52359877559829882, 0.0 },
 251   { 0.69813170079773179, 0.0000000000000000, 0.69813170079773179, 0.0 },
 252   { 0.87266462599716477, 0.0000000000000000, 0.87266462599716477, 0.0 },
 253   { 1.0471975511965976, 0.0000000000000000, 1.0471975511965976, 0.0 },
 254   { 1.2217304763960306, 0.0000000000000000, 1.2217304763960306, 0.0 },
 255   { 1.3962634015954636, 0.0000000000000000, 1.3962634015954636, 0.0 },
 256   { 1.5707963267948966, 0.0000000000000000, 1.5707963267948966, 0.0 },
 257 };
 258 const double toler010 = 2.5000000000000020e-13;
 259
 260 // Test data for k=0.10000000000000009.
 261 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 8
 262 // max(|f - f_Boost| / |f_Boost|): 3.1875595485348024e-16
 263 // mean(f - f_Boost): -4.7184478546569152e-17
 264 // variance(f - f_Boost): 2.7486111305082032e-34
 265 // stddev(f - f_Boost): 1.6578935823834422e-17
 266 const testcase_ellint_2<double>
 267 data011[10] =
 268 {
 269   { 0.0000000000000000, 0.10000000000000009, 0.0000000000000000, 0.0 },
 270   { 0.17452411766649942, 0.10000000000000009, 0.17453292519943295, 0.0 },
 271   { 0.34899665805442409, 0.10000000000000009, 0.34906585039886590, 0.0 },
 272   { 0.52337222400508787, 0.10000000000000009, 0.52359877559829882, 0.0 },
 273   { 0.69761705217284864, 0.10000000000000009, 0.69813170079773179, 0.0 },
 274   { 0.87171309273007491, 0.10000000000000009, 0.87266462599716477, 0.0 },
 275   { 1.0456602197056326, 0.10000000000000009, 1.0471975511965976, 0.0 },
 276   { 1.2194762899272027, 0.10000000000000009, 1.2217304763960306, 0.0 },
 277   { 1.3931950229892747, 0.10000000000000009, 1.3962634015954636, 0.0 },
 278   { 1.5668619420216683, 0.10000000000000009, 1.5707963267948966, 0.0 },
 279 };
 280 const double toler011 = 2.5000000000000020e-13;
 281
 282 // Test data for k=0.20000000000000018.
 283 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 6
 284 // max(|f - f_Boost| / |f_Boost|): 4.2658819988515356e-16
 285 // mean(f - f_Boost): -5.2735593669694933e-17
 286 // variance(f - f_Boost): 3.0473442641042680e-32
 287 // stddev(f - f_Boost): 1.7456644190978597e-16
 288 const testcase_ellint_2<double>
 289 data012[10] =
 290 {
 291   { 0.0000000000000000, 0.20000000000000018, 0.0000000000000000, 0.0 },
 292   { 0.17449769027652809, 0.20000000000000018, 0.17453292519943295, 0.0 },
 293   { 0.34878893400762090, 0.20000000000000018, 0.34906585039886590, 0.0 },
 294   { 0.52269152856057410, 0.20000000000000018, 0.52359877559829882, 0.0 },
 295   { 0.69606913360157574, 0.20000000000000018, 0.69813170079773179, 0.0 },
 296   { 0.86884782374863379, 0.20000000000000018, 0.87266462599716477, 0.0 },
 297   { 1.0410255369689567, 0.20000000000000018, 1.0471975511965976, 0.0 },
 298   { 1.2126730391631364, 0.20000000000000018, 1.2217304763960306, 0.0 },
 299   { 1.3839259540325151, 0.20000000000000018, 1.3962634015954636, 0.0 },
 300   { 1.5549685462425291, 0.20000000000000018, 1.5707963267948966, 0.0 },
 301 };
 302 const double toler012 = 2.5000000000000020e-13;
 303
 304 // Test data for k=0.30000000000000004.
 305 // max(|f - f_Boost|): 6.6613381477509392e-16 at index 9
 306 // max(|f - f_Boost| / |f_Boost|): 4.3401048387253188e-16
 307 // mean(f - f_Boost): 7.2164496600635178e-17
 308 // variance(f - f_Boost): 4.3555500115139682e-32
 309 // stddev(f - f_Boost): 2.0869954507650391e-16
 310 const testcase_ellint_2<double>
 311 data013[10] =
 312 {
 313   { 0.0000000000000000, 0.30000000000000004, 0.0000000000000000, 0.0 },
 314   { 0.17445362864048913, 0.30000000000000004, 0.17453292519943295, 0.0 },
 315   { 0.34844223535713470, 0.30000000000000004, 0.34906585039886590, 0.0 },
 316   { 0.52155353877411759, 0.30000000000000004, 0.52359877559829882, 0.0 },
 317   { 0.69347584418369890, 0.30000000000000004, 0.69813170079773179, 0.0 },
 318   { 0.86403609928237657, 0.30000000000000004, 0.87266462599716477, 0.0 },
 319   { 1.0332234514065408, 0.30000000000000004, 1.0471975511965976, 0.0 },
 320   { 1.2011943182068923, 0.30000000000000004, 1.2217304763960306, 0.0 },
 321   { 1.3682566113689625, 0.30000000000000004, 1.3962634015954636, 0.0 },
 322   { 1.5348334649232489, 0.30000000000000004, 1.5707963267948966, 0.0 },
 323 };
 324 const double toler013 = 2.5000000000000020e-13;
 325
 326 // Test data for k=0.40000000000000013.
 327 // max(|f - f_Boost|): 1.7763568394002505e-15 at index 9
 328 // max(|f - f_Boost| / |f_Boost|): 1.1795655454506157e-15
 329 // mean(f - f_Boost): 2.0816681711721685e-16
 330 // variance(f - f_Boost): 3.0360740073926687e-31
 331 // stddev(f - f_Boost): 5.5100580826273227e-16
 332 const testcase_ellint_2<double>
 333 data014[10] =
 334 {
 335   { 0.0000000000000000, 0.40000000000000013, 0.0000000000000000, 0.0 },
 336   { 0.17439190872481267, 0.40000000000000013, 0.17453292519943295, 0.0 },
 337   { 0.34795581767099210, 0.40000000000000013, 0.34906585039886590, 0.0 },
 338   { 0.51995290683804463, 0.40000000000000013, 0.52359877559829882, 0.0 },
 339   { 0.68981638464431527, 0.40000000000000013, 0.69813170079773179, 0.0 },
 340   { 0.85722088859936030, 0.40000000000000013, 0.87266462599716477, 0.0 },
 341   { 1.0221301327876993, 0.40000000000000013, 1.0471975511965976, 0.0 },
 342   { 1.1848138019818375, 0.40000000000000013, 1.2217304763960306, 0.0 },
 343   { 1.3458259266501531, 0.40000000000000013, 1.3962634015954636, 0.0 },
 344   { 1.5059416123600402, 0.40000000000000013, 1.5707963267948966, 0.0 },
 345 };
 346 const double toler014 = 2.5000000000000020e-13;
 347
 348 // Test data for k=0.50000000000000000.
 349 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 7
 350 // max(|f - f_Boost| / |f_Boost|): 3.8178992821201131e-16
 351 // mean(f - f_Boost): -4.9960036108132046e-17
 352 // variance(f - f_Boost): 3.0133908324921077e-32
 353 // stddev(f - f_Boost): 1.7359121039073689e-16
 354 const testcase_ellint_2<double>
 355 data015[10] =
 356 {
 357   { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000, 0.0 },
 358   { 0.17431249677315908, 0.50000000000000000, 0.17453292519943295, 0.0 },
 359   { 0.34732862537770803, 0.50000000000000000, 0.34906585039886590, 0.0 },
 360   { 0.51788193485993794, 0.50000000000000000, 0.52359877559829882, 0.0 },
 361   { 0.68506022954164547, 0.50000000000000000, 0.69813170079773179, 0.0 },
 362   { 0.84831662803347208, 0.50000000000000000, 0.87266462599716477, 0.0 },
 363   { 1.0075555551444719, 0.50000000000000000, 1.0471975511965976, 0.0 },
 364   { 1.1631768599287302, 0.50000000000000000, 1.2217304763960306, 0.0 },
 365   { 1.3160584048772548, 0.50000000000000000, 1.3962634015954636, 0.0 },
 366   { 1.4674622093394272, 0.50000000000000000, 1.5707963267948966, 0.0 },
 367 };
 368 const double toler015 = 2.5000000000000020e-13;
 369
 370 // Test data for k=0.60000000000000009.
 371 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 7
 372 // max(|f - f_Boost| / |f_Boost|): 3.9101039108874066e-16
 373 // mean(f - f_Boost): 1.9428902930940238e-17
 374 // variance(f - f_Boost): 7.1986981476874020e-33
 375 // stddev(f - f_Boost): 8.4845142157270271e-17
 376 const testcase_ellint_2<double>
 377 data016[10] =
 378 {
 379   { 0.0000000000000000, 0.60000000000000009, 0.0000000000000000, 0.0 },
 380   { 0.17421534919599127, 0.60000000000000009, 0.17453292519943295, 0.0 },
 381   { 0.34655927787174096, 0.60000000000000009, 0.34906585039886590, 0.0 },
 382   { 0.51533034538432143, 0.60000000000000009, 0.52359877559829882, 0.0 },
 383   { 0.67916550597453018, 0.60000000000000009, 0.69813170079773179, 0.0 },
 384   { 0.83720218180349881, 0.60000000000000009, 0.87266462599716477, 0.0 },
 385   { 0.98922159354937755, 0.60000000000000009, 1.0471975511965976, 0.0 },
 386   { 1.1357478470419360, 0.60000000000000009, 1.2217304763960306, 0.0 },
 387   { 1.2780617372844061, 0.60000000000000009, 1.3962634015954636, 0.0 },
 388   { 1.4180833944487241, 0.60000000000000009, 1.5707963267948966, 0.0 },
 389 };
 390 const double toler016 = 2.5000000000000020e-13;
 391
 392 // Test data for k=0.70000000000000018.
 393 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 6
 394 // max(|f - f_Boost| / |f_Boost|): 4.5937579711009016e-16
 395 // mean(f - f_Boost): 6.1062266354383615e-17
 396 // variance(f - f_Boost): 1.8112301165881739e-32
 397 // stddev(f - f_Boost): 1.3458194962877355e-16
 398 const testcase_ellint_2<double>
 399 data017[10] =
 400 {
 401   { 0.0000000000000000, 0.70000000000000018, 0.0000000000000000, 0.0 },
 402   { 0.17410041242702540, 0.70000000000000018, 0.17453292519943295, 0.0 },
 403   { 0.34564605085764760, 0.70000000000000018, 0.34906585039886590, 0.0 },
 404   { 0.51228495693314657, 0.70000000000000018, 0.52359877559829882, 0.0 },
 405   { 0.67207654098799519, 0.70000000000000018, 0.69813170079773179, 0.0 },
 406   { 0.82370932631556493, 0.70000000000000018, 0.87266462599716477, 0.0 },
 407   { 0.96672313309452806, 0.70000000000000018, 1.0471975511965976, 0.0 },
 408   { 1.1017090644949501, 0.70000000000000018, 1.2217304763960306, 0.0 },
 409   { 1.2304180097292916, 0.70000000000000018, 1.3962634015954636, 0.0 },
 410   { 1.3556611355719552, 0.70000000000000018, 1.5707963267948966, 0.0 },
 411 };
 412 const double toler017 = 2.5000000000000020e-13;
 413
 414 // Test data for k=0.80000000000000004.
 415 // max(|f - f_Boost|): 1.3322676295501878e-15 at index 9
 416 // max(|f - f_Boost| / |f_Boost|): 1.0438106231598255e-15
 417 // mean(f - f_Boost): 1.8318679906315082e-16
 418 // variance(f - f_Boost): 1.6301071049293564e-31
 419 // stddev(f - f_Boost): 4.0374584888632060e-16
 420 const testcase_ellint_2<double>
 421 data018[10] =
 422 {
 423   { 0.0000000000000000, 0.80000000000000004, 0.0000000000000000, 0.0 },
 424   { 0.17396762274534805, 0.80000000000000004, 0.17453292519943295, 0.0 },
 425   { 0.34458685226969321, 0.80000000000000004, 0.34906585039886590, 0.0 },
 426   { 0.50872923654502433, 0.80000000000000004, 0.52359877559829882, 0.0 },
 427   { 0.66372016539176226, 0.80000000000000004, 0.69813170079773179, 0.0 },
 428   { 0.80760344410167406, 0.80000000000000004, 0.87266462599716477, 0.0 },
 429   { 0.93945480372495072, 0.80000000000000004, 1.0471975511965976, 0.0 },
 430   { 1.0597473310395040, 0.80000000000000004, 1.2217304763960306, 0.0 },
 431   { 1.1706981862452359, 0.80000000000000004, 1.3962634015954636, 0.0 },
 432   { 1.2763499431699064, 0.80000000000000004, 1.5707963267948966, 0.0 },
 433 };
 434 const double toler018 = 2.5000000000000020e-13;
 435
 436 // Test data for k=0.90000000000000013.
 437 // max(|f - f_Boost|): 6.6613381477509392e-16 at index 7
 438 // max(|f - f_Boost| / |f_Boost|): 6.6116483711056727e-16
 439 // mean(f - f_Boost): 1.3877787807814457e-17
 440 // variance(f - f_Boost): 2.3776912893669577e-35
 441 // stddev(f - f_Boost): 4.8761575952454181e-18
 442 const testcase_ellint_2<double>
 443 data019[10] =
 444 {
 445   { 0.0000000000000000, 0.90000000000000013, 0.0000000000000000, 0.0 },
 446   { 0.17381690606167963, 0.90000000000000013, 0.17453292519943295, 0.0 },
 447   { 0.34337919186972055, 0.90000000000000013, 0.34906585039886590, 0.0 },
 448   { 0.50464268659856337, 0.90000000000000013, 0.52359877559829882, 0.0 },
 449   { 0.65400003842368593, 0.90000000000000013, 0.69813170079773179, 0.0 },
 450   { 0.78854928419904635, 0.90000000000000013, 0.87266462599716477, 0.0 },
 451   { 0.90645698626315385, 0.90000000000000013, 1.0471975511965976, 0.0 },
 452   { 1.0075154899135927, 0.90000000000000013, 1.2217304763960306, 0.0 },
 453   { 1.0940135583194068, 0.90000000000000013, 1.3962634015954636, 0.0 },
 454   { 1.1716970527816140, 0.90000000000000013, 1.5707963267948966, 0.0 },
 455 };
 456 const double toler019 = 2.5000000000000020e-13;
 457
 458 template<typename Ret, unsigned int Num>
 459   void
 460   test(const testcase_ellint_2<Ret> (&data)[Num], Ret toler)
 461   {
 462     bool test __attribute__((unused)) = true;
 463     const Ret eps = std::numeric_limits<Ret>::epsilon();
 464     Ret max_abs_diff = -Ret(1);
 465     Ret max_abs_frac = -Ret(1);
 466     unsigned int num_datum = Num;
 467     for (unsigned int i = 0; i < num_datum; ++i)
 468       {
 469         const Ret f = std::ellint_2(data[i].k, data[i].phi);
 470         const Ret f0 = data[i].f0;
 471         const Ret diff = f - f0;
 472         if (std::abs(diff) > max_abs_diff)
 473           max_abs_diff = std::abs(diff);
 474         if (std::abs(f0) > Ret(10) * eps
 475          && std::abs(f) > Ret(10) * eps)
 476           {
 477             const Ret frac = diff / f0;
 478             if (std::abs(frac) > max_abs_frac)
 479               max_abs_frac = std::abs(frac);
 480           }
 481       }
 482     VERIFY(max_abs_frac < toler);
 483   }
 484
 485 int
 486 main()
 487 {
 488   test(data001, toler001);
 489   test(data002, toler002);
 490   test(data003, toler003);
 491   test(data004, toler004);
 492   test(data005, toler005);
 493   test(data006, toler006);
 494   test(data007, toler007);
 495   test(data008, toler008);
 496   test(data009, toler009);
 497   test(data010, toler010);
 498   test(data011, toler011);
 499   test(data012, toler012);
 500   test(data013, toler013);
 501   test(data014, toler014);
 502   test(data015, toler015);
 503   test(data016, toler016);
 504   test(data017, toler017);
 505   test(data018, toler018);
 506   test(data019, toler019);
 507   return 0;
 508 }