libstdc++-v3/testsuite/special_functions/13_ellint_3/check_value.cc

   1 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
   2 //
   3 // Copyright (C) 2016 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 //  ellint_3
  21 //  Compare against values generated by the GNU Scientific Library.
  22 //  The GSL can be found on the web: http://www.gnu.org/software/gsl/
  23 #include <limits>
  24 #include <cmath>
  25 #if defined(__TEST_DEBUG)
  26 #  include <iostream>
  27 #  define VERIFY(A) \
  28   if (!(A)) \
  29     { \
  30       std::cout << "line " << __LINE__ \
  31         << "  max_abs_frac = " << max_abs_frac \
  32         << std::endl; \
  33     }
  34 #else
  35 #  include <testsuite_hooks.h>
  36 #endif
  37 #include <specfun_testcase.h>
  38
  39
  40 // Test data for k=-0.90000000000000002, nu=0.0000000000000000.
  41 // max(|f - f_GSL|): 4.4408920985006262e-16
  42 // max(|f - f_GSL| / |f_GSL|): 2.9686139313362077e-16
  43 const testcase_ellint_3<double>
  44 data001[10] =
  45 {
  46   { 0.0000000000000000, -0.90000000000000002, 0.0000000000000000,
  47           0.0000000000000000 },
  48   { 0.17525427376115024, -0.90000000000000002, 0.0000000000000000,
  49           0.17453292519943295 },
  50   { 0.35492464591297446, -0.90000000000000002, 0.0000000000000000,
  51           0.34906585039886590 },
  52   { 0.54388221416157112, -0.90000000000000002, 0.0000000000000000,
  53           0.52359877559829882 },
  54   { 0.74797400423532490, -0.90000000000000002, 0.0000000000000000,
  55           0.69813170079773179 },
  56   { 0.97463898451966458, -0.90000000000000002, 0.0000000000000000,
  57           0.87266462599716477 },
  58   { 1.2334463254523440, -0.90000000000000002, 0.0000000000000000,
  59           1.0471975511965976 },
  60   { 1.5355247765594913, -0.90000000000000002, 0.0000000000000000,
  61           1.2217304763960306 },
  62   { 1.8882928567775121, -0.90000000000000002, 0.0000000000000000,
  63           1.3962634015954636 },
  64   { 2.2805491384227703, -0.90000000000000002, 0.0000000000000000,
  65           1.5707963267948966 },
  66 };
  67 const double toler001 = 2.5000000000000020e-13;
  68
  69 // Test data for k=-0.90000000000000002, nu=0.10000000000000001.
  70 // max(|f - f_GSL|): 4.4408920985006262e-16
  71 // max(|f - f_GSL| / |f_GSL|): 3.0141810743801079e-16
  72 const testcase_ellint_3<double>
  73 data002[10] =
  74 {
  75   { 0.0000000000000000, -0.90000000000000002, 0.10000000000000001,
  76           0.0000000000000000 },
  77   { 0.17507714233254656, -0.90000000000000002, 0.10000000000000001,
  78           0.17453292519943295 },
  79   { 0.35350932904326521, -0.90000000000000002, 0.10000000000000001,
  80           0.34906585039886590 },
  81   { 0.53911129989870976, -0.90000000000000002, 0.10000000000000001,
  82           0.52359877559829882 },
  83   { 0.73666644254508395, -0.90000000000000002, 0.10000000000000001,
  84           0.69813170079773179 },
  85   { 0.95250736612100195, -0.90000000000000002, 0.10000000000000001,
  86           0.87266462599716477 },
  87   { 1.1950199550905594, -0.90000000000000002, 0.10000000000000001,
  88           1.0471975511965976 },
  89   { 1.4741687286340850, -0.90000000000000002, 0.10000000000000001,
  90           1.2217304763960306 },
  91   { 1.7968678183506057, -0.90000000000000002, 0.10000000000000001,
  92           1.3962634015954636 },
  93   { 2.1537868513875287, -0.90000000000000002, 0.10000000000000001,
  94           1.5707963267948966 },
  95 };
  96 const double toler002 = 2.5000000000000020e-13;
  97
  98 // Test data for k=-0.90000000000000002, nu=0.20000000000000001.
  99 // max(|f - f_GSL|): 2.2204460492503131e-16
 100 // max(|f - f_GSL| / |f_GSL|): 3.0588292817405780e-16
 101 const testcase_ellint_3<double>
 102 data003[10] =
 103 {
 104   { 0.0000000000000000, -0.90000000000000002, 0.20000000000000001,
 105           0.0000000000000000 },
 106   { 0.17490065089140927, -0.90000000000000002, 0.20000000000000001,
 107           0.17453292519943295 },
 108   { 0.35211377590661436, -0.90000000000000002, 0.20000000000000001,
 109           0.34906585039886590 },
 110   { 0.53448220334204100, -0.90000000000000002, 0.20000000000000001,
 111           0.52359877559829882 },
 112   { 0.72591368943179579, -0.90000000000000002, 0.20000000000000001,
 113           0.69813170079773179 },
 114   { 0.93192539780038763, -0.90000000000000002, 0.20000000000000001,
 115           0.87266462599716477 },
 116   { 1.1600809679692683, -0.90000000000000002, 0.20000000000000001,
 117           1.0471975511965976 },
 118   { 1.4195407225882510, -0.90000000000000002, 0.20000000000000001,
 119           1.2217304763960306 },
 120   { 1.7168966476424525, -0.90000000000000002, 0.20000000000000001,
 121           1.3962634015954636 },
 122   { 2.0443194576468890, -0.90000000000000002, 0.20000000000000001,
 123           1.5707963267948966 },
 124 };
 125 const double toler003 = 2.5000000000000020e-13;
 126
 127 // Test data for k=-0.90000000000000002, nu=0.29999999999999999.
 128 // max(|f - f_GSL|): 4.4408920985006262e-16
 129 // max(|f - f_GSL| / |f_GSL|): 3.2403611223075570e-16
 130 const testcase_ellint_3<double>
 131 data004[10] =
 132 {
 133   { 0.0000000000000000, -0.90000000000000002, 0.29999999999999999,
 134           0.0000000000000000 },
 135   { 0.17472479532647531, -0.90000000000000002, 0.29999999999999999,
 136           0.17453292519943295 },
 137   { 0.35073750187374114, -0.90000000000000002, 0.29999999999999999,
 138           0.34906585039886590 },
 139   { 0.52998766129466957, -0.90000000000000002, 0.29999999999999999,
 140           0.52359877559829882 },
 141   { 0.71566993548699553, -0.90000000000000002, 0.29999999999999999,
 142           0.69813170079773179 },
 143   { 0.91271517762560195, -0.90000000000000002, 0.29999999999999999,
 144           0.87266462599716477 },
 145   { 1.1281241199843370, -0.90000000000000002, 0.29999999999999999,
 146           1.0471975511965976 },
 147   { 1.3704929576917451, -0.90000000000000002, 0.29999999999999999,
 148           1.2217304763960306 },
 149   { 1.6461981511487713, -0.90000000000000002, 0.29999999999999999,
 150           1.3962634015954636 },
 151   { 1.9486280260314426, -0.90000000000000002, 0.29999999999999999,
 152           1.5707963267948966 },
 153 };
 154 const double toler004 = 2.5000000000000020e-13;
 155
 156 // Test data for k=-0.90000000000000002, nu=0.40000000000000002.
 157 // max(|f - f_GSL|): 4.4408920985006262e-16
 158 // max(|f - f_GSL| / |f_GSL|): 3.3487482375512111e-16
 159 const testcase_ellint_3<double>
 160 data005[10] =
 161 {
 162   { 0.0000000000000000, -0.90000000000000002, 0.40000000000000002,
 163           0.0000000000000000 },
 164   { 0.17454957156468837, -0.90000000000000002, 0.40000000000000002,
 165           0.17453292519943295 },
 166   { 0.34938003933330430, -0.90000000000000002, 0.40000000000000002,
 167           0.34906585039886590 },
 168   { 0.52562093533067433, -0.90000000000000002, 0.40000000000000002,
 169           0.52359877559829882 },
 170   { 0.70589461324915670, -0.90000000000000002, 0.40000000000000002,
 171           0.69813170079773179 },
 172   { 0.89472658511942849, -0.90000000000000002, 0.40000000000000002,
 173           0.87266462599716477 },
 174   { 1.0987419542323440, -0.90000000000000002, 0.40000000000000002,
 175           1.0471975511965976 },
 176   { 1.3261349565496303, -0.90000000000000002, 0.40000000000000002,
 177           1.2217304763960306 },
 178   { 1.5831293909853765, -0.90000000000000002, 0.40000000000000002,
 179           1.3962634015954636 },
 180   { 1.8641114227238349, -0.90000000000000002, 0.40000000000000002,
 181           1.5707963267948966 },
 182 };
 183 const double toler005 = 2.5000000000000020e-13;
 184
 185 // Test data for k=-0.90000000000000002, nu=0.50000000000000000.
 186 // max(|f - f_GSL|): 4.4408920985006262e-16
 187 // max(|f - f_GSL| / |f_GSL|): 3.4538944656036724e-16
 188 const testcase_ellint_3<double>
 189 data006[10] =
 190 {
 191   { 0.0000000000000000, -0.90000000000000002, 0.50000000000000000,
 192           0.0000000000000000 },
 193   { 0.17437497557073334, -0.90000000000000002, 0.50000000000000000,
 194           0.17453292519943295 },
 195   { 0.34804093691586013, -0.90000000000000002, 0.50000000000000000,
 196           0.34906585039886590 },
 197   { 0.52137576320372891, -0.90000000000000002, 0.50000000000000000,
 198           0.52359877559829882 },
 199   { 0.69655163996912262, -0.90000000000000002, 0.50000000000000000,
 200           0.69813170079773179 },
 201   { 0.87783188683054236, -0.90000000000000002, 0.50000000000000000,
 202           0.87266462599716477 },
 203   { 1.0716015959755185, -0.90000000000000002, 0.50000000000000000,
 204           1.0471975511965976 },
 205   { 1.2857636916026749, -0.90000000000000002, 0.50000000000000000,
 206           1.2217304763960306 },
 207   { 1.5264263913252363, -0.90000000000000002, 0.50000000000000000,
 208           1.3962634015954636 },
 209   { 1.7888013241937861, -0.90000000000000002, 0.50000000000000000,
 210           1.5707963267948966 },
 211 };
 212 const double toler006 = 2.5000000000000020e-13;
 213
 214 // Test data for k=-0.90000000000000002, nu=0.59999999999999998.
 215 // max(|f - f_GSL|): 4.4408920985006262e-16
 216 // max(|f - f_GSL| / |f_GSL|): 3.5560830683344639e-16
 217 const testcase_ellint_3<double>
 218 data007[10] =
 219 {
 220   { 0.0000000000000000, -0.90000000000000002, 0.59999999999999998,
 221           0.0000000000000000 },
 222   { 0.17420100334657812, -0.90000000000000002, 0.59999999999999998,
 223           0.17453292519943295 },
 224   { 0.34671975876122157, -0.90000000000000002, 0.59999999999999998,
 225           0.34906585039886590 },
 226   { 0.51724631570707946, -0.90000000000000002, 0.59999999999999998,
 227           0.52359877559829882 },
 228   { 0.68760879113743023, -0.90000000000000002, 0.59999999999999998,
 229           0.69813170079773179 },
 230   { 0.86192157779698364, -0.90000000000000002, 0.59999999999999998,
 231           0.87266462599716477 },
 232   { 1.0464279696166354, -0.90000000000000002, 0.59999999999999998,
 233           1.0471975511965976 },
 234   { 1.2488156247094007, -0.90000000000000002, 0.59999999999999998,
 235           1.2217304763960306 },
 236   { 1.4750988777188472, -0.90000000000000002, 0.59999999999999998,
 237           1.3962634015954636 },
 238   { 1.7211781128919523, -0.90000000000000002, 0.59999999999999998,
 239           1.5707963267948966 },
 240 };
 241 const double toler007 = 2.5000000000000020e-13;
 242
 243 // Test data for k=-0.90000000000000002, nu=0.69999999999999996.
 244 // max(|f - f_GSL|): 6.6613381477509392e-16
 245 // max(|f - f_GSL| / |f_GSL|): 5.4833366769839281e-16
 246 const testcase_ellint_3<double>
 247 data008[10] =
 248 {
 249   { 0.0000000000000000, -0.90000000000000002, 0.69999999999999996,
 250           0.0000000000000000 },
 251   { 0.17402765093102207, -0.90000000000000002, 0.69999999999999996,
 252           0.17453292519943295 },
 253   { 0.34541608382635131, -0.90000000000000002, 0.69999999999999996,
 254           0.34906585039886590 },
 255   { 0.51322715827061682, -0.90000000000000002, 0.69999999999999996,
 256           0.52359877559829882 },
 257   { 0.67903717872440272, -0.90000000000000002, 0.69999999999999996,
 258           0.69813170079773179 },
 259   { 0.84690113601682671, -0.90000000000000002, 0.69999999999999996,
 260           0.87266462599716477 },
 261   { 1.0229914311548418, -0.90000000000000002, 0.69999999999999996,
 262           1.0471975511965976 },
 263   { 1.2148329639709381, -0.90000000000000002, 0.69999999999999996,
 264           1.2217304763960306 },
 265   { 1.4283586501307803, -0.90000000000000002, 0.69999999999999996,
 266           1.3962634015954636 },
 267   { 1.6600480747670940, -0.90000000000000002, 0.69999999999999996,
 268           1.5707963267948966 },
 269 };
 270 const double toler008 = 2.5000000000000020e-13;
 271
 272 // Test data for k=-0.90000000000000002, nu=0.80000000000000004.
 273 // max(|f - f_GSL|): 4.4408920985006262e-16
 274 // max(|f - f_GSL| / |f_GSL|): 3.7525301941362493e-16
 275 const testcase_ellint_3<double>
 276 data009[10] =
 277 {
 278   { 0.0000000000000000, -0.90000000000000002, 0.80000000000000004,
 279           0.0000000000000000 },
 280   { 0.17385491439925146, -0.90000000000000002, 0.80000000000000004,
 281           0.17453292519943295 },
 282   { 0.34412950523113928, -0.90000000000000002, 0.80000000000000004,
 283           0.34906585039886590 },
 284   { 0.50931321668729590, -0.90000000000000002, 0.80000000000000004,
 285           0.52359877559829882 },
 286   { 0.67081081392296327, -0.90000000000000002, 0.80000000000000004,
 287           0.69813170079773179 },
 288   { 0.83268846097293259, -0.90000000000000002, 0.80000000000000004,
 289           0.87266462599716477 },
 290   { 1.0010985015814027, -0.90000000000000002, 0.80000000000000004,
 291           1.0471975511965976 },
 292   { 1.1834394045489680, -0.90000000000000002, 0.80000000000000004,
 293           1.2217304763960306 },
 294   { 1.3855695891683186, -0.90000000000000002, 0.80000000000000004,
 295           1.3962634015954636 },
 296   { 1.6044591960982202, -0.90000000000000002, 0.80000000000000004,
 297           1.5707963267948966 },
 298 };
 299 const double toler009 = 2.5000000000000020e-13;
 300
 301 // Test data for k=-0.90000000000000002, nu=0.90000000000000002.
 302 // max(|f - f_GSL|): 4.4408920985006262e-16
 303 // max(|f - f_GSL| / |f_GSL|): 3.8471853989694167e-16
 304 const testcase_ellint_3<double>
 305 data010[10] =
 306 {
 307   { 0.0000000000000000, -0.90000000000000002, 0.90000000000000002,
 308           0.0000000000000000 },
 309   { 0.17368278986240135, -0.90000000000000002, 0.90000000000000002,
 310           0.17453292519943295 },
 311   { 0.34285962963961397, -0.90000000000000002, 0.90000000000000002,
 312           0.34906585039886590 },
 313   { 0.50549974644993312, -0.90000000000000002, 0.90000000000000002,
 314           0.52359877559829882 },
 315   { 0.66290623857720876, -0.90000000000000002, 0.90000000000000002,
 316           0.69813170079773179 },
 317   { 0.81921183128847175, -0.90000000000000002, 0.90000000000000002,
 318           0.87266462599716477 },
 319   { 0.98058481956066390, -0.90000000000000002, 0.90000000000000002,
 320           1.0471975511965976 },
 321   { 1.1543223520473569, -0.90000000000000002, 0.90000000000000002,
 322           1.2217304763960306 },
 323   { 1.3462119782292938, -0.90000000000000002, 0.90000000000000002,
 324           1.3962634015954636 },
 325   { 1.5536420236310946, -0.90000000000000002, 0.90000000000000002,
 326           1.5707963267948966 },
 327 };
 328 const double toler010 = 2.5000000000000020e-13;
 329
 330 // Test data for k=-0.80000000000000004, nu=0.0000000000000000.
 331 // max(|f - f_GSL|): 4.4408920985006262e-16
 332 // max(|f - f_GSL| / |f_GSL|): 4.1175183168766718e-16
 333 const testcase_ellint_3<double>
 334 data011[10] =
 335 {
 336   { 0.0000000000000000, -0.80000000000000004, 0.0000000000000000,
 337           0.0000000000000000 },
 338   { 0.17510154241338899, -0.80000000000000004, 0.0000000000000000,
 339           0.17453292519943295 },
 340   { 0.35365068839779390, -0.80000000000000004, 0.0000000000000000,
 341           0.34906585039886590 },
 342   { 0.53926804409084550, -0.80000000000000004, 0.0000000000000000,
 343           0.52359877559829882 },
 344   { 0.73587926028070361, -0.80000000000000004, 0.0000000000000000,
 345           0.69813170079773179 },
 346   { 0.94770942970071170, -0.80000000000000004, 0.0000000000000000,
 347           0.87266462599716477 },
 348   { 1.1789022995388236, -0.80000000000000004, 0.0000000000000000,
 349           1.0471975511965976 },
 350   { 1.4323027881876009, -0.80000000000000004, 0.0000000000000000,
 351           1.2217304763960306 },
 352   { 1.7069629739121674, -0.80000000000000004, 0.0000000000000000,
 353           1.3962634015954636 },
 354   { 1.9953027776647296, -0.80000000000000004, 0.0000000000000000,
 355           1.5707963267948966 },
 356 };
 357 const double toler011 = 2.5000000000000020e-13;
 358
 359 // Test data for k=-0.80000000000000004, nu=0.10000000000000001.
 360 // max(|f - f_GSL|): 4.4408920985006262e-16
 361 // max(|f - f_GSL| / |f_GSL|): 4.1537164503193145e-16
 362 const testcase_ellint_3<double>
 363 data012[10] =
 364 {
 365   { 0.0000000000000000, -0.80000000000000004, 0.10000000000000001,
 366           0.0000000000000000 },
 367   { 0.17492468824017163, -0.80000000000000004, 0.10000000000000001,
 368           0.17453292519943295 },
 369   { 0.35224443521476911, -0.80000000000000004, 0.10000000000000001,
 370           0.34906585039886590 },
 371   { 0.53456851853226950, -0.80000000000000004, 0.10000000000000001,
 372           0.52359877559829882 },
 373   { 0.72488875602364922, -0.80000000000000004, 0.10000000000000001,
 374           0.69813170079773179 },
 375   { 0.92661354274638952, -0.80000000000000004, 0.10000000000000001,
 376           0.87266462599716477 },
 377   { 1.1432651144499075, -0.80000000000000004, 0.10000000000000001,
 378           1.0471975511965976 },
 379   { 1.3774479927211429, -0.80000000000000004, 0.10000000000000001,
 380           1.2217304763960306 },
 381   { 1.6287092337196041, -0.80000000000000004, 0.10000000000000001,
 382           1.3962634015954636 },
 383   { 1.8910755418379521, -0.80000000000000004, 0.10000000000000001,
 384           1.5707963267948966 },
 385 };
 386 const double toler012 = 2.5000000000000020e-13;
 387
 388 // Test data for k=-0.80000000000000004, nu=0.20000000000000001.
 389 // max(|f - f_GSL|): 4.4408920985006262e-16
 390 // max(|f - f_GSL| / |f_GSL|): 4.1894552974436829e-16
 391 const testcase_ellint_3<double>
 392 data013[10] =
 393 {
 394   { 0.0000000000000000, -0.80000000000000004, 0.20000000000000001,
 395           0.0000000000000000 },
 396   { 0.17474847286224940, -0.80000000000000004, 0.20000000000000001,
 397           0.17453292519943295 },
 398   { 0.35085779529084682, -0.80000000000000004, 0.20000000000000001,
 399           0.34906585039886590 },
 400   { 0.53000829263059146, -0.80000000000000004, 0.20000000000000001,
 401           0.52359877559829882 },
 402   { 0.71443466027453384, -0.80000000000000004, 0.20000000000000001,
 403           0.69813170079773179 },
 404   { 0.90698196872715420, -0.80000000000000004, 0.20000000000000001,
 405           0.87266462599716477 },
 406   { 1.1108198200558579, -0.80000000000000004, 0.20000000000000001,
 407           1.0471975511965976 },
 408   { 1.3284988909963957, -0.80000000000000004, 0.20000000000000001,
 409           1.2217304763960306 },
 410   { 1.5600369318140328, -0.80000000000000004, 0.20000000000000001,
 411           1.3962634015954636 },
 412   { 1.8007226661734588, -0.80000000000000004, 0.20000000000000001,
 413           1.5707963267948966 },
 414 };
 415 const double toler013 = 2.5000000000000020e-13;
 416
 417 // Test data for k=-0.80000000000000004, nu=0.29999999999999999.
 418 // max(|f - f_GSL|): 4.4408920985006262e-16
 419 // max(|f - f_GSL| / |f_GSL|): 4.2247517409029886e-16
 420 const testcase_ellint_3<double>
 421 data014[10] =
 422 {
 423   { 0.0000000000000000, -0.80000000000000004, 0.29999999999999999,
 424           0.0000000000000000 },
 425   { 0.17457289217669889, -0.80000000000000004, 0.29999999999999999,
 426           0.17453292519943295 },
 427   { 0.34949028801501258, -0.80000000000000004, 0.29999999999999999,
 428           0.34906585039886590 },
 429   { 0.52558024362769307, -0.80000000000000004, 0.29999999999999999,
 430           0.52359877559829882 },
 431   { 0.70447281740094891, -0.80000000000000004, 0.29999999999999999,
 432           0.69813170079773179 },
 433   { 0.88864745641528986, -0.80000000000000004, 0.29999999999999999,
 434           0.87266462599716477 },
 435   { 1.0811075819341462, -0.80000000000000004, 0.29999999999999999,
 436           1.0471975511965976 },
 437   { 1.2844589654082377, -0.80000000000000004, 0.29999999999999999,
 438           1.2217304763960306 },
 439   { 1.4991461361277847, -0.80000000000000004, 0.29999999999999999,
 440           1.3962634015954636 },
 441   { 1.7214611048717301, -0.80000000000000004, 0.29999999999999999,
 442           1.5707963267948966 },
 443 };
 444 const double toler014 = 2.5000000000000020e-13;
 445
 446 // Test data for k=-0.80000000000000004, nu=0.40000000000000002.
 447 // max(|f - f_GSL|): 4.4408920985006262e-16
 448 // max(|f - f_GSL| / |f_GSL|): 4.2596216594752862e-16
 449 const testcase_ellint_3<double>
 450 data015[10] =
 451 {
 452   { 0.0000000000000000, -0.80000000000000004, 0.40000000000000002,
 453           0.0000000000000000 },
 454   { 0.17439794211872175, -0.80000000000000004, 0.40000000000000002,
 455           0.17453292519943295 },
 456   { 0.34814144964568972, -0.80000000000000004, 0.40000000000000002,
 457           0.34906585039886590 },
 458   { 0.52127776285273064, -0.80000000000000004, 0.40000000000000002,
 459           0.52359877559829882 },
 460   { 0.69496411438966588, -0.80000000000000004, 0.40000000000000002,
 461           0.69813170079773179 },
 462   { 0.87146878427509589, -0.80000000000000004, 0.40000000000000002,
 463           0.87266462599716477 },
 464   { 1.0537579024937762, -0.80000000000000004, 0.40000000000000002,
 465           1.0471975511965976 },
 466   { 1.2445534387922637, -0.80000000000000004, 0.40000000000000002,
 467           1.2217304763960306 },
 468   { 1.4446769766361993, -0.80000000000000004, 0.40000000000000002,
 469           1.3962634015954636 },
 470   { 1.6512267838651289, -0.80000000000000004, 0.40000000000000002,
 471           1.5707963267948966 },
 472 };
 473 const double toler015 = 2.5000000000000020e-13;
 474
 475 // Test data for k=-0.80000000000000004, nu=0.50000000000000000.
 476 // max(|f - f_GSL|): 4.4408920985006262e-16
 477 // max(|f - f_GSL| / |f_GSL|): 4.2940800093915668e-16
 478 const testcase_ellint_3<double>
 479 data016[10] =
 480 {
 481   { 0.0000000000000000, -0.80000000000000004, 0.50000000000000000,
 482           0.0000000000000000 },
 483   { 0.17422361866118044, -0.80000000000000004, 0.50000000000000000,
 484           0.17453292519943295 },
 485   { 0.34681083254170475, -0.80000000000000004, 0.50000000000000000,
 486           0.34906585039886590 },
 487   { 0.51709470815494440, -0.80000000000000004, 0.50000000000000000,
 488           0.52359877559829882 },
 489   { 0.68587375344080237, -0.80000000000000004, 0.50000000000000000,
 490           0.69813170079773179 },
 491   { 0.85532571852810624, -0.80000000000000004, 0.50000000000000000,
 492           0.87266462599716477 },
 493   { 1.0284677391874903, -0.80000000000000004, 0.50000000000000000,
 494           1.0471975511965976 },
 495   { 1.2081693942686225, -0.80000000000000004, 0.50000000000000000,
 496           1.2217304763960306 },
 497   { 1.3955803006426311, -0.80000000000000004, 0.50000000000000000,
 498           1.3962634015954636 },
 499   { 1.5884528947755532, -0.80000000000000004, 0.50000000000000000,
 500           1.5707963267948966 },
 501 };
 502 const double toler016 = 2.5000000000000020e-13;
 503
 504 // Test data for k=-0.80000000000000004, nu=0.59999999999999998.
 505 // max(|f - f_GSL|): 4.4408920985006262e-16
 506 // max(|f - f_GSL| / |f_GSL|): 4.3281408974056389e-16
 507 const testcase_ellint_3<double>
 508 data017[10] =
 509 {
 510   { 0.0000000000000000, -0.80000000000000004, 0.59999999999999998,
 511           0.0000000000000000 },
 512   { 0.17404991781414089, -0.80000000000000004, 0.59999999999999998,
 513           0.17453292519943295 },
 514   { 0.34549800443625167, -0.80000000000000004, 0.59999999999999998,
 515           0.34906585039886590 },
 516   { 0.51302536167001545, -0.80000000000000004, 0.59999999999999998,
 517           0.52359877559829882 },
 518   { 0.67717065003912236, -0.80000000000000004, 0.59999999999999998,
 519           0.69813170079773179 },
 520   { 0.84011512421134416, -0.80000000000000004, 0.59999999999999998,
 521           0.87266462599716477 },
 522   { 1.0049863847088740, -0.80000000000000004, 0.59999999999999998,
 523           1.0471975511965976 },
 524   { 1.1748145941898920, -0.80000000000000004, 0.59999999999999998,
 525           1.2217304763960306 },
 526   { 1.3510319699755071, -0.80000000000000004, 0.59999999999999998,
 527           1.3962634015954636 },
 528   { 1.5319262547427865, -0.80000000000000004, 0.59999999999999998,
 529           1.5707963267948966 },
 530 };
 531 const double toler017 = 2.5000000000000020e-13;
 532
 533 // Test data for k=-0.80000000000000004, nu=0.69999999999999996.
 534 // max(|f - f_GSL|): 2.2204460492503131e-16
 535 // max(|f - f_GSL| / |f_GSL|): 4.3618176466061808e-16
 536 const testcase_ellint_3<double>
 537 data018[10] =
 538 {
 539   { 0.0000000000000000, -0.80000000000000004, 0.69999999999999996,
 540           0.0000000000000000 },
 541   { 0.17387683562442199, -0.80000000000000004, 0.69999999999999996,
 542           0.17453292519943295 },
 543   { 0.34420254775101611, -0.80000000000000004, 0.69999999999999996,
 544           0.34906585039886590 },
 545   { 0.50906439222143673, -0.80000000000000004, 0.69999999999999996,
 546           0.52359877559829882 },
 547   { 0.66882693152688422, -0.80000000000000004, 0.69999999999999996,
 548           0.69813170079773179 },
 549   { 0.82574792844091316, -0.80000000000000004, 0.69999999999999996,
 550           0.87266462599716477 },
 551   { 0.98310431309490931, -0.80000000000000004, 0.69999999999999996,
 552           1.0471975511965976 },
 553   { 1.1440884535113258, -0.80000000000000004, 0.69999999999999996,
 554           1.2217304763960306 },
 555   { 1.3103743938952537, -0.80000000000000004, 0.69999999999999996,
 556           1.3962634015954636 },
 557   { 1.4806912324625332, -0.80000000000000004, 0.69999999999999996,
 558           1.5707963267948966 },
 559 };
 560 const double toler018 = 2.5000000000000020e-13;
 561
 562 // Test data for k=-0.80000000000000004, nu=0.80000000000000004.
 563 // max(|f - f_GSL|): 4.4408920985006262e-16
 564 // max(|f - f_GSL| / |f_GSL|): 4.3951228558314112e-16
 565 const testcase_ellint_3<double>
 566 data019[10] =
 567 {
 568   { 0.0000000000000000, -0.80000000000000004, 0.80000000000000004,
 569           0.0000000000000000 },
 570   { 0.17370436817515203, -0.80000000000000004, 0.80000000000000004,
 571           0.17453292519943295 },
 572   { 0.34292405894783395, -0.80000000000000004, 0.80000000000000004,
 573           0.34906585039886590 },
 574   { 0.50520682176250076, -0.80000000000000004, 0.80000000000000004,
 575           0.52359877559829882 },
 576   { 0.66081751679736178, -0.80000000000000004, 0.80000000000000004,
 577           0.69813170079773179 },
 578   { 0.81214672249355102, -0.80000000000000004, 0.80000000000000004,
 579           0.87266462599716477 },
 580   { 0.96264481387685552, -0.80000000000000004, 0.80000000000000004,
 581           1.0471975511965976 },
 582   { 1.1156611352656258, -0.80000000000000004, 0.80000000000000004,
 583           1.2217304763960306 },
 584   { 1.2730756225143889, -0.80000000000000004, 0.80000000000000004,
 585           1.3962634015954636 },
 586   { 1.4339837018309471, -0.80000000000000004, 0.80000000000000004,
 587           1.5707963267948966 },
 588 };
 589 const double toler019 = 2.5000000000000020e-13;
 590
 591 // Test data for k=-0.80000000000000004, nu=0.90000000000000002.
 592 // max(|f - f_GSL|): 3.3306690738754696e-16
 593 // max(|f - f_GSL| / |f_GSL|): 4.4280684534289690e-16
 594 const testcase_ellint_3<double>
 595 data020[10] =
 596 {
 597   { 0.0000000000000000, -0.80000000000000004, 0.90000000000000002,
 598           0.0000000000000000 },
 599   { 0.17353251158533151, -0.80000000000000004, 0.90000000000000002,
 600           0.17453292519943295 },
 601   { 0.34166214791545768, -0.80000000000000004, 0.90000000000000002,
 602           0.34906585039886590 },
 603   { 0.50144799535130569, -0.80000000000000004, 0.90000000000000002,
 604           0.52359877559829882 },
 605   { 0.65311976193814425, -0.80000000000000004, 0.90000000000000002,
 606           0.69813170079773179 },
 607   { 0.79924384892320866, -0.80000000000000004, 0.90000000000000002,
 608           0.87266462599716477 },
 609   { 0.94345762353365603, -0.80000000000000004, 0.90000000000000002,
 610           1.0471975511965976 },
 611   { 1.0892582069219161, -0.80000000000000004, 0.90000000000000002,
 612           1.2217304763960306 },
 613   { 1.2387000876610268, -0.80000000000000004, 0.90000000000000002,
 614           1.3962634015954636 },
 615   { 1.3911845406776222, -0.80000000000000004, 0.90000000000000002,
 616           1.5707963267948966 },
 617 };
 618 const double toler020 = 2.5000000000000020e-13;
 619
 620 // Test data for k=-0.69999999999999996, nu=0.0000000000000000.
 621 // max(|f - f_GSL|): 3.3306690738754696e-16
 622 // max(|f - f_GSL| / |f_GSL|): 3.5930208052157665e-16
 623 const testcase_ellint_3<double>
 624 data021[10] =
 625 {
 626   { 0.0000000000000000, -0.69999999999999996, 0.0000000000000000,
 627           0.0000000000000000 },
 628   { 0.17496737466916723, -0.69999999999999996, 0.0000000000000000,
 629           0.17453292519943295 },
 630   { 0.35254687535677925, -0.69999999999999996, 0.0000000000000000,
 631           0.34906585039886590 },
 632   { 0.53536740275997119, -0.69999999999999996, 0.0000000000000000,
 633           0.52359877559829882 },
 634   { 0.72603797651684454, -0.69999999999999996, 0.0000000000000000,
 635           0.69813170079773179 },
 636   { 0.92698296348313458, -0.69999999999999996, 0.0000000000000000,
 637           0.87266462599716477 },
 638   { 1.1400447527693316, -0.69999999999999996, 0.0000000000000000,
 639           1.0471975511965976 },
 640   { 1.3657668117194073, -0.69999999999999996, 0.0000000000000000,
 641           1.2217304763960306 },
 642   { 1.6024686895959159, -0.69999999999999996, 0.0000000000000000,
 643           1.3962634015954636 },
 644   { 1.8456939983747236, -0.69999999999999996, 0.0000000000000000,
 645           1.5707963267948966 },
 646 };
 647 const double toler021 = 2.5000000000000020e-13;
 648
 649 // Test data for k=-0.69999999999999996, nu=0.10000000000000001.
 650 // max(|f - f_GSL|): 3.3306690738754696e-16
 651 // max(|f - f_GSL| / |f_GSL|): 3.6735282577377367e-16
 652 const testcase_ellint_3<double>
 653 data022[10] =
 654 {
 655   { 0.0000000000000000, -0.69999999999999996, 0.10000000000000001,
 656           0.0000000000000000 },
 657   { 0.17479076384884684, -0.69999999999999996, 0.10000000000000001,
 658           0.17453292519943295 },
 659   { 0.35114844900396364, -0.69999999999999996, 0.10000000000000001,
 660           0.34906585039886590 },
 661   { 0.53072776947527001, -0.69999999999999996, 0.10000000000000001,
 662           0.52359877559829882 },
 663   { 0.71530198262386235, -0.69999999999999996, 0.10000000000000001,
 664           0.69813170079773179 },
 665   { 0.90666760677828306, -0.69999999999999996, 0.10000000000000001,
 666           0.87266462599716477 },
 667   { 1.1063366517438080, -0.69999999999999996, 0.10000000000000001,
 668           1.0471975511965976 },
 669   { 1.3149477243092149, -0.69999999999999996, 0.10000000000000001,
 670           1.2217304763960306 },
 671   { 1.5314886725038925, -0.69999999999999996, 0.10000000000000001,
 672           1.3962634015954636 },
 673   { 1.7528050171757608, -0.69999999999999996, 0.10000000000000001,
 674           1.5707963267948966 },
 675 };
 676 const double toler022 = 2.5000000000000020e-13;
 677
 678 // Test data for k=-0.69999999999999996, nu=0.20000000000000001.
 679 // max(|f - f_GSL|): 3.3306690738754696e-16
 680 // max(|f - f_GSL| / |f_GSL|): 3.7517969287516802e-16
 681 const testcase_ellint_3<double>
 682 data023[10] =
 683 {
 684   { 0.0000000000000000, -0.69999999999999996, 0.20000000000000001,
 685           0.0000000000000000 },
 686   { 0.17461479077791475, -0.69999999999999996, 0.20000000000000001,
 687           0.17453292519943295 },
 688   { 0.34976950621407538, -0.69999999999999996, 0.20000000000000001,
 689           0.34906585039886590 },
 690   { 0.52622533231350177, -0.69999999999999996, 0.20000000000000001,
 691           0.52359877559829882 },
 692   { 0.70508774017895215, -0.69999999999999996, 0.20000000000000001,
 693           0.69813170079773179 },
 694   { 0.88775302531730294, -0.69999999999999996, 0.20000000000000001,
 695           0.87266462599716477 },
 696   { 1.0756195476149006, -0.69999999999999996, 0.20000000000000001,
 697           1.0471975511965976 },
 698   { 1.2695349716654374, -0.69999999999999996, 0.20000000000000001,
 699           1.2217304763960306 },
 700   { 1.4690814617070540, -0.69999999999999996, 0.20000000000000001,
 701           1.3962634015954636 },
 702   { 1.6721098780092145, -0.69999999999999996, 0.20000000000000001,
 703           1.5707963267948966 },
 704 };
 705 const double toler023 = 2.5000000000000020e-13;
 706
 707 // Test data for k=-0.69999999999999996, nu=0.29999999999999999.
 708 // max(|f - f_GSL|): 4.4408920985006262e-16
 709 // max(|f - f_GSL| / |f_GSL|): 3.8280039841080712e-16
 710 const testcase_ellint_3<double>
 711 data024[10] =
 712 {
 713   { 0.0000000000000000, -0.69999999999999996, 0.29999999999999999,
 714           0.0000000000000000 },
 715   { 0.17443945136076175, -0.69999999999999996, 0.29999999999999999,
 716           0.17453292519943295 },
 717   { 0.34840956983535287, -0.69999999999999996, 0.29999999999999999,
 718           0.34906585039886590 },
 719   { 0.52185308551329168, -0.69999999999999996, 0.29999999999999999,
 720           0.52359877559829882 },
 721   { 0.69535240431168255, -0.69999999999999996, 0.29999999999999999,
 722           0.69813170079773179 },
 723   { 0.87007983473964923, -0.69999999999999996, 0.29999999999999999,
 724           0.87266462599716477 },
 725   { 1.0474657975577066, -0.69999999999999996, 0.29999999999999999,
 726           1.0471975511965976 },
 727   { 1.2286225419931891, -0.69999999999999996, 0.29999999999999999,
 728           1.2217304763960306 },
 729   { 1.4136490671013271, -0.69999999999999996, 0.29999999999999999,
 730           1.3962634015954636 },
 731   { 1.6011813647733213, -0.69999999999999996, 0.29999999999999999,
 732           1.5707963267948966 },
 733 };
 734 const double toler024 = 2.5000000000000020e-13;
 735
 736 // Test data for k=-0.69999999999999996, nu=0.40000000000000002.
 737 // max(|f - f_GSL|): 4.4408920985006262e-16
 738 // max(|f - f_GSL| / |f_GSL|): 4.3472957053482092e-16
 739 const testcase_ellint_3<double>
 740 data025[10] =
 741 {
 742   { 0.0000000000000000, -0.69999999999999996, 0.40000000000000002,
 743           0.0000000000000000 },
 744   { 0.17426474153983229, -0.69999999999999996, 0.40000000000000002,
 745           0.17453292519943295 },
 746   { 0.34706817945773732, -0.69999999999999996, 0.40000000000000002,
 747           0.34906585039886590 },
 748   { 0.51760452851738148, -0.69999999999999996, 0.40000000000000002,
 749           0.52359877559829882 },
 750   { 0.68605801534722755, -0.69999999999999996, 0.40000000000000002,
 751           0.69813170079773179 },
 752   { 0.85351339387296532, -0.69999999999999996, 0.40000000000000002,
 753           0.87266462599716477 },
 754   { 1.0215297967969539, -0.69999999999999996, 0.40000000000000002,
 755           1.0471975511965976 },
 756   { 1.1915051074460530, -0.69999999999999996, 0.40000000000000002,
 757           1.2217304763960306 },
 758   { 1.3639821911744707, -0.69999999999999996, 0.40000000000000002,
 759           1.3962634015954636 },
 760   { 1.5382162002954762, -0.69999999999999996, 0.40000000000000002,
 761           1.5707963267948966 },
 762 };
 763 const double toler025 = 2.5000000000000020e-13;
 764
 765 // Test data for k=-0.69999999999999996, nu=0.50000000000000000.
 766 // max(|f - f_GSL|): 3.3306690738754696e-16
 767 // max(|f - f_GSL| / |f_GSL|): 3.9748346743390620e-16
 768 const testcase_ellint_3<double>
 769 data026[10] =
 770 {
 771   { 0.0000000000000000, -0.69999999999999996, 0.50000000000000000,
 772           0.0000000000000000 },
 773   { 0.17409065729516096, -0.69999999999999996, 0.50000000000000000,
 774           0.17453292519943295 },
 775   { 0.34574489064986091, -0.69999999999999996, 0.50000000000000000,
 776           0.34906585039886590 },
 777   { 0.51347361925579782, -0.69999999999999996, 0.50000000000000000,
 778           0.52359877559829882 },
 779   { 0.67717079489579279, -0.69999999999999996, 0.50000000000000000,
 780           0.69813170079773179 },
 781   { 0.83793902055292280, -0.69999999999999996, 0.50000000000000000,
 782           0.87266462599716477 },
 783   { 0.99752863545289705, -0.69999999999999996, 0.50000000000000000,
 784           1.0471975511965976 },
 785   { 1.1576240080401501, -0.69999999999999996, 0.50000000000000000,
 786           1.2217304763960306 },
 787   { 1.3191464023923762, -0.69999999999999996, 0.50000000000000000,
 788           1.3962634015954636 },
 789   { 1.4818433192178544, -0.69999999999999996, 0.50000000000000000,
 790           1.5707963267948966 },
 791 };
 792 const double toler026 = 2.5000000000000020e-13;
 793
 794 // Test data for k=-0.69999999999999996, nu=0.59999999999999998.
 795 // max(|f - f_GSL|): 3.3306690738754696e-16
 796 // max(|f - f_GSL| / |f_GSL|): 4.0457157538295173e-16
 797 const testcase_ellint_3<double>
 798 data027[10] =
 799 {
 800   { 0.0000000000000000, -0.69999999999999996, 0.59999999999999998,
 801           0.0000000000000000 },
 802   { 0.17391719464391614, -0.69999999999999996, 0.59999999999999998,
 803           0.17453292519943295 },
 804   { 0.34443927423869031, -0.69999999999999996, 0.59999999999999998,
 805           0.34906585039886590 },
 806   { 0.50945473266486063, -0.69999999999999996, 0.59999999999999998,
 807           0.52359877559829882 },
 808   { 0.66866056326513812, -0.69999999999999996, 0.59999999999999998,
 809           0.69813170079773179 },
 810   { 0.82325830002337352, -0.69999999999999996, 0.59999999999999998,
 811           0.87266462599716477 },
 812   { 0.97522808245669368, -0.69999999999999996, 0.59999999999999998,
 813           1.0471975511965976 },
 814   { 1.1265300613705285, -0.69999999999999996, 0.59999999999999998,
 815           1.2217304763960306 },
 816   { 1.2784066076152001, -0.69999999999999996, 0.59999999999999998,
 817           1.3962634015954636 },
 818   { 1.4309994736080540, -0.69999999999999996, 0.59999999999999998,
 819           1.5707963267948966 },
 820 };
 821 const double toler027 = 2.5000000000000020e-13;
 822
 823 // Test data for k=-0.69999999999999996, nu=0.69999999999999996.
 824 // max(|f - f_GSL|): 4.4408920985006262e-16
 825 // max(|f - f_GSL| / |f_GSL|): 5.4867405596732161e-16
 826 const testcase_ellint_3<double>
 827 data028[10] =
 828 {
 829   { 0.0000000000000000, -0.69999999999999996, 0.69999999999999996,
 830           0.0000000000000000 },
 831   { 0.17374434963995031, -0.69999999999999996, 0.69999999999999996,
 832           0.17453292519943295 },
 833   { 0.34315091562900674, -0.69999999999999996, 0.69999999999999996,
 834           0.34906585039886590 },
 835   { 0.50554262375653347, -0.69999999999999996, 0.69999999999999996,
 836           0.52359877559829882 },
 837   { 0.66050025406305801, -0.69999999999999996, 0.69999999999999996,
 838           0.69813170079773179 },
 839   { 0.80938620118847404, -0.69999999999999996, 0.69999999999999996,
 840           0.87266462599716477 },
 841   { 0.95443223855852144, -0.69999999999999996, 0.69999999999999996,
 842           1.0471975511965976 },
 843   { 1.0978573207128304, -0.69999999999999996, 0.69999999999999996,
 844           1.2217304763960306 },
 845   { 1.2411754575007123, -0.69999999999999996, 0.69999999999999996,
 846           1.3962634015954636 },
 847   { 1.3848459188329196, -0.69999999999999996, 0.69999999999999996,
 848           1.5707963267948966 },
 849 };
 850 const double toler028 = 2.5000000000000020e-13;
 851
 852 // Test data for k=-0.69999999999999996, nu=0.80000000000000004.
 853 // max(|f - f_GSL|): 4.4408920985006262e-16
 854 // max(|f - f_GSL| / |f_GSL|): 4.1829502028913879e-16
 855 const testcase_ellint_3<double>
 856 data029[10] =
 857 {
 858   { 0.0000000000000000, -0.69999999999999996, 0.80000000000000004,
 859           0.0000000000000000 },
 860   { 0.17357211837335740, -0.69999999999999996, 0.80000000000000004,
 861           0.17453292519943295 },
 862   { 0.34187941416012108, -0.69999999999999996, 0.80000000000000004,
 863           0.34906585039886590 },
 864   { 0.50173239465478259, -0.69999999999999996, 0.80000000000000004,
 865           0.52359877559829882 },
 866   { 0.65266550725988315, -0.69999999999999996, 0.80000000000000004,
 867           0.69813170079773179 },
 868   { 0.79624879865249298, -0.69999999999999996, 0.80000000000000004,
 869           0.87266462599716477 },
 870   { 0.93497577043296920, -0.69999999999999996, 0.80000000000000004,
 871           1.0471975511965976 },
 872   { 1.0713041566930750, -0.69999999999999996, 0.80000000000000004,
 873           1.2217304763960306 },
 874   { 1.2069772023255654, -0.69999999999999996, 0.80000000000000004,
 875           1.3962634015954636 },
 876   { 1.3427110650397531, -0.69999999999999996, 0.80000000000000004,
 877           1.5707963267948966 },
 878 };
 879 const double toler029 = 2.5000000000000020e-13;
 880
 881 // Test data for k=-0.69999999999999996, nu=0.90000000000000002.
 882 // max(|f - f_GSL|): 3.3306690738754696e-16
 883 // max(|f - f_GSL| / |f_GSL|): 4.2494869624129105e-16
 884 const testcase_ellint_3<double>
 885 data030[10] =
 886 {
 887   { 0.0000000000000000, -0.69999999999999996, 0.90000000000000002,
 888           0.0000000000000000 },
 889   { 0.17340049697003637, -0.69999999999999996, 0.90000000000000002,
 890           0.17453292519943295 },
 891   { 0.34062438249741556, -0.69999999999999996, 0.90000000000000002,
 892           0.34906585039886590 },
 893   { 0.49801946510076867, -0.69999999999999996, 0.90000000000000002,
 894           0.52359877559829882 },
 895   { 0.64513432604750476, -0.69999999999999996, 0.90000000000000002,
 896           0.69813170079773179 },
 897   { 0.78378145487573758, -0.69999999999999996, 0.90000000000000002,
 898           0.87266462599716477 },
 899   { 0.91671799500854623, -0.69999999999999996, 0.90000000000000002,
 900           1.0471975511965976 },
 901   { 1.0466193579463123, -0.69999999999999996, 0.90000000000000002,
 902           1.2217304763960306 },
 903   { 1.1754218079199146, -0.69999999999999996, 0.90000000000000002,
 904           1.3962634015954636 },
 905   { 1.3040500499695913, -0.69999999999999996, 0.90000000000000002,
 906           1.5707963267948966 },
 907 };
 908 const double toler030 = 2.5000000000000020e-13;
 909
 910 // Test data for k=-0.59999999999999998, nu=0.0000000000000000.
 911 // max(|f - f_GSL|): 4.4408920985006262e-16
 912 // max(|f - f_GSL| / |f_GSL|): 2.8964816695821429e-16
 913 const testcase_ellint_3<double>
 914 data031[10] =
 915 {
 916   { 0.0000000000000000, -0.59999999999999998, 0.0000000000000000,
 917           0.0000000000000000 },
 918   { 0.17485154362988359, -0.59999999999999998, 0.0000000000000000,
 919           0.17453292519943295 },
 920   { 0.35160509865544326, -0.59999999999999998, 0.0000000000000000,
 921           0.34906585039886590 },
 922   { 0.53210652578446138, -0.59999999999999998, 0.0000000000000000,
 923           0.52359877559829882 },
 924   { 0.71805304664485659, -0.59999999999999998, 0.0000000000000000,
 925           0.69813170079773179 },
 926   { 0.91082759030195970, -0.59999999999999998, 0.0000000000000000,
 927           0.87266462599716477 },
 928   { 1.1112333229323361, -0.59999999999999998, 0.0000000000000000,
 929           1.0471975511965976 },
 930   { 1.3191461190365270, -0.59999999999999998, 0.0000000000000000,
 931           1.2217304763960306 },
 932   { 1.5332022105084773, -0.59999999999999998, 0.0000000000000000,
 933           1.3962634015954636 },
 934   { 1.7507538029157526, -0.59999999999999998, 0.0000000000000000,
 935           1.5707963267948966 },
 936 };
 937 const double toler031 = 2.5000000000000020e-13;
 938
 939 // Test data for k=-0.59999999999999998, nu=0.10000000000000001.
 940 // max(|f - f_GSL|): 4.4408920985006262e-16
 941 // max(|f - f_GSL| / |f_GSL|): 2.6674242225057385e-16
 942 const testcase_ellint_3<double>
 943 data032[10] =
 944 {
 945   { 0.0000000000000000, -0.59999999999999998, 0.10000000000000001,
 946           0.0000000000000000 },
 947   { 0.17467514275022011, -0.59999999999999998, 0.10000000000000001,
 948           0.17453292519943295 },
 949   { 0.35021333086258255, -0.59999999999999998, 0.10000000000000001,
 950           0.34906585039886590 },
 951   { 0.52751664092962691, -0.59999999999999998, 0.10000000000000001,
 952           0.52359877559829882 },
 953   { 0.70752126971957874, -0.59999999999999998, 0.10000000000000001,
 954           0.69813170079773179 },
 955   { 0.89111058756112871, -0.59999999999999998, 0.10000000000000001,
 956           0.87266462599716477 },
 957   { 1.0789241202877768, -0.59999999999999998, 0.10000000000000001,
 958           1.0471975511965976 },
 959   { 1.2710800210399946, -0.59999999999999998, 0.10000000000000001,
 960           1.2217304763960306 },
 961   { 1.4669060574440276, -0.59999999999999998, 0.10000000000000001,
 962           1.3962634015954636 },
 963   { 1.6648615773343014, -0.59999999999999998, 0.10000000000000001,
 964           1.5707963267948966 },
 965 };
 966 const double toler032 = 2.5000000000000020e-13;
 967
 968 // Test data for k=-0.59999999999999998, nu=0.20000000000000001.
 969 // max(|f - f_GSL|): 6.6613381477509392e-16
 970 // max(|f - f_GSL| / |f_GSL|): 4.1891472451898755e-16
 971 const testcase_ellint_3<double>
 972 data033[10] =
 973 {
 974   { 0.0000000000000000, -0.59999999999999998, 0.20000000000000001,
 975           0.0000000000000000 },
 976   { 0.17449937871800650, -0.59999999999999998, 0.20000000000000001,
 977           0.17453292519943295 },
 978   { 0.34884093647346553, -0.59999999999999998, 0.20000000000000001,
 979           0.34906585039886590 },
 980   { 0.52306221119844087, -0.59999999999999998, 0.20000000000000001,
 981           0.52359877559829882 },
 982   { 0.69749955678982223, -0.59999999999999998, 0.20000000000000001,
 983           0.69813170079773179 },
 984   { 0.87274610682416853, -0.59999999999999998, 0.20000000000000001,
 985           0.87266462599716477 },
 986   { 1.0494620540750792, -0.59999999999999998, 0.20000000000000001,
 987           1.0471975511965976 },
 988   { 1.2280847305507339, -0.59999999999999998, 0.20000000000000001,
 989           1.2217304763960306 },
 990   { 1.4085436279696886, -0.59999999999999998, 0.20000000000000001,
 991           1.3962634015954636 },
 992   { 1.5901418016279374, -0.59999999999999998, 0.20000000000000001,
 993           1.5707963267948966 },
 994 };
 995 const double toler033 = 2.5000000000000020e-13;
 996
 997 // Test data for k=-0.59999999999999998, nu=0.29999999999999999.
 998 // max(|f - f_GSL|): 4.4408920985006262e-16
 999 // max(|f - f_GSL| / |f_GSL|): 2.9132420715478757e-16
1000 const testcase_ellint_3<double>
1001 data034[10] =
1002 {
1003   { 0.0000000000000000, -0.59999999999999998, 0.29999999999999999,
1004           0.0000000000000000 },
1005   { 0.17432424744393932, -0.59999999999999998, 0.29999999999999999,
1006           0.17453292519943295 },
1007   { 0.34748744127146447, -0.59999999999999998, 0.29999999999999999,
1008           0.34906585039886590 },
1009   { 0.51873632743924825, -0.59999999999999998, 0.29999999999999999,
1010           0.52359877559829882 },
1011   { 0.68794610396313116, -0.59999999999999998, 0.29999999999999999,
1012           0.69813170079773179 },
1013   { 0.85558070175468726, -0.59999999999999998, 0.29999999999999999,
1014           0.87266462599716477 },
1015   { 1.0224416343605653, -0.59999999999999998, 0.29999999999999999,
1016           1.0471975511965976 },
1017   { 1.1893144457936788, -0.59999999999999998, 0.29999999999999999,
1018           1.2217304763960306 },
1019   { 1.3566435377982575, -0.59999999999999998, 0.29999999999999999,
1020           1.3962634015954636 },
1021   { 1.5243814243493585, -0.59999999999999998, 0.29999999999999999,
1022           1.5707963267948966 },
1023 };
1024 const double toler034 = 2.5000000000000020e-13;
1025
1026 // Test data for k=-0.59999999999999998, nu=0.40000000000000002.
1027 // max(|f - f_GSL|): 4.4408920985006262e-16
1028 // max(|f - f_GSL| / |f_GSL|): 3.3897581541285558e-16
1029 const testcase_ellint_3<double>
1030 data035[10] =
1031 {
1032   { 0.0000000000000000, -0.59999999999999998, 0.40000000000000002,
1033           0.0000000000000000 },
1034   { 0.17414974487670717, -0.59999999999999998, 0.40000000000000002,
1035           0.17453292519943295 },
1036   { 0.34615238767335027, -0.59999999999999998, 0.40000000000000002,
1037           0.34906585039886590 },
1038   { 0.51453257838108557, -0.59999999999999998, 0.40000000000000002,
1039           0.52359877559829882 },
1040   { 0.67882386787534399, -0.59999999999999998, 0.40000000000000002,
1041           0.69813170079773179 },
1042   { 0.83948470233173578, -0.59999999999999998, 0.40000000000000002,
1043           0.87266462599716477 },
1044   { 0.99753496200073977, -0.59999999999999998, 0.40000000000000002,
1045           1.0471975511965976 },
1046   { 1.1541101404388487, -0.59999999999999998, 0.40000000000000002,
1047           1.2217304763960306 },
1048   { 1.3100911323398814, -0.59999999999999998, 0.40000000000000002,
1049           1.3962634015954636 },
1050   { 1.4659345278069984, -0.59999999999999998, 0.40000000000000002,
1051           1.5707963267948966 },
1052 };
1053 const double toler035 = 2.5000000000000020e-13;
1054
1055 // Test data for k=-0.59999999999999998, nu=0.50000000000000000.
1056 // max(|f - f_GSL|): 4.4408920985006262e-16
1057 // max(|f - f_GSL| / |f_GSL|): 3.5022138270566200e-16
1058 const testcase_ellint_3<double>
1059 data036[10] =
1060 {
1061   { 0.0000000000000000, -0.59999999999999998, 0.50000000000000000,
1062           0.0000000000000000 },
1063   { 0.17397586700252807, -0.59999999999999998, 0.50000000000000000,
1064           0.17453292519943295 },
1065   { 0.34483533397138516, -0.59999999999999998, 0.50000000000000000,
1066           0.34906585039886590 },
1067   { 0.51044500461706477, -0.59999999999999998, 0.50000000000000000,
1068           0.52359877559829882 },
1069   { 0.67009988034712664, -0.59999999999999998, 0.50000000000000000,
1070           0.69813170079773179 },
1071   { 0.82434762375735193, -0.59999999999999998, 0.50000000000000000,
1072           0.87266462599716477 },
1073   { 0.97447346702798998, -0.59999999999999998, 0.50000000000000000,
1074           1.0471975511965976 },
1075   { 1.1219494000522143, -0.59999999999999998, 0.50000000000000000,
1076           1.2217304763960306 },
1077   { 1.2680242605954484, -0.59999999999999998, 0.50000000000000000,
1078           1.3962634015954636 },
1079   { 1.4135484285693078, -0.59999999999999998, 0.50000000000000000,
1080           1.5707963267948966 },
1081 };
1082 const double toler036 = 2.5000000000000020e-13;
1083
1084 // Test data for k=-0.59999999999999998, nu=0.59999999999999998.
1085 // max(|f - f_GSL|): 4.4408920985006262e-16
1086 // max(|f - f_GSL| / |f_GSL|): 3.2504224329684343e-16
1087 const testcase_ellint_3<double>
1088 data037[10] =
1089 {
1090   { 0.0000000000000000, -0.59999999999999998, 0.59999999999999998,
1091           0.0000000000000000 },
1092   { 0.17380260984469353, -0.59999999999999998, 0.59999999999999998,
1093           0.17453292519943295 },
1094   { 0.34353585361777839, -0.59999999999999998, 0.59999999999999998,
1095           0.34906585039886590 },
1096   { 0.50646805774321380, -0.59999999999999998, 0.59999999999999998,
1097           0.52359877559829882 },
1098   { 0.66174468108625506, -0.59999999999999998, 0.59999999999999998,
1099           0.69813170079773179 },
1100   { 0.81007462280278408, -0.59999999999999998, 0.59999999999999998,
1101           0.87266462599716477 },
1102   { 0.95303466945718729, -0.59999999999999998, 0.59999999999999998,
1103           1.0471975511965976 },
1104   { 1.0924118588677505, -0.59999999999999998, 0.59999999999999998,
1105           1.2217304763960306 },
1106   { 1.2297640574847937, -0.59999999999999998, 0.59999999999999998,
1107           1.3962634015954636 },
1108   { 1.3662507535812816, -0.59999999999999998, 0.59999999999999998,
1109           1.5707963267948966 },
1110 };
1111 const double toler037 = 2.5000000000000020e-13;
1112
1113 // Test data for k=-0.59999999999999998, nu=0.69999999999999996.
1114 // max(|f - f_GSL|): 4.4408920985006262e-16
1115 // max(|f - f_GSL| / |f_GSL|): 3.3559889697529752e-16
1116 const testcase_ellint_3<double>
1117 data038[10] =
1118 {
1119   { 0.0000000000000000, -0.59999999999999998, 0.69999999999999996,
1120           0.0000000000000000 },
1121   { 0.17362996946312007, -0.59999999999999998, 0.69999999999999996,
1122           0.17453292519943295 },
1123   { 0.34225353454870588, -0.59999999999999998, 0.69999999999999996,
1124           0.34906585039886590 },
1125   { 0.50259656397799524, -0.59999999999999998, 0.69999999999999996,
1126           0.52359877559829882 },
1127   { 0.65373184496628933, -0.59999999999999998, 0.69999999999999996,
1128           0.69813170079773179 },
1129   { 0.79658372884056439, -0.59999999999999998, 0.69999999999999996,
1130           0.87266462599716477 },
1131   { 0.93303240100245421, -0.59999999999999998, 0.69999999999999996,
1132           1.0471975511965976 },
1133   { 1.0651547944716557, -0.59999999999999998, 0.69999999999999996,
1134           1.2217304763960306 },
1135   { 1.1947676204853441, -0.59999999999999998, 0.69999999999999996,
1136           1.3962634015954636 },
1137   { 1.3232737468822813, -0.59999999999999998, 0.69999999999999996,
1138           1.5707963267948966 },
1139 };
1140 const double toler038 = 2.5000000000000020e-13;
1141
1142 // Test data for k=-0.59999999999999998, nu=0.80000000000000004.
1143 // max(|f - f_GSL|): 6.6613381477509392e-16
1144 // max(|f - f_GSL| / |f_GSL|): 5.1879494682720725e-16
1145 const testcase_ellint_3<double>
1146 data039[10] =
1147 {
1148   { 0.0000000000000000, -0.59999999999999998, 0.80000000000000004,
1149           0.0000000000000000 },
1150   { 0.17345794195390685, -0.59999999999999998, 0.80000000000000004,
1151           0.17453292519943295 },
1152   { 0.34098797854531027, -0.59999999999999998, 0.80000000000000004,
1153           0.34906585039886590 },
1154   { 0.49882569168826213, -0.59999999999999998, 0.80000000000000004,
1155           0.52359877559829882 },
1156   { 0.64603758566475511, -0.59999999999999998, 0.80000000000000004,
1157           0.69813170079773179 },
1158   { 0.78380365594769730, -0.59999999999999998, 0.80000000000000004,
1159           0.87266462599716477 },
1160   { 0.91430946255611190, -0.59999999999999998, 0.80000000000000004,
1161           1.0471975511965976 },
1162   { 1.0398955217270607, -0.59999999999999998, 0.80000000000000004,
1163           1.2217304763960306 },
1164   { 1.1625948314277679, -0.59999999999999998, 0.80000000000000004,
1165           1.3962634015954636 },
1166   { 1.2840021261752192, -0.59999999999999998, 0.80000000000000004,
1167           1.5707963267948966 },
1168 };
1169 const double toler039 = 2.5000000000000020e-13;
1170
1171 // Test data for k=-0.59999999999999998, nu=0.90000000000000002.
1172 // max(|f - f_GSL|): 2.2204460492503131e-16
1173 // max(|f - f_GSL| / |f_GSL|): 3.4768329326726447e-16
1174 const testcase_ellint_3<double>
1175 data040[10] =
1176 {
1177   { 0.0000000000000000, -0.59999999999999998, 0.90000000000000002,
1178           0.0000000000000000 },
1179   { 0.17328652344890030, -0.59999999999999998, 0.90000000000000002,
1180           0.17453292519943295 },
1181   { 0.33973880062929018, -0.59999999999999998, 0.90000000000000002,
1182           0.34906585039886590 },
1183   { 0.49515092233122743, -0.59999999999999998, 0.90000000000000002,
1184           0.52359877559829882 },
1185   { 0.63864042139737043, -0.59999999999999998, 0.90000000000000002,
1186           0.69813170079773179 },
1187   { 0.77167205646538850, -0.59999999999999998, 0.90000000000000002,
1188           0.87266462599716477 },
1189   { 0.89673202848034383, -0.59999999999999998, 0.90000000000000002,
1190           1.0471975511965976 },
1191   { 1.0163984492661304, -0.59999999999999998, 0.90000000000000002,
1192           1.2217304763960306 },
1193   { 1.1328845785162431, -0.59999999999999998, 0.90000000000000002,
1194           1.3962634015954636 },
1195   { 1.2479362973851875, -0.59999999999999998, 0.90000000000000002,
1196           1.5707963267948966 },
1197 };
1198 const double toler040 = 2.5000000000000020e-13;
1199
1200 // Test data for k=-0.50000000000000000, nu=0.0000000000000000.
1201 // max(|f - f_GSL|): 2.2204460492503131e-16
1202 // max(|f - f_GSL| / |f_GSL|): 3.1201497220602069e-16
1203 const testcase_ellint_3<double>
1204 data041[10] =
1205 {
1206   { 0.0000000000000000, -0.50000000000000000, 0.0000000000000000,
1207           0.0000000000000000 },
1208   { 0.17475385514035785, -0.50000000000000000, 0.0000000000000000,
1209           0.17453292519943295 },
1210   { 0.35081868470101585, -0.50000000000000000, 0.0000000000000000,
1211           0.34906585039886590 },
1212   { 0.52942862705190574, -0.50000000000000000, 0.0000000000000000,
1213           0.52359877559829882 },
1214   { 0.71164727562630314, -0.50000000000000000, 0.0000000000000000,
1215           0.69813170079773179 },
1216   { 0.89824523594227768, -0.50000000000000000, 0.0000000000000000,
1217           0.87266462599716477 },
1218   { 1.0895506700518851, -0.50000000000000000, 0.0000000000000000,
1219           1.0471975511965976 },
1220   { 1.2853005857432931, -0.50000000000000000, 0.0000000000000000,
1221           1.2217304763960306 },
1222   { 1.4845545520549484, -0.50000000000000000, 0.0000000000000000,
1223           1.3962634015954636 },
1224   { 1.6857503548125963, -0.50000000000000000, 0.0000000000000000,
1225           1.5707963267948966 },
1226 };
1227 const double toler041 = 2.5000000000000020e-13;
1228
1229 // Test data for k=-0.50000000000000000, nu=0.10000000000000001.
1230 // max(|f - f_GSL|): 2.2204460492503131e-16
1231 // max(|f - f_GSL| / |f_GSL|): 3.1662857256911530e-16
1232 const testcase_ellint_3<double>
1233 data042[10] =
1234 {
1235   { 0.0000000000000000, -0.50000000000000000, 0.10000000000000001,
1236           0.0000000000000000 },
1237   { 0.17457763120814676, -0.50000000000000000, 0.10000000000000001,
1238           0.17453292519943295 },
1239   { 0.34943246340849154, -0.50000000000000000, 0.10000000000000001,
1240           0.34906585039886590 },
1241   { 0.52487937869610790, -0.50000000000000000, 0.10000000000000001,
1242           0.52359877559829882 },
1243   { 0.70127785096388384, -0.50000000000000000, 0.10000000000000001,
1244           0.69813170079773179 },
1245   { 0.87898815988624479, -0.50000000000000000, 0.10000000000000001,
1246           0.87266462599716477 },
1247   { 1.0582764576094172, -0.50000000000000000, 0.10000000000000001,
1248           1.0471975511965976 },
1249   { 1.2391936844060205, -0.50000000000000000, 0.10000000000000001,
1250           1.2217304763960306 },
1251   { 1.4214793542995841, -0.50000000000000000, 0.10000000000000001,
1252           1.3962634015954636 },
1253   { 1.6045524936084892, -0.50000000000000000, 0.10000000000000001,
1254           1.5707963267948966 },
1255 };
1256 const double toler042 = 2.5000000000000020e-13;
1257
1258 // Test data for k=-0.50000000000000000, nu=0.20000000000000001.
1259 // max(|f - f_GSL|): 2.2204460492503131e-16
1260 // max(|f - f_GSL| / |f_GSL|): 3.2114786773102175e-16
1261 const testcase_ellint_3<double>
1262 data043[10] =
1263 {
1264   { 0.0000000000000000, -0.50000000000000000, 0.20000000000000001,
1265           0.0000000000000000 },
1266   { 0.17440204336345433, -0.50000000000000000, 0.20000000000000001,
1267           0.17453292519943295 },
1268   { 0.34806552388338824, -0.50000000000000000, 0.20000000000000001,
1269           0.34906585039886590 },
1270   { 0.52046416757129810, -0.50000000000000000, 0.20000000000000001,
1271           0.52359877559829882 },
1272   { 0.69140924550993865, -0.50000000000000000, 0.20000000000000001,
1273           0.69813170079773179 },
1274   { 0.86104678636125520, -0.50000000000000000, 0.20000000000000001,
1275           0.87266462599716477 },
1276   { 1.0297439459053981, -0.50000000000000000, 0.20000000000000001,
1277           1.0471975511965976 },
1278   { 1.1979214112912033, -0.50000000000000000, 0.20000000000000001,
1279           1.2217304763960306 },
1280   { 1.3659033858648930, -0.50000000000000000, 0.20000000000000001,
1281           1.3962634015954636 },
1282   { 1.5338490483665983, -0.50000000000000000, 0.20000000000000001,
1283           1.5707963267948966 },
1284 };
1285 const double toler043 = 2.5000000000000020e-13;
1286
1287 // Test data for k=-0.50000000000000000, nu=0.29999999999999999.
1288 // max(|f - f_GSL|): 2.2204460492503131e-16
1289 // max(|f - f_GSL| / |f_GSL|): 3.2557837230041312e-16
1290 const testcase_ellint_3<double>
1291 data044[10] =
1292 {
1293   { 0.0000000000000000, -0.50000000000000000, 0.29999999999999999,
1294           0.0000000000000000 },
1295   { 0.17422708752228896, -0.50000000000000000, 0.29999999999999999,
1296           0.17453292519943295 },
1297   { 0.34671739434855858, -0.50000000000000000, 0.29999999999999999,
1298           0.34906585039886590 },
1299   { 0.51617616305641878, -0.50000000000000000, 0.29999999999999999,
1300           0.52359877559829882 },
1301   { 0.68200047612545167, -0.50000000000000000, 0.29999999999999999,
1302           0.69813170079773179 },
1303   { 0.84427217869498372, -0.50000000000000000, 0.29999999999999999,
1304           0.87266462599716477 },
1305   { 1.0035637821389782, -0.50000000000000000, 0.29999999999999999,
1306           1.0471975511965976 },
1307   { 1.1606800483933111, -0.50000000000000000, 0.29999999999999999,
1308           1.2217304763960306 },
1309   { 1.3164407134643459, -0.50000000000000000, 0.29999999999999999,
1310           1.3962634015954636 },
1311   { 1.4715681939859637, -0.50000000000000000, 0.29999999999999999,
1312           1.5707963267948966 },
1313 };
1314 const double toler044 = 2.5000000000000020e-13;
1315
1316 // Test data for k=-0.50000000000000000, nu=0.40000000000000002.
1317 // max(|f - f_GSL|): 2.2204460492503131e-16
1318 // max(|f - f_GSL| / |f_GSL|): 3.2992508582900068e-16
1319 const testcase_ellint_3<double>
1320 data045[10] =
1321 {
1322   { 0.0000000000000000, -0.50000000000000000, 0.40000000000000002,
1323           0.0000000000000000 },
1324   { 0.17405275963859917, -0.50000000000000000, 0.40000000000000002,
1325           0.17453292519943295 },
1326   { 0.34538761957029329, -0.50000000000000000, 0.40000000000000002,
1327           0.34906585039886590 },
1328   { 0.51200902646603907, -0.50000000000000000, 0.40000000000000002,
1329           0.52359877559829882 },
1330   { 0.67301522212868792, -0.50000000000000000, 0.40000000000000002,
1331           0.69813170079773179 },
1332   { 0.82853844466313320, -0.50000000000000000, 0.40000000000000002,
1333           0.87266462599716477 },
1334   { 0.97942097862681488, -0.50000000000000000, 0.40000000000000002,
1335           1.0471975511965976 },
1336   { 1.1268429801220614, -0.50000000000000000, 0.40000000000000002,
1337           1.2217304763960306 },
1338   { 1.2720406704533922, -0.50000000000000000, 0.40000000000000002,
1339           1.3962634015954636 },
1340   { 1.4161679518465340, -0.50000000000000000, 0.40000000000000002,
1341           1.5707963267948966 },
1342 };
1343 const double toler045 = 2.5000000000000020e-13;
1344
1345 // Test data for k=-0.50000000000000000, nu=0.50000000000000000.
1346 // max(|f - f_GSL|): 2.2204460492503131e-16
1347 // max(|f - f_GSL| / |f_GSL|): 3.3419255755184137e-16
1348 const testcase_ellint_3<double>
1349 data046[10] =
1350 {
1351   { 0.0000000000000000, -0.50000000000000000, 0.50000000000000000,
1352           0.0000000000000000 },
1353   { 0.17387905570381157, -0.50000000000000000, 0.50000000000000000,
1354           0.17453292519943295 },
1355   { 0.34407576010465207, -0.50000000000000000, 0.50000000000000000,
1356           0.34906585039886590 },
1357   { 0.50795686560160824, -0.50000000000000000, 0.50000000000000000,
1358           0.52359877559829882 },
1359   { 0.66442115453330164, -0.50000000000000000, 0.50000000000000000,
1360           0.69813170079773179 },
1361   { 0.81373829119355345, -0.50000000000000000, 0.50000000000000000,
1362           0.87266462599716477 },
1363   { 0.95705743313235825, -0.50000000000000000, 0.50000000000000000,
1364           1.0471975511965976 },
1365   { 1.0959131991362554, -0.50000000000000000, 0.50000000000000000,
1366           1.2217304763960306 },
1367   { 1.2318900529754597, -0.50000000000000000, 0.50000000000000000,
1368           1.3962634015954636 },
1369   { 1.3664739530045971, -0.50000000000000000, 0.50000000000000000,
1370           1.5707963267948966 },
1371 };
1372 const double toler046 = 2.5000000000000020e-13;
1373
1374 // Test data for k=-0.50000000000000000, nu=0.59999999999999998.
1375 // max(|f - f_GSL|): 2.2204460492503131e-16
1376 // max(|f - f_GSL| / |f_GSL|): 3.3838494104749599e-16
1377 const testcase_ellint_3<double>
1378 data047[10] =
1379 {
1380   { 0.0000000000000000, -0.50000000000000000, 0.59999999999999998,
1381           0.0000000000000000 },
1382   { 0.17370597174637581, -0.50000000000000000, 0.59999999999999998,
1383           0.17453292519943295 },
1384   { 0.34278139158591414, -0.50000000000000000, 0.59999999999999998,
1385           0.34906585039886590 },
1386   { 0.50401419439302708, -0.50000000000000000, 0.59999999999999998,
1387           0.52359877559829882 },
1388   { 0.65618938076167210, -0.50000000000000000, 0.59999999999999998,
1389           0.69813170079773179 },
1390   { 0.79977959248855424, -0.50000000000000000, 0.59999999999999998,
1391           0.87266462599716477 },
1392   { 0.93625925190753545, -0.50000000000000000, 0.59999999999999998,
1393           1.0471975511965976 },
1394   { 1.0674905658379708, -0.50000000000000000, 0.59999999999999998,
1395           1.2217304763960306 },
1396   { 1.1953481298023050, -0.50000000000000000, 0.59999999999999998,
1397           1.3962634015954636 },
1398   { 1.3215740290190876, -0.50000000000000000, 0.59999999999999998,
1399           1.5707963267948966 },
1400 };
1401 const double toler047 = 2.5000000000000020e-13;
1402
1403 // Test data for k=-0.50000000000000000, nu=0.69999999999999996.
1404 // max(|f - f_GSL|): 2.2204460492503131e-16
1405 // max(|f - f_GSL| / |f_GSL|): 3.4250604066951477e-16
1406 const testcase_ellint_3<double>
1407 data048[10] =
1408 {
1409   { 0.0000000000000000, -0.50000000000000000, 0.69999999999999996,
1410           0.0000000000000000 },
1411   { 0.17353350383131641, -0.50000000000000000, 0.69999999999999996,
1412           0.17453292519943295 },
1413   { 0.34150410405436771, -0.50000000000000000, 0.69999999999999996,
1414           0.34906585039886590 },
1415   { 0.50017589696443487, -0.50000000000000000, 0.69999999999999996,
1416           0.52359877559829882 },
1417   { 0.64829398188419951, -0.50000000000000000, 0.69999999999999996,
1418           0.69813170079773179 },
1419   { 0.78658270782402073, -0.50000000000000000, 0.69999999999999996,
1420           0.87266462599716477 },
1421   { 0.91684738336675053, -0.50000000000000000, 0.69999999999999996,
1422           1.0471975511965976 },
1423   { 1.0412486789555935, -0.50000000000000000, 0.69999999999999996,
1424           1.2217304763960306 },
1425   { 1.1619021847612001, -0.50000000000000000, 0.69999999999999996,
1426           1.3962634015954636 },
1427   { 1.2807475181182502, -0.50000000000000000, 0.69999999999999996,
1428           1.5707963267948966 },
1429 };
1430 const double toler048 = 2.5000000000000020e-13;
1431
1432 // Test data for k=-0.50000000000000000, nu=0.80000000000000004.
1433 // max(|f - f_GSL|): 4.4408920985006262e-16
1434 // max(|f - f_GSL| / |f_GSL|): 3.5715240651179632e-16
1435 const testcase_ellint_3<double>
1436 data049[10] =
1437 {
1438   { 0.0000000000000000, -0.50000000000000000, 0.80000000000000004,
1439           0.0000000000000000 },
1440   { 0.17336164805979126, -0.50000000000000000, 0.80000000000000004,
1441           0.17453292519943295 },
1442   { 0.34024350132086773, -0.50000000000000000, 0.80000000000000004,
1443           0.34906585039886590 },
1444   { 0.49643719555734073, -0.50000000000000000, 0.80000000000000004,
1445           0.52359877559829882 },
1446   { 0.64071162456976150, -0.50000000000000000, 0.80000000000000004,
1447           0.69813170079773179 },
1448   { 0.77407836177211908, -0.50000000000000000, 0.80000000000000004,
1449           0.87266462599716477 },
1450   { 0.89867058251905652, -0.50000000000000000, 0.80000000000000004,
1451           1.0471975511965976 },
1452   { 1.0169181822134910, -0.50000000000000000, 0.80000000000000004,
1453           1.2217304763960306 },
1454   { 1.1311363312779448, -0.50000000000000000, 0.80000000000000004,
1455           1.3962634015954636 },
1456   { 1.2434165408189539, -0.50000000000000000, 0.80000000000000004,
1457           1.5707963267948966 },
1458 };
1459 const double toler049 = 2.5000000000000020e-13;
1460
1461 // Test data for k=-0.50000000000000000, nu=0.90000000000000002.
1462 // max(|f - f_GSL|): 4.4408920985006262e-16
1463 // max(|f - f_GSL| / |f_GSL|): 4.4664649039489274e-16
1464 const testcase_ellint_3<double>
1465 data050[10] =
1466 {
1467   { 0.0000000000000000, -0.50000000000000000, 0.90000000000000002,
1468           0.0000000000000000 },
1469   { 0.17319040056865681, -0.50000000000000000, 0.90000000000000002,
1470           0.17453292519943295 },
1471   { 0.33899920036578557, -0.50000000000000000, 0.90000000000000002,
1472           0.34906585039886590 },
1473   { 0.49279362182695174, -0.50000000000000000, 0.90000000000000002,
1474           0.52359877559829882 },
1475   { 0.63342123379746151, -0.50000000000000000, 0.90000000000000002,
1476           0.69813170079773179 },
1477   { 0.76220595179550321, -0.50000000000000000, 0.90000000000000002,
1478           0.87266462599716477 },
1479   { 0.88160004743532294, -0.50000000000000000, 0.90000000000000002,
1480           1.0471975511965976 },
1481   { 0.99427448642310123, -0.50000000000000000, 0.90000000000000002,
1482           1.2217304763960306 },
1483   { 1.1027091512470095, -0.50000000000000000, 0.90000000000000002,
1484           1.3962634015954636 },
1485   { 1.2091116095504744, -0.50000000000000000, 0.90000000000000002,
1486           1.5707963267948966 },
1487 };
1488 const double toler050 = 2.5000000000000020e-13;
1489
1490 // Test data for k=-0.40000000000000002, nu=0.0000000000000000.
1491 // max(|f - f_GSL|): 6.6613381477509392e-16
1492 // max(|f - f_GSL| / |f_GSL|): 4.0617918857203532e-16
1493 const testcase_ellint_3<double>
1494 data051[10] =
1495 {
1496   { 0.0000000000000000, -0.40000000000000002, 0.0000000000000000,
1497           0.0000000000000000 },
1498   { 0.17467414669441528, -0.40000000000000002, 0.0000000000000000,
1499           0.17453292519943295 },
1500   { 0.35018222772483443, -0.40000000000000002, 0.0000000000000000,
1501           0.34906585039886590 },
1502   { 0.52729015917508737, -0.40000000000000002, 0.0000000000000000,
1503           0.52359877559829882 },
1504   { 0.70662374407341244, -0.40000000000000002, 0.0000000000000000,
1505           0.69813170079773179 },
1506   { 0.88859210497602170, -0.40000000000000002, 0.0000000000000000,
1507           0.87266462599716477 },
1508   { 1.0733136290471379, -0.40000000000000002, 0.0000000000000000,
1509           1.0471975511965976 },
1510   { 1.2605612170157061, -0.40000000000000002, 0.0000000000000000,
1511           1.2217304763960306 },
1512   { 1.4497513956433439, -0.40000000000000002, 0.0000000000000000,
1513           1.3962634015954636 },
1514   { 1.6399998658645112, -0.40000000000000002, 0.0000000000000000,
1515           1.5707963267948966 },
1516 };
1517 const double toler051 = 2.5000000000000020e-13;
1518
1519 // Test data for k=-0.40000000000000002, nu=0.10000000000000001.
1520 // max(|f - f_GSL|): 6.6613381477509392e-16
1521 // max(|f - f_GSL| / |f_GSL|): 4.2644663257577874e-16
1522 const testcase_ellint_3<double>
1523 data052[10] =
1524 {
1525   { 0.0000000000000000, -0.40000000000000002, 0.10000000000000001,
1526           0.0000000000000000 },
1527   { 0.17449806706684670, -0.40000000000000002, 0.10000000000000001,
1528           0.17453292519943295 },
1529   { 0.34880048623856075, -0.40000000000000002, 0.10000000000000001,
1530           0.34906585039886590 },
1531   { 0.52277322065757392, -0.40000000000000002, 0.10000000000000001,
1532           0.52359877559829882 },
1533   { 0.69638072056918365, -0.40000000000000002, 0.10000000000000001,
1534           0.69813170079773179 },
1535   { 0.86968426619831540, -0.40000000000000002, 0.10000000000000001,
1536           0.87266462599716477 },
1537   { 1.0428044206578095, -0.40000000000000002, 0.10000000000000001,
1538           1.0471975511965976 },
1539   { 1.2158651158274378, -0.40000000000000002, 0.10000000000000001,
1540           1.2217304763960306 },
1541   { 1.3889447129893324, -0.40000000000000002, 0.10000000000000001,
1542           1.3962634015954636 },
1543   { 1.5620566886683604, -0.40000000000000002, 0.10000000000000001,
1544           1.5707963267948966 },
1545 };
1546 const double toler052 = 2.5000000000000020e-13;
1547
1548 // Test data for k=-0.40000000000000002, nu=0.20000000000000001.
1549 // max(|f - f_GSL|): 6.6613381477509392e-16
1550 // max(|f - f_GSL| / |f_GSL|): 4.4583049464169287e-16
1551 const testcase_ellint_3<double>
1552 data053[10] =
1553 {
1554   { 0.0000000000000000, -0.40000000000000002, 0.20000000000000001,
1555           0.0000000000000000 },
1556   { 0.17432262290723397, -0.40000000000000002, 0.20000000000000001,
1557           0.17453292519943295 },
1558   { 0.34743795258968596, -0.40000000000000002, 0.20000000000000001,
1559           0.34906585039886590 },
1560   { 0.51838919472805101, -0.40000000000000002, 0.20000000000000001,
1561           0.52359877559829882 },
1562   { 0.68663134739057907, -0.40000000000000002, 0.20000000000000001,
1563           0.69813170079773179 },
1564   { 0.85206432981833979, -0.40000000000000002, 0.20000000000000001,
1565           0.87266462599716477 },
1566   { 1.0149595349004430, -0.40000000000000002, 0.20000000000000001,
1567           1.0471975511965976 },
1568   { 1.1758349405464676, -0.40000000000000002, 0.20000000000000001,
1569           1.2217304763960306 },
1570   { 1.3353337673882637, -0.40000000000000002, 0.20000000000000001,
1571           1.3962634015954636 },
1572   { 1.4941414344266770, -0.40000000000000002, 0.20000000000000001,
1573           1.5707963267948966 },
1574 };
1575 const double toler053 = 2.5000000000000020e-13;
1576
1577 // Test data for k=-0.40000000000000002, nu=0.29999999999999999.
1578 // max(|f - f_GSL|): 8.8817841970012523e-16
1579 // max(|f - f_GSL| / |f_GSL|): 6.1925080711125793e-16
1580 const testcase_ellint_3<double>
1581 data054[10] =
1582 {
1583   { 0.0000000000000000, -0.40000000000000002, 0.29999999999999999,
1584           0.0000000000000000 },
1585   { 0.17414781013591540, -0.40000000000000002, 0.29999999999999999,
1586           0.17453292519943295 },
1587   { 0.34609415696777285, -0.40000000000000002, 0.29999999999999999,
1588           0.34906585039886590 },
1589   { 0.51413131295862535, -0.40000000000000002, 0.29999999999999999,
1590           0.52359877559829882 },
1591   { 0.67733527622935630, -0.40000000000000002, 0.29999999999999999,
1592           0.69813170079773179 },
1593   { 0.83558675182733266, -0.40000000000000002, 0.29999999999999999,
1594           0.87266462599716477 },
1595   { 0.98940140808865906, -0.40000000000000002, 0.29999999999999999,
1596           1.0471975511965976 },
1597   { 1.1396968797728058, -0.40000000000000002, 0.29999999999999999,
1598           1.2217304763960306 },
1599   { 1.2875920037865090, -0.40000000000000002, 0.29999999999999999,
1600           1.3962634015954636 },
1601   { 1.4342789859950078, -0.40000000000000002, 0.29999999999999999,
1602           1.5707963267948966 },
1603 };
1604 const double toler054 = 2.5000000000000020e-13;
1605
1606 // Test data for k=-0.40000000000000002, nu=0.40000000000000002.
1607 // max(|f - f_GSL|): 6.6613381477509392e-16
1608 // max(|f - f_GSL| / |f_GSL|): 4.8235661108581362e-16
1609 const testcase_ellint_3<double>
1610 data055[10] =
1611 {
1612   { 0.0000000000000000, -0.40000000000000002, 0.40000000000000002,
1613           0.0000000000000000 },
1614   { 0.17397362471112707, -0.40000000000000002, 0.40000000000000002,
1615           0.17453292519943295 },
1616   { 0.34476864603333196, -0.40000000000000002, 0.40000000000000002,
1617           0.34906585039886590 },
1618   { 0.50999329415379346, -0.40000000000000002, 0.40000000000000002,
1619           0.52359877559829882 },
1620   { 0.66845674551396006, -0.40000000000000002, 0.40000000000000002,
1621           0.69813170079773179 },
1622   { 0.82012848346231748, -0.40000000000000002, 0.40000000000000002,
1623           0.87266462599716477 },
1624   { 0.96582449258349057, -0.40000000000000002, 0.40000000000000002,
1625           1.0471975511965976 },
1626   { 1.1068473749476286, -0.40000000000000002, 0.40000000000000002,
1627           1.2217304763960306 },
1628   { 1.2447132729159989, -0.40000000000000002, 0.40000000000000002,
1629           1.3962634015954636 },
1630   { 1.3809986210732901, -0.40000000000000002, 0.40000000000000002,
1631           1.5707963267948966 },
1632 };
1633 const double toler055 = 2.5000000000000020e-13;
1634
1635 // Test data for k=-0.40000000000000002, nu=0.50000000000000000.
1636 // max(|f - f_GSL|): 6.6613381477509392e-16
1637 // max(|f - f_GSL| / |f_GSL|): 4.9965792755639576e-16
1638 const testcase_ellint_3<double>
1639 data056[10] =
1640 {
1641   { 0.0000000000000000, -0.40000000000000002, 0.50000000000000000,
1642           0.0000000000000000 },
1643   { 0.17380006262854136, -0.40000000000000002, 0.50000000000000000,
1644           0.17453292519943295 },
1645   { 0.34346098216756610, -0.40000000000000002, 0.50000000000000000,
1646           0.34906585039886590 },
1647   { 0.50596929935059420, -0.40000000000000002, 0.50000000000000000,
1648           0.52359877559829882 },
1649   { 0.65996392089131251, -0.40000000000000002, 0.50000000000000000,
1650           0.69813170079773179 },
1651   { 0.80558463511364786, -0.40000000000000002, 0.50000000000000000,
1652           0.87266462599716477 },
1653   { 0.94397834522857704, -0.40000000000000002, 0.50000000000000000,
1654           1.0471975511965976 },
1655   { 1.0768075114108115, -0.40000000000000002, 0.50000000000000000,
1656           1.2217304763960306 },
1657   { 1.2059184624251333, -0.40000000000000002, 0.50000000000000000,
1658           1.3962634015954636 },
1659   { 1.3331797176377398, -0.40000000000000002, 0.50000000000000000,
1660           1.5707963267948966 },
1661 };
1662 const double toler056 = 2.5000000000000020e-13;
1663
1664 // Test data for k=-0.40000000000000002, nu=0.59999999999999998.
1665 // max(|f - f_GSL|): 6.6613381477509392e-16
1666 // max(|f - f_GSL| / |f_GSL|): 5.1640223038298069e-16
1667 const testcase_ellint_3<double>
1668 data057[10] =
1669 {
1670   { 0.0000000000000000, -0.40000000000000002, 0.59999999999999998,
1671           0.0000000000000000 },
1672   { 0.17362711992081245, -0.40000000000000002, 0.59999999999999998,
1673           0.17453292519943295 },
1674   { 0.34217074276403953, -0.40000000000000002, 0.59999999999999998,
1675           0.34906585039886590 },
1676   { 0.50205389185761606, -0.40000000000000002, 0.59999999999999998,
1677           0.52359877559829882 },
1678   { 0.65182834920372734, -0.40000000000000002, 0.59999999999999998,
1679           0.69813170079773179 },
1680   { 0.79186512820565136, -0.40000000000000002, 0.59999999999999998,
1681           0.87266462599716477 },
1682   { 0.92365535916287134, -0.40000000000000002, 0.59999999999999998,
1683           1.0471975511965976 },
1684   { 1.0491915663957907, -0.40000000000000002, 0.59999999999999998,
1685           1.2217304763960306 },
1686   { 1.1705934291745106, -0.40000000000000002, 0.59999999999999998,
1687           1.3962634015954636 },
1688   { 1.2899514672527024, -0.40000000000000002, 0.59999999999999998,
1689           1.5707963267948966 },
1690 };
1691 const double toler057 = 2.5000000000000020e-13;
1692
1693 // Test data for k=-0.40000000000000002, nu=0.69999999999999996.
1694 // max(|f - f_GSL|): 6.6613381477509392e-16
1695 // max(|f - f_GSL| / |f_GSL|): 5.3264047918332349e-16
1696 const testcase_ellint_3<double>
1697 data058[10] =
1698 {
1699   { 0.0000000000000000, -0.40000000000000002, 0.69999999999999996,
1700           0.0000000000000000 },
1701   { 0.17345479265712868, -0.40000000000000002, 0.69999999999999996,
1702           0.17453292519943295 },
1703   { 0.34089751955950354, -0.40000000000000002, 0.69999999999999996,
1704           0.34906585039886590 },
1705   { 0.49824200167361332, -0.40000000000000002, 0.69999999999999996,
1706           0.52359877559829882 },
1707   { 0.64402450341199402, -0.40000000000000002, 0.69999999999999996,
1708           0.69813170079773179 },
1709   { 0.77889207804122873, -0.40000000000000002, 0.69999999999999996,
1710           0.87266462599716477 },
1711   { 0.90468169720957992, -0.40000000000000002, 0.69999999999999996,
1712           1.0471975511965976 },
1713   { 1.0236847823692916, -0.40000000000000002, 0.69999999999999996,
1714           1.2217304763960306 },
1715   { 1.1382465247425166, -0.40000000000000002, 0.69999999999999996,
1716           1.3962634015954636 },
1717   { 1.2506255923253344, -0.40000000000000002, 0.69999999999999996,
1718           1.5707963267948966 },
1719 };
1720 const double toler058 = 2.5000000000000020e-13;
1721
1722 // Test data for k=-0.40000000000000002, nu=0.80000000000000004.
1723 // max(|f - f_GSL|): 6.6613381477509392e-16
1724 // max(|f - f_GSL| / |f_GSL|): 6.6611561645571024e-16
1725 const testcase_ellint_3<double>
1726 data059[10] =
1727 {
1728   { 0.0000000000000000, -0.40000000000000002, 0.80000000000000004,
1729           0.0000000000000000 },
1730   { 0.17328307694277154, -0.40000000000000002, 0.80000000000000004,
1731           0.17453292519943295 },
1732   { 0.33964091800132007, -0.40000000000000002, 0.80000000000000004,
1733           0.34906585039886590 },
1734   { 0.49452889372467440, -0.40000000000000002, 0.80000000000000004,
1735           0.52359877559829882 },
1736   { 0.63652940095937316, -0.40000000000000002, 0.80000000000000004,
1737           0.69813170079773179 },
1738   { 0.76659772511159097, -0.40000000000000002, 0.80000000000000004,
1739           0.87266462599716477 },
1740   { 0.88691047977338111, -0.40000000000000002, 0.80000000000000004,
1741           1.0471975511965976 },
1742   { 1.0000273200611638, -0.40000000000000002, 0.80000000000000004,
1743           1.2217304763960306 },
1744   { 1.1084787902188009, -0.40000000000000002, 0.80000000000000004,
1745           1.3962634015954636 },
1746   { 1.2146499565727209, -0.40000000000000002, 0.80000000000000004,
1747           1.5707963267948966 },
1748 };
1749 const double toler059 = 2.5000000000000020e-13;
1750
1751 // Test data for k=-0.40000000000000002, nu=0.90000000000000002.
1752 // max(|f - f_GSL|): 6.6613381477509392e-16
1753 // max(|f - f_GSL| / |f_GSL|): 5.6376730823308004e-16
1754 const testcase_ellint_3<double>
1755 data060[10] =
1756 {
1757   { 0.0000000000000000, -0.40000000000000002, 0.90000000000000002,
1758           0.0000000000000000 },
1759   { 0.17311196891868127, -0.40000000000000002, 0.90000000000000002,
1760           0.17453292519943295 },
1761   { 0.33840055664911906, -0.40000000000000002, 0.90000000000000002,
1762           0.34906585039886590 },
1763   { 0.49091013944075329, -0.40000000000000002, 0.90000000000000002,
1764           0.52359877559829882 },
1765   { 0.62932228186809580, -0.40000000000000002, 0.90000000000000002,
1766           0.69813170079773179 },
1767   { 0.75492278323019801, -0.40000000000000002, 0.90000000000000002,
1768           0.87266462599716477 },
1769   { 0.87021659043854294, -0.40000000000000002, 0.90000000000000002,
1770           1.0471975511965976 },
1771   { 0.97800245228239246, -0.40000000000000002, 0.90000000000000002,
1772           1.2217304763960306 },
1773   { 1.0809625773173697, -0.40000000000000002, 0.90000000000000002,
1774           1.3962634015954636 },
1775   { 1.1815758115929846, -0.40000000000000002, 0.90000000000000002,
1776           1.5707963267948966 },
1777 };
1778 const double toler060 = 2.5000000000000020e-13;
1779
1780 // Test data for k=-0.30000000000000004, nu=0.0000000000000000.
1781 // max(|f - f_GSL|): 8.8817841970012523e-16
1782 // max(|f - f_GSL| / |f_GSL|): 6.3361874537309281e-16
1783 const testcase_ellint_3<double>
1784 data061[10] =
1785 {
1786   { 0.0000000000000000, -0.30000000000000004, 0.0000000000000000,
1787           0.0000000000000000 },
1788   { 0.17461228653000099, -0.30000000000000004, 0.0000000000000000,
1789           0.17453292519943295 },
1790   { 0.34969146102798415, -0.30000000000000004, 0.0000000000000000,
1791           0.34906585039886590 },
1792   { 0.52565822873726320, -0.30000000000000004, 0.0000000000000000,
1793           0.52359877559829882 },
1794   { 0.70284226512408532, -0.30000000000000004, 0.0000000000000000,
1795           0.69813170079773179 },
1796   { 0.88144139195111182, -0.30000000000000004, 0.0000000000000000,
1797           0.87266462599716477 },
1798   { 1.0614897067260520, -0.30000000000000004, 0.0000000000000000,
1799           1.0471975511965976 },
1800   { 1.2428416824174218, -0.30000000000000004, 0.0000000000000000,
1801           1.2217304763960306 },
1802   { 1.4251795877015927, -0.30000000000000004, 0.0000000000000000,
1803           1.3962634015954636 },
1804   { 1.6080486199305128, -0.30000000000000004, 0.0000000000000000,
1805           1.5707963267948966 },
1806 };
1807 const double toler061 = 2.5000000000000020e-13;
1808
1809 // Test data for k=-0.30000000000000004, nu=0.10000000000000001.
1810 // max(|f - f_GSL|): 8.8817841970012523e-16
1811 // max(|f - f_GSL| / |f_GSL|): 6.3908043711907203e-16
1812 const testcase_ellint_3<double>
1813 data062[10] =
1814 {
1815   { 0.0000000000000000, -0.30000000000000004, 0.10000000000000001,
1816           0.0000000000000000 },
1817   { 0.17443631884814376, -0.30000000000000004, 0.10000000000000001,
1818           0.17453292519943295 },
1819   { 0.34831316835124926, -0.30000000000000004, 0.10000000000000001,
1820           0.34906585039886590 },
1821   { 0.52116586276523857, -0.30000000000000004, 0.10000000000000001,
1822           0.52359877559829882 },
1823   { 0.69269385837910036, -0.30000000000000004, 0.10000000000000001,
1824           0.69813170079773179 },
1825   { 0.86279023163070856, -0.30000000000000004, 0.10000000000000001,
1826           0.87266462599716477 },
1827   { 1.0315321461438263, -0.30000000000000004, 0.10000000000000001,
1828           1.0471975511965976 },
1829   { 1.1991449111869024, -0.30000000000000004, 0.10000000000000001,
1830           1.2217304763960306 },
1831   { 1.3659561780923213, -0.30000000000000004, 0.10000000000000001,
1832           1.3962634015954636 },
1833   { 1.5323534693557528, -0.30000000000000004, 0.10000000000000001,
1834           1.5707963267948966 },
1835 };
1836 const double toler062 = 2.5000000000000020e-13;
1837
1838 // Test data for k=-0.30000000000000004, nu=0.20000000000000001.
1839 // max(|f - f_GSL|): 8.8817841970012523e-16
1840 // max(|f - f_GSL| / |f_GSL|): 6.4447238179454079e-16
1841 const testcase_ellint_3<double>
1842 data063[10] =
1843 {
1844   { 0.0000000000000000, -0.30000000000000004, 0.20000000000000001,
1845           0.0000000000000000 },
1846   { 0.17426098615372088, -0.30000000000000004, 0.20000000000000001,
1847           0.17453292519943295 },
1848   { 0.34695402664689923, -0.30000000000000004, 0.20000000000000001,
1849           0.34906585039886590 },
1850   { 0.51680555567038933, -0.30000000000000004, 0.20000000000000001,
1851           0.52359877559829882 },
1852   { 0.68303375225260210, -0.30000000000000004, 0.20000000000000001,
1853           0.69813170079773179 },
1854   { 0.84540662891295026, -0.30000000000000004, 0.20000000000000001,
1855           0.87266462599716477 },
1856   { 1.0041834051646927, -0.30000000000000004, 0.20000000000000001,
1857           1.0471975511965976 },
1858   { 1.1599952702345711, -0.30000000000000004, 0.20000000000000001,
1859           1.2217304763960306 },
1860   { 1.3137179520499165, -0.30000000000000004, 0.20000000000000001,
1861           1.3962634015954636 },
1862   { 1.4663658145259877, -0.30000000000000004, 0.20000000000000001,
1863           1.5707963267948966 },
1864 };
1865 const double toler063 = 2.5000000000000020e-13;
1866
1867 // Test data for k=-0.30000000000000004, nu=0.29999999999999999.
1868 // max(|f - f_GSL|): 8.8817841970012523e-16
1869 // max(|f - f_GSL| / |f_GSL|): 6.4979715256503266e-16
1870 const testcase_ellint_3<double>
1871 data064[10] =
1872 {
1873   { 0.0000000000000000, -0.30000000000000004, 0.29999999999999999,
1874           0.0000000000000000 },
1875   { 0.17408628437042842, -0.30000000000000004, 0.29999999999999999,
1876           0.17453292519943295 },
1877   { 0.34561356761638401, -0.30000000000000004, 0.29999999999999999,
1878           0.34906585039886590 },
1879   { 0.51257058617875850, -0.30000000000000004, 0.29999999999999999,
1880           0.52359877559829882 },
1881   { 0.67382207124602878, -0.30000000000000004, 0.29999999999999999,
1882           0.69813170079773179 },
1883   { 0.82914751587825131, -0.30000000000000004, 0.29999999999999999,
1884           0.87266462599716477 },
1885   { 0.97907434814374938, -0.30000000000000004, 0.29999999999999999,
1886           1.0471975511965976 },
1887   { 1.1246399297351584, -0.30000000000000004, 0.29999999999999999,
1888           1.2217304763960306 },
1889   { 1.2671793970398149, -0.30000000000000004, 0.29999999999999999,
1890           1.3962634015954636 },
1891   { 1.4081767433479091, -0.30000000000000004, 0.29999999999999999,
1892           1.5707963267948966 },
1893 };
1894 const double toler064 = 2.5000000000000020e-13;
1895
1896 // Test data for k=-0.30000000000000004, nu=0.40000000000000002.
1897 // max(|f - f_GSL|): 8.8817841970012523e-16
1898 // max(|f - f_GSL| / |f_GSL|): 6.5505716921759864e-16
1899 const testcase_ellint_3<double>
1900 data065[10] =
1901 {
1902   { 0.0000000000000000, -0.30000000000000004, 0.40000000000000002,
1903           0.0000000000000000 },
1904   { 0.17391220945982727, -0.30000000000000004, 0.40000000000000002,
1905           0.17453292519943295 },
1906   { 0.34429133937639689, -0.30000000000000004, 0.40000000000000002,
1907           0.34906585039886590 },
1908   { 0.50845471668581632, -0.30000000000000004, 0.40000000000000002,
1909           0.52359877559829882 },
1910   { 0.66502347027873854, -0.30000000000000004, 0.40000000000000002,
1911           0.69813170079773179 },
1912   { 0.81389191978012254, -0.30000000000000004, 0.40000000000000002,
1913           0.87266462599716477 },
1914   { 0.95590618002140570, -0.30000000000000004, 0.40000000000000002,
1915           1.0471975511965976 },
1916   { 1.0924915195213121, -0.30000000000000004, 0.40000000000000002,
1917           1.2217304763960306 },
1918   { 1.2253651604038061, -0.30000000000000004, 0.40000000000000002,
1919           1.3962634015954636 },
1920   { 1.3563643538969763, -0.30000000000000004, 0.40000000000000002,
1921           1.5707963267948966 },
1922 };
1923 const double toler065 = 2.5000000000000020e-13;
1924
1925 // Test data for k=-0.30000000000000004, nu=0.50000000000000000.
1926 // max(|f - f_GSL|): 8.8817841970012523e-16
1927 // max(|f - f_GSL| / |f_GSL|): 6.7807908859023716e-16
1928 const testcase_ellint_3<double>
1929 data066[10] =
1930 {
1931   { 0.0000000000000000, -0.30000000000000004, 0.50000000000000000,
1932           0.0000000000000000 },
1933   { 0.17373875742088232, -0.30000000000000004, 0.50000000000000000,
1934           0.17453292519943295 },
1935   { 0.34298690571124157, -0.30000000000000004, 0.50000000000000000,
1936           0.34906585039886590 },
1937   { 0.50445214859646936, -0.30000000000000004, 0.50000000000000000,
1938           0.52359877559829882 },
1939   { 0.65660648352418516, -0.30000000000000004, 0.50000000000000000,
1940           0.69813170079773179 },
1941   { 0.79953670639287289, -0.30000000000000004, 0.50000000000000000,
1942           0.87266462599716477 },
1943   { 0.93443393926588536, -0.30000000000000004, 0.50000000000000000,
1944           1.0471975511965976 },
1945   { 1.0630838369016911, -0.30000000000000004, 0.50000000000000000,
1946           1.2217304763960306 },
1947   { 1.1875197325653029, -0.30000000000000004, 0.50000000000000000,
1948           1.3962634015954636 },
1949   { 1.3098448759814962, -0.30000000000000004, 0.50000000000000000,
1950           1.5707963267948966 },
1951 };
1952 const double toler066 = 2.5000000000000020e-13;
1953
1954 // Test data for k=-0.30000000000000004, nu=0.59999999999999998.
1955 // max(|f - f_GSL|): 8.8817841970012523e-16
1956 // max(|f - f_GSL| / |f_GSL|): 7.0057999499931649e-16
1957 const testcase_ellint_3<double>
1958 data067[10] =
1959 {
1960   { 0.0000000000000000, -0.30000000000000004, 0.59999999999999998,
1961           0.0000000000000000 },
1962   { 0.17356592428950823, -0.30000000000000004, 0.59999999999999998,
1963           0.17453292519943295 },
1964   { 0.34169984536697379, -0.30000000000000004, 0.59999999999999998,
1965           0.34906585039886590 },
1966   { 0.50055748266498457, -0.30000000000000004, 0.59999999999999998,
1967           0.52359877559829882 },
1968   { 0.64854298527106768, -0.30000000000000004, 0.59999999999999998,
1969           0.69813170079773179 },
1970   { 0.78599329284207431, -0.30000000000000004, 0.59999999999999998,
1971           0.87266462599716477 },
1972   { 0.91445452089128199, -0.30000000000000004, 0.59999999999999998,
1973           1.0471975511965976 },
1974   { 1.0360412952290587, -0.30000000000000004, 0.59999999999999998,
1975           1.2217304763960306 },
1976   { 1.1530473919778641, -0.30000000000000004, 0.59999999999999998,
1977           1.3962634015954636 },
1978   { 1.2677758800420669, -0.30000000000000004, 0.59999999999999998,
1979           1.5707963267948966 },
1980 };
1981 const double toler067 = 2.5000000000000020e-13;
1982
1983 // Test data for k=-0.30000000000000004, nu=0.69999999999999996.
1984 // max(|f - f_GSL|): 8.8817841970012523e-16
1985 // max(|f - f_GSL| / |f_GSL|): 7.2239502844122443e-16
1986 const testcase_ellint_3<double>
1987 data068[10] =
1988 {
1989   { 0.0000000000000000, -0.30000000000000004, 0.69999999999999996,
1990           0.0000000000000000 },
1991   { 0.17339370613812224, -0.30000000000000004, 0.69999999999999996,
1992           0.17453292519943295 },
1993   { 0.34042975138455933, -0.30000000000000004, 0.69999999999999996,
1994           0.34906585039886590 },
1995   { 0.49676568368075985, -0.30000000000000004, 0.69999999999999996,
1996           0.52359877559829882 },
1997   { 0.64080774055753720, -0.30000000000000004, 0.69999999999999996,
1998           0.69813170079773179 },
1999   { 0.77318507779667278, -0.30000000000000004, 0.69999999999999996,
2000           0.87266462599716477 },
2001   { 0.89579782346548609, -0.30000000000000004, 0.69999999999999996,
2002           1.0471975511965976 },
2003   { 1.0110573286052202, -0.30000000000000004, 0.69999999999999996,
2004           1.2217304763960306 },
2005   { 1.1214710972949635, -0.30000000000000004, 0.69999999999999996,
2006           1.3962634015954636 },
2007   { 1.2294913236274982, -0.30000000000000004, 0.69999999999999996,
2008           1.5707963267948966 },
2009 };
2010 const double toler068 = 2.5000000000000020e-13;
2011
2012 // Test data for k=-0.30000000000000004, nu=0.80000000000000004.
2013 // max(|f - f_GSL|): 8.8817841970012523e-16
2014 // max(|f - f_GSL| / |f_GSL|): 7.4358357000101250e-16
2015 const testcase_ellint_3<double>
2016 data069[10] =
2017 {
2018   { 0.0000000000000000, -0.30000000000000004, 0.80000000000000004,
2019           0.0000000000000000 },
2020   { 0.17322209907520358, -0.30000000000000004, 0.80000000000000004,
2021           0.17453292519943295 },
2022   { 0.33917623046949996, -0.30000000000000004, 0.80000000000000004,
2023           0.34906585039886590 },
2024   { 0.49307204894329176, -0.30000000000000004, 0.80000000000000004,
2025           0.52359877559829882 },
2026   { 0.63337802830291734, -0.30000000000000004, 0.80000000000000004,
2027           0.69813170079773179 },
2028   { 0.76104540997689407, -0.30000000000000004, 0.80000000000000004,
2029           0.87266462599716477 },
2030   { 0.87832009635450714, -0.30000000000000004, 0.80000000000000004,
2031           1.0471975511965976 },
2032   { 0.98787879723171790, -0.30000000000000004, 0.80000000000000004,
2033           1.2217304763960306 },
2034   { 1.0924036340069339, -0.30000000000000004, 0.80000000000000004,
2035           1.3962634015954636 },
2036   { 1.1944567571590048, -0.30000000000000004, 0.80000000000000004,
2037           1.5707963267948966 },
2038 };
2039 const double toler069 = 2.5000000000000020e-13;
2040
2041 // Test data for k=-0.30000000000000004, nu=0.90000000000000002.
2042 // max(|f - f_GSL|): 8.8817841970012523e-16
2043 // max(|f - f_GSL| / |f_GSL|): 7.6419688299804087e-16
2044 const testcase_ellint_3<double>
2045 data070[10] =
2046 {
2047   { 0.0000000000000000, -0.30000000000000004, 0.90000000000000002,
2048           0.0000000000000000 },
2049   { 0.17305109924485945, -0.30000000000000004, 0.90000000000000002,
2050           0.17453292519943295 },
2051   { 0.33793890239556984, -0.30000000000000004, 0.90000000000000002,
2052           0.34906585039886590 },
2053   { 0.48947218005089738, -0.30000000000000004, 0.90000000000000002,
2054           0.52359877559829882 },
2055   { 0.62623332340775151, -0.30000000000000004, 0.90000000000000002,
2056           0.69813170079773179 },
2057   { 0.74951596581511148, -0.30000000000000004, 0.90000000000000002,
2058           0.87266462599716477 },
2059   { 0.86189886597755994, -0.30000000000000004, 0.90000000000000002,
2060           1.0471975511965976 },
2061   { 0.96629451153092005, -0.30000000000000004, 0.90000000000000002,
2062           1.2217304763960306 },
2063   { 1.0655269133492682, -0.30000000000000004, 0.90000000000000002,
2064           1.3962634015954636 },
2065   { 1.1622376896064914, -0.30000000000000004, 0.90000000000000002,
2066           1.5707963267948966 },
2067 };
2068 const double toler070 = 2.5000000000000020e-13;
2069
2070 // Test data for k=-0.19999999999999996, nu=0.0000000000000000.
2071 // max(|f - f_GSL|): 4.4408920985006262e-16
2072 // max(|f - f_GSL| / |f_GSL|): 4.2156475739151676e-16
2073 const testcase_ellint_3<double>
2074 data071[10] =
2075 {
2076   { 0.0000000000000000, -0.19999999999999996, 0.0000000000000000,
2077           0.0000000000000000 },
2078   { 0.17456817290292809, -0.19999999999999996, 0.0000000000000000,
2079           0.17453292519943295 },
2080   { 0.34934315932086801, -0.19999999999999996, 0.0000000000000000,
2081           0.34906585039886590 },
2082   { 0.52450880529443988, -0.19999999999999996, 0.0000000000000000,
2083           0.52359877559829882 },
2084   { 0.70020491009844876, -0.19999999999999996, 0.0000000000000000,
2085           0.69813170079773179 },
2086   { 0.87651006649967955, -0.19999999999999996, 0.0000000000000000,
2087           0.87266462599716477 },
2088   { 1.0534305870298994, -0.19999999999999996, 0.0000000000000000,
2089           1.0471975511965976 },
2090   { 1.2308975521670784, -0.19999999999999996, 0.0000000000000000,
2091           1.2217304763960306 },
2092   { 1.4087733584990738, -0.19999999999999996, 0.0000000000000000,
2093           1.3962634015954636 },
2094   { 1.5868678474541660, -0.19999999999999996, 0.0000000000000000,
2095           1.5707963267948966 },
2096 };
2097 const double toler071 = 2.5000000000000020e-13;
2098
2099 // Test data for k=-0.19999999999999996, nu=0.10000000000000001.
2100 // max(|f - f_GSL|): 4.4408920985006262e-16
2101 // max(|f - f_GSL| / |f_GSL|): 4.3374593253183472e-16
2102 const testcase_ellint_3<double>
2103 data072[10] =
2104 {
2105   { 0.0000000000000000, -0.19999999999999996, 0.10000000000000001,
2106           0.0000000000000000 },
2107   { 0.17439228502691748, -0.19999999999999996, 0.10000000000000001,
2108           0.17453292519943295 },
2109   { 0.34796731137565740, -0.19999999999999996, 0.10000000000000001,
2110           0.34906585039886590 },
2111   { 0.52003370294544848, -0.19999999999999996, 0.10000000000000001,
2112           0.52359877559829882 },
2113   { 0.69012222258631462, -0.19999999999999996, 0.10000000000000001,
2114           0.69813170079773179 },
2115   { 0.85803491465566772, -0.19999999999999996, 0.10000000000000001,
2116           0.87266462599716477 },
2117   { 1.0238463961099364, -0.19999999999999996, 0.10000000000000001,
2118           1.0471975511965976 },
2119   { 1.1878691059202153, -0.19999999999999996, 0.10000000000000001,
2120           1.2217304763960306 },
2121   { 1.3505985031831940, -0.19999999999999996, 0.10000000000000001,
2122           1.3962634015954636 },
2123   { 1.5126513474261087, -0.19999999999999996, 0.10000000000000001,
2124           1.5707963267948966 },
2125 };
2126 const double toler072 = 2.5000000000000020e-13;
2127
2128 // Test data for k=-0.19999999999999996, nu=0.20000000000000001.
2129 // max(|f - f_GSL|): 4.4408920985006262e-16
2130 // max(|f - f_GSL| / |f_GSL|): 4.4549984059502760e-16
2131 const testcase_ellint_3<double>
2132 data073[10] =
2133 {
2134   { 0.0000000000000000, -0.19999999999999996, 0.20000000000000001,
2135           0.0000000000000000 },
2136   { 0.17421703179583747, -0.19999999999999996, 0.20000000000000001,
2137           0.17453292519943295 },
2138   { 0.34661057411998791, -0.19999999999999996, 0.20000000000000001,
2139           0.34906585039886590 },
2140   { 0.51569006052647393, -0.19999999999999996, 0.20000000000000001,
2141           0.52359877559829882 },
2142   { 0.68052412821107244, -0.19999999999999996, 0.20000000000000001,
2143           0.69813170079773179 },
2144   { 0.84081341263313825, -0.19999999999999996, 0.20000000000000001,
2145           0.87266462599716477 },
2146   { 0.99683359988842890, -0.19999999999999996, 0.20000000000000001,
2147           1.0471975511965976 },
2148   { 1.1493086715118852, -0.19999999999999996, 0.20000000000000001,
2149           1.2217304763960306 },
2150   { 1.2992699693957541, -0.19999999999999996, 0.20000000000000001,
2151           1.3962634015954636 },
2152   { 1.4479323932249564, -0.19999999999999996, 0.20000000000000001,
2153           1.5707963267948966 },
2154 };
2155 const double toler073 = 2.5000000000000020e-13;
2156
2157 // Test data for k=-0.19999999999999996, nu=0.29999999999999999.
2158 // max(|f - f_GSL|): 6.6613381477509392e-16
2159 // max(|f - f_GSL| / |f_GSL|): 5.3140668101543467e-16
2160 const testcase_ellint_3<double>
2161 data074[10] =
2162 {
2163   { 0.0000000000000000, -0.19999999999999996, 0.29999999999999999,
2164           0.0000000000000000 },
2165   { 0.17404240913577704, -0.19999999999999996, 0.29999999999999999,
2166           0.17453292519943295 },
2167   { 0.34527248032587193, -0.19999999999999996, 0.29999999999999999,
2168           0.34906585039886590 },
2169   { 0.51147118981668416, -0.19999999999999996, 0.29999999999999999,
2170           0.52359877559829882 },
2171   { 0.67137107867777601, -0.19999999999999996, 0.29999999999999999,
2172           0.69813170079773179 },
2173   { 0.82470418188668893, -0.19999999999999996, 0.29999999999999999,
2174           0.87266462599716477 },
2175   { 0.97202873223594299, -0.19999999999999996, 0.29999999999999999,
2176           1.0471975511965976 },
2177   { 1.1144773569375266, -0.19999999999999996, 0.29999999999999999,
2178           1.2217304763960306 },
2179   { 1.2535292433701000, -0.19999999999999996, 0.29999999999999999,
2180           1.3962634015954636 },
2181   { 1.3908453514752477, -0.19999999999999996, 0.29999999999999999,
2182           1.5707963267948966 },
2183 };
2184 const double toler074 = 2.5000000000000020e-13;
2185
2186 // Test data for k=-0.19999999999999996, nu=0.40000000000000002.
2187 // max(|f - f_GSL|): 4.4408920985006262e-16
2188 // max(|f - f_GSL| / |f_GSL|): 4.6788709752760483e-16
2189 const testcase_ellint_3<double>
2190 data075[10] =
2191 {
2192   { 0.0000000000000000, -0.19999999999999996, 0.40000000000000002,
2193           0.0000000000000000 },
2194   { 0.17386841301066674, -0.19999999999999996, 0.40000000000000002,
2195           0.17453292519943295 },
2196   { 0.34395257914113253, -0.19999999999999996, 0.40000000000000002,
2197           0.34906585039886590 },
2198   { 0.50737088376869466, -0.19999999999999996, 0.40000000000000002,
2199           0.52359877559829882 },
2200   { 0.66262801717277631, -0.19999999999999996, 0.40000000000000002,
2201           0.69813170079773179 },
2202   { 0.80958766645079094, -0.19999999999999996, 0.40000000000000002,
2203           0.87266462599716477 },
2204   { 0.94913754236162040, -0.19999999999999996, 0.40000000000000002,
2205           1.0471975511965976 },
2206   { 1.0827985514222997, -0.19999999999999996, 0.40000000000000002,
2207           1.2217304763960306 },
2208   { 1.2124212429050478, -0.19999999999999996, 0.40000000000000002,
2209           1.3962634015954636 },
2210   { 1.3400002519661005, -0.19999999999999996, 0.40000000000000002,
2211           1.5707963267948966 },
2212 };
2213 const double toler075 = 2.5000000000000020e-13;
2214
2215 // Test data for k=-0.19999999999999996, nu=0.50000000000000000.
2216 // max(|f - f_GSL|): 4.4408920985006262e-16
2217 // max(|f - f_GSL| / |f_GSL|): 3.7788201301356829e-16
2218 const testcase_ellint_3<double>
2219 data076[10] =
2220 {
2221   { 0.0000000000000000, -0.19999999999999996, 0.50000000000000000,
2222           0.0000000000000000 },
2223   { 0.17369503942181799, -0.19999999999999996, 0.50000000000000000,
2224           0.17453292519943295 },
2225   { 0.34265043534362660, -0.19999999999999996, 0.50000000000000000,
2226           0.34906585039886590 },
2227   { 0.50338337208655415, -0.19999999999999996, 0.50000000000000000,
2228           0.52359877559829882 },
2229   { 0.65426373297163609, -0.19999999999999996, 0.50000000000000000,
2230           0.69813170079773179 },
2231   { 0.79536193036145808, -0.19999999999999996, 0.50000000000000000,
2232           0.87266462599716477 },
2233   { 0.92791875910061605, -0.19999999999999996, 0.50000000000000000,
2234           1.0471975511965976 },
2235   { 1.0538145052725829, -0.19999999999999996, 0.50000000000000000,
2236           1.2217304763960306 },
2237   { 1.1752060022875899, -0.19999999999999996, 0.50000000000000000,
2238           1.3962634015954636 },
2239   { 1.2943374404397372, -0.19999999999999996, 0.50000000000000000,
2240           1.5707963267948966 },
2241 };
2242 const double toler076 = 2.5000000000000020e-13;
2243
2244 // Test data for k=-0.19999999999999996, nu=0.59999999999999998.
2245 // max(|f - f_GSL|): 4.4408920985006262e-16
2246 // max(|f - f_GSL| / |f_GSL|): 4.8899223779598256e-16
2247 const testcase_ellint_3<double>
2248 data077[10] =
2249 {
2250   { 0.0000000000000000, -0.19999999999999996, 0.59999999999999998,
2251           0.0000000000000000 },
2252   { 0.17352228440746925, -0.19999999999999996, 0.59999999999999998,
2253           0.17453292519943295 },
2254   { 0.34136562863713626, -0.19999999999999996, 0.59999999999999998,
2255           0.34906585039886590 },
2256   { 0.49950328177638481, -0.19999999999999996, 0.59999999999999998,
2257           0.52359877559829882 },
2258   { 0.64625032705690799, -0.19999999999999996, 0.59999999999999998,
2259           0.69813170079773179 },
2260   { 0.78193941198403083, -0.19999999999999996, 0.59999999999999998,
2261           0.87266462599716477 },
2262   { 0.90817230934317128, -0.19999999999999996, 0.59999999999999998,
2263           1.0471975511965976 },
2264   { 1.0271563751276462, -0.19999999999999996, 0.59999999999999998,
2265           1.2217304763960306 },
2266   { 1.1412999379040518, -0.19999999999999996, 0.59999999999999998,
2267           1.3962634015954636 },
2268   { 1.2530330675914556, -0.19999999999999996, 0.59999999999999998,
2269           1.5707963267948966 },
2270 };
2271 const double toler077 = 2.5000000000000020e-13;
2272
2273 // Test data for k=-0.19999999999999996, nu=0.69999999999999996.
2274 // max(|f - f_GSL|): 6.6613381477509392e-16
2275 // max(|f - f_GSL| / |f_GSL|): 5.9999318361775115e-16
2276 const testcase_ellint_3<double>
2277 data078[10] =
2278 {
2279   { 0.0000000000000000, -0.19999999999999996, 0.69999999999999996,
2280           0.0000000000000000 },
2281   { 0.17335014404233895, -0.19999999999999996, 0.69999999999999996,
2282           0.17453292519943295 },
2283   { 0.34009775298617811, -0.19999999999999996, 0.69999999999999996,
2284           0.34906585039886590 },
2285   { 0.49572560201923810, -0.19999999999999996, 0.69999999999999996,
2286           0.52359877559829882 },
2287   { 0.63856276669886503, -0.19999999999999996, 0.69999999999999996,
2288           0.69813170079773179 },
2289   { 0.76924438644867565, -0.19999999999999996, 0.69999999999999996,
2290           0.87266462599716477 },
2291   { 0.88973060843856466, -0.19999999999999996, 0.69999999999999996,
2292           1.0471975511965976 },
2293   { 1.0025230471636377, -0.19999999999999996, 0.69999999999999996,
2294           1.2217304763960306 },
2295   { 1.1102356376093103, -0.19999999999999996, 0.69999999999999996,
2296           1.3962634015954636 },
2297   { 1.2154356555075863, -0.19999999999999996, 0.69999999999999996,
2298           1.5707963267948966 },
2299 };
2300 const double toler078 = 2.5000000000000020e-13;
2301
2302 // Test data for k=-0.19999999999999996, nu=0.80000000000000004.
2303 // max(|f - f_GSL|): 4.4408920985006262e-16
2304 // max(|f - f_GSL| / |f_GSL|): 5.0901276230707249e-16
2305 const testcase_ellint_3<double>
2306 data079[10] =
2307 {
2308   { 0.0000000000000000, -0.19999999999999996, 0.80000000000000004,
2309           0.0000000000000000 },
2310   { 0.17317861443718538, -0.19999999999999996, 0.80000000000000004,
2311           0.17453292519943295 },
2312   { 0.33884641598718701, -0.19999999999999996, 0.80000000000000004,
2313           0.34906585039886590 },
2314   { 0.49204565281259494, -0.19999999999999996, 0.80000000000000004,
2315           0.52359877559829882 },
2316   { 0.63117851188220320, -0.19999999999999996, 0.80000000000000004,
2317           0.69813170079773179 },
2318   { 0.75721095949544170, -0.19999999999999996, 0.80000000000000004,
2319           0.87266462599716477 },
2320   { 0.87245201443919118, -0.19999999999999996, 0.80000000000000004,
2321           1.0471975511965976 },
2322   { 0.97966584238831089, -0.19999999999999996, 0.80000000000000004,
2323           1.2217304763960306 },
2324   { 1.0816336325174360, -0.19999999999999996, 0.80000000000000004,
2325           1.3962634015954636 },
2326   { 1.1810223448909909, -0.19999999999999996, 0.80000000000000004,
2327           1.5707963267948966 },
2328 };
2329 const double toler079 = 2.5000000000000020e-13;
2330
2331 // Test data for k=-0.19999999999999996, nu=0.90000000000000002.
2332 // max(|f - f_GSL|): 6.6613381477509392e-16
2333 // max(|f - f_GSL| / |f_GSL|): 6.4833128442756722e-16
2334 const testcase_ellint_3<double>
2335 data080[10] =
2336 {
2337   { 0.0000000000000000, -0.19999999999999996, 0.90000000000000002,
2338           0.0000000000000000 },
2339   { 0.17300769173837277, -0.19999999999999996, 0.90000000000000002,
2340           0.17453292519943295 },
2341   { 0.33761123827372508, -0.19999999999999996, 0.90000000000000002,
2342           0.34906585039886590 },
2343   { 0.48845905690769426, -0.19999999999999996, 0.90000000000000002,
2344           0.52359877559829882 },
2345   { 0.62407720017324952, -0.19999999999999996, 0.90000000000000002,
2346           0.69813170079773179 },
2347   { 0.74578146525124289, -0.19999999999999996, 0.90000000000000002,
2348           0.87266462599716477 },
2349   { 0.85621583540073076, -0.19999999999999996, 0.90000000000000002,
2350           1.0471975511965976 },
2351   { 0.95837725988001199, -0.19999999999999996, 0.90000000000000002,
2352           1.2217304763960306 },
2353   { 1.0551821412633928, -0.19999999999999996, 0.90000000000000002,
2354           1.3962634015954636 },
2355   { 1.1493679916141861, -0.19999999999999996, 0.90000000000000002,
2356           1.5707963267948966 },
2357 };
2358 const double toler080 = 2.5000000000000020e-13;
2359
2360 // Test data for k=-0.099999999999999978, nu=0.0000000000000000.
2361 // max(|f - f_GSL|): 4.4408920985006262e-16
2362 // max(|f - f_GSL| / |f_GSL|): 3.1735566504509650e-16
2363 const testcase_ellint_3<double>
2364 data081[10] =
2365 {
2366   { 0.0000000000000000, -0.099999999999999978, 0.0000000000000000,
2367           0.0000000000000000 },
2368   { 0.17454173353063659, -0.099999999999999978, 0.0000000000000000,
2369           0.17453292519943295 },
2370   { 0.34913506721468091, -0.099999999999999978, 0.0000000000000000,
2371           0.34906585039886590 },
2372   { 0.52382550016538942, -0.099999999999999978, 0.0000000000000000,
2373           0.52359877559829882 },
2374   { 0.69864700854177020, -0.099999999999999978, 0.0000000000000000,
2375           0.69813170079773179 },
2376   { 0.87361792586964870, -0.099999999999999978, 0.0000000000000000,
2377           0.87266462599716477 },
2378   { 1.0487386319621683, -0.099999999999999978, 0.0000000000000000,
2379           1.0471975511965976 },
2380   { 1.2239913752078757, -0.099999999999999978, 0.0000000000000000,
2381           1.2217304763960306 },
2382   { 1.3993423113684049, -0.099999999999999978, 0.0000000000000000,
2383           1.3962634015954636 },
2384   { 1.5747455615173562, -0.099999999999999978, 0.0000000000000000,
2385           1.5707963267948966 },
2386 };
2387 const double toler081 = 2.5000000000000020e-13;
2388
2389 // Test data for k=-0.099999999999999978, nu=0.10000000000000001.
2390 // max(|f - f_GSL|): 4.4408920985006262e-16
2391 // max(|f - f_GSL| / |f_GSL|): 3.3097339877269682e-16
2392 const testcase_ellint_3<double>
2393 data082[10] =
2394 {
2395   { 0.0000000000000000, -0.099999999999999978, 0.10000000000000001,
2396           0.0000000000000000 },
2397   { 0.17436589347616613, -0.099999999999999978, 0.10000000000000001,
2398           0.17453292519943295 },
2399   { 0.34776067871237359, -0.099999999999999978, 0.10000000000000001,
2400           0.34906585039886590 },
2401   { 0.51936064354727796, -0.099999999999999978, 0.10000000000000001,
2402           0.52359877559829882 },
2403   { 0.68860303749364349, -0.099999999999999978, 0.10000000000000001,
2404           0.69813170079773179 },
2405   { 0.85524561882332051, -0.099999999999999978, 0.10000000000000001,
2406           0.87266462599716477 },
2407   { 1.0193708301908335, -0.099999999999999978, 0.10000000000000001,
2408           1.0471975511965976 },
2409   { 1.1813474067123044, -0.099999999999999978, 0.10000000000000001,
2410           1.2217304763960306 },
2411   { 1.3417670770424983, -0.099999999999999978, 0.10000000000000001,
2412           1.3962634015954636 },
2413   { 1.5013711111199950, -0.099999999999999978, 0.10000000000000001,
2414           1.5707963267948966 },
2415 };
2416 const double toler082 = 2.5000000000000020e-13;
2417
2418 // Test data for k=-0.099999999999999978, nu=0.20000000000000001.
2419 // max(|f - f_GSL|): 4.4408920985006262e-16
2420 // max(|f - f_GSL| / |f_GSL|): 3.4399947764827574e-16
2421 const testcase_ellint_3<double>
2422 data083[10] =
2423 {
2424   { 0.0000000000000000, -0.099999999999999978, 0.20000000000000001,
2425           0.0000000000000000 },
2426   { 0.17419068786141340, -0.099999999999999978, 0.20000000000000001,
2427           0.17453292519943295 },
2428   { 0.34640537686230133, -0.099999999999999978, 0.20000000000000001,
2429           0.34906585039886590 },
2430   { 0.51502689171753946, -0.099999999999999978, 0.20000000000000001,
2431           0.52359877559829882 },
2432   { 0.67904147863672715, -0.099999999999999978, 0.20000000000000001,
2433           0.69813170079773179 },
2434   { 0.83811885126105179, -0.099999999999999978, 0.20000000000000001,
2435           0.87266462599716477 },
2436   { 0.99255278555742787, -0.099999999999999978, 0.20000000000000001,
2437           1.0471975511965976 },
2438   { 1.1431260546194930, -0.099999999999999978, 0.20000000000000001,
2439           1.2217304763960306 },
2440   { 1.2909589656532101, -0.099999999999999978, 0.20000000000000001,
2441           1.3962634015954636 },
2442   { 1.4373749386463430, -0.099999999999999978, 0.20000000000000001,
2443           1.5707963267948966 },
2444 };
2445 const double toler083 = 2.5000000000000020e-13;
2446
2447 // Test data for k=-0.099999999999999978, nu=0.29999999999999999.
2448 // max(|f - f_GSL|): 4.4408920985006262e-16
2449 // max(|f - f_GSL| / |f_GSL|): 3.5650492137236872e-16
2450 const testcase_ellint_3<double>
2451 data084[10] =
2452 {
2453   { 0.0000000000000000, -0.099999999999999978, 0.29999999999999999,
2454           0.0000000000000000 },
2455   { 0.17401611261390104, -0.099999999999999978, 0.29999999999999999,
2456           0.17453292519943295 },
2457   { 0.34506869507511773, -0.099999999999999978, 0.29999999999999999,
2458           0.34906585039886590 },
2459   { 0.51081757604259859, -0.099999999999999978, 0.29999999999999999,
2460           0.52359877559829882 },
2461   { 0.66992297597712303, -0.099999999999999978, 0.29999999999999999,
2462           0.69813170079773179 },
2463   { 0.82209722856174228, -0.099999999999999978, 0.29999999999999999,
2464           0.87266462599716477 },
2465   { 0.96792430487669590, -0.099999999999999978, 0.29999999999999999,
2466           1.0471975511965976 },
2467   { 1.1085964108954092, -0.099999999999999978, 0.29999999999999999,
2468           1.2217304763960306 },
2469   { 1.2456748370836999, -0.099999999999999978, 0.29999999999999999,
2470           1.3962634015954636 },
2471   { 1.3809159606704959, -0.099999999999999978, 0.29999999999999999,
2472           1.5707963267948966 },
2473 };
2474 const double toler084 = 2.5000000000000020e-13;
2475
2476 // Test data for k=-0.099999999999999978, nu=0.40000000000000002.
2477 // max(|f - f_GSL|): 4.4408920985006262e-16
2478 // max(|f - f_GSL| / |f_GSL|): 3.6854758534459740e-16
2479 const testcase_ellint_3<double>
2480 data085[10] =
2481 {
2482   { 0.0000000000000000, -0.099999999999999978, 0.40000000000000002,
2483           0.0000000000000000 },
2484   { 0.17384216369897931, -0.099999999999999978, 0.40000000000000002,
2485           0.17453292519943295 },
2486   { 0.34375018311376787, -0.099999999999999978, 0.40000000000000002,
2487           0.34906585039886590 },
2488   { 0.50672650758380455, -0.099999999999999978, 0.40000000000000002,
2489           0.52359877559829882 },
2490   { 0.66121264213337616, -0.099999999999999978, 0.40000000000000002,
2491           0.69813170079773179 },
2492   { 0.80706202005774441, -0.099999999999999978, 0.40000000000000002,
2493           0.87266462599716477 },
2494   { 0.94519376138245870, -0.099999999999999978, 0.40000000000000002,
2495           1.0471975511965976 },
2496   { 1.0771880300759584, -0.099999999999999978, 0.40000000000000002,
2497           1.2217304763960306 },
2498   { 1.2049711557188272, -0.099999999999999978, 0.40000000000000002,
2499           1.3962634015954636 },
2500   { 1.3306223265207477, -0.099999999999999978, 0.40000000000000002,
2501           1.5707963267948966 },
2502 };
2503 const double toler085 = 2.5000000000000020e-13;
2504
2505 // Test data for k=-0.099999999999999978, nu=0.50000000000000000.
2506 // max(|f - f_GSL|): 4.4408920985006262e-16
2507 // max(|f - f_GSL| / |f_GSL|): 3.8017534281650347e-16
2508 const testcase_ellint_3<double>
2509 data086[10] =
2510 {
2511   { 0.0000000000000000, -0.099999999999999978, 0.50000000000000000,
2512           0.0000000000000000 },
2513   { 0.17366883711936548, -0.099999999999999978, 0.50000000000000000,
2514           0.17453292519943295 },
2515   { 0.34244940634881882, -0.099999999999999978, 0.50000000000000000,
2516           0.34906585039886590 },
2517   { 0.50274793281634367, -0.099999999999999978, 0.50000000000000000,
2518           0.52359877559829882 },
2519   { 0.65287941633275082, -0.099999999999999978, 0.50000000000000000,
2520           0.69813170079773179 },
2521   { 0.79291198790315398, -0.099999999999999978, 0.50000000000000000,
2522           0.87266462599716477 },
2523   { 0.92412201537880323, -0.099999999999999978, 0.50000000000000000,
2524           1.0471975511965976 },
2525   { 1.0484480076799372, -0.099999999999999978, 0.50000000000000000,
2526           1.2217304763960306 },
2527   { 1.1681168130475206, -0.099999999999999978, 0.50000000000000000,
2528           1.3962634015954636 },
2529   { 1.2854480708580160, -0.099999999999999978, 0.50000000000000000,
2530           1.5707963267948966 },
2531 };
2532 const double toler086 = 2.5000000000000020e-13;
2533
2534 // Test data for k=-0.099999999999999978, nu=0.59999999999999998.
2535 // max(|f - f_GSL|): 4.4408920985006262e-16
2536 // max(|f - f_GSL| / |f_GSL|): 3.9142834151672032e-16
2537 const testcase_ellint_3<double>
2538 data087[10] =
2539 {
2540   { 0.0000000000000000, -0.099999999999999978, 0.59999999999999998,
2541           0.0000000000000000 },
2542   { 0.17349612891469013, -0.099999999999999978, 0.59999999999999998,
2543           0.17453292519943295 },
2544   { 0.34116594505539444, -0.099999999999999978, 0.59999999999999998,
2545           0.34906585039886590 },
2546   { 0.49887649430466674, -0.099999999999999978, 0.59999999999999998,
2547           0.52359877559829882 },
2548   { 0.64489553282165146, -0.099999999999999978, 0.59999999999999998,
2549           0.69813170079773179 },
2550   { 0.77956016553782437, -0.099999999999999978, 0.59999999999999998,
2551           0.87266462599716477 },
2552   { 0.90451074530096287, -0.099999999999999978, 0.59999999999999998,
2553           1.0471975511965976 },
2554   { 1.0220113666961632, -0.099999999999999978, 0.59999999999999998,
2555           1.2217304763960306 },
2556   { 1.1345351441065563, -0.099999999999999978, 0.59999999999999998,
2557           1.3962634015954636 },
2558   { 1.2445798942989255, -0.099999999999999978, 0.59999999999999998,
2559           1.5707963267948966 },
2560 };
2561 const double toler087 = 2.5000000000000020e-13;
2562
2563 // Test data for k=-0.099999999999999978, nu=0.69999999999999996.
2564 // max(|f - f_GSL|): 6.6613381477509392e-16
2565 // max(|f - f_GSL| / |f_GSL|): 5.5172091551439012e-16
2566 const testcase_ellint_3<double>
2567 data088[10] =
2568 {
2569   { 0.0000000000000000, -0.099999999999999978, 0.69999999999999996,
2570           0.0000000000000000 },
2571   { 0.17332403516105047, -0.099999999999999978, 0.69999999999999996,
2572           0.17453292519943295 },
2573   { 0.33989939374896883, -0.099999999999999978, 0.69999999999999996,
2574           0.34906585039886590 },
2575   { 0.49510719568614070, -0.099999999999999978, 0.69999999999999996,
2576           0.52359877559829882 },
2577   { 0.63723607776354974, -0.099999999999999978, 0.69999999999999996,
2578           0.69813170079773179 },
2579   { 0.76693133887935327, -0.099999999999999978, 0.69999999999999996,
2580           0.87266462599716477 },
2581   { 0.88619382078823805, -0.099999999999999978, 0.69999999999999996,
2582           1.0471975511965976 },
2583   { 0.99758012018676490, -0.099999999999999978, 0.69999999999999996,
2584           1.2217304763960306 },
2585   { 1.1037642270814410, -0.099999999999999978, 0.69999999999999996,
2586           1.3962634015954636 },
2587   { 1.2073745911083185, -0.099999999999999978, 0.69999999999999996,
2588           1.5707963267948966 },
2589 };
2590 const double toler088 = 2.5000000000000020e-13;
2591
2592 // Test data for k=-0.099999999999999978, nu=0.80000000000000004.
2593 // max(|f - f_GSL|): 4.4408920985006262e-16
2594 // max(|f - f_GSL| / |f_GSL|): 4.1294144515772258e-16
2595 const testcase_ellint_3<double>
2596 data089[10] =
2597 {
2598   { 0.0000000000000000, -0.099999999999999978, 0.80000000000000004,
2599           0.0000000000000000 },
2600   { 0.17315255197057014, -0.099999999999999978, 0.80000000000000004,
2601           0.17453292519943295 },
2602   { 0.33864936055747991, -0.099999999999999978, 0.80000000000000004,
2603           0.34906585039886590 },
2604   { 0.49143537041117613, -0.099999999999999978, 0.80000000000000004,
2605           0.52359877559829882 },
2606   { 0.62987861760047492, -0.099999999999999978, 0.80000000000000004,
2607           0.69813170079773179 },
2608   { 0.75496005490917517, -0.099999999999999978, 0.80000000000000004,
2609           0.87266462599716477 },
2610   { 0.86903081862701881, -0.099999999999999978, 0.80000000000000004,
2611           1.0471975511965976 },
2612   { 0.97490814820725591, -0.099999999999999978, 0.80000000000000004,
2613           1.2217304763960306 },
2614   { 1.0754290107171083, -0.099999999999999978, 0.80000000000000004,
2615           1.3962634015954636 },
2616   { 1.1733158866987732, -0.099999999999999978, 0.80000000000000004,
2617           1.5707963267948966 },
2618 };
2619 const double toler089 = 2.5000000000000020e-13;
2620
2621 // Test data for k=-0.099999999999999978, nu=0.90000000000000002.
2622 // max(|f - f_GSL|): 4.4408920985006262e-16
2623 // max(|f - f_GSL| / |f_GSL|): 4.2325599449457852e-16
2624 const testcase_ellint_3<double>
2625 data090[10] =
2626 {
2627   { 0.0000000000000000, -0.099999999999999978, 0.90000000000000002,
2628           0.0000000000000000 },
2629   { 0.17298167549096563, -0.099999999999999978, 0.90000000000000002,
2630           0.17453292519943295 },
2631   { 0.33741546662741589, -0.099999999999999978, 0.90000000000000002,
2632           0.34906585039886590 },
2633   { 0.48785665376856868, -0.099999999999999978, 0.90000000000000002,
2634           0.52359877559829882 },
2635   { 0.62280288554518959, -0.099999999999999978, 0.90000000000000002,
2636           0.69813170079773179 },
2637   { 0.74358903115455188, -0.099999999999999978, 0.90000000000000002,
2638           0.87266462599716477 },
2639   { 0.85290207679298335, -0.099999999999999978, 0.90000000000000002,
2640           1.0471975511965976 },
2641   { 0.95379006645397379, -0.099999999999999978, 0.90000000000000002,
2642           1.2217304763960306 },
2643   { 1.0492213119872327, -0.099999999999999978, 0.90000000000000002,
2644           1.3962634015954636 },
2645   { 1.1419839485283374, -0.099999999999999978, 0.90000000000000002,
2646           1.5707963267948966 },
2647 };
2648 const double toler090 = 2.5000000000000020e-13;
2649
2650 // Test data for k=0.0000000000000000, nu=0.0000000000000000.
2651 // max(|f - f_GSL|): 2.2204460492503131e-16
2652 // max(|f - f_GSL| / |f_GSL|): 2.1203697876423452e-16
2653 const testcase_ellint_3<double>
2654 data091[10] =
2655 {
2656   { 0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
2657           0.0000000000000000 },
2658   { 0.17453292519943292, 0.0000000000000000, 0.0000000000000000,
2659           0.17453292519943295 },
2660   { 0.34906585039886584, 0.0000000000000000, 0.0000000000000000,
2661           0.34906585039886590 },
2662   { 0.52359877559829870, 0.0000000000000000, 0.0000000000000000,
2663           0.52359877559829882 },
2664   { 0.69813170079773168, 0.0000000000000000, 0.0000000000000000,
2665           0.69813170079773179 },
2666   { 0.87266462599716477, 0.0000000000000000, 0.0000000000000000,
2667           0.87266462599716477 },
2668   { 1.0471975511965974, 0.0000000000000000, 0.0000000000000000,
2669           1.0471975511965976 },
2670   { 1.2217304763960304, 0.0000000000000000, 0.0000000000000000,
2671           1.2217304763960306 },
2672   { 1.3962634015954631, 0.0000000000000000, 0.0000000000000000,
2673           1.3962634015954636 },
2674   { 1.5707963267948966, 0.0000000000000000, 0.0000000000000000,
2675           1.5707963267948966 },
2676 };
2677 const double toler091 = 2.5000000000000020e-13;
2678
2679 // Test data for k=0.0000000000000000, nu=0.10000000000000001.
2680 // max(|f - f_GSL|): 2.2204460492503131e-16
2681 // max(|f - f_GSL| / |f_GSL|): 2.1813975824747021e-16
2682 const testcase_ellint_3<double>
2683 data092[10] =
2684 {
2685   { 0.0000000000000000, 0.0000000000000000, 0.10000000000000001,
2686           0.0000000000000000 },
2687   { 0.17435710107516605, 0.0000000000000000, 0.10000000000000001,
2688           0.17453292519943295 },
2689   { 0.34769194715329604, 0.0000000000000000, 0.10000000000000001,
2690           0.34906585039886590 },
2691   { 0.51913731575866107, 0.0000000000000000, 0.10000000000000001,
2692           0.52359877559829882 },
2693   { 0.68810051897078450, 0.0000000000000000, 0.10000000000000001,
2694           0.69813170079773179 },
2695   { 0.85432615661706823, 0.0000000000000000, 0.10000000000000001,
2696           0.87266462599716477 },
2697   { 1.0179006647340794, 0.0000000000000000, 0.10000000000000001,
2698           1.0471975511965976 },
2699   { 1.1792120640746322, 0.0000000000000000, 0.10000000000000001,
2700           1.2217304763960306 },
2701   { 1.3388834245070498, 0.0000000000000000, 0.10000000000000001,
2702           1.3962634015954636 },
2703   { 1.4976955329233277, 0.0000000000000000, 0.10000000000000001,
2704           1.5707963267948966 },
2705 };
2706 const double toler092 = 2.5000000000000020e-13;
2707
2708 // Test data for k=0.0000000000000000, nu=0.20000000000000001.
2709 // max(|f - f_GSL|): 2.2204460492503131e-16
2710 // max(|f - f_GSL| / |f_GSL|): 2.2402804784409065e-16
2711 const testcase_ellint_3<double>
2712 data093[10] =
2713 {
2714   { 0.0000000000000000, 0.0000000000000000, 0.20000000000000001,
2715           0.0000000000000000 },
2716   { 0.17418191132226074, 0.0000000000000000, 0.20000000000000001,
2717           0.17453292519943295 },
2718   { 0.34633712256943405, 0.0000000000000000, 0.20000000000000001,
2719           0.34906585039886590 },
2720   { 0.51480684302043700, 0.0000000000000000, 0.20000000000000001,
2721           0.52359877559829882 },
2722   { 0.67855102942481937, 0.0000000000000000, 0.20000000000000001,
2723           0.69813170079773179 },
2724   { 0.83723056090326253, 0.0000000000000000, 0.20000000000000001,
2725           0.87266462599716477 },
2726   { 0.99114645269578161, 0.0000000000000000, 0.20000000000000001,
2727           1.0471975511965976 },
2728   { 1.1411014627915537, 0.0000000000000000, 0.20000000000000001,
2729           1.2217304763960306 },
2730   { 1.2882448138013969, 0.0000000000000000, 0.20000000000000001,
2731           1.3962634015954636 },
2732   { 1.4339343023863691, 0.0000000000000000, 0.20000000000000001,
2733           1.5707963267948966 },
2734 };
2735 const double toler093 = 2.5000000000000020e-13;
2736
2737 // Test data for k=0.0000000000000000, nu=0.29999999999999999.
2738 // max(|f - f_GSL|): 2.2204460492503131e-16
2739 // max(|f - f_GSL| / |f_GSL|): 2.2972291118632678e-16
2740 const testcase_ellint_3<double>
2741 data094[10] =
2742 {
2743   { 0.0000000000000000, 0.0000000000000000, 0.29999999999999999,
2744           0.0000000000000000 },
2745   { 0.17400735186871724, 0.0000000000000000, 0.29999999999999999,
2746           0.17453292519943295 },
2747   { 0.34500091027020219, 0.0000000000000000, 0.29999999999999999,
2748           0.34906585039886590 },
2749   { 0.51060069523901530, 0.0000000000000000, 0.29999999999999999,
2750           0.52359877559829882 },
2751   { 0.66944393961375448, 0.0000000000000000, 0.29999999999999999,
2752           0.69813170079773179 },
2753   { 0.82123776744538157, 0.0000000000000000, 0.29999999999999999,
2754           0.87266462599716477 },
2755   { 0.96657579245516501, 0.0000000000000000, 0.29999999999999999,
2756           1.0471975511965976 },
2757   { 1.1066703663542414, 0.0000000000000000, 0.29999999999999999,
2758           1.2217304763960306 },
2759   { 1.2431094251944901, 0.0000000000000000, 0.29999999999999999,
2760           1.3962634015954636 },
2761   { 1.3776795151134889, 0.0000000000000000, 0.29999999999999999,
2762           1.5707963267948966 },
2763 };
2764 const double toler094 = 2.5000000000000020e-13;
2765
2766 // Test data for k=0.0000000000000000, nu=0.40000000000000002.
2767 // max(|f - f_GSL|): 2.2204460492503131e-16
2768 // max(|f - f_GSL| / |f_GSL|): 2.3524218164111537e-16
2769 const testcase_ellint_3<double>
2770 data095[10] =
2771 {
2772   { 0.0000000000000000, 0.0000000000000000, 0.40000000000000002,
2773           0.0000000000000000 },
2774   { 0.17383341868035862, 0.0000000000000000, 0.40000000000000002,
2775           0.17453292519943295 },
2776   { 0.34368286022299821, 0.0000000000000000, 0.40000000000000002,
2777           0.34906585039886590 },
2778   { 0.50651268947499395, 0.0000000000000000, 0.40000000000000002,
2779           0.52359877559829882 },
2780   { 0.66074441806097539, 0.0000000000000000, 0.40000000000000002,
2781           0.69813170079773179 },
2782   { 0.80622931670113474, 0.0000000000000000, 0.40000000000000002,
2783           0.87266462599716477 },
2784   { 0.94389791565435210, 0.0000000000000000, 0.40000000000000002,
2785           1.0471975511965976 },
2786   { 1.0753503387899728, 0.0000000000000000, 0.40000000000000002,
2787           1.2217304763960306 },
2788   { 1.2025374759127518, 0.0000000000000000, 0.40000000000000002,
2789           1.3962634015954636 },
2790   { 1.3275651989026320, 0.0000000000000000, 0.40000000000000002,
2791           1.5707963267948966 },
2792 };
2793 const double toler095 = 2.5000000000000020e-13;
2794
2795 // Test data for k=0.0000000000000000, nu=0.50000000000000000.
2796 // max(|f - f_GSL|): 3.3306690738754696e-16
2797 // max(|f - f_GSL| / |f_GSL|): 3.6090167266677240e-16
2798 const testcase_ellint_3<double>
2799 data096[10] =
2800 {
2801   { 0.0000000000000000, 0.0000000000000000, 0.50000000000000000,
2802           0.0000000000000000 },
2803   { 0.17366010776037044, 0.0000000000000000, 0.50000000000000000,
2804           0.17453292519943295 },
2805   { 0.34238253799539309, 0.0000000000000000, 0.50000000000000000,
2806           0.34906585039886590 },
2807   { 0.50253707775976397, 0.0000000000000000, 0.50000000000000000,
2808           0.52359877559829882 },
2809   { 0.65242145347295766, 0.0000000000000000, 0.50000000000000000,
2810           0.69813170079773179 },
2811   { 0.79210420018698058, 0.0000000000000000, 0.50000000000000000,
2812           0.87266462599716477 },
2813   { 0.92287437995632171, 0.0000000000000000, 0.50000000000000000,
2814           1.0471975511965976 },
2815   { 1.0466900550798659, 0.0000000000000000, 0.50000000000000000,
2816           1.2217304763960306 },
2817   { 1.1658007366618623, 0.0000000000000000, 0.50000000000000000,
2818           1.3962634015954636 },
2819   { 1.2825498301618641, 0.0000000000000000, 0.50000000000000000,
2820           1.5707963267948966 },
2821 };
2822 const double toler096 = 2.5000000000000020e-13;
2823
2824 // Test data for k=0.0000000000000000, nu=0.59999999999999998.
2825 // max(|f - f_GSL|): 2.2204460492503131e-16
2826 // max(|f - f_GSL| / |f_GSL|): 2.4581288258006758e-16
2827 const testcase_ellint_3<double>
2828 data097[10] =
2829 {
2830   { 0.0000000000000000, 0.0000000000000000, 0.59999999999999998,
2831           0.0000000000000000 },
2832   { 0.17348741514884700, 0.0000000000000000, 0.59999999999999998,
2833           0.17453292519943295 },
2834   { 0.34109952405241289, 0.0000000000000000, 0.59999999999999998,
2835           0.34906585039886590 },
2836   { 0.49866850781226285, 0.0000000000000000, 0.59999999999999998,
2837           0.52359877559829882 },
2838   { 0.64444732407062499, 0.0000000000000000, 0.59999999999999998,
2839           0.69813170079773179 },
2840   { 0.77877564686544720, 0.0000000000000000, 0.59999999999999998,
2841           0.87266462599716477 },
2842   { 0.90330743691883475, 0.0000000000000000, 0.59999999999999998,
2843           1.0471975511965976 },
2844   { 1.0203257987604104, 0.0000000000000000, 0.59999999999999998,
2845           1.2217304763960306 },
2846   { 1.1323247918768629, 0.0000000000000000, 0.59999999999999998,
2847           1.3962634015954636 },
2848   { 1.2418235332245127, 0.0000000000000000, 0.59999999999999998,
2849           1.5707963267948966 },
2850 };
2851 const double toler097 = 2.5000000000000020e-13;
2852
2853 // Test data for k=0.0000000000000000, nu=0.69999999999999996.
2854 // max(|f - f_GSL|): 2.2204460492503131e-16
2855 // max(|f - f_GSL| / |f_GSL|): 2.5088894797856263e-16
2856 const testcase_ellint_3<double>
2857 data098[10] =
2858 {
2859   { 0.0000000000000000, 0.0000000000000000, 0.69999999999999996,
2860           0.0000000000000000 },
2861   { 0.17331533692234474, 0.0000000000000000, 0.69999999999999996,
2862           0.17453292519943295 },
2863   { 0.33983341309265935, 0.0000000000000000, 0.69999999999999996,
2864           0.34906585039886590 },
2865   { 0.49490198805931979, 0.0000000000000000, 0.69999999999999996,
2866           0.52359877559829882 },
2867   { 0.63679715525145297, 0.0000000000000000, 0.69999999999999996,
2868           0.69813170079773179 },
2869   { 0.76616861049481944, 0.0000000000000000, 0.69999999999999996,
2870           0.87266462599716477 },
2871   { 0.88503143209004198, 0.0000000000000000, 0.69999999999999996,
2872           1.0471975511965976 },
2873   { 0.99596060249112173, 0.0000000000000000, 0.69999999999999996,
2874           1.2217304763960306 },
2875   { 1.1016495050260424, 0.0000000000000000, 0.69999999999999996,
2876           1.3962634015954636 },
2877   { 1.2047457872617382, 0.0000000000000000, 0.69999999999999996,
2878           1.5707963267948966 },
2879 };
2880 const double toler098 = 2.5000000000000020e-13;
2881
2882 // Test data for k=0.0000000000000000, nu=0.80000000000000004.
2883 // max(|f - f_GSL|): 3.3306690738754696e-16
2884 // max(|f - f_GSL| / |f_GSL|): 3.8375904358197891e-16
2885 const testcase_ellint_3<double>
2886 data099[10] =
2887 {
2888   { 0.0000000000000000, 0.0000000000000000, 0.80000000000000004,
2889           0.0000000000000000 },
2890   { 0.17314386919344210, 0.0000000000000000, 0.80000000000000004,
2891           0.17453292519943295 },
2892   { 0.33858381342073240, 0.0000000000000000, 0.80000000000000004,
2893           0.34906585039886590 },
2894   { 0.49123285640844727, 0.0000000000000000, 0.80000000000000004,
2895           0.52359877559829882 },
2896   { 0.62944854858904509, 0.0000000000000000, 0.80000000000000004,
2897           0.69813170079773179 },
2898   { 0.75421778305499343, 0.0000000000000000, 0.80000000000000004,
2899           0.87266462599716477 },
2900   { 0.86790634112156617, 0.0000000000000000, 0.80000000000000004,
2901           1.0471975511965976 },
2902   { 0.97334918087427558, 0.0000000000000000, 0.80000000000000004,
2903           1.2217304763960306 },
2904   { 1.0734012615283985, 0.0000000000000000, 0.80000000000000004,
2905           1.3962634015954636 },
2906   { 1.1708024551734544, 0.0000000000000000, 0.80000000000000004,
2907           1.5707963267948966 },
2908 };
2909 const double toler099 = 2.5000000000000020e-13;
2910
2911 // Test data for k=0.0000000000000000, nu=0.90000000000000002.
2912 // max(|f - f_GSL|): 1.1102230246251565e-16
2913 // max(|f - f_GSL| / |f_GSL|): 1.7838310376154469e-16
2914 const testcase_ellint_3<double>
2915 data100[10] =
2916 {
2917   { 0.0000000000000000, 0.0000000000000000, 0.90000000000000002,
2918           0.0000000000000000 },
2919   { 0.17297300811030597, 0.0000000000000000, 0.90000000000000002,
2920           0.17453292519943295 },
2921   { 0.33735034635360817, 0.0000000000000000, 0.90000000000000002,
2922           0.34906585039886590 },
2923   { 0.48765675230233130, 0.0000000000000000, 0.90000000000000002,
2924           0.52359877559829882 },
2925   { 0.62238126886123568, 0.0000000000000000, 0.90000000000000002,
2926           0.69813170079773179 },
2927   { 0.74286600807269243, 0.0000000000000000, 0.90000000000000002,
2928           0.87266462599716477 },
2929   { 0.85181283909264949, 0.0000000000000000, 0.90000000000000002,
2930           1.0471975511965976 },
2931   { 0.95228683995371133, 0.0000000000000000, 0.90000000000000002,
2932           1.2217304763960306 },
2933   { 1.0472730487412552, 0.0000000000000000, 0.90000000000000002,
2934           1.3962634015954636 },
2935   { 1.1395754288497419, 0.0000000000000000, 0.90000000000000002,
2936           1.5707963267948966 },
2937 };
2938 const double toler100 = 2.5000000000000020e-13;
2939
2940 // Test data for k=0.10000000000000009, nu=0.0000000000000000.
2941 // max(|f - f_GSL|): 4.4408920985006262e-16
2942 // max(|f - f_GSL| / |f_GSL|): 3.1735566504509650e-16
2943 const testcase_ellint_3<double>
2944 data101[10] =
2945 {
2946   { 0.0000000000000000, 0.10000000000000009, 0.0000000000000000,
2947           0.0000000000000000 },
2948   { 0.17454173353063659, 0.10000000000000009, 0.0000000000000000,
2949           0.17453292519943295 },
2950   { 0.34913506721468091, 0.10000000000000009, 0.0000000000000000,
2951           0.34906585039886590 },
2952   { 0.52382550016538942, 0.10000000000000009, 0.0000000000000000,
2953           0.52359877559829882 },
2954   { 0.69864700854177020, 0.10000000000000009, 0.0000000000000000,
2955           0.69813170079773179 },
2956   { 0.87361792586964870, 0.10000000000000009, 0.0000000000000000,
2957           0.87266462599716477 },
2958   { 1.0487386319621683, 0.10000000000000009, 0.0000000000000000,
2959           1.0471975511965976 },
2960   { 1.2239913752078757, 0.10000000000000009, 0.0000000000000000,
2961           1.2217304763960306 },
2962   { 1.3993423113684049, 0.10000000000000009, 0.0000000000000000,
2963           1.3962634015954636 },
2964   { 1.5747455615173562, 0.10000000000000009, 0.0000000000000000,
2965           1.5707963267948966 },
2966 };
2967 const double toler101 = 2.5000000000000020e-13;
2968
2969 // Test data for k=0.10000000000000009, nu=0.10000000000000001.
2970 // max(|f - f_GSL|): 4.4408920985006262e-16
2971 // max(|f - f_GSL| / |f_GSL|): 3.3097339877269682e-16
2972 const testcase_ellint_3<double>
2973 data102[10] =
2974 {
2975   { 0.0000000000000000, 0.10000000000000009, 0.10000000000000001,
2976           0.0000000000000000 },
2977   { 0.17436589347616613, 0.10000000000000009, 0.10000000000000001,
2978           0.17453292519943295 },
2979   { 0.34776067871237359, 0.10000000000000009, 0.10000000000000001,
2980           0.34906585039886590 },
2981   { 0.51936064354727796, 0.10000000000000009, 0.10000000000000001,
2982           0.52359877559829882 },
2983   { 0.68860303749364349, 0.10000000000000009, 0.10000000000000001,
2984           0.69813170079773179 },
2985   { 0.85524561882332051, 0.10000000000000009, 0.10000000000000001,
2986           0.87266462599716477 },
2987   { 1.0193708301908335, 0.10000000000000009, 0.10000000000000001,
2988           1.0471975511965976 },
2989   { 1.1813474067123044, 0.10000000000000009, 0.10000000000000001,
2990           1.2217304763960306 },
2991   { 1.3417670770424983, 0.10000000000000009, 0.10000000000000001,
2992           1.3962634015954636 },
2993   { 1.5013711111199950, 0.10000000000000009, 0.10000000000000001,
2994           1.5707963267948966 },
2995 };
2996 const double toler102 = 2.5000000000000020e-13;
2997
2998 // Test data for k=0.10000000000000009, nu=0.20000000000000001.
2999 // max(|f - f_GSL|): 4.4408920985006262e-16
3000 // max(|f - f_GSL| / |f_GSL|): 3.4399947764827574e-16
3001 const testcase_ellint_3<double>
3002 data103[10] =
3003 {
3004   { 0.0000000000000000, 0.10000000000000009, 0.20000000000000001,
3005           0.0000000000000000 },
3006   { 0.17419068786141340, 0.10000000000000009, 0.20000000000000001,
3007           0.17453292519943295 },
3008   { 0.34640537686230133, 0.10000000000000009, 0.20000000000000001,
3009           0.34906585039886590 },
3010   { 0.51502689171753946, 0.10000000000000009, 0.20000000000000001,
3011           0.52359877559829882 },
3012   { 0.67904147863672715, 0.10000000000000009, 0.20000000000000001,
3013           0.69813170079773179 },
3014   { 0.83811885126105179, 0.10000000000000009, 0.20000000000000001,
3015           0.87266462599716477 },
3016   { 0.99255278555742787, 0.10000000000000009, 0.20000000000000001,
3017           1.0471975511965976 },
3018   { 1.1431260546194930, 0.10000000000000009, 0.20000000000000001,
3019           1.2217304763960306 },
3020   { 1.2909589656532101, 0.10000000000000009, 0.20000000000000001,
3021           1.3962634015954636 },
3022   { 1.4373749386463430, 0.10000000000000009, 0.20000000000000001,
3023           1.5707963267948966 },
3024 };
3025 const double toler103 = 2.5000000000000020e-13;
3026
3027 // Test data for k=0.10000000000000009, nu=0.29999999999999999.
3028 // max(|f - f_GSL|): 4.4408920985006262e-16
3029 // max(|f - f_GSL| / |f_GSL|): 3.5650492137236872e-16
3030 const testcase_ellint_3<double>
3031 data104[10] =
3032 {
3033   { 0.0000000000000000, 0.10000000000000009, 0.29999999999999999,
3034           0.0000000000000000 },
3035   { 0.17401611261390104, 0.10000000000000009, 0.29999999999999999,
3036           0.17453292519943295 },
3037   { 0.34506869507511773, 0.10000000000000009, 0.29999999999999999,
3038           0.34906585039886590 },
3039   { 0.51081757604259859, 0.10000000000000009, 0.29999999999999999,
3040           0.52359877559829882 },
3041   { 0.66992297597712303, 0.10000000000000009, 0.29999999999999999,
3042           0.69813170079773179 },
3043   { 0.82209722856174228, 0.10000000000000009, 0.29999999999999999,
3044           0.87266462599716477 },
3045   { 0.96792430487669590, 0.10000000000000009, 0.29999999999999999,
3046           1.0471975511965976 },
3047   { 1.1085964108954092, 0.10000000000000009, 0.29999999999999999,
3048           1.2217304763960306 },
3049   { 1.2456748370836999, 0.10000000000000009, 0.29999999999999999,
3050           1.3962634015954636 },
3051   { 1.3809159606704959, 0.10000000000000009, 0.29999999999999999,
3052           1.5707963267948966 },
3053 };
3054 const double toler104 = 2.5000000000000020e-13;
3055
3056 // Test data for k=0.10000000000000009, nu=0.40000000000000002.
3057 // max(|f - f_GSL|): 4.4408920985006262e-16
3058 // max(|f - f_GSL| / |f_GSL|): 3.6854758534459740e-16
3059 const testcase_ellint_3<double>
3060 data105[10] =
3061 {
3062   { 0.0000000000000000, 0.10000000000000009, 0.40000000000000002,
3063           0.0000000000000000 },
3064   { 0.17384216369897931, 0.10000000000000009, 0.40000000000000002,
3065           0.17453292519943295 },
3066   { 0.34375018311376787, 0.10000000000000009, 0.40000000000000002,
3067           0.34906585039886590 },
3068   { 0.50672650758380455, 0.10000000000000009, 0.40000000000000002,
3069           0.52359877559829882 },
3070   { 0.66121264213337616, 0.10000000000000009, 0.40000000000000002,
3071           0.69813170079773179 },
3072   { 0.80706202005774441, 0.10000000000000009, 0.40000000000000002,
3073           0.87266462599716477 },
3074   { 0.94519376138245870, 0.10000000000000009, 0.40000000000000002,
3075           1.0471975511965976 },
3076   { 1.0771880300759584, 0.10000000000000009, 0.40000000000000002,
3077           1.2217304763960306 },
3078   { 1.2049711557188272, 0.10000000000000009, 0.40000000000000002,
3079           1.3962634015954636 },
3080   { 1.3306223265207477, 0.10000000000000009, 0.40000000000000002,
3081           1.5707963267948966 },
3082 };
3083 const double toler105 = 2.5000000000000020e-13;
3084
3085 // Test data for k=0.10000000000000009, nu=0.50000000000000000.
3086 // max(|f - f_GSL|): 4.4408920985006262e-16
3087 // max(|f - f_GSL| / |f_GSL|): 3.8017534281650347e-16
3088 const testcase_ellint_3<double>
3089 data106[10] =
3090 {
3091   { 0.0000000000000000, 0.10000000000000009, 0.50000000000000000,
3092           0.0000000000000000 },
3093   { 0.17366883711936548, 0.10000000000000009, 0.50000000000000000,
3094           0.17453292519943295 },
3095   { 0.34244940634881882, 0.10000000000000009, 0.50000000000000000,
3096           0.34906585039886590 },
3097   { 0.50274793281634367, 0.10000000000000009, 0.50000000000000000,
3098           0.52359877559829882 },
3099   { 0.65287941633275082, 0.10000000000000009, 0.50000000000000000,
3100           0.69813170079773179 },
3101   { 0.79291198790315398, 0.10000000000000009, 0.50000000000000000,
3102           0.87266462599716477 },
3103   { 0.92412201537880323, 0.10000000000000009, 0.50000000000000000,
3104           1.0471975511965976 },
3105   { 1.0484480076799372, 0.10000000000000009, 0.50000000000000000,
3106           1.2217304763960306 },
3107   { 1.1681168130475206, 0.10000000000000009, 0.50000000000000000,
3108           1.3962634015954636 },
3109   { 1.2854480708580160, 0.10000000000000009, 0.50000000000000000,
3110           1.5707963267948966 },
3111 };
3112 const double toler106 = 2.5000000000000020e-13;
3113
3114 // Test data for k=0.10000000000000009, nu=0.59999999999999998.
3115 // max(|f - f_GSL|): 4.4408920985006262e-16
3116 // max(|f - f_GSL| / |f_GSL|): 3.9142834151672032e-16
3117 const testcase_ellint_3<double>
3118 data107[10] =
3119 {
3120   { 0.0000000000000000, 0.10000000000000009, 0.59999999999999998,
3121           0.0000000000000000 },
3122   { 0.17349612891469013, 0.10000000000000009, 0.59999999999999998,
3123           0.17453292519943295 },
3124   { 0.34116594505539444, 0.10000000000000009, 0.59999999999999998,
3125           0.34906585039886590 },
3126   { 0.49887649430466674, 0.10000000000000009, 0.59999999999999998,
3127           0.52359877559829882 },
3128   { 0.64489553282165146, 0.10000000000000009, 0.59999999999999998,
3129           0.69813170079773179 },
3130   { 0.77956016553782437, 0.10000000000000009, 0.59999999999999998,
3131           0.87266462599716477 },
3132   { 0.90451074530096287, 0.10000000000000009, 0.59999999999999998,
3133           1.0471975511965976 },
3134   { 1.0220113666961632, 0.10000000000000009, 0.59999999999999998,
3135           1.2217304763960306 },
3136   { 1.1345351441065563, 0.10000000000000009, 0.59999999999999998,
3137           1.3962634015954636 },
3138   { 1.2445798942989255, 0.10000000000000009, 0.59999999999999998,
3139           1.5707963267948966 },
3140 };
3141 const double toler107 = 2.5000000000000020e-13;
3142
3143 // Test data for k=0.10000000000000009, nu=0.69999999999999996.
3144 // max(|f - f_GSL|): 6.6613381477509392e-16
3145 // max(|f - f_GSL| / |f_GSL|): 5.5172091551439012e-16
3146 const testcase_ellint_3<double>
3147 data108[10] =
3148 {
3149   { 0.0000000000000000, 0.10000000000000009, 0.69999999999999996,
3150           0.0000000000000000 },
3151   { 0.17332403516105047, 0.10000000000000009, 0.69999999999999996,
3152           0.17453292519943295 },
3153   { 0.33989939374896883, 0.10000000000000009, 0.69999999999999996,
3154           0.34906585039886590 },
3155   { 0.49510719568614070, 0.10000000000000009, 0.69999999999999996,
3156           0.52359877559829882 },
3157   { 0.63723607776354974, 0.10000000000000009, 0.69999999999999996,
3158           0.69813170079773179 },
3159   { 0.76693133887935327, 0.10000000000000009, 0.69999999999999996,
3160           0.87266462599716477 },
3161   { 0.88619382078823805, 0.10000000000000009, 0.69999999999999996,
3162           1.0471975511965976 },
3163   { 0.99758012018676490, 0.10000000000000009, 0.69999999999999996,
3164           1.2217304763960306 },
3165   { 1.1037642270814410, 0.10000000000000009, 0.69999999999999996,
3166           1.3962634015954636 },
3167   { 1.2073745911083185, 0.10000000000000009, 0.69999999999999996,
3168           1.5707963267948966 },
3169 };
3170 const double toler108 = 2.5000000000000020e-13;
3171
3172 // Test data for k=0.10000000000000009, nu=0.80000000000000004.
3173 // max(|f - f_GSL|): 4.4408920985006262e-16
3174 // max(|f - f_GSL| / |f_GSL|): 4.1294144515772258e-16
3175 const testcase_ellint_3<double>
3176 data109[10] =
3177 {
3178   { 0.0000000000000000, 0.10000000000000009, 0.80000000000000004,
3179           0.0000000000000000 },
3180   { 0.17315255197057014, 0.10000000000000009, 0.80000000000000004,
3181           0.17453292519943295 },
3182   { 0.33864936055747991, 0.10000000000000009, 0.80000000000000004,
3183           0.34906585039886590 },
3184   { 0.49143537041117613, 0.10000000000000009, 0.80000000000000004,
3185           0.52359877559829882 },
3186   { 0.62987861760047492, 0.10000000000000009, 0.80000000000000004,
3187           0.69813170079773179 },
3188   { 0.75496005490917517, 0.10000000000000009, 0.80000000000000004,
3189           0.87266462599716477 },
3190   { 0.86903081862701881, 0.10000000000000009, 0.80000000000000004,
3191           1.0471975511965976 },
3192   { 0.97490814820725591, 0.10000000000000009, 0.80000000000000004,
3193           1.2217304763960306 },
3194   { 1.0754290107171083, 0.10000000000000009, 0.80000000000000004,
3195           1.3962634015954636 },
3196   { 1.1733158866987732, 0.10000000000000009, 0.80000000000000004,
3197           1.5707963267948966 },
3198 };
3199 const double toler109 = 2.5000000000000020e-13;
3200
3201 // Test data for k=0.10000000000000009, nu=0.90000000000000002.
3202 // max(|f - f_GSL|): 4.4408920985006262e-16
3203 // max(|f - f_GSL| / |f_GSL|): 4.2325599449457852e-16
3204 const testcase_ellint_3<double>
3205 data110[10] =
3206 {
3207   { 0.0000000000000000, 0.10000000000000009, 0.90000000000000002,
3208           0.0000000000000000 },
3209   { 0.17298167549096563, 0.10000000000000009, 0.90000000000000002,
3210           0.17453292519943295 },
3211   { 0.33741546662741589, 0.10000000000000009, 0.90000000000000002,
3212           0.34906585039886590 },
3213   { 0.48785665376856868, 0.10000000000000009, 0.90000000000000002,
3214           0.52359877559829882 },
3215   { 0.62280288554518959, 0.10000000000000009, 0.90000000000000002,
3216           0.69813170079773179 },
3217   { 0.74358903115455188, 0.10000000000000009, 0.90000000000000002,
3218           0.87266462599716477 },
3219   { 0.85290207679298335, 0.10000000000000009, 0.90000000000000002,
3220           1.0471975511965976 },
3221   { 0.95379006645397379, 0.10000000000000009, 0.90000000000000002,
3222           1.2217304763960306 },
3223   { 1.0492213119872327, 0.10000000000000009, 0.90000000000000002,
3224           1.3962634015954636 },
3225   { 1.1419839485283374, 0.10000000000000009, 0.90000000000000002,
3226           1.5707963267948966 },
3227 };
3228 const double toler110 = 2.5000000000000020e-13;
3229
3230 // Test data for k=0.19999999999999996, nu=0.0000000000000000.
3231 // max(|f - f_GSL|): 4.4408920985006262e-16
3232 // max(|f - f_GSL| / |f_GSL|): 4.2156475739151676e-16
3233 const testcase_ellint_3<double>
3234 data111[10] =
3235 {
3236   { 0.0000000000000000, 0.19999999999999996, 0.0000000000000000,
3237           0.0000000000000000 },
3238   { 0.17456817290292809, 0.19999999999999996, 0.0000000000000000,
3239           0.17453292519943295 },
3240   { 0.34934315932086801, 0.19999999999999996, 0.0000000000000000,
3241           0.34906585039886590 },
3242   { 0.52450880529443988, 0.19999999999999996, 0.0000000000000000,
3243           0.52359877559829882 },
3244   { 0.70020491009844876, 0.19999999999999996, 0.0000000000000000,
3245           0.69813170079773179 },
3246   { 0.87651006649967955, 0.19999999999999996, 0.0000000000000000,
3247           0.87266462599716477 },
3248   { 1.0534305870298994, 0.19999999999999996, 0.0000000000000000,
3249           1.0471975511965976 },
3250   { 1.2308975521670784, 0.19999999999999996, 0.0000000000000000,
3251           1.2217304763960306 },
3252   { 1.4087733584990738, 0.19999999999999996, 0.0000000000000000,
3253           1.3962634015954636 },
3254   { 1.5868678474541660, 0.19999999999999996, 0.0000000000000000,
3255           1.5707963267948966 },
3256 };
3257 const double toler111 = 2.5000000000000020e-13;
3258
3259 // Test data for k=0.19999999999999996, nu=0.10000000000000001.
3260 // max(|f - f_GSL|): 4.4408920985006262e-16
3261 // max(|f - f_GSL| / |f_GSL|): 4.3374593253183472e-16
3262 const testcase_ellint_3<double>
3263 data112[10] =
3264 {
3265   { 0.0000000000000000, 0.19999999999999996, 0.10000000000000001,
3266           0.0000000000000000 },
3267   { 0.17439228502691748, 0.19999999999999996, 0.10000000000000001,
3268           0.17453292519943295 },
3269   { 0.34796731137565740, 0.19999999999999996, 0.10000000000000001,
3270           0.34906585039886590 },
3271   { 0.52003370294544848, 0.19999999999999996, 0.10000000000000001,
3272           0.52359877559829882 },
3273   { 0.69012222258631462, 0.19999999999999996, 0.10000000000000001,
3274           0.69813170079773179 },
3275   { 0.85803491465566772, 0.19999999999999996, 0.10000000000000001,
3276           0.87266462599716477 },
3277   { 1.0238463961099364, 0.19999999999999996, 0.10000000000000001,
3278           1.0471975511965976 },
3279   { 1.1878691059202153, 0.19999999999999996, 0.10000000000000001,
3280           1.2217304763960306 },
3281   { 1.3505985031831940, 0.19999999999999996, 0.10000000000000001,
3282           1.3962634015954636 },
3283   { 1.5126513474261087, 0.19999999999999996, 0.10000000000000001,
3284           1.5707963267948966 },
3285 };
3286 const double toler112 = 2.5000000000000020e-13;
3287
3288 // Test data for k=0.19999999999999996, nu=0.20000000000000001.
3289 // max(|f - f_GSL|): 4.4408920985006262e-16
3290 // max(|f - f_GSL| / |f_GSL|): 4.4549984059502760e-16
3291 const testcase_ellint_3<double>
3292 data113[10] =
3293 {
3294   { 0.0000000000000000, 0.19999999999999996, 0.20000000000000001,
3295           0.0000000000000000 },
3296   { 0.17421703179583747, 0.19999999999999996, 0.20000000000000001,
3297           0.17453292519943295 },
3298   { 0.34661057411998791, 0.19999999999999996, 0.20000000000000001,
3299           0.34906585039886590 },
3300   { 0.51569006052647393, 0.19999999999999996, 0.20000000000000001,
3301           0.52359877559829882 },
3302   { 0.68052412821107244, 0.19999999999999996, 0.20000000000000001,
3303           0.69813170079773179 },
3304   { 0.84081341263313825, 0.19999999999999996, 0.20000000000000001,
3305           0.87266462599716477 },
3306   { 0.99683359988842890, 0.19999999999999996, 0.20000000000000001,
3307           1.0471975511965976 },
3308   { 1.1493086715118852, 0.19999999999999996, 0.20000000000000001,
3309           1.2217304763960306 },
3310   { 1.2992699693957541, 0.19999999999999996, 0.20000000000000001,
3311           1.3962634015954636 },
3312   { 1.4479323932249564, 0.19999999999999996, 0.20000000000000001,
3313           1.5707963267948966 },
3314 };
3315 const double toler113 = 2.5000000000000020e-13;
3316
3317 // Test data for k=0.19999999999999996, nu=0.29999999999999999.
3318 // max(|f - f_GSL|): 6.6613381477509392e-16
3319 // max(|f - f_GSL| / |f_GSL|): 5.3140668101543467e-16
3320 const testcase_ellint_3<double>
3321 data114[10] =
3322 {
3323   { 0.0000000000000000, 0.19999999999999996, 0.29999999999999999,
3324           0.0000000000000000 },
3325   { 0.17404240913577704, 0.19999999999999996, 0.29999999999999999,
3326           0.17453292519943295 },
3327   { 0.34527248032587193, 0.19999999999999996, 0.29999999999999999,
3328           0.34906585039886590 },
3329   { 0.51147118981668416, 0.19999999999999996, 0.29999999999999999,
3330           0.52359877559829882 },
3331   { 0.67137107867777601, 0.19999999999999996, 0.29999999999999999,
3332           0.69813170079773179 },
3333   { 0.82470418188668893, 0.19999999999999996, 0.29999999999999999,
3334           0.87266462599716477 },
3335   { 0.97202873223594299, 0.19999999999999996, 0.29999999999999999,
3336           1.0471975511965976 },
3337   { 1.1144773569375266, 0.19999999999999996, 0.29999999999999999,
3338           1.2217304763960306 },
3339   { 1.2535292433701000, 0.19999999999999996, 0.29999999999999999,
3340           1.3962634015954636 },
3341   { 1.3908453514752477, 0.19999999999999996, 0.29999999999999999,
3342           1.5707963267948966 },
3343 };
3344 const double toler114 = 2.5000000000000020e-13;
3345
3346 // Test data for k=0.19999999999999996, nu=0.40000000000000002.
3347 // max(|f - f_GSL|): 4.4408920985006262e-16
3348 // max(|f - f_GSL| / |f_GSL|): 4.6788709752760483e-16
3349 const testcase_ellint_3<double>
3350 data115[10] =
3351 {
3352   { 0.0000000000000000, 0.19999999999999996, 0.40000000000000002,
3353           0.0000000000000000 },
3354   { 0.17386841301066674, 0.19999999999999996, 0.40000000000000002,
3355           0.17453292519943295 },
3356   { 0.34395257914113253, 0.19999999999999996, 0.40000000000000002,
3357           0.34906585039886590 },
3358   { 0.50737088376869466, 0.19999999999999996, 0.40000000000000002,
3359           0.52359877559829882 },
3360   { 0.66262801717277631, 0.19999999999999996, 0.40000000000000002,
3361           0.69813170079773179 },
3362   { 0.80958766645079094, 0.19999999999999996, 0.40000000000000002,
3363           0.87266462599716477 },
3364   { 0.94913754236162040, 0.19999999999999996, 0.40000000000000002,
3365           1.0471975511965976 },
3366   { 1.0827985514222997, 0.19999999999999996, 0.40000000000000002,
3367           1.2217304763960306 },
3368   { 1.2124212429050478, 0.19999999999999996, 0.40000000000000002,
3369           1.3962634015954636 },
3370   { 1.3400002519661005, 0.19999999999999996, 0.40000000000000002,
3371           1.5707963267948966 },
3372 };
3373 const double toler115 = 2.5000000000000020e-13;
3374
3375 // Test data for k=0.19999999999999996, nu=0.50000000000000000.
3376 // max(|f - f_GSL|): 4.4408920985006262e-16
3377 // max(|f - f_GSL| / |f_GSL|): 3.7788201301356829e-16
3378 const testcase_ellint_3<double>
3379 data116[10] =
3380 {
3381   { 0.0000000000000000, 0.19999999999999996, 0.50000000000000000,
3382           0.0000000000000000 },
3383   { 0.17369503942181799, 0.19999999999999996, 0.50000000000000000,
3384           0.17453292519943295 },
3385   { 0.34265043534362660, 0.19999999999999996, 0.50000000000000000,
3386           0.34906585039886590 },
3387   { 0.50338337208655415, 0.19999999999999996, 0.50000000000000000,
3388           0.52359877559829882 },
3389   { 0.65426373297163609, 0.19999999999999996, 0.50000000000000000,
3390           0.69813170079773179 },
3391   { 0.79536193036145808, 0.19999999999999996, 0.50000000000000000,
3392           0.87266462599716477 },
3393   { 0.92791875910061605, 0.19999999999999996, 0.50000000000000000,
3394           1.0471975511965976 },
3395   { 1.0538145052725829, 0.19999999999999996, 0.50000000000000000,
3396           1.2217304763960306 },
3397   { 1.1752060022875899, 0.19999999999999996, 0.50000000000000000,
3398           1.3962634015954636 },
3399   { 1.2943374404397372, 0.19999999999999996, 0.50000000000000000,
3400           1.5707963267948966 },
3401 };
3402 const double toler116 = 2.5000000000000020e-13;
3403
3404 // Test data for k=0.19999999999999996, nu=0.59999999999999998.
3405 // max(|f - f_GSL|): 4.4408920985006262e-16
3406 // max(|f - f_GSL| / |f_GSL|): 4.8899223779598256e-16
3407 const testcase_ellint_3<double>
3408 data117[10] =
3409 {
3410   { 0.0000000000000000, 0.19999999999999996, 0.59999999999999998,
3411           0.0000000000000000 },
3412   { 0.17352228440746925, 0.19999999999999996, 0.59999999999999998,
3413           0.17453292519943295 },
3414   { 0.34136562863713626, 0.19999999999999996, 0.59999999999999998,
3415           0.34906585039886590 },
3416   { 0.49950328177638481, 0.19999999999999996, 0.59999999999999998,
3417           0.52359877559829882 },
3418   { 0.64625032705690799, 0.19999999999999996, 0.59999999999999998,
3419           0.69813170079773179 },
3420   { 0.78193941198403083, 0.19999999999999996, 0.59999999999999998,
3421           0.87266462599716477 },
3422   { 0.90817230934317128, 0.19999999999999996, 0.59999999999999998,
3423           1.0471975511965976 },
3424   { 1.0271563751276462, 0.19999999999999996, 0.59999999999999998,
3425           1.2217304763960306 },
3426   { 1.1412999379040518, 0.19999999999999996, 0.59999999999999998,
3427           1.3962634015954636 },
3428   { 1.2530330675914556, 0.19999999999999996, 0.59999999999999998,
3429           1.5707963267948966 },
3430 };
3431 const double toler117 = 2.5000000000000020e-13;
3432
3433 // Test data for k=0.19999999999999996, nu=0.69999999999999996.
3434 // max(|f - f_GSL|): 6.6613381477509392e-16
3435 // max(|f - f_GSL| / |f_GSL|): 5.9999318361775115e-16
3436 const testcase_ellint_3<double>
3437 data118[10] =
3438 {
3439   { 0.0000000000000000, 0.19999999999999996, 0.69999999999999996,
3440           0.0000000000000000 },
3441   { 0.17335014404233895, 0.19999999999999996, 0.69999999999999996,
3442           0.17453292519943295 },
3443   { 0.34009775298617811, 0.19999999999999996, 0.69999999999999996,
3444           0.34906585039886590 },
3445   { 0.49572560201923810, 0.19999999999999996, 0.69999999999999996,
3446           0.52359877559829882 },
3447   { 0.63856276669886503, 0.19999999999999996, 0.69999999999999996,
3448           0.69813170079773179 },
3449   { 0.76924438644867565, 0.19999999999999996, 0.69999999999999996,
3450           0.87266462599716477 },
3451   { 0.88973060843856466, 0.19999999999999996, 0.69999999999999996,
3452           1.0471975511965976 },
3453   { 1.0025230471636377, 0.19999999999999996, 0.69999999999999996,
3454           1.2217304763960306 },
3455   { 1.1102356376093103, 0.19999999999999996, 0.69999999999999996,
3456           1.3962634015954636 },
3457   { 1.2154356555075863, 0.19999999999999996, 0.69999999999999996,
3458           1.5707963267948966 },
3459 };
3460 const double toler118 = 2.5000000000000020e-13;
3461
3462 // Test data for k=0.19999999999999996, nu=0.80000000000000004.
3463 // max(|f - f_GSL|): 4.4408920985006262e-16
3464 // max(|f - f_GSL| / |f_GSL|): 5.0901276230707249e-16
3465 const testcase_ellint_3<double>
3466 data119[10] =
3467 {
3468   { 0.0000000000000000, 0.19999999999999996, 0.80000000000000004,
3469           0.0000000000000000 },
3470   { 0.17317861443718538, 0.19999999999999996, 0.80000000000000004,
3471           0.17453292519943295 },
3472   { 0.33884641598718701, 0.19999999999999996, 0.80000000000000004,
3473           0.34906585039886590 },
3474   { 0.49204565281259494, 0.19999999999999996, 0.80000000000000004,
3475           0.52359877559829882 },
3476   { 0.63117851188220320, 0.19999999999999996, 0.80000000000000004,
3477           0.69813170079773179 },
3478   { 0.75721095949544170, 0.19999999999999996, 0.80000000000000004,
3479           0.87266462599716477 },
3480   { 0.87245201443919118, 0.19999999999999996, 0.80000000000000004,
3481           1.0471975511965976 },
3482   { 0.97966584238831089, 0.19999999999999996, 0.80000000000000004,
3483           1.2217304763960306 },
3484   { 1.0816336325174360, 0.19999999999999996, 0.80000000000000004,
3485           1.3962634015954636 },
3486   { 1.1810223448909909, 0.19999999999999996, 0.80000000000000004,
3487           1.5707963267948966 },
3488 };
3489 const double toler119 = 2.5000000000000020e-13;
3490
3491 // Test data for k=0.19999999999999996, nu=0.90000000000000002.
3492 // max(|f - f_GSL|): 6.6613381477509392e-16
3493 // max(|f - f_GSL| / |f_GSL|): 6.4833128442756722e-16
3494 const testcase_ellint_3<double>
3495 data120[10] =
3496 {
3497   { 0.0000000000000000, 0.19999999999999996, 0.90000000000000002,
3498           0.0000000000000000 },
3499   { 0.17300769173837277, 0.19999999999999996, 0.90000000000000002,
3500           0.17453292519943295 },
3501   { 0.33761123827372508, 0.19999999999999996, 0.90000000000000002,
3502           0.34906585039886590 },
3503   { 0.48845905690769426, 0.19999999999999996, 0.90000000000000002,
3504           0.52359877559829882 },
3505   { 0.62407720017324952, 0.19999999999999996, 0.90000000000000002,
3506           0.69813170079773179 },
3507   { 0.74578146525124289, 0.19999999999999996, 0.90000000000000002,
3508           0.87266462599716477 },
3509   { 0.85621583540073076, 0.19999999999999996, 0.90000000000000002,
3510           1.0471975511965976 },
3511   { 0.95837725988001199, 0.19999999999999996, 0.90000000000000002,
3512           1.2217304763960306 },
3513   { 1.0551821412633928, 0.19999999999999996, 0.90000000000000002,
3514           1.3962634015954636 },
3515   { 1.1493679916141861, 0.19999999999999996, 0.90000000000000002,
3516           1.5707963267948966 },
3517 };
3518 const double toler120 = 2.5000000000000020e-13;
3519
3520 // Test data for k=0.30000000000000004, nu=0.0000000000000000.
3521 // max(|f - f_GSL|): 8.8817841970012523e-16
3522 // max(|f - f_GSL| / |f_GSL|): 6.3361874537309281e-16
3523 const testcase_ellint_3<double>
3524 data121[10] =
3525 {
3526   { 0.0000000000000000, 0.30000000000000004, 0.0000000000000000,
3527           0.0000000000000000 },
3528   { 0.17461228653000099, 0.30000000000000004, 0.0000000000000000,
3529           0.17453292519943295 },
3530   { 0.34969146102798415, 0.30000000000000004, 0.0000000000000000,
3531           0.34906585039886590 },
3532   { 0.52565822873726320, 0.30000000000000004, 0.0000000000000000,
3533           0.52359877559829882 },
3534   { 0.70284226512408532, 0.30000000000000004, 0.0000000000000000,
3535           0.69813170079773179 },
3536   { 0.88144139195111182, 0.30000000000000004, 0.0000000000000000,
3537           0.87266462599716477 },
3538   { 1.0614897067260520, 0.30000000000000004, 0.0000000000000000,
3539           1.0471975511965976 },
3540   { 1.2428416824174218, 0.30000000000000004, 0.0000000000000000,
3541           1.2217304763960306 },
3542   { 1.4251795877015927, 0.30000000000000004, 0.0000000000000000,
3543           1.3962634015954636 },
3544   { 1.6080486199305128, 0.30000000000000004, 0.0000000000000000,
3545           1.5707963267948966 },
3546 };
3547 const double toler121 = 2.5000000000000020e-13;
3548
3549 // Test data for k=0.30000000000000004, nu=0.10000000000000001.
3550 // max(|f - f_GSL|): 8.8817841970012523e-16
3551 // max(|f - f_GSL| / |f_GSL|): 6.3908043711907203e-16
3552 const testcase_ellint_3<double>
3553 data122[10] =
3554 {
3555   { 0.0000000000000000, 0.30000000000000004, 0.10000000000000001,
3556           0.0000000000000000 },
3557   { 0.17443631884814376, 0.30000000000000004, 0.10000000000000001,
3558           0.17453292519943295 },
3559   { 0.34831316835124926, 0.30000000000000004, 0.10000000000000001,
3560           0.34906585039886590 },
3561   { 0.52116586276523857, 0.30000000000000004, 0.10000000000000001,
3562           0.52359877559829882 },
3563   { 0.69269385837910036, 0.30000000000000004, 0.10000000000000001,
3564           0.69813170079773179 },
3565   { 0.86279023163070856, 0.30000000000000004, 0.10000000000000001,
3566           0.87266462599716477 },
3567   { 1.0315321461438263, 0.30000000000000004, 0.10000000000000001,
3568           1.0471975511965976 },
3569   { 1.1991449111869024, 0.30000000000000004, 0.10000000000000001,
3570           1.2217304763960306 },
3571   { 1.3659561780923213, 0.30000000000000004, 0.10000000000000001,
3572           1.3962634015954636 },
3573   { 1.5323534693557528, 0.30000000000000004, 0.10000000000000001,
3574           1.5707963267948966 },
3575 };
3576 const double toler122 = 2.5000000000000020e-13;
3577
3578 // Test data for k=0.30000000000000004, nu=0.20000000000000001.
3579 // max(|f - f_GSL|): 8.8817841970012523e-16
3580 // max(|f - f_GSL| / |f_GSL|): 6.4447238179454079e-16
3581 const testcase_ellint_3<double>
3582 data123[10] =
3583 {
3584   { 0.0000000000000000, 0.30000000000000004, 0.20000000000000001,
3585           0.0000000000000000 },
3586   { 0.17426098615372088, 0.30000000000000004, 0.20000000000000001,
3587           0.17453292519943295 },
3588   { 0.34695402664689923, 0.30000000000000004, 0.20000000000000001,
3589           0.34906585039886590 },
3590   { 0.51680555567038933, 0.30000000000000004, 0.20000000000000001,
3591           0.52359877559829882 },
3592   { 0.68303375225260210, 0.30000000000000004, 0.20000000000000001,
3593           0.69813170079773179 },
3594   { 0.84540662891295026, 0.30000000000000004, 0.20000000000000001,
3595           0.87266462599716477 },
3596   { 1.0041834051646927, 0.30000000000000004, 0.20000000000000001,
3597           1.0471975511965976 },
3598   { 1.1599952702345711, 0.30000000000000004, 0.20000000000000001,
3599           1.2217304763960306 },
3600   { 1.3137179520499165, 0.30000000000000004, 0.20000000000000001,
3601           1.3962634015954636 },
3602   { 1.4663658145259877, 0.30000000000000004, 0.20000000000000001,
3603           1.5707963267948966 },
3604 };
3605 const double toler123 = 2.5000000000000020e-13;
3606
3607 // Test data for k=0.30000000000000004, nu=0.29999999999999999.
3608 // max(|f - f_GSL|): 8.8817841970012523e-16
3609 // max(|f - f_GSL| / |f_GSL|): 6.4979715256503266e-16
3610 const testcase_ellint_3<double>
3611 data124[10] =
3612 {
3613   { 0.0000000000000000, 0.30000000000000004, 0.29999999999999999,
3614           0.0000000000000000 },
3615   { 0.17408628437042842, 0.30000000000000004, 0.29999999999999999,
3616           0.17453292519943295 },
3617   { 0.34561356761638401, 0.30000000000000004, 0.29999999999999999,
3618           0.34906585039886590 },
3619   { 0.51257058617875850, 0.30000000000000004, 0.29999999999999999,
3620           0.52359877559829882 },
3621   { 0.67382207124602878, 0.30000000000000004, 0.29999999999999999,
3622           0.69813170079773179 },
3623   { 0.82914751587825131, 0.30000000000000004, 0.29999999999999999,
3624           0.87266462599716477 },
3625   { 0.97907434814374938, 0.30000000000000004, 0.29999999999999999,
3626           1.0471975511965976 },
3627   { 1.1246399297351584, 0.30000000000000004, 0.29999999999999999,
3628           1.2217304763960306 },
3629   { 1.2671793970398149, 0.30000000000000004, 0.29999999999999999,
3630           1.3962634015954636 },
3631   { 1.4081767433479091, 0.30000000000000004, 0.29999999999999999,
3632           1.5707963267948966 },
3633 };
3634 const double toler124 = 2.5000000000000020e-13;
3635
3636 // Test data for k=0.30000000000000004, nu=0.40000000000000002.
3637 // max(|f - f_GSL|): 8.8817841970012523e-16
3638 // max(|f - f_GSL| / |f_GSL|): 6.5505716921759864e-16
3639 const testcase_ellint_3<double>
3640 data125[10] =
3641 {
3642   { 0.0000000000000000, 0.30000000000000004, 0.40000000000000002,
3643           0.0000000000000000 },
3644   { 0.17391220945982727, 0.30000000000000004, 0.40000000000000002,
3645           0.17453292519943295 },
3646   { 0.34429133937639689, 0.30000000000000004, 0.40000000000000002,
3647           0.34906585039886590 },
3648   { 0.50845471668581632, 0.30000000000000004, 0.40000000000000002,
3649           0.52359877559829882 },
3650   { 0.66502347027873854, 0.30000000000000004, 0.40000000000000002,
3651           0.69813170079773179 },
3652   { 0.81389191978012254, 0.30000000000000004, 0.40000000000000002,
3653           0.87266462599716477 },
3654   { 0.95590618002140570, 0.30000000000000004, 0.40000000000000002,
3655           1.0471975511965976 },
3656   { 1.0924915195213121, 0.30000000000000004, 0.40000000000000002,
3657           1.2217304763960306 },
3658   { 1.2253651604038061, 0.30000000000000004, 0.40000000000000002,
3659           1.3962634015954636 },
3660   { 1.3563643538969763, 0.30000000000000004, 0.40000000000000002,
3661           1.5707963267948966 },
3662 };
3663 const double toler125 = 2.5000000000000020e-13;
3664
3665 // Test data for k=0.30000000000000004, nu=0.50000000000000000.
3666 // max(|f - f_GSL|): 8.8817841970012523e-16
3667 // max(|f - f_GSL| / |f_GSL|): 6.7807908859023716e-16
3668 const testcase_ellint_3<double>
3669 data126[10] =
3670 {
3671   { 0.0000000000000000, 0.30000000000000004, 0.50000000000000000,
3672           0.0000000000000000 },
3673   { 0.17373875742088232, 0.30000000000000004, 0.50000000000000000,
3674           0.17453292519943295 },
3675   { 0.34298690571124157, 0.30000000000000004, 0.50000000000000000,
3676           0.34906585039886590 },
3677   { 0.50445214859646936, 0.30000000000000004, 0.50000000000000000,
3678           0.52359877559829882 },
3679   { 0.65660648352418516, 0.30000000000000004, 0.50000000000000000,
3680           0.69813170079773179 },
3681   { 0.79953670639287289, 0.30000000000000004, 0.50000000000000000,
3682           0.87266462599716477 },
3683   { 0.93443393926588536, 0.30000000000000004, 0.50000000000000000,
3684           1.0471975511965976 },
3685   { 1.0630838369016911, 0.30000000000000004, 0.50000000000000000,
3686           1.2217304763960306 },
3687   { 1.1875197325653029, 0.30000000000000004, 0.50000000000000000,
3688           1.3962634015954636 },
3689   { 1.3098448759814962, 0.30000000000000004, 0.50000000000000000,
3690           1.5707963267948966 },
3691 };
3692 const double toler126 = 2.5000000000000020e-13;
3693
3694 // Test data for k=0.30000000000000004, nu=0.59999999999999998.
3695 // max(|f - f_GSL|): 8.8817841970012523e-16
3696 // max(|f - f_GSL| / |f_GSL|): 7.0057999499931649e-16
3697 const testcase_ellint_3<double>
3698 data127[10] =
3699 {
3700   { 0.0000000000000000, 0.30000000000000004, 0.59999999999999998,
3701           0.0000000000000000 },
3702   { 0.17356592428950823, 0.30000000000000004, 0.59999999999999998,
3703           0.17453292519943295 },
3704   { 0.34169984536697379, 0.30000000000000004, 0.59999999999999998,
3705           0.34906585039886590 },
3706   { 0.50055748266498457, 0.30000000000000004, 0.59999999999999998,
3707           0.52359877559829882 },
3708   { 0.64854298527106768, 0.30000000000000004, 0.59999999999999998,
3709           0.69813170079773179 },
3710   { 0.78599329284207431, 0.30000000000000004, 0.59999999999999998,
3711           0.87266462599716477 },
3712   { 0.91445452089128199, 0.30000000000000004, 0.59999999999999998,
3713           1.0471975511965976 },
3714   { 1.0360412952290587, 0.30000000000000004, 0.59999999999999998,
3715           1.2217304763960306 },
3716   { 1.1530473919778641, 0.30000000000000004, 0.59999999999999998,
3717           1.3962634015954636 },
3718   { 1.2677758800420669, 0.30000000000000004, 0.59999999999999998,
3719           1.5707963267948966 },
3720 };
3721 const double toler127 = 2.5000000000000020e-13;
3722
3723 // Test data for k=0.30000000000000004, nu=0.69999999999999996.
3724 // max(|f - f_GSL|): 8.8817841970012523e-16
3725 // max(|f - f_GSL| / |f_GSL|): 7.2239502844122443e-16
3726 const testcase_ellint_3<double>
3727 data128[10] =
3728 {
3729   { 0.0000000000000000, 0.30000000000000004, 0.69999999999999996,
3730           0.0000000000000000 },
3731   { 0.17339370613812224, 0.30000000000000004, 0.69999999999999996,
3732           0.17453292519943295 },
3733   { 0.34042975138455933, 0.30000000000000004, 0.69999999999999996,
3734           0.34906585039886590 },
3735   { 0.49676568368075985, 0.30000000000000004, 0.69999999999999996,
3736           0.52359877559829882 },
3737   { 0.64080774055753720, 0.30000000000000004, 0.69999999999999996,
3738           0.69813170079773179 },
3739   { 0.77318507779667278, 0.30000000000000004, 0.69999999999999996,
3740           0.87266462599716477 },
3741   { 0.89579782346548609, 0.30000000000000004, 0.69999999999999996,
3742           1.0471975511965976 },
3743   { 1.0110573286052202, 0.30000000000000004, 0.69999999999999996,
3744           1.2217304763960306 },
3745   { 1.1214710972949635, 0.30000000000000004, 0.69999999999999996,
3746           1.3962634015954636 },
3747   { 1.2294913236274982, 0.30000000000000004, 0.69999999999999996,
3748           1.5707963267948966 },
3749 };
3750 const double toler128 = 2.5000000000000020e-13;
3751
3752 // Test data for k=0.30000000000000004, nu=0.80000000000000004.
3753 // max(|f - f_GSL|): 8.8817841970012523e-16
3754 // max(|f - f_GSL| / |f_GSL|): 7.4358357000101250e-16
3755 const testcase_ellint_3<double>
3756 data129[10] =
3757 {
3758   { 0.0000000000000000, 0.30000000000000004, 0.80000000000000004,
3759           0.0000000000000000 },
3760   { 0.17322209907520358, 0.30000000000000004, 0.80000000000000004,
3761           0.17453292519943295 },
3762   { 0.33917623046949996, 0.30000000000000004, 0.80000000000000004,
3763           0.34906585039886590 },
3764   { 0.49307204894329176, 0.30000000000000004, 0.80000000000000004,
3765           0.52359877559829882 },
3766   { 0.63337802830291734, 0.30000000000000004, 0.80000000000000004,
3767           0.69813170079773179 },
3768   { 0.76104540997689407, 0.30000000000000004, 0.80000000000000004,
3769           0.87266462599716477 },
3770   { 0.87832009635450714, 0.30000000000000004, 0.80000000000000004,
3771           1.0471975511965976 },
3772   { 0.98787879723171790, 0.30000000000000004, 0.80000000000000004,
3773           1.2217304763960306 },
3774   { 1.0924036340069339, 0.30000000000000004, 0.80000000000000004,
3775           1.3962634015954636 },
3776   { 1.1944567571590048, 0.30000000000000004, 0.80000000000000004,
3777           1.5707963267948966 },
3778 };
3779 const double toler129 = 2.5000000000000020e-13;
3780
3781 // Test data for k=0.30000000000000004, nu=0.90000000000000002.
3782 // max(|f - f_GSL|): 8.8817841970012523e-16
3783 // max(|f - f_GSL| / |f_GSL|): 7.6419688299804087e-16
3784 const testcase_ellint_3<double>
3785 data130[10] =
3786 {
3787   { 0.0000000000000000, 0.30000000000000004, 0.90000000000000002,
3788           0.0000000000000000 },
3789   { 0.17305109924485945, 0.30000000000000004, 0.90000000000000002,
3790           0.17453292519943295 },
3791   { 0.33793890239556984, 0.30000000000000004, 0.90000000000000002,
3792           0.34906585039886590 },
3793   { 0.48947218005089738, 0.30000000000000004, 0.90000000000000002,
3794           0.52359877559829882 },
3795   { 0.62623332340775151, 0.30000000000000004, 0.90000000000000002,
3796           0.69813170079773179 },
3797   { 0.74951596581511148, 0.30000000000000004, 0.90000000000000002,
3798           0.87266462599716477 },
3799   { 0.86189886597755994, 0.30000000000000004, 0.90000000000000002,
3800           1.0471975511965976 },
3801   { 0.96629451153092005, 0.30000000000000004, 0.90000000000000002,
3802           1.2217304763960306 },
3803   { 1.0655269133492682, 0.30000000000000004, 0.90000000000000002,
3804           1.3962634015954636 },
3805   { 1.1622376896064914, 0.30000000000000004, 0.90000000000000002,
3806           1.5707963267948966 },
3807 };
3808 const double toler130 = 2.5000000000000020e-13;
3809
3810 // Test data for k=0.39999999999999991, nu=0.0000000000000000.
3811 // max(|f - f_GSL|): 8.8817841970012523e-16
3812 // max(|f - f_GSL| / |f_GSL|): 5.4157225142938039e-16
3813 const testcase_ellint_3<double>
3814 data131[10] =
3815 {
3816   { 0.0000000000000000, 0.39999999999999991, 0.0000000000000000,
3817           0.0000000000000000 },
3818   { 0.17467414669441528, 0.39999999999999991, 0.0000000000000000,
3819           0.17453292519943295 },
3820   { 0.35018222772483443, 0.39999999999999991, 0.0000000000000000,
3821           0.34906585039886590 },
3822   { 0.52729015917508737, 0.39999999999999991, 0.0000000000000000,
3823           0.52359877559829882 },
3824   { 0.70662374407341244, 0.39999999999999991, 0.0000000000000000,
3825           0.69813170079773179 },
3826   { 0.88859210497602170, 0.39999999999999991, 0.0000000000000000,
3827           0.87266462599716477 },
3828   { 1.0733136290471379, 0.39999999999999991, 0.0000000000000000,
3829           1.0471975511965976 },
3830   { 1.2605612170157061, 0.39999999999999991, 0.0000000000000000,
3831           1.2217304763960306 },
3832   { 1.4497513956433439, 0.39999999999999991, 0.0000000000000000,
3833           1.3962634015954636 },
3834   { 1.6399998658645112, 0.39999999999999991, 0.0000000000000000,
3835           1.5707963267948966 },
3836 };
3837 const double toler131 = 2.5000000000000020e-13;
3838
3839 // Test data for k=0.39999999999999991, nu=0.10000000000000001.
3840 // max(|f - f_GSL|): 8.8817841970012523e-16
3841 // max(|f - f_GSL| / |f_GSL|): 5.6859551010103832e-16
3842 const testcase_ellint_3<double>
3843 data132[10] =
3844 {
3845   { 0.0000000000000000, 0.39999999999999991, 0.10000000000000001,
3846           0.0000000000000000 },
3847   { 0.17449806706684670, 0.39999999999999991, 0.10000000000000001,
3848           0.17453292519943295 },
3849   { 0.34880048623856075, 0.39999999999999991, 0.10000000000000001,
3850           0.34906585039886590 },
3851   { 0.52277322065757392, 0.39999999999999991, 0.10000000000000001,
3852           0.52359877559829882 },
3853   { 0.69638072056918365, 0.39999999999999991, 0.10000000000000001,
3854           0.69813170079773179 },
3855   { 0.86968426619831540, 0.39999999999999991, 0.10000000000000001,
3856           0.87266462599716477 },
3857   { 1.0428044206578095, 0.39999999999999991, 0.10000000000000001,
3858           1.0471975511965976 },
3859   { 1.2158651158274378, 0.39999999999999991, 0.10000000000000001,
3860           1.2217304763960306 },
3861   { 1.3889447129893324, 0.39999999999999991, 0.10000000000000001,
3862           1.3962634015954636 },
3863   { 1.5620566886683604, 0.39999999999999991, 0.10000000000000001,
3864           1.5707963267948966 },
3865 };
3866 const double toler132 = 2.5000000000000020e-13;
3867
3868 // Test data for k=0.39999999999999991, nu=0.20000000000000001.
3869 // max(|f - f_GSL|): 8.8817841970012523e-16
3870 // max(|f - f_GSL| / |f_GSL|): 5.9444065952225719e-16
3871 const testcase_ellint_3<double>
3872 data133[10] =
3873 {
3874   { 0.0000000000000000, 0.39999999999999991, 0.20000000000000001,
3875           0.0000000000000000 },
3876   { 0.17432262290723397, 0.39999999999999991, 0.20000000000000001,
3877           0.17453292519943295 },
3878   { 0.34743795258968596, 0.39999999999999991, 0.20000000000000001,
3879           0.34906585039886590 },
3880   { 0.51838919472805112, 0.39999999999999991, 0.20000000000000001,
3881           0.52359877559829882 },
3882   { 0.68663134739057907, 0.39999999999999991, 0.20000000000000001,
3883           0.69813170079773179 },
3884   { 0.85206432981833979, 0.39999999999999991, 0.20000000000000001,
3885           0.87266462599716477 },
3886   { 1.0149595349004430, 0.39999999999999991, 0.20000000000000001,
3887           1.0471975511965976 },
3888   { 1.1758349405464676, 0.39999999999999991, 0.20000000000000001,
3889           1.2217304763960306 },
3890   { 1.3353337673882637, 0.39999999999999991, 0.20000000000000001,
3891           1.3962634015954636 },
3892   { 1.4941414344266770, 0.39999999999999991, 0.20000000000000001,
3893           1.5707963267948966 },
3894 };
3895 const double toler133 = 2.5000000000000020e-13;
3896
3897 // Test data for k=0.39999999999999991, nu=0.29999999999999999.
3898 // max(|f - f_GSL|): 1.1102230246251565e-15
3899 // max(|f - f_GSL| / |f_GSL|): 7.7406350888907249e-16
3900 const testcase_ellint_3<double>
3901 data134[10] =
3902 {
3903   { 0.0000000000000000, 0.39999999999999991, 0.29999999999999999,
3904           0.0000000000000000 },
3905   { 0.17414781013591540, 0.39999999999999991, 0.29999999999999999,
3906           0.17453292519943295 },
3907   { 0.34609415696777285, 0.39999999999999991, 0.29999999999999999,
3908           0.34906585039886590 },
3909   { 0.51413131295862535, 0.39999999999999991, 0.29999999999999999,
3910           0.52359877559829882 },
3911   { 0.67733527622935630, 0.39999999999999991, 0.29999999999999999,
3912           0.69813170079773179 },
3913   { 0.83558675182733266, 0.39999999999999991, 0.29999999999999999,
3914           0.87266462599716477 },
3915   { 0.98940140808865906, 0.39999999999999991, 0.29999999999999999,
3916           1.0471975511965976 },
3917   { 1.1396968797728058, 0.39999999999999991, 0.29999999999999999,
3918           1.2217304763960306 },
3919   { 1.2875920037865090, 0.39999999999999991, 0.29999999999999999,
3920           1.3962634015954636 },
3921   { 1.4342789859950078, 0.39999999999999991, 0.29999999999999999,
3922           1.5707963267948966 },
3923 };
3924 const double toler134 = 2.5000000000000020e-13;
3925
3926 // Test data for k=0.39999999999999991, nu=0.40000000000000002.
3927 // max(|f - f_GSL|): 8.8817841970012523e-16
3928 // max(|f - f_GSL| / |f_GSL|): 6.4314214811441816e-16
3929 const testcase_ellint_3<double>
3930 data135[10] =
3931 {
3932   { 0.0000000000000000, 0.39999999999999991, 0.40000000000000002,
3933           0.0000000000000000 },
3934   { 0.17397362471112707, 0.39999999999999991, 0.40000000000000002,
3935           0.17453292519943295 },
3936   { 0.34476864603333196, 0.39999999999999991, 0.40000000000000002,
3937           0.34906585039886590 },
3938   { 0.50999329415379346, 0.39999999999999991, 0.40000000000000002,
3939           0.52359877559829882 },
3940   { 0.66845674551396006, 0.39999999999999991, 0.40000000000000002,
3941           0.69813170079773179 },
3942   { 0.82012848346231748, 0.39999999999999991, 0.40000000000000002,
3943           0.87266462599716477 },
3944   { 0.96582449258349057, 0.39999999999999991, 0.40000000000000002,
3945           1.0471975511965976 },
3946   { 1.1068473749476286, 0.39999999999999991, 0.40000000000000002,
3947           1.2217304763960306 },
3948   { 1.2447132729159989, 0.39999999999999991, 0.40000000000000002,
3949           1.3962634015954636 },
3950   { 1.3809986210732901, 0.39999999999999991, 0.40000000000000002,
3951           1.5707963267948966 },
3952 };
3953 const double toler135 = 2.5000000000000020e-13;
3954
3955 // Test data for k=0.39999999999999991, nu=0.50000000000000000.
3956 // max(|f - f_GSL|): 8.8817841970012523e-16
3957 // max(|f - f_GSL| / |f_GSL|): 6.6621057007519435e-16
3958 const testcase_ellint_3<double>
3959 data136[10] =
3960 {
3961   { 0.0000000000000000, 0.39999999999999991, 0.50000000000000000,
3962           0.0000000000000000 },
3963   { 0.17380006262854136, 0.39999999999999991, 0.50000000000000000,
3964           0.17453292519943295 },
3965   { 0.34346098216756610, 0.39999999999999991, 0.50000000000000000,
3966           0.34906585039886590 },
3967   { 0.50596929935059420, 0.39999999999999991, 0.50000000000000000,
3968           0.52359877559829882 },
3969   { 0.65996392089131251, 0.39999999999999991, 0.50000000000000000,
3970           0.69813170079773179 },
3971   { 0.80558463511364786, 0.39999999999999991, 0.50000000000000000,
3972           0.87266462599716477 },
3973   { 0.94397834522857704, 0.39999999999999991, 0.50000000000000000,
3974           1.0471975511965976 },
3975   { 1.0768075114108115, 0.39999999999999991, 0.50000000000000000,
3976           1.2217304763960306 },
3977   { 1.2059184624251333, 0.39999999999999991, 0.50000000000000000,
3978           1.3962634015954636 },
3979   { 1.3331797176377398, 0.39999999999999991, 0.50000000000000000,
3980           1.5707963267948966 },
3981 };
3982 const double toler136 = 2.5000000000000020e-13;
3983
3984 // Test data for k=0.39999999999999991, nu=0.59999999999999998.
3985 // max(|f - f_GSL|): 8.8817841970012523e-16
3986 // max(|f - f_GSL| / |f_GSL|): 6.8853630717730749e-16
3987 const testcase_ellint_3<double>
3988 data137[10] =
3989 {
3990   { 0.0000000000000000, 0.39999999999999991, 0.59999999999999998,
3991           0.0000000000000000 },
3992   { 0.17362711992081245, 0.39999999999999991, 0.59999999999999998,
3993           0.17453292519943295 },
3994   { 0.34217074276403953, 0.39999999999999991, 0.59999999999999998,
3995           0.34906585039886590 },
3996   { 0.50205389185761606, 0.39999999999999991, 0.59999999999999998,
3997           0.52359877559829882 },
3998   { 0.65182834920372734, 0.39999999999999991, 0.59999999999999998,
3999           0.69813170079773179 },
4000   { 0.79186512820565136, 0.39999999999999991, 0.59999999999999998,
4001           0.87266462599716477 },
4002   { 0.92365535916287134, 0.39999999999999991, 0.59999999999999998,
4003           1.0471975511965976 },
4004   { 1.0491915663957907, 0.39999999999999991, 0.59999999999999998,
4005           1.2217304763960306 },
4006   { 1.1705934291745106, 0.39999999999999991, 0.59999999999999998,
4007           1.3962634015954636 },
4008   { 1.2899514672527024, 0.39999999999999991, 0.59999999999999998,
4009           1.5707963267948966 },
4010 };
4011 const double toler137 = 2.5000000000000020e-13;
4012
4013 // Test data for k=0.39999999999999991, nu=0.69999999999999996.
4014 // max(|f - f_GSL|): 8.8817841970012523e-16
4015 // max(|f - f_GSL| / |f_GSL|): 7.1018730557776469e-16
4016 const testcase_ellint_3<double>
4017 data138[10] =
4018 {
4019   { 0.0000000000000000, 0.39999999999999991, 0.69999999999999996,
4020           0.0000000000000000 },
4021   { 0.17345479265712868, 0.39999999999999991, 0.69999999999999996,
4022           0.17453292519943295 },
4023   { 0.34089751955950354, 0.39999999999999991, 0.69999999999999996,
4024           0.34906585039886590 },
4025   { 0.49824200167361332, 0.39999999999999991, 0.69999999999999996,
4026           0.52359877559829882 },
4027   { 0.64402450341199402, 0.39999999999999991, 0.69999999999999996,
4028           0.69813170079773179 },
4029   { 0.77889207804122873, 0.39999999999999991, 0.69999999999999996,
4030           0.87266462599716477 },
4031   { 0.90468169720957992, 0.39999999999999991, 0.69999999999999996,
4032           1.0471975511965976 },
4033   { 1.0236847823692916, 0.39999999999999991, 0.69999999999999996,
4034           1.2217304763960306 },
4035   { 1.1382465247425166, 0.39999999999999991, 0.69999999999999996,
4036           1.3962634015954636 },
4037   { 1.2506255923253344, 0.39999999999999991, 0.69999999999999996,
4038           1.5707963267948966 },
4039 };
4040 const double toler138 = 2.5000000000000020e-13;
4041
4042 // Test data for k=0.39999999999999991, nu=0.80000000000000004.
4043 // max(|f - f_GSL|): 8.8817841970012523e-16
4044 // max(|f - f_GSL| / |f_GSL|): 7.3122171115555478e-16
4045 const testcase_ellint_3<double>
4046 data139[10] =
4047 {
4048   { 0.0000000000000000, 0.39999999999999991, 0.80000000000000004,
4049           0.0000000000000000 },
4050   { 0.17328307694277154, 0.39999999999999991, 0.80000000000000004,
4051           0.17453292519943295 },
4052   { 0.33964091800132007, 0.39999999999999991, 0.80000000000000004,
4053           0.34906585039886590 },
4054   { 0.49452889372467440, 0.39999999999999991, 0.80000000000000004,
4055           0.52359877559829882 },
4056   { 0.63652940095937316, 0.39999999999999991, 0.80000000000000004,
4057           0.69813170079773179 },
4058   { 0.76659772511159097, 0.39999999999999991, 0.80000000000000004,
4059           0.87266462599716477 },
4060   { 0.88691047977338111, 0.39999999999999991, 0.80000000000000004,
4061           1.0471975511965976 },
4062   { 1.0000273200611638, 0.39999999999999991, 0.80000000000000004,
4063           1.2217304763960306 },
4064   { 1.1084787902188009, 0.39999999999999991, 0.80000000000000004,
4065           1.3962634015954636 },
4066   { 1.2146499565727209, 0.39999999999999991, 0.80000000000000004,
4067           1.5707963267948966 },
4068 };
4069 const double toler139 = 2.5000000000000020e-13;
4070
4071 // Test data for k=0.39999999999999991, nu=0.90000000000000002.
4072 // max(|f - f_GSL|): 8.8817841970012523e-16
4073 // max(|f - f_GSL| / |f_GSL|): 7.5168974431077345e-16
4074 const testcase_ellint_3<double>
4075 data140[10] =
4076 {
4077   { 0.0000000000000000, 0.39999999999999991, 0.90000000000000002,
4078           0.0000000000000000 },
4079   { 0.17311196891868127, 0.39999999999999991, 0.90000000000000002,
4080           0.17453292519943295 },
4081   { 0.33840055664911906, 0.39999999999999991, 0.90000000000000002,
4082           0.34906585039886590 },
4083   { 0.49091013944075329, 0.39999999999999991, 0.90000000000000002,
4084           0.52359877559829882 },
4085   { 0.62932228186809580, 0.39999999999999991, 0.90000000000000002,
4086           0.69813170079773179 },
4087   { 0.75492278323019801, 0.39999999999999991, 0.90000000000000002,
4088           0.87266462599716477 },
4089   { 0.87021659043854294, 0.39999999999999991, 0.90000000000000002,
4090           1.0471975511965976 },
4091   { 0.97800245228239246, 0.39999999999999991, 0.90000000000000002,
4092           1.2217304763960306 },
4093   { 1.0809625773173697, 0.39999999999999991, 0.90000000000000002,
4094           1.3962634015954636 },
4095   { 1.1815758115929846, 0.39999999999999991, 0.90000000000000002,
4096           1.5707963267948966 },
4097 };
4098 const double toler140 = 2.5000000000000020e-13;
4099
4100 // Test data for k=0.50000000000000000, nu=0.0000000000000000.
4101 // max(|f - f_GSL|): 2.2204460492503131e-16
4102 // max(|f - f_GSL| / |f_GSL|): 3.1201497220602069e-16
4103 const testcase_ellint_3<double>
4104 data141[10] =
4105 {
4106   { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000,
4107           0.0000000000000000 },
4108   { 0.17475385514035785, 0.50000000000000000, 0.0000000000000000,
4109           0.17453292519943295 },
4110   { 0.35081868470101585, 0.50000000000000000, 0.0000000000000000,
4111           0.34906585039886590 },
4112   { 0.52942862705190574, 0.50000000000000000, 0.0000000000000000,
4113           0.52359877559829882 },
4114   { 0.71164727562630314, 0.50000000000000000, 0.0000000000000000,
4115           0.69813170079773179 },
4116   { 0.89824523594227768, 0.50000000000000000, 0.0000000000000000,
4117           0.87266462599716477 },
4118   { 1.0895506700518851, 0.50000000000000000, 0.0000000000000000,
4119           1.0471975511965976 },
4120   { 1.2853005857432931, 0.50000000000000000, 0.0000000000000000,
4121           1.2217304763960306 },
4122   { 1.4845545520549484, 0.50000000000000000, 0.0000000000000000,
4123           1.3962634015954636 },
4124   { 1.6857503548125963, 0.50000000000000000, 0.0000000000000000,
4125           1.5707963267948966 },
4126 };
4127 const double toler141 = 2.5000000000000020e-13;
4128
4129 // Test data for k=0.50000000000000000, nu=0.10000000000000001.
4130 // max(|f - f_GSL|): 2.2204460492503131e-16
4131 // max(|f - f_GSL| / |f_GSL|): 3.1662857256911530e-16
4132 const testcase_ellint_3<double>
4133 data142[10] =
4134 {
4135   { 0.0000000000000000, 0.50000000000000000, 0.10000000000000001,
4136           0.0000000000000000 },
4137   { 0.17457763120814676, 0.50000000000000000, 0.10000000000000001,
4138           0.17453292519943295 },
4139   { 0.34943246340849154, 0.50000000000000000, 0.10000000000000001,
4140           0.34906585039886590 },
4141   { 0.52487937869610790, 0.50000000000000000, 0.10000000000000001,
4142           0.52359877559829882 },
4143   { 0.70127785096388384, 0.50000000000000000, 0.10000000000000001,
4144           0.69813170079773179 },
4145   { 0.87898815988624479, 0.50000000000000000, 0.10000000000000001,
4146           0.87266462599716477 },
4147   { 1.0582764576094172, 0.50000000000000000, 0.10000000000000001,
4148           1.0471975511965976 },
4149   { 1.2391936844060205, 0.50000000000000000, 0.10000000000000001,
4150           1.2217304763960306 },
4151   { 1.4214793542995841, 0.50000000000000000, 0.10000000000000001,
4152           1.3962634015954636 },
4153   { 1.6045524936084892, 0.50000000000000000, 0.10000000000000001,
4154           1.5707963267948966 },
4155 };
4156 const double toler142 = 2.5000000000000020e-13;
4157
4158 // Test data for k=0.50000000000000000, nu=0.20000000000000001.
4159 // max(|f - f_GSL|): 2.2204460492503131e-16
4160 // max(|f - f_GSL| / |f_GSL|): 3.2114786773102175e-16
4161 const testcase_ellint_3<double>
4162 data143[10] =
4163 {
4164   { 0.0000000000000000, 0.50000000000000000, 0.20000000000000001,
4165           0.0000000000000000 },
4166   { 0.17440204336345433, 0.50000000000000000, 0.20000000000000001,
4167           0.17453292519943295 },
4168   { 0.34806552388338824, 0.50000000000000000, 0.20000000000000001,
4169           0.34906585039886590 },
4170   { 0.52046416757129810, 0.50000000000000000, 0.20000000000000001,
4171           0.52359877559829882 },
4172   { 0.69140924550993865, 0.50000000000000000, 0.20000000000000001,
4173           0.69813170079773179 },
4174   { 0.86104678636125520, 0.50000000000000000, 0.20000000000000001,
4175           0.87266462599716477 },
4176   { 1.0297439459053981, 0.50000000000000000, 0.20000000000000001,
4177           1.0471975511965976 },
4178   { 1.1979214112912033, 0.50000000000000000, 0.20000000000000001,
4179           1.2217304763960306 },
4180   { 1.3659033858648930, 0.50000000000000000, 0.20000000000000001,
4181           1.3962634015954636 },
4182   { 1.5338490483665983, 0.50000000000000000, 0.20000000000000001,
4183           1.5707963267948966 },
4184 };
4185 const double toler143 = 2.5000000000000020e-13;
4186
4187 // Test data for k=0.50000000000000000, nu=0.29999999999999999.
4188 // max(|f - f_GSL|): 2.2204460492503131e-16
4189 // max(|f - f_GSL| / |f_GSL|): 3.2557837230041312e-16
4190 const testcase_ellint_3<double>
4191 data144[10] =
4192 {
4193   { 0.0000000000000000, 0.50000000000000000, 0.29999999999999999,
4194           0.0000000000000000 },
4195   { 0.17422708752228896, 0.50000000000000000, 0.29999999999999999,
4196           0.17453292519943295 },
4197   { 0.34671739434855858, 0.50000000000000000, 0.29999999999999999,
4198           0.34906585039886590 },
4199   { 0.51617616305641878, 0.50000000000000000, 0.29999999999999999,
4200           0.52359877559829882 },
4201   { 0.68200047612545167, 0.50000000000000000, 0.29999999999999999,
4202           0.69813170079773179 },
4203   { 0.84427217869498372, 0.50000000000000000, 0.29999999999999999,
4204           0.87266462599716477 },
4205   { 1.0035637821389782, 0.50000000000000000, 0.29999999999999999,
4206           1.0471975511965976 },
4207   { 1.1606800483933111, 0.50000000000000000, 0.29999999999999999,
4208           1.2217304763960306 },
4209   { 1.3164407134643459, 0.50000000000000000, 0.29999999999999999,
4210           1.3962634015954636 },
4211   { 1.4715681939859637, 0.50000000000000000, 0.29999999999999999,
4212           1.5707963267948966 },
4213 };
4214 const double toler144 = 2.5000000000000020e-13;
4215
4216 // Test data for k=0.50000000000000000, nu=0.40000000000000002.
4217 // max(|f - f_GSL|): 2.2204460492503131e-16
4218 // max(|f - f_GSL| / |f_GSL|): 3.2992508582900068e-16
4219 const testcase_ellint_3<double>
4220 data145[10] =
4221 {
4222   { 0.0000000000000000, 0.50000000000000000, 0.40000000000000002,
4223           0.0000000000000000 },
4224   { 0.17405275963859917, 0.50000000000000000, 0.40000000000000002,
4225           0.17453292519943295 },
4226   { 0.34538761957029329, 0.50000000000000000, 0.40000000000000002,
4227           0.34906585039886590 },
4228   { 0.51200902646603907, 0.50000000000000000, 0.40000000000000002,
4229           0.52359877559829882 },
4230   { 0.67301522212868792, 0.50000000000000000, 0.40000000000000002,
4231           0.69813170079773179 },
4232   { 0.82853844466313320, 0.50000000000000000, 0.40000000000000002,
4233           0.87266462599716477 },
4234   { 0.97942097862681488, 0.50000000000000000, 0.40000000000000002,
4235           1.0471975511965976 },
4236   { 1.1268429801220614, 0.50000000000000000, 0.40000000000000002,
4237           1.2217304763960306 },
4238   { 1.2720406704533922, 0.50000000000000000, 0.40000000000000002,
4239           1.3962634015954636 },
4240   { 1.4161679518465340, 0.50000000000000000, 0.40000000000000002,
4241           1.5707963267948966 },
4242 };
4243 const double toler145 = 2.5000000000000020e-13;
4244
4245 // Test data for k=0.50000000000000000, nu=0.50000000000000000.
4246 // max(|f - f_GSL|): 2.2204460492503131e-16
4247 // max(|f - f_GSL| / |f_GSL|): 3.3419255755184137e-16
4248 const testcase_ellint_3<double>
4249 data146[10] =
4250 {
4251   { 0.0000000000000000, 0.50000000000000000, 0.50000000000000000,
4252           0.0000000000000000 },
4253   { 0.17387905570381157, 0.50000000000000000, 0.50000000000000000,
4254           0.17453292519943295 },
4255   { 0.34407576010465207, 0.50000000000000000, 0.50000000000000000,
4256           0.34906585039886590 },
4257   { 0.50795686560160824, 0.50000000000000000, 0.50000000000000000,
4258           0.52359877559829882 },
4259   { 0.66442115453330164, 0.50000000000000000, 0.50000000000000000,
4260           0.69813170079773179 },
4261   { 0.81373829119355345, 0.50000000000000000, 0.50000000000000000,
4262           0.87266462599716477 },
4263   { 0.95705743313235825, 0.50000000000000000, 0.50000000000000000,
4264           1.0471975511965976 },
4265   { 1.0959131991362554, 0.50000000000000000, 0.50000000000000000,
4266           1.2217304763960306 },
4267   { 1.2318900529754597, 0.50000000000000000, 0.50000000000000000,
4268           1.3962634015954636 },
4269   { 1.3664739530045971, 0.50000000000000000, 0.50000000000000000,
4270           1.5707963267948966 },
4271 };
4272 const double toler146 = 2.5000000000000020e-13;
4273
4274 // Test data for k=0.50000000000000000, nu=0.59999999999999998.
4275 // max(|f - f_GSL|): 2.2204460492503131e-16
4276 // max(|f - f_GSL| / |f_GSL|): 3.3838494104749599e-16
4277 const testcase_ellint_3<double>
4278 data147[10] =
4279 {
4280   { 0.0000000000000000, 0.50000000000000000, 0.59999999999999998,
4281           0.0000000000000000 },
4282   { 0.17370597174637581, 0.50000000000000000, 0.59999999999999998,
4283           0.17453292519943295 },
4284   { 0.34278139158591414, 0.50000000000000000, 0.59999999999999998,
4285           0.34906585039886590 },
4286   { 0.50401419439302708, 0.50000000000000000, 0.59999999999999998,
4287           0.52359877559829882 },
4288   { 0.65618938076167210, 0.50000000000000000, 0.59999999999999998,
4289           0.69813170079773179 },
4290   { 0.79977959248855424, 0.50000000000000000, 0.59999999999999998,
4291           0.87266462599716477 },
4292   { 0.93625925190753545, 0.50000000000000000, 0.59999999999999998,
4293           1.0471975511965976 },
4294   { 1.0674905658379708, 0.50000000000000000, 0.59999999999999998,
4295           1.2217304763960306 },
4296   { 1.1953481298023050, 0.50000000000000000, 0.59999999999999998,
4297           1.3962634015954636 },
4298   { 1.3215740290190876, 0.50000000000000000, 0.59999999999999998,
4299           1.5707963267948966 },
4300 };
4301 const double toler147 = 2.5000000000000020e-13;
4302
4303 // Test data for k=0.50000000000000000, nu=0.69999999999999996.
4304 // max(|f - f_GSL|): 2.2204460492503131e-16
4305 // max(|f - f_GSL| / |f_GSL|): 3.4250604066951477e-16
4306 const testcase_ellint_3<double>
4307 data148[10] =
4308 {
4309   { 0.0000000000000000, 0.50000000000000000, 0.69999999999999996,
4310           0.0000000000000000 },
4311   { 0.17353350383131641, 0.50000000000000000, 0.69999999999999996,
4312           0.17453292519943295 },
4313   { 0.34150410405436771, 0.50000000000000000, 0.69999999999999996,
4314           0.34906585039886590 },
4315   { 0.50017589696443487, 0.50000000000000000, 0.69999999999999996,
4316           0.52359877559829882 },
4317   { 0.64829398188419951, 0.50000000000000000, 0.69999999999999996,
4318           0.69813170079773179 },
4319   { 0.78658270782402073, 0.50000000000000000, 0.69999999999999996,
4320           0.87266462599716477 },
4321   { 0.91684738336675053, 0.50000000000000000, 0.69999999999999996,
4322           1.0471975511965976 },
4323   { 1.0412486789555935, 0.50000000000000000, 0.69999999999999996,
4324           1.2217304763960306 },
4325   { 1.1619021847612001, 0.50000000000000000, 0.69999999999999996,
4326           1.3962634015954636 },
4327   { 1.2807475181182502, 0.50000000000000000, 0.69999999999999996,
4328           1.5707963267948966 },
4329 };
4330 const double toler148 = 2.5000000000000020e-13;
4331
4332 // Test data for k=0.50000000000000000, nu=0.80000000000000004.
4333 // max(|f - f_GSL|): 4.4408920985006262e-16
4334 // max(|f - f_GSL| / |f_GSL|): 3.5715240651179632e-16
4335 const testcase_ellint_3<double>
4336 data149[10] =
4337 {
4338   { 0.0000000000000000, 0.50000000000000000, 0.80000000000000004,
4339           0.0000000000000000 },
4340   { 0.17336164805979126, 0.50000000000000000, 0.80000000000000004,
4341           0.17453292519943295 },
4342   { 0.34024350132086773, 0.50000000000000000, 0.80000000000000004,
4343           0.34906585039886590 },
4344   { 0.49643719555734073, 0.50000000000000000, 0.80000000000000004,
4345           0.52359877559829882 },
4346   { 0.64071162456976150, 0.50000000000000000, 0.80000000000000004,
4347           0.69813170079773179 },
4348   { 0.77407836177211908, 0.50000000000000000, 0.80000000000000004,
4349           0.87266462599716477 },
4350   { 0.89867058251905652, 0.50000000000000000, 0.80000000000000004,
4351           1.0471975511965976 },
4352   { 1.0169181822134910, 0.50000000000000000, 0.80000000000000004,
4353           1.2217304763960306 },
4354   { 1.1311363312779448, 0.50000000000000000, 0.80000000000000004,
4355           1.3962634015954636 },
4356   { 1.2434165408189539, 0.50000000000000000, 0.80000000000000004,
4357           1.5707963267948966 },
4358 };
4359 const double toler149 = 2.5000000000000020e-13;
4360
4361 // Test data for k=0.50000000000000000, nu=0.90000000000000002.
4362 // max(|f - f_GSL|): 4.4408920985006262e-16
4363 // max(|f - f_GSL| / |f_GSL|): 4.4664649039489274e-16
4364 const testcase_ellint_3<double>
4365 data150[10] =
4366 {
4367   { 0.0000000000000000, 0.50000000000000000, 0.90000000000000002,
4368           0.0000000000000000 },
4369   { 0.17319040056865681, 0.50000000000000000, 0.90000000000000002,
4370           0.17453292519943295 },
4371   { 0.33899920036578557, 0.50000000000000000, 0.90000000000000002,
4372           0.34906585039886590 },
4373   { 0.49279362182695174, 0.50000000000000000, 0.90000000000000002,
4374           0.52359877559829882 },
4375   { 0.63342123379746151, 0.50000000000000000, 0.90000000000000002,
4376           0.69813170079773179 },
4377   { 0.76220595179550321, 0.50000000000000000, 0.90000000000000002,
4378           0.87266462599716477 },
4379   { 0.88160004743532294, 0.50000000000000000, 0.90000000000000002,
4380           1.0471975511965976 },
4381   { 0.99427448642310123, 0.50000000000000000, 0.90000000000000002,
4382           1.2217304763960306 },
4383   { 1.1027091512470095, 0.50000000000000000, 0.90000000000000002,
4384           1.3962634015954636 },
4385   { 1.2091116095504744, 0.50000000000000000, 0.90000000000000002,
4386           1.5707963267948966 },
4387 };
4388 const double toler150 = 2.5000000000000020e-13;
4389
4390 // Test data for k=0.60000000000000009, nu=0.0000000000000000.
4391 // max(|f - f_GSL|): 4.4408920985006262e-16
4392 // max(|f - f_GSL| / |f_GSL|): 3.3664899092028927e-16
4393 const testcase_ellint_3<double>
4394 data151[10] =
4395 {
4396   { 0.0000000000000000, 0.60000000000000009, 0.0000000000000000,
4397           0.0000000000000000 },
4398   { 0.17485154362988359, 0.60000000000000009, 0.0000000000000000,
4399           0.17453292519943295 },
4400   { 0.35160509865544326, 0.60000000000000009, 0.0000000000000000,
4401           0.34906585039886590 },
4402   { 0.53210652578446138, 0.60000000000000009, 0.0000000000000000,
4403           0.52359877559829882 },
4404   { 0.71805304664485659, 0.60000000000000009, 0.0000000000000000,
4405           0.69813170079773179 },
4406   { 0.91082759030195970, 0.60000000000000009, 0.0000000000000000,
4407           0.87266462599716477 },
4408   { 1.1112333229323361, 0.60000000000000009, 0.0000000000000000,
4409           1.0471975511965976 },
4410   { 1.3191461190365270, 0.60000000000000009, 0.0000000000000000,
4411           1.2217304763960306 },
4412   { 1.5332022105084775, 0.60000000000000009, 0.0000000000000000,
4413           1.3962634015954636 },
4414   { 1.7507538029157526, 0.60000000000000009, 0.0000000000000000,
4415           1.5707963267948966 },
4416 };
4417 const double toler151 = 2.5000000000000020e-13;
4418
4419 // Test data for k=0.60000000000000009, nu=0.10000000000000001.
4420 // max(|f - f_GSL|): 4.4408920985006262e-16
4421 // max(|f - f_GSL| / |f_GSL|): 3.4937942733669112e-16
4422 const testcase_ellint_3<double>
4423 data152[10] =
4424 {
4425   { 0.0000000000000000, 0.60000000000000009, 0.10000000000000001,
4426           0.0000000000000000 },
4427   { 0.17467514275022011, 0.60000000000000009, 0.10000000000000001,
4428           0.17453292519943295 },
4429   { 0.35021333086258255, 0.60000000000000009, 0.10000000000000001,
4430           0.34906585039886590 },
4431   { 0.52751664092962691, 0.60000000000000009, 0.10000000000000001,
4432           0.52359877559829882 },
4433   { 0.70752126971957874, 0.60000000000000009, 0.10000000000000001,
4434           0.69813170079773179 },
4435   { 0.89111058756112871, 0.60000000000000009, 0.10000000000000001,
4436           0.87266462599716477 },
4437   { 1.0789241202877768, 0.60000000000000009, 0.10000000000000001,
4438           1.0471975511965976 },
4439   { 1.2710800210399946, 0.60000000000000009, 0.10000000000000001,
4440           1.2217304763960306 },
4441   { 1.4669060574440276, 0.60000000000000009, 0.10000000000000001,
4442           1.3962634015954636 },
4443   { 1.6648615773343014, 0.60000000000000009, 0.10000000000000001,
4444           1.5707963267948966 },
4445 };
4446 const double toler152 = 2.5000000000000020e-13;
4447
4448 // Test data for k=0.60000000000000009, nu=0.20000000000000001.
4449 // max(|f - f_GSL|): 6.6613381477509392e-16
4450 // max(|f - f_GSL| / |f_GSL|): 4.1891472451898755e-16
4451 const testcase_ellint_3<double>
4452 data153[10] =
4453 {
4454   { 0.0000000000000000, 0.60000000000000009, 0.20000000000000001,
4455           0.0000000000000000 },
4456   { 0.17449937871800650, 0.60000000000000009, 0.20000000000000001,
4457           0.17453292519943295 },
4458   { 0.34884093647346553, 0.60000000000000009, 0.20000000000000001,
4459           0.34906585039886590 },
4460   { 0.52306221119844087, 0.60000000000000009, 0.20000000000000001,
4461           0.52359877559829882 },
4462   { 0.69749955678982223, 0.60000000000000009, 0.20000000000000001,
4463           0.69813170079773179 },
4464   { 0.87274610682416853, 0.60000000000000009, 0.20000000000000001,
4465           0.87266462599716477 },
4466   { 1.0494620540750792, 0.60000000000000009, 0.20000000000000001,
4467           1.0471975511965976 },
4468   { 1.2280847305507339, 0.60000000000000009, 0.20000000000000001,
4469           1.2217304763960306 },
4470   { 1.4085436279696888, 0.60000000000000009, 0.20000000000000001,
4471           1.3962634015954636 },
4472   { 1.5901418016279374, 0.60000000000000009, 0.20000000000000001,
4473           1.5707963267948966 },
4474 };
4475 const double toler153 = 2.5000000000000020e-13;
4476
4477 // Test data for k=0.60000000000000009, nu=0.29999999999999999.
4478 // max(|f - f_GSL|): 4.4408920985006262e-16
4479 // max(|f - f_GSL| / |f_GSL|): 3.7339932380431439e-16
4480 const testcase_ellint_3<double>
4481 data154[10] =
4482 {
4483   { 0.0000000000000000, 0.60000000000000009, 0.29999999999999999,
4484           0.0000000000000000 },
4485   { 0.17432424744393932, 0.60000000000000009, 0.29999999999999999,
4486           0.17453292519943295 },
4487   { 0.34748744127146447, 0.60000000000000009, 0.29999999999999999,
4488           0.34906585039886590 },
4489   { 0.51873632743924825, 0.60000000000000009, 0.29999999999999999,
4490           0.52359877559829882 },
4491   { 0.68794610396313116, 0.60000000000000009, 0.29999999999999999,
4492           0.69813170079773179 },
4493   { 0.85558070175468726, 0.60000000000000009, 0.29999999999999999,
4494           0.87266462599716477 },
4495   { 1.0224416343605653, 0.60000000000000009, 0.29999999999999999,
4496           1.0471975511965976 },
4497   { 1.1893144457936788, 0.60000000000000009, 0.29999999999999999,
4498           1.2217304763960306 },
4499   { 1.3566435377982575, 0.60000000000000009, 0.29999999999999999,
4500           1.3962634015954636 },
4501   { 1.5243814243493585, 0.60000000000000009, 0.29999999999999999,
4502           1.5707963267948966 },
4503 };
4504 const double toler154 = 2.5000000000000020e-13;
4505
4506 // Test data for k=0.60000000000000009, nu=0.40000000000000002.
4507 // max(|f - f_GSL|): 6.6613381477509392e-16
4508 // max(|f - f_GSL| / |f_GSL|): 4.5440898085101625e-16
4509 const testcase_ellint_3<double>
4510 data155[10] =
4511 {
4512   { 0.0000000000000000, 0.60000000000000009, 0.40000000000000002,
4513           0.0000000000000000 },
4514   { 0.17414974487670717, 0.60000000000000009, 0.40000000000000002,
4515           0.17453292519943295 },
4516   { 0.34615238767335027, 0.60000000000000009, 0.40000000000000002,
4517           0.34906585039886590 },
4518   { 0.51453257838108557, 0.60000000000000009, 0.40000000000000002,
4519           0.52359877559829882 },
4520   { 0.67882386787534399, 0.60000000000000009, 0.40000000000000002,
4521           0.69813170079773179 },
4522   { 0.83948470233173578, 0.60000000000000009, 0.40000000000000002,
4523           0.87266462599716477 },
4524   { 0.99753496200073977, 0.60000000000000009, 0.40000000000000002,
4525           1.0471975511965976 },
4526   { 1.1541101404388487, 0.60000000000000009, 0.40000000000000002,
4527           1.2217304763960306 },
4528   { 1.3100911323398816, 0.60000000000000009, 0.40000000000000002,
4529           1.3962634015954636 },
4530   { 1.4659345278069984, 0.60000000000000009, 0.40000000000000002,
4531           1.5707963267948966 },
4532 };
4533 const double toler155 = 2.5000000000000020e-13;
4534
4535 // Test data for k=0.60000000000000009, nu=0.50000000000000000.
4536 // max(|f - f_GSL|): 6.6613381477509392e-16
4537 // max(|f - f_GSL| / |f_GSL|): 4.7124937590522226e-16
4538 const testcase_ellint_3<double>
4539 data156[10] =
4540 {
4541   { 0.0000000000000000, 0.60000000000000009, 0.50000000000000000,
4542           0.0000000000000000 },
4543   { 0.17397586700252807, 0.60000000000000009, 0.50000000000000000,
4544           0.17453292519943295 },
4545   { 0.34483533397138516, 0.60000000000000009, 0.50000000000000000,
4546           0.34906585039886590 },
4547   { 0.51044500461706477, 0.60000000000000009, 0.50000000000000000,
4548           0.52359877559829882 },
4549   { 0.67009988034712664, 0.60000000000000009, 0.50000000000000000,
4550           0.69813170079773179 },
4551   { 0.82434762375735193, 0.60000000000000009, 0.50000000000000000,
4552           0.87266462599716477 },
4553   { 0.97447346702798998, 0.60000000000000009, 0.50000000000000000,
4554           1.0471975511965976 },
4555   { 1.1219494000522143, 0.60000000000000009, 0.50000000000000000,
4556           1.2217304763960306 },
4557   { 1.2680242605954486, 0.60000000000000009, 0.50000000000000000,
4558           1.3962634015954636 },
4559   { 1.4135484285693078, 0.60000000000000009, 0.50000000000000000,
4560           1.5707963267948966 },
4561 };
4562 const double toler156 = 2.5000000000000020e-13;
4563
4564 // Test data for k=0.60000000000000009, nu=0.59999999999999998.
4565 // max(|f - f_GSL|): 4.4408920985006262e-16
4566 // max(|f - f_GSL| / |f_GSL|): 4.0652177678695900e-16
4567 const testcase_ellint_3<double>
4568 data157[10] =
4569 {
4570   { 0.0000000000000000, 0.60000000000000009, 0.59999999999999998,
4571           0.0000000000000000 },
4572   { 0.17380260984469353, 0.60000000000000009, 0.59999999999999998,
4573           0.17453292519943295 },
4574   { 0.34353585361777839, 0.60000000000000009, 0.59999999999999998,
4575           0.34906585039886590 },
4576   { 0.50646805774321380, 0.60000000000000009, 0.59999999999999998,
4577           0.52359877559829882 },
4578   { 0.66174468108625506, 0.60000000000000009, 0.59999999999999998,
4579           0.69813170079773179 },
4580   { 0.81007462280278408, 0.60000000000000009, 0.59999999999999998,
4581           0.87266462599716477 },
4582   { 0.95303466945718729, 0.60000000000000009, 0.59999999999999998,
4583           1.0471975511965976 },
4584   { 1.0924118588677505, 0.60000000000000009, 0.59999999999999998,
4585           1.2217304763960306 },
4586   { 1.2297640574847937, 0.60000000000000009, 0.59999999999999998,
4587           1.3962634015954636 },
4588   { 1.3662507535812816, 0.60000000000000009, 0.59999999999999998,
4589           1.5707963267948966 },
4590 };
4591 const double toler157 = 2.5000000000000020e-13;
4592
4593 // Test data for k=0.60000000000000009, nu=0.69999999999999996.
4594 // max(|f - f_GSL|): 4.4408920985006262e-16
4595 // max(|f - f_GSL| / |f_GSL|): 4.1692457486457856e-16
4596 const testcase_ellint_3<double>
4597 data158[10] =
4598 {
4599   { 0.0000000000000000, 0.60000000000000009, 0.69999999999999996,
4600           0.0000000000000000 },
4601   { 0.17362996946312007, 0.60000000000000009, 0.69999999999999996,
4602           0.17453292519943295 },
4603   { 0.34225353454870588, 0.60000000000000009, 0.69999999999999996,
4604           0.34906585039886590 },
4605   { 0.50259656397799524, 0.60000000000000009, 0.69999999999999996,
4606           0.52359877559829882 },
4607   { 0.65373184496628933, 0.60000000000000009, 0.69999999999999996,
4608           0.69813170079773179 },
4609   { 0.79658372884056439, 0.60000000000000009, 0.69999999999999996,
4610           0.87266462599716477 },
4611   { 0.93303240100245421, 0.60000000000000009, 0.69999999999999996,
4612           1.0471975511965976 },
4613   { 1.0651547944716557, 0.60000000000000009, 0.69999999999999996,
4614           1.2217304763960306 },
4615   { 1.1947676204853441, 0.60000000000000009, 0.69999999999999996,
4616           1.3962634015954636 },
4617   { 1.3232737468822813, 0.60000000000000009, 0.69999999999999996,
4618           1.5707963267948966 },
4619 };
4620 const double toler158 = 2.5000000000000020e-13;
4621
4622 // Test data for k=0.60000000000000009, nu=0.80000000000000004.
4623 // max(|f - f_GSL|): 4.4408920985006262e-16
4624 // max(|f - f_GSL| / |f_GSL|): 4.2705175719241326e-16
4625 const testcase_ellint_3<double>
4626 data159[10] =
4627 {
4628   { 0.0000000000000000, 0.60000000000000009, 0.80000000000000004,
4629           0.0000000000000000 },
4630   { 0.17345794195390685, 0.60000000000000009, 0.80000000000000004,
4631           0.17453292519943295 },
4632   { 0.34098797854531027, 0.60000000000000009, 0.80000000000000004,
4633           0.34906585039886590 },
4634   { 0.49882569168826213, 0.60000000000000009, 0.80000000000000004,
4635           0.52359877559829882 },
4636   { 0.64603758566475511, 0.60000000000000009, 0.80000000000000004,
4637           0.69813170079773179 },
4638   { 0.78380365594769730, 0.60000000000000009, 0.80000000000000004,
4639           0.87266462599716477 },
4640   { 0.91430946255611190, 0.60000000000000009, 0.80000000000000004,
4641           1.0471975511965976 },
4642   { 1.0398955217270607, 0.60000000000000009, 0.80000000000000004,
4643           1.2217304763960306 },
4644   { 1.1625948314277679, 0.60000000000000009, 0.80000000000000004,
4645           1.3962634015954636 },
4646   { 1.2840021261752192, 0.60000000000000009, 0.80000000000000004,
4647           1.5707963267948966 },
4648 };
4649 const double toler159 = 2.5000000000000020e-13;
4650
4651 // Test data for k=0.60000000000000009, nu=0.90000000000000002.
4652 // max(|f - f_GSL|): 4.4408920985006262e-16
4653 // max(|f - f_GSL| / |f_GSL|): 3.5585887739668036e-16
4654 const testcase_ellint_3<double>
4655 data160[10] =
4656 {
4657   { 0.0000000000000000, 0.60000000000000009, 0.90000000000000002,
4658           0.0000000000000000 },
4659   { 0.17328652344890030, 0.60000000000000009, 0.90000000000000002,
4660           0.17453292519943295 },
4661   { 0.33973880062929018, 0.60000000000000009, 0.90000000000000002,
4662           0.34906585039886590 },
4663   { 0.49515092233122743, 0.60000000000000009, 0.90000000000000002,
4664           0.52359877559829882 },
4665   { 0.63864042139737043, 0.60000000000000009, 0.90000000000000002,
4666           0.69813170079773179 },
4667   { 0.77167205646538850, 0.60000000000000009, 0.90000000000000002,
4668           0.87266462599716477 },
4669   { 0.89673202848034383, 0.60000000000000009, 0.90000000000000002,
4670           1.0471975511965976 },
4671   { 1.0163984492661304, 0.60000000000000009, 0.90000000000000002,
4672           1.2217304763960306 },
4673   { 1.1328845785162431, 0.60000000000000009, 0.90000000000000002,
4674           1.3962634015954636 },
4675   { 1.2479362973851873, 0.60000000000000009, 0.90000000000000002,
4676           1.5707963267948966 },
4677 };
4678 const double toler160 = 2.5000000000000020e-13;
4679
4680 // Test data for k=0.69999999999999996, nu=0.0000000000000000.
4681 // max(|f - f_GSL|): 3.3306690738754696e-16
4682 // max(|f - f_GSL| / |f_GSL|): 3.5930208052157665e-16
4683 const testcase_ellint_3<double>
4684 data161[10] =
4685 {
4686   { 0.0000000000000000, 0.69999999999999996, 0.0000000000000000,
4687           0.0000000000000000 },
4688   { 0.17496737466916723, 0.69999999999999996, 0.0000000000000000,
4689           0.17453292519943295 },
4690   { 0.35254687535677925, 0.69999999999999996, 0.0000000000000000,
4691           0.34906585039886590 },
4692   { 0.53536740275997119, 0.69999999999999996, 0.0000000000000000,
4693           0.52359877559829882 },
4694   { 0.72603797651684454, 0.69999999999999996, 0.0000000000000000,
4695           0.69813170079773179 },
4696   { 0.92698296348313458, 0.69999999999999996, 0.0000000000000000,
4697           0.87266462599716477 },
4698   { 1.1400447527693316, 0.69999999999999996, 0.0000000000000000,
4699           1.0471975511965976 },
4700   { 1.3657668117194073, 0.69999999999999996, 0.0000000000000000,
4701           1.2217304763960306 },
4702   { 1.6024686895959159, 0.69999999999999996, 0.0000000000000000,
4703           1.3962634015954636 },
4704   { 1.8456939983747236, 0.69999999999999996, 0.0000000000000000,
4705           1.5707963267948966 },
4706 };
4707 const double toler161 = 2.5000000000000020e-13;
4708
4709 // Test data for k=0.69999999999999996, nu=0.10000000000000001.
4710 // max(|f - f_GSL|): 3.3306690738754696e-16
4711 // max(|f - f_GSL| / |f_GSL|): 3.6735282577377367e-16
4712 const testcase_ellint_3<double>
4713 data162[10] =
4714 {
4715   { 0.0000000000000000, 0.69999999999999996, 0.10000000000000001,
4716           0.0000000000000000 },
4717   { 0.17479076384884684, 0.69999999999999996, 0.10000000000000001,
4718           0.17453292519943295 },
4719   { 0.35114844900396364, 0.69999999999999996, 0.10000000000000001,
4720           0.34906585039886590 },
4721   { 0.53072776947527001, 0.69999999999999996, 0.10000000000000001,
4722           0.52359877559829882 },
4723   { 0.71530198262386235, 0.69999999999999996, 0.10000000000000001,
4724           0.69813170079773179 },
4725   { 0.90666760677828306, 0.69999999999999996, 0.10000000000000001,
4726           0.87266462599716477 },
4727   { 1.1063366517438080, 0.69999999999999996, 0.10000000000000001,
4728           1.0471975511965976 },
4729   { 1.3149477243092149, 0.69999999999999996, 0.10000000000000001,
4730           1.2217304763960306 },
4731   { 1.5314886725038925, 0.69999999999999996, 0.10000000000000001,
4732           1.3962634015954636 },
4733   { 1.7528050171757608, 0.69999999999999996, 0.10000000000000001,
4734           1.5707963267948966 },
4735 };
4736 const double toler162 = 2.5000000000000020e-13;
4737
4738 // Test data for k=0.69999999999999996, nu=0.20000000000000001.
4739 // max(|f - f_GSL|): 3.3306690738754696e-16
4740 // max(|f - f_GSL| / |f_GSL|): 3.7517969287516802e-16
4741 const testcase_ellint_3<double>
4742 data163[10] =
4743 {
4744   { 0.0000000000000000, 0.69999999999999996, 0.20000000000000001,
4745           0.0000000000000000 },
4746   { 0.17461479077791475, 0.69999999999999996, 0.20000000000000001,
4747           0.17453292519943295 },
4748   { 0.34976950621407538, 0.69999999999999996, 0.20000000000000001,
4749           0.34906585039886590 },
4750   { 0.52622533231350177, 0.69999999999999996, 0.20000000000000001,
4751           0.52359877559829882 },
4752   { 0.70508774017895215, 0.69999999999999996, 0.20000000000000001,
4753           0.69813170079773179 },
4754   { 0.88775302531730294, 0.69999999999999996, 0.20000000000000001,
4755           0.87266462599716477 },
4756   { 1.0756195476149006, 0.69999999999999996, 0.20000000000000001,
4757           1.0471975511965976 },
4758   { 1.2695349716654374, 0.69999999999999996, 0.20000000000000001,
4759           1.2217304763960306 },
4760   { 1.4690814617070540, 0.69999999999999996, 0.20000000000000001,
4761           1.3962634015954636 },
4762   { 1.6721098780092145, 0.69999999999999996, 0.20000000000000001,
4763           1.5707963267948966 },
4764 };
4765 const double toler163 = 2.5000000000000020e-13;
4766
4767 // Test data for k=0.69999999999999996, nu=0.29999999999999999.
4768 // max(|f - f_GSL|): 4.4408920985006262e-16
4769 // max(|f - f_GSL| / |f_GSL|): 3.8280039841080712e-16
4770 const testcase_ellint_3<double>
4771 data164[10] =
4772 {
4773   { 0.0000000000000000, 0.69999999999999996, 0.29999999999999999,
4774           0.0000000000000000 },
4775   { 0.17443945136076175, 0.69999999999999996, 0.29999999999999999,
4776           0.17453292519943295 },
4777   { 0.34840956983535287, 0.69999999999999996, 0.29999999999999999,
4778           0.34906585039886590 },
4779   { 0.52185308551329168, 0.69999999999999996, 0.29999999999999999,
4780           0.52359877559829882 },
4781   { 0.69535240431168255, 0.69999999999999996, 0.29999999999999999,
4782           0.69813170079773179 },
4783   { 0.87007983473964923, 0.69999999999999996, 0.29999999999999999,
4784           0.87266462599716477 },
4785   { 1.0474657975577066, 0.69999999999999996, 0.29999999999999999,
4786           1.0471975511965976 },
4787   { 1.2286225419931891, 0.69999999999999996, 0.29999999999999999,
4788           1.2217304763960306 },
4789   { 1.4136490671013271, 0.69999999999999996, 0.29999999999999999,
4790           1.3962634015954636 },
4791   { 1.6011813647733213, 0.69999999999999996, 0.29999999999999999,
4792           1.5707963267948966 },
4793 };
4794 const double toler164 = 2.5000000000000020e-13;
4795
4796 // Test data for k=0.69999999999999996, nu=0.40000000000000002.
4797 // max(|f - f_GSL|): 4.4408920985006262e-16
4798 // max(|f - f_GSL| / |f_GSL|): 4.3472957053482092e-16
4799 const testcase_ellint_3<double>
4800 data165[10] =
4801 {
4802   { 0.0000000000000000, 0.69999999999999996, 0.40000000000000002,
4803           0.0000000000000000 },
4804   { 0.17426474153983229, 0.69999999999999996, 0.40000000000000002,
4805           0.17453292519943295 },
4806   { 0.34706817945773732, 0.69999999999999996, 0.40000000000000002,
4807           0.34906585039886590 },
4808   { 0.51760452851738148, 0.69999999999999996, 0.40000000000000002,
4809           0.52359877559829882 },
4810   { 0.68605801534722755, 0.69999999999999996, 0.40000000000000002,
4811           0.69813170079773179 },
4812   { 0.85351339387296532, 0.69999999999999996, 0.40000000000000002,
4813           0.87266462599716477 },
4814   { 1.0215297967969539, 0.69999999999999996, 0.40000000000000002,
4815           1.0471975511965976 },
4816   { 1.1915051074460530, 0.69999999999999996, 0.40000000000000002,
4817           1.2217304763960306 },
4818   { 1.3639821911744707, 0.69999999999999996, 0.40000000000000002,
4819           1.3962634015954636 },
4820   { 1.5382162002954762, 0.69999999999999996, 0.40000000000000002,
4821           1.5707963267948966 },
4822 };
4823 const double toler165 = 2.5000000000000020e-13;
4824
4825 // Test data for k=0.69999999999999996, nu=0.50000000000000000.
4826 // max(|f - f_GSL|): 3.3306690738754696e-16
4827 // max(|f - f_GSL| / |f_GSL|): 3.9748346743390620e-16
4828 const testcase_ellint_3<double>
4829 data166[10] =
4830 {
4831   { 0.0000000000000000, 0.69999999999999996, 0.50000000000000000,
4832           0.0000000000000000 },
4833   { 0.17409065729516096, 0.69999999999999996, 0.50000000000000000,
4834           0.17453292519943295 },
4835   { 0.34574489064986091, 0.69999999999999996, 0.50000000000000000,
4836           0.34906585039886590 },
4837   { 0.51347361925579782, 0.69999999999999996, 0.50000000000000000,
4838           0.52359877559829882 },
4839   { 0.67717079489579279, 0.69999999999999996, 0.50000000000000000,
4840           0.69813170079773179 },
4841   { 0.83793902055292280, 0.69999999999999996, 0.50000000000000000,
4842           0.87266462599716477 },
4843   { 0.99752863545289705, 0.69999999999999996, 0.50000000000000000,
4844           1.0471975511965976 },
4845   { 1.1576240080401501, 0.69999999999999996, 0.50000000000000000,
4846           1.2217304763960306 },
4847   { 1.3191464023923762, 0.69999999999999996, 0.50000000000000000,
4848           1.3962634015954636 },
4849   { 1.4818433192178544, 0.69999999999999996, 0.50000000000000000,
4850           1.5707963267948966 },
4851 };
4852 const double toler166 = 2.5000000000000020e-13;
4853
4854 // Test data for k=0.69999999999999996, nu=0.59999999999999998.
4855 // max(|f - f_GSL|): 3.3306690738754696e-16
4856 // max(|f - f_GSL| / |f_GSL|): 4.0457157538295173e-16
4857 const testcase_ellint_3<double>
4858 data167[10] =
4859 {
4860   { 0.0000000000000000, 0.69999999999999996, 0.59999999999999998,
4861           0.0000000000000000 },
4862   { 0.17391719464391614, 0.69999999999999996, 0.59999999999999998,
4863           0.17453292519943295 },
4864   { 0.34443927423869031, 0.69999999999999996, 0.59999999999999998,
4865           0.34906585039886590 },
4866   { 0.50945473266486063, 0.69999999999999996, 0.59999999999999998,
4867           0.52359877559829882 },
4868   { 0.66866056326513812, 0.69999999999999996, 0.59999999999999998,
4869           0.69813170079773179 },
4870   { 0.82325830002337352, 0.69999999999999996, 0.59999999999999998,
4871           0.87266462599716477 },
4872   { 0.97522808245669368, 0.69999999999999996, 0.59999999999999998,
4873           1.0471975511965976 },
4874   { 1.1265300613705285, 0.69999999999999996, 0.59999999999999998,
4875           1.2217304763960306 },
4876   { 1.2784066076152001, 0.69999999999999996, 0.59999999999999998,
4877           1.3962634015954636 },
4878   { 1.4309994736080540, 0.69999999999999996, 0.59999999999999998,
4879           1.5707963267948966 },
4880 };
4881 const double toler167 = 2.5000000000000020e-13;
4882
4883 // Test data for k=0.69999999999999996, nu=0.69999999999999996.
4884 // max(|f - f_GSL|): 4.4408920985006262e-16
4885 // max(|f - f_GSL| / |f_GSL|): 5.4867405596732161e-16
4886 const testcase_ellint_3<double>
4887 data168[10] =
4888 {
4889   { 0.0000000000000000, 0.69999999999999996, 0.69999999999999996,
4890           0.0000000000000000 },
4891   { 0.17374434963995031, 0.69999999999999996, 0.69999999999999996,
4892           0.17453292519943295 },
4893   { 0.34315091562900674, 0.69999999999999996, 0.69999999999999996,
4894           0.34906585039886590 },
4895   { 0.50554262375653347, 0.69999999999999996, 0.69999999999999996,
4896           0.52359877559829882 },
4897   { 0.66050025406305801, 0.69999999999999996, 0.69999999999999996,
4898           0.69813170079773179 },
4899   { 0.80938620118847404, 0.69999999999999996, 0.69999999999999996,
4900           0.87266462599716477 },
4901   { 0.95443223855852144, 0.69999999999999996, 0.69999999999999996,
4902           1.0471975511965976 },
4903   { 1.0978573207128304, 0.69999999999999996, 0.69999999999999996,
4904           1.2217304763960306 },
4905   { 1.2411754575007123, 0.69999999999999996, 0.69999999999999996,
4906           1.3962634015954636 },
4907   { 1.3848459188329196, 0.69999999999999996, 0.69999999999999996,
4908           1.5707963267948966 },
4909 };
4910 const double toler168 = 2.5000000000000020e-13;
4911
4912 // Test data for k=0.69999999999999996, nu=0.80000000000000004.
4913 // max(|f - f_GSL|): 4.4408920985006262e-16
4914 // max(|f - f_GSL| / |f_GSL|): 4.1829502028913879e-16
4915 const testcase_ellint_3<double>
4916 data169[10] =
4917 {
4918   { 0.0000000000000000, 0.69999999999999996, 0.80000000000000004,
4919           0.0000000000000000 },
4920   { 0.17357211837335740, 0.69999999999999996, 0.80000000000000004,
4921           0.17453292519943295 },
4922   { 0.34187941416012108, 0.69999999999999996, 0.80000000000000004,
4923           0.34906585039886590 },
4924   { 0.50173239465478259, 0.69999999999999996, 0.80000000000000004,
4925           0.52359877559829882 },
4926   { 0.65266550725988315, 0.69999999999999996, 0.80000000000000004,
4927           0.69813170079773179 },
4928   { 0.79624879865249298, 0.69999999999999996, 0.80000000000000004,
4929           0.87266462599716477 },
4930   { 0.93497577043296920, 0.69999999999999996, 0.80000000000000004,
4931           1.0471975511965976 },
4932   { 1.0713041566930750, 0.69999999999999996, 0.80000000000000004,
4933           1.2217304763960306 },
4934   { 1.2069772023255654, 0.69999999999999996, 0.80000000000000004,
4935           1.3962634015954636 },
4936   { 1.3427110650397531, 0.69999999999999996, 0.80000000000000004,
4937           1.5707963267948966 },
4938 };
4939 const double toler169 = 2.5000000000000020e-13;
4940
4941 // Test data for k=0.69999999999999996, nu=0.90000000000000002.
4942 // max(|f - f_GSL|): 3.3306690738754696e-16
4943 // max(|f - f_GSL| / |f_GSL|): 4.2494869624129105e-16
4944 const testcase_ellint_3<double>
4945 data170[10] =
4946 {
4947   { 0.0000000000000000, 0.69999999999999996, 0.90000000000000002,
4948           0.0000000000000000 },
4949   { 0.17340049697003637, 0.69999999999999996, 0.90000000000000002,
4950           0.17453292519943295 },
4951   { 0.34062438249741556, 0.69999999999999996, 0.90000000000000002,
4952           0.34906585039886590 },
4953   { 0.49801946510076867, 0.69999999999999996, 0.90000000000000002,
4954           0.52359877559829882 },
4955   { 0.64513432604750476, 0.69999999999999996, 0.90000000000000002,
4956           0.69813170079773179 },
4957   { 0.78378145487573758, 0.69999999999999996, 0.90000000000000002,
4958           0.87266462599716477 },
4959   { 0.91671799500854623, 0.69999999999999996, 0.90000000000000002,
4960           1.0471975511965976 },
4961   { 1.0466193579463123, 0.69999999999999996, 0.90000000000000002,
4962           1.2217304763960306 },
4963   { 1.1754218079199146, 0.69999999999999996, 0.90000000000000002,
4964           1.3962634015954636 },
4965   { 1.3040500499695913, 0.69999999999999996, 0.90000000000000002,
4966           1.5707963267948966 },
4967 };
4968 const double toler170 = 2.5000000000000020e-13;
4969
4970 // Test data for k=0.80000000000000004, nu=0.0000000000000000.
4971 // max(|f - f_GSL|): 4.4408920985006262e-16
4972 // max(|f - f_GSL| / |f_GSL|): 4.1175183168766718e-16
4973 const testcase_ellint_3<double>
4974 data171[10] =
4975 {
4976   { 0.0000000000000000, 0.80000000000000004, 0.0000000000000000,
4977           0.0000000000000000 },
4978   { 0.17510154241338899, 0.80000000000000004, 0.0000000000000000,
4979           0.17453292519943295 },
4980   { 0.35365068839779390, 0.80000000000000004, 0.0000000000000000,
4981           0.34906585039886590 },
4982   { 0.53926804409084550, 0.80000000000000004, 0.0000000000000000,
4983           0.52359877559829882 },
4984   { 0.73587926028070361, 0.80000000000000004, 0.0000000000000000,
4985           0.69813170079773179 },
4986   { 0.94770942970071170, 0.80000000000000004, 0.0000000000000000,
4987           0.87266462599716477 },
4988   { 1.1789022995388236, 0.80000000000000004, 0.0000000000000000,
4989           1.0471975511965976 },
4990   { 1.4323027881876009, 0.80000000000000004, 0.0000000000000000,
4991           1.2217304763960306 },
4992   { 1.7069629739121674, 0.80000000000000004, 0.0000000000000000,
4993           1.3962634015954636 },
4994   { 1.9953027776647296, 0.80000000000000004, 0.0000000000000000,
4995           1.5707963267948966 },
4996 };
4997 const double toler171 = 2.5000000000000020e-13;
4998
4999 // Test data for k=0.80000000000000004, nu=0.10000000000000001.
5000 // max(|f - f_GSL|): 4.4408920985006262e-16
5001 // max(|f - f_GSL| / |f_GSL|): 4.1537164503193145e-16
5002 const testcase_ellint_3<double>
5003 data172[10] =
5004 {
5005   { 0.0000000000000000, 0.80000000000000004, 0.10000000000000001,
5006           0.0000000000000000 },
5007   { 0.17492468824017163, 0.80000000000000004, 0.10000000000000001,
5008           0.17453292519943295 },
5009   { 0.35224443521476911, 0.80000000000000004, 0.10000000000000001,
5010           0.34906585039886590 },
5011   { 0.53456851853226950, 0.80000000000000004, 0.10000000000000001,
5012           0.52359877559829882 },
5013   { 0.72488875602364922, 0.80000000000000004, 0.10000000000000001,
5014           0.69813170079773179 },
5015   { 0.92661354274638952, 0.80000000000000004, 0.10000000000000001,
5016           0.87266462599716477 },
5017   { 1.1432651144499075, 0.80000000000000004, 0.10000000000000001,
5018           1.0471975511965976 },
5019   { 1.3774479927211429, 0.80000000000000004, 0.10000000000000001,
5020           1.2217304763960306 },
5021   { 1.6287092337196041, 0.80000000000000004, 0.10000000000000001,
5022           1.3962634015954636 },
5023   { 1.8910755418379521, 0.80000000000000004, 0.10000000000000001,
5024           1.5707963267948966 },
5025 };
5026 const double toler172 = 2.5000000000000020e-13;
5027
5028 // Test data for k=0.80000000000000004, nu=0.20000000000000001.
5029 // max(|f - f_GSL|): 4.4408920985006262e-16
5030 // max(|f - f_GSL| / |f_GSL|): 4.1894552974436829e-16
5031 const testcase_ellint_3<double>
5032 data173[10] =
5033 {
5034   { 0.0000000000000000, 0.80000000000000004, 0.20000000000000001,
5035           0.0000000000000000 },
5036   { 0.17474847286224940, 0.80000000000000004, 0.20000000000000001,
5037           0.17453292519943295 },
5038   { 0.35085779529084682, 0.80000000000000004, 0.20000000000000001,
5039           0.34906585039886590 },
5040   { 0.53000829263059146, 0.80000000000000004, 0.20000000000000001,
5041           0.52359877559829882 },
5042   { 0.71443466027453384, 0.80000000000000004, 0.20000000000000001,
5043           0.69813170079773179 },
5044   { 0.90698196872715420, 0.80000000000000004, 0.20000000000000001,
5045           0.87266462599716477 },
5046   { 1.1108198200558579, 0.80000000000000004, 0.20000000000000001,
5047           1.0471975511965976 },
5048   { 1.3284988909963957, 0.80000000000000004, 0.20000000000000001,
5049           1.2217304763960306 },
5050   { 1.5600369318140328, 0.80000000000000004, 0.20000000000000001,
5051           1.3962634015954636 },
5052   { 1.8007226661734588, 0.80000000000000004, 0.20000000000000001,
5053           1.5707963267948966 },
5054 };
5055 const double toler173 = 2.5000000000000020e-13;
5056
5057 // Test data for k=0.80000000000000004, nu=0.29999999999999999.
5058 // max(|f - f_GSL|): 4.4408920985006262e-16
5059 // max(|f - f_GSL| / |f_GSL|): 4.2247517409029886e-16
5060 const testcase_ellint_3<double>
5061 data174[10] =
5062 {
5063   { 0.0000000000000000, 0.80000000000000004, 0.29999999999999999,
5064           0.0000000000000000 },
5065   { 0.17457289217669889, 0.80000000000000004, 0.29999999999999999,
5066           0.17453292519943295 },
5067   { 0.34949028801501258, 0.80000000000000004, 0.29999999999999999,
5068           0.34906585039886590 },
5069   { 0.52558024362769307, 0.80000000000000004, 0.29999999999999999,
5070           0.52359877559829882 },
5071   { 0.70447281740094891, 0.80000000000000004, 0.29999999999999999,
5072           0.69813170079773179 },
5073   { 0.88864745641528986, 0.80000000000000004, 0.29999999999999999,
5074           0.87266462599716477 },
5075   { 1.0811075819341462, 0.80000000000000004, 0.29999999999999999,
5076           1.0471975511965976 },
5077   { 1.2844589654082377, 0.80000000000000004, 0.29999999999999999,
5078           1.2217304763960306 },
5079   { 1.4991461361277847, 0.80000000000000004, 0.29999999999999999,
5080           1.3962634015954636 },
5081   { 1.7214611048717301, 0.80000000000000004, 0.29999999999999999,
5082           1.5707963267948966 },
5083 };
5084 const double toler174 = 2.5000000000000020e-13;
5085
5086 // Test data for k=0.80000000000000004, nu=0.40000000000000002.
5087 // max(|f - f_GSL|): 4.4408920985006262e-16
5088 // max(|f - f_GSL| / |f_GSL|): 4.2596216594752862e-16
5089 const testcase_ellint_3<double>
5090 data175[10] =
5091 {
5092   { 0.0000000000000000, 0.80000000000000004, 0.40000000000000002,
5093           0.0000000000000000 },
5094   { 0.17439794211872175, 0.80000000000000004, 0.40000000000000002,
5095           0.17453292519943295 },
5096   { 0.34814144964568972, 0.80000000000000004, 0.40000000000000002,
5097           0.34906585039886590 },
5098   { 0.52127776285273064, 0.80000000000000004, 0.40000000000000002,
5099           0.52359877559829882 },
5100   { 0.69496411438966588, 0.80000000000000004, 0.40000000000000002,
5101           0.69813170079773179 },
5102   { 0.87146878427509589, 0.80000000000000004, 0.40000000000000002,
5103           0.87266462599716477 },
5104   { 1.0537579024937762, 0.80000000000000004, 0.40000000000000002,
5105           1.0471975511965976 },
5106   { 1.2445534387922637, 0.80000000000000004, 0.40000000000000002,
5107           1.2217304763960306 },
5108   { 1.4446769766361993, 0.80000000000000004, 0.40000000000000002,
5109           1.3962634015954636 },
5110   { 1.6512267838651289, 0.80000000000000004, 0.40000000000000002,
5111           1.5707963267948966 },
5112 };
5113 const double toler175 = 2.5000000000000020e-13;
5114
5115 // Test data for k=0.80000000000000004, nu=0.50000000000000000.
5116 // max(|f - f_GSL|): 4.4408920985006262e-16
5117 // max(|f - f_GSL| / |f_GSL|): 4.2940800093915668e-16
5118 const testcase_ellint_3<double>
5119 data176[10] =
5120 {
5121   { 0.0000000000000000, 0.80000000000000004, 0.50000000000000000,
5122           0.0000000000000000 },
5123   { 0.17422361866118044, 0.80000000000000004, 0.50000000000000000,
5124           0.17453292519943295 },
5125   { 0.34681083254170475, 0.80000000000000004, 0.50000000000000000,
5126           0.34906585039886590 },
5127   { 0.51709470815494440, 0.80000000000000004, 0.50000000000000000,
5128           0.52359877559829882 },
5129   { 0.68587375344080237, 0.80000000000000004, 0.50000000000000000,
5130           0.69813170079773179 },
5131   { 0.85532571852810624, 0.80000000000000004, 0.50000000000000000,
5132           0.87266462599716477 },
5133   { 1.0284677391874903, 0.80000000000000004, 0.50000000000000000,
5134           1.0471975511965976 },
5135   { 1.2081693942686225, 0.80000000000000004, 0.50000000000000000,
5136           1.2217304763960306 },
5137   { 1.3955803006426311, 0.80000000000000004, 0.50000000000000000,
5138           1.3962634015954636 },
5139   { 1.5884528947755532, 0.80000000000000004, 0.50000000000000000,
5140           1.5707963267948966 },
5141 };
5142 const double toler176 = 2.5000000000000020e-13;
5143
5144 // Test data for k=0.80000000000000004, nu=0.59999999999999998.
5145 // max(|f - f_GSL|): 4.4408920985006262e-16
5146 // max(|f - f_GSL| / |f_GSL|): 4.3281408974056389e-16
5147 const testcase_ellint_3<double>
5148 data177[10] =
5149 {
5150   { 0.0000000000000000, 0.80000000000000004, 0.59999999999999998,
5151           0.0000000000000000 },
5152   { 0.17404991781414089, 0.80000000000000004, 0.59999999999999998,
5153           0.17453292519943295 },
5154   { 0.34549800443625167, 0.80000000000000004, 0.59999999999999998,
5155           0.34906585039886590 },
5156   { 0.51302536167001545, 0.80000000000000004, 0.59999999999999998,
5157           0.52359877559829882 },
5158   { 0.67717065003912236, 0.80000000000000004, 0.59999999999999998,
5159           0.69813170079773179 },
5160   { 0.84011512421134416, 0.80000000000000004, 0.59999999999999998,
5161           0.87266462599716477 },
5162   { 1.0049863847088740, 0.80000000000000004, 0.59999999999999998,
5163           1.0471975511965976 },
5164   { 1.1748145941898920, 0.80000000000000004, 0.59999999999999998,
5165           1.2217304763960306 },
5166   { 1.3510319699755071, 0.80000000000000004, 0.59999999999999998,
5167           1.3962634015954636 },
5168   { 1.5319262547427865, 0.80000000000000004, 0.59999999999999998,
5169           1.5707963267948966 },
5170 };
5171 const double toler177 = 2.5000000000000020e-13;
5172
5173 // Test data for k=0.80000000000000004, nu=0.69999999999999996.
5174 // max(|f - f_GSL|): 2.2204460492503131e-16
5175 // max(|f - f_GSL| / |f_GSL|): 4.3618176466061808e-16
5176 const testcase_ellint_3<double>
5177 data178[10] =
5178 {
5179   { 0.0000000000000000, 0.80000000000000004, 0.69999999999999996,
5180           0.0000000000000000 },
5181   { 0.17387683562442199, 0.80000000000000004, 0.69999999999999996,
5182           0.17453292519943295 },
5183   { 0.34420254775101611, 0.80000000000000004, 0.69999999999999996,
5184           0.34906585039886590 },
5185   { 0.50906439222143673, 0.80000000000000004, 0.69999999999999996,
5186           0.52359877559829882 },
5187   { 0.66882693152688422, 0.80000000000000004, 0.69999999999999996,
5188           0.69813170079773179 },
5189   { 0.82574792844091316, 0.80000000000000004, 0.69999999999999996,
5190           0.87266462599716477 },
5191   { 0.98310431309490931, 0.80000000000000004, 0.69999999999999996,
5192           1.0471975511965976 },
5193   { 1.1440884535113258, 0.80000000000000004, 0.69999999999999996,
5194           1.2217304763960306 },
5195   { 1.3103743938952537, 0.80000000000000004, 0.69999999999999996,
5196           1.3962634015954636 },
5197   { 1.4806912324625332, 0.80000000000000004, 0.69999999999999996,
5198           1.5707963267948966 },
5199 };
5200 const double toler178 = 2.5000000000000020e-13;
5201
5202 // Test data for k=0.80000000000000004, nu=0.80000000000000004.
5203 // max(|f - f_GSL|): 4.4408920985006262e-16
5204 // max(|f - f_GSL| / |f_GSL|): 4.3951228558314112e-16
5205 const testcase_ellint_3<double>
5206 data179[10] =
5207 {
5208   { 0.0000000000000000, 0.80000000000000004, 0.80000000000000004,
5209           0.0000000000000000 },
5210   { 0.17370436817515203, 0.80000000000000004, 0.80000000000000004,
5211           0.17453292519943295 },
5212   { 0.34292405894783395, 0.80000000000000004, 0.80000000000000004,
5213           0.34906585039886590 },
5214   { 0.50520682176250076, 0.80000000000000004, 0.80000000000000004,
5215           0.52359877559829882 },
5216   { 0.66081751679736178, 0.80000000000000004, 0.80000000000000004,
5217           0.69813170079773179 },
5218   { 0.81214672249355102, 0.80000000000000004, 0.80000000000000004,
5219           0.87266462599716477 },
5220   { 0.96264481387685552, 0.80000000000000004, 0.80000000000000004,
5221           1.0471975511965976 },
5222   { 1.1156611352656258, 0.80000000000000004, 0.80000000000000004,
5223           1.2217304763960306 },
5224   { 1.2730756225143889, 0.80000000000000004, 0.80000000000000004,
5225           1.3962634015954636 },
5226   { 1.4339837018309471, 0.80000000000000004, 0.80000000000000004,
5227           1.5707963267948966 },
5228 };
5229 const double toler179 = 2.5000000000000020e-13;
5230
5231 // Test data for k=0.80000000000000004, nu=0.90000000000000002.
5232 // max(|f - f_GSL|): 3.3306690738754696e-16
5233 // max(|f - f_GSL| / |f_GSL|): 4.4280684534289690e-16
5234 const testcase_ellint_3<double>
5235 data180[10] =
5236 {
5237   { 0.0000000000000000, 0.80000000000000004, 0.90000000000000002,
5238           0.0000000000000000 },
5239   { 0.17353251158533151, 0.80000000000000004, 0.90000000000000002,
5240           0.17453292519943295 },
5241   { 0.34166214791545768, 0.80000000000000004, 0.90000000000000002,
5242           0.34906585039886590 },
5243   { 0.50144799535130569, 0.80000000000000004, 0.90000000000000002,
5244           0.52359877559829882 },
5245   { 0.65311976193814425, 0.80000000000000004, 0.90000000000000002,
5246           0.69813170079773179 },
5247   { 0.79924384892320866, 0.80000000000000004, 0.90000000000000002,
5248           0.87266462599716477 },
5249   { 0.94345762353365603, 0.80000000000000004, 0.90000000000000002,
5250           1.0471975511965976 },
5251   { 1.0892582069219161, 0.80000000000000004, 0.90000000000000002,
5252           1.2217304763960306 },
5253   { 1.2387000876610268, 0.80000000000000004, 0.90000000000000002,
5254           1.3962634015954636 },
5255   { 1.3911845406776222, 0.80000000000000004, 0.90000000000000002,
5256           1.5707963267948966 },
5257 };
5258 const double toler180 = 2.5000000000000020e-13;
5259
5260 // Test data for k=0.89999999999999991, nu=0.0000000000000000.
5261 // max(|f - f_GSL|): 8.8817841970012523e-16
5262 // max(|f - f_GSL| / |f_GSL|): 3.8945813740035884e-16
5263 const testcase_ellint_3<double>
5264 data181[10] =
5265 {
5266   { 0.0000000000000000, 0.89999999999999991, 0.0000000000000000,
5267           0.0000000000000000 },
5268   { 0.17525427376115024, 0.89999999999999991, 0.0000000000000000,
5269           0.17453292519943295 },
5270   { 0.35492464591297446, 0.89999999999999991, 0.0000000000000000,
5271           0.34906585039886590 },
5272   { 0.54388221416157112, 0.89999999999999991, 0.0000000000000000,
5273           0.52359877559829882 },
5274   { 0.74797400423532490, 0.89999999999999991, 0.0000000000000000,
5275           0.69813170079773179 },
5276   { 0.97463898451966458, 0.89999999999999991, 0.0000000000000000,
5277           0.87266462599716477 },
5278   { 1.2334463254523440, 0.89999999999999991, 0.0000000000000000,
5279           1.0471975511965976 },
5280   { 1.5355247765594910, 0.89999999999999991, 0.0000000000000000,
5281           1.2217304763960306 },
5282   { 1.8882928567775117, 0.89999999999999991, 0.0000000000000000,
5283           1.3962634015954636 },
5284   { 2.2805491384227703, 0.89999999999999991, 0.0000000000000000,
5285           1.5707963267948966 },
5286 };
5287 const double toler181 = 2.5000000000000020e-13;
5288
5289 // Test data for k=0.89999999999999991, nu=0.10000000000000001.
5290 // max(|f - f_GSL|): 8.8817841970012523e-16
5291 // max(|f - f_GSL| / |f_GSL|): 4.1237990617685137e-16
5292 const testcase_ellint_3<double>
5293 data182[10] =
5294 {
5295   { 0.0000000000000000, 0.89999999999999991, 0.10000000000000001,
5296           0.0000000000000000 },
5297   { 0.17507714233254656, 0.89999999999999991, 0.10000000000000001,
5298           0.17453292519943295 },
5299   { 0.35350932904326521, 0.89999999999999991, 0.10000000000000001,
5300           0.34906585039886590 },
5301   { 0.53911129989870976, 0.89999999999999991, 0.10000000000000001,
5302           0.52359877559829882 },
5303   { 0.73666644254508395, 0.89999999999999991, 0.10000000000000001,
5304           0.69813170079773179 },
5305   { 0.95250736612100195, 0.89999999999999991, 0.10000000000000001,
5306           0.87266462599716477 },
5307   { 1.1950199550905594, 0.89999999999999991, 0.10000000000000001,
5308           1.0471975511965976 },
5309   { 1.4741687286340848, 0.89999999999999991, 0.10000000000000001,
5310           1.2217304763960306 },
5311   { 1.7968678183506053, 0.89999999999999991, 0.10000000000000001,
5312           1.3962634015954636 },
5313   { 2.1537868513875287, 0.89999999999999991, 0.10000000000000001,
5314           1.5707963267948966 },
5315 };
5316 const double toler182 = 2.5000000000000020e-13;
5317
5318 // Test data for k=0.89999999999999991, nu=0.20000000000000001.
5319 // max(|f - f_GSL|): 8.8817841970012523e-16
5320 // max(|f - f_GSL| / |f_GSL|): 4.3446165733924066e-16
5321 const testcase_ellint_3<double>
5322 data183[10] =
5323 {
5324   { 0.0000000000000000, 0.89999999999999991, 0.20000000000000001,
5325           0.0000000000000000 },
5326   { 0.17490065089140927, 0.89999999999999991, 0.20000000000000001,
5327           0.17453292519943295 },
5328   { 0.35211377590661436, 0.89999999999999991, 0.20000000000000001,
5329           0.34906585039886590 },
5330   { 0.53448220334204100, 0.89999999999999991, 0.20000000000000001,
5331           0.52359877559829882 },
5332   { 0.72591368943179579, 0.89999999999999991, 0.20000000000000001,
5333           0.69813170079773179 },
5334   { 0.93192539780038763, 0.89999999999999991, 0.20000000000000001,
5335           0.87266462599716477 },
5336   { 1.1600809679692683, 0.89999999999999991, 0.20000000000000001,
5337           1.0471975511965976 },
5338   { 1.4195407225882508, 0.89999999999999991, 0.20000000000000001,
5339           1.2217304763960306 },
5340   { 1.7168966476424521, 0.89999999999999991, 0.20000000000000001,
5341           1.3962634015954636 },
5342   { 2.0443194576468895, 0.89999999999999991, 0.20000000000000001,
5343           1.5707963267948966 },
5344 };
5345 const double toler183 = 2.5000000000000020e-13;
5346
5347 // Test data for k=0.89999999999999991, nu=0.29999999999999999.
5348 // max(|f - f_GSL|): 1.1102230246251565e-15
5349 // max(|f - f_GSL| / |f_GSL|): 5.6974600067013622e-16
5350 const testcase_ellint_3<double>
5351 data184[10] =
5352 {
5353   { 0.0000000000000000, 0.89999999999999991, 0.29999999999999999,
5354           0.0000000000000000 },
5355   { 0.17472479532647531, 0.89999999999999991, 0.29999999999999999,
5356           0.17453292519943295 },
5357   { 0.35073750187374114, 0.89999999999999991, 0.29999999999999999,
5358           0.34906585039886590 },
5359   { 0.52998766129466957, 0.89999999999999991, 0.29999999999999999,
5360           0.52359877559829882 },
5361   { 0.71566993548699553, 0.89999999999999991, 0.29999999999999999,
5362           0.69813170079773179 },
5363   { 0.91271517762560195, 0.89999999999999991, 0.29999999999999999,
5364           0.87266462599716477 },
5365   { 1.1281241199843370, 0.89999999999999991, 0.29999999999999999,
5366           1.0471975511965976 },
5367   { 1.3704929576917448, 0.89999999999999991, 0.29999999999999999,
5368           1.2217304763960306 },
5369   { 1.6461981511487711, 0.89999999999999991, 0.29999999999999999,
5370           1.3962634015954636 },
5371   { 1.9486280260314426, 0.89999999999999991, 0.29999999999999999,
5372           1.5707963267948966 },
5373 };
5374 const double toler184 = 2.5000000000000020e-13;
5375
5376 // Test data for k=0.89999999999999991, nu=0.40000000000000002.
5377 // max(|f - f_GSL|): 8.8817841970012523e-16
5378 // max(|f - f_GSL| / |f_GSL|): 4.7646208744449464e-16
5379 const testcase_ellint_3<double>
5380 data185[10] =
5381 {
5382   { 0.0000000000000000, 0.89999999999999991, 0.40000000000000002,
5383           0.0000000000000000 },
5384   { 0.17454957156468837, 0.89999999999999991, 0.40000000000000002,
5385           0.17453292519943295 },
5386   { 0.34938003933330430, 0.89999999999999991, 0.40000000000000002,
5387           0.34906585039886590 },
5388   { 0.52562093533067433, 0.89999999999999991, 0.40000000000000002,
5389           0.52359877559829882 },
5390   { 0.70589461324915670, 0.89999999999999991, 0.40000000000000002,
5391           0.69813170079773179 },
5392   { 0.89472658511942849, 0.89999999999999991, 0.40000000000000002,
5393           0.87266462599716477 },
5394   { 1.0987419542323440, 0.89999999999999991, 0.40000000000000002,
5395           1.0471975511965976 },
5396   { 1.3261349565496301, 0.89999999999999991, 0.40000000000000002,
5397           1.2217304763960306 },
5398   { 1.5831293909853763, 0.89999999999999991, 0.40000000000000002,
5399           1.3962634015954636 },
5400   { 1.8641114227238351, 0.89999999999999991, 0.40000000000000002,
5401           1.5707963267948966 },
5402 };
5403 const double toler185 = 2.5000000000000020e-13;
5404
5405 // Test data for k=0.89999999999999991, nu=0.50000000000000000.
5406 // max(|f - f_GSL|): 8.8817841970012523e-16
5407 // max(|f - f_GSL| / |f_GSL|): 4.9652155758573562e-16
5408 const testcase_ellint_3<double>
5409 data186[10] =
5410 {
5411   { 0.0000000000000000, 0.89999999999999991, 0.50000000000000000,
5412           0.0000000000000000 },
5413   { 0.17437497557073334, 0.89999999999999991, 0.50000000000000000,
5414           0.17453292519943295 },
5415   { 0.34804093691586013, 0.89999999999999991, 0.50000000000000000,
5416           0.34906585039886590 },
5417   { 0.52137576320372891, 0.89999999999999991, 0.50000000000000000,
5418           0.52359877559829882 },
5419   { 0.69655163996912262, 0.89999999999999991, 0.50000000000000000,
5420           0.69813170079773179 },
5421   { 0.87783188683054236, 0.89999999999999991, 0.50000000000000000,
5422           0.87266462599716477 },
5423   { 1.0716015959755185, 0.89999999999999991, 0.50000000000000000,
5424           1.0471975511965976 },
5425   { 1.2857636916026749, 0.89999999999999991, 0.50000000000000000,
5426           1.2217304763960306 },
5427   { 1.5264263913252358, 0.89999999999999991, 0.50000000000000000,
5428           1.3962634015954636 },
5429   { 1.7888013241937863, 0.89999999999999991, 0.50000000000000000,
5430           1.5707963267948966 },
5431 };
5432 const double toler186 = 2.5000000000000020e-13;
5433
5434 // Test data for k=0.89999999999999991, nu=0.59999999999999998.
5435 // max(|f - f_GSL|): 6.6613381477509392e-16
5436 // max(|f - f_GSL| / |f_GSL|): 3.8702201113622378e-16
5437 const testcase_ellint_3<double>
5438 data187[10] =
5439 {
5440   { 0.0000000000000000, 0.89999999999999991, 0.59999999999999998,
5441           0.0000000000000000 },
5442   { 0.17420100334657812, 0.89999999999999991, 0.59999999999999998,
5443           0.17453292519943295 },
5444   { 0.34671975876122157, 0.89999999999999991, 0.59999999999999998,
5445           0.34906585039886590 },
5446   { 0.51724631570707946, 0.89999999999999991, 0.59999999999999998,
5447           0.52359877559829882 },
5448   { 0.68760879113743023, 0.89999999999999991, 0.59999999999999998,
5449           0.69813170079773179 },
5450   { 0.86192157779698364, 0.89999999999999991, 0.59999999999999998,
5451           0.87266462599716477 },
5452   { 1.0464279696166354, 0.89999999999999991, 0.59999999999999998,
5453           1.0471975511965976 },
5454   { 1.2488156247094004, 0.89999999999999991, 0.59999999999999998,
5455           1.2217304763960306 },
5456   { 1.4750988777188470, 0.89999999999999991, 0.59999999999999998,
5457           1.3962634015954636 },
5458   { 1.7211781128919525, 0.89999999999999991, 0.59999999999999998,
5459           1.5707963267948966 },
5460 };
5461 const double toler187 = 2.5000000000000020e-13;
5462
5463 // Test data for k=0.89999999999999991, nu=0.69999999999999996.
5464 // max(|f - f_GSL|): 4.4408920985006262e-16
5465 // max(|f - f_GSL| / |f_GSL|): 4.3410843563834748e-16
5466 const testcase_ellint_3<double>
5467 data188[10] =
5468 {
5469   { 0.0000000000000000, 0.89999999999999991, 0.69999999999999996,
5470           0.0000000000000000 },
5471   { 0.17402765093102207, 0.89999999999999991, 0.69999999999999996,
5472           0.17453292519943295 },
5473   { 0.34541608382635131, 0.89999999999999991, 0.69999999999999996,
5474           0.34906585039886590 },
5475   { 0.51322715827061682, 0.89999999999999991, 0.69999999999999996,
5476           0.52359877559829882 },
5477   { 0.67903717872440272, 0.89999999999999991, 0.69999999999999996,
5478           0.69813170079773179 },
5479   { 0.84690113601682671, 0.89999999999999991, 0.69999999999999996,
5480           0.87266462599716477 },
5481   { 1.0229914311548418, 0.89999999999999991, 0.69999999999999996,
5482           1.0471975511965976 },
5483   { 1.2148329639709381, 0.89999999999999991, 0.69999999999999996,
5484           1.2217304763960306 },
5485   { 1.4283586501307799, 0.89999999999999991, 0.69999999999999996,
5486           1.3962634015954636 },
5487   { 1.6600480747670940, 0.89999999999999991, 0.69999999999999996,
5488           1.5707963267948966 },
5489 };
5490 const double toler188 = 2.5000000000000020e-13;
5491
5492 // Test data for k=0.89999999999999991, nu=0.80000000000000004.
5493 // max(|f - f_GSL|): 4.4408920985006262e-16
5494 // max(|f - f_GSL| / |f_GSL|): 3.3100928058463168e-16
5495 const testcase_ellint_3<double>
5496 data189[10] =
5497 {
5498   { 0.0000000000000000, 0.89999999999999991, 0.80000000000000004,
5499           0.0000000000000000 },
5500   { 0.17385491439925146, 0.89999999999999991, 0.80000000000000004,
5501           0.17453292519943295 },
5502   { 0.34412950523113928, 0.89999999999999991, 0.80000000000000004,
5503           0.34906585039886590 },
5504   { 0.50931321668729590, 0.89999999999999991, 0.80000000000000004,
5505           0.52359877559829882 },
5506   { 0.67081081392296327, 0.89999999999999991, 0.80000000000000004,
5507           0.69813170079773179 },
5508   { 0.83268846097293259, 0.89999999999999991, 0.80000000000000004,
5509           0.87266462599716477 },
5510   { 1.0010985015814027, 0.89999999999999991, 0.80000000000000004,
5511           1.0471975511965976 },
5512   { 1.1834394045489678, 0.89999999999999991, 0.80000000000000004,
5513           1.2217304763960306 },
5514   { 1.3855695891683182, 0.89999999999999991, 0.80000000000000004,
5515           1.3962634015954636 },
5516   { 1.6044591960982202, 0.89999999999999991, 0.80000000000000004,
5517           1.5707963267948966 },
5518 };
5519 const double toler189 = 2.5000000000000020e-13;
5520
5521 // Test data for k=0.89999999999999991, nu=0.90000000000000002.
5522 // max(|f - f_GSL|): 8.8817841970012523e-16
5523 // max(|f - f_GSL| / |f_GSL|): 5.7167507456081732e-16
5524 const testcase_ellint_3<double>
5525 data190[10] =
5526 {
5527   { 0.0000000000000000, 0.89999999999999991, 0.90000000000000002,
5528           0.0000000000000000 },
5529   { 0.17368278986240135, 0.89999999999999991, 0.90000000000000002,
5530           0.17453292519943295 },
5531   { 0.34285962963961397, 0.89999999999999991, 0.90000000000000002,
5532           0.34906585039886590 },
5533   { 0.50549974644993312, 0.89999999999999991, 0.90000000000000002,
5534           0.52359877559829882 },
5535   { 0.66290623857720876, 0.89999999999999991, 0.90000000000000002,
5536           0.69813170079773179 },
5537   { 0.81921183128847175, 0.89999999999999991, 0.90000000000000002,
5538           0.87266462599716477 },
5539   { 0.98058481956066390, 0.89999999999999991, 0.90000000000000002,
5540           1.0471975511965976 },
5541   { 1.1543223520473569, 0.89999999999999991, 0.90000000000000002,
5542           1.2217304763960306 },
5543   { 1.3462119782292934, 0.89999999999999991, 0.90000000000000002,
5544           1.3962634015954636 },
5545   { 1.5536420236310948, 0.89999999999999991, 0.90000000000000002,
5546           1.5707963267948966 },
5547 };
5548 const double toler190 = 2.5000000000000020e-13;
5549
5550 template<typename Tp, unsigned int Num>
5551   void
5552   test(const testcase_ellint_3<Tp> (&data)[Num], Tp toler)
5553   {
5554     bool test __attribute__((unused)) = true;
5555     const Tp eps = std::numeric_limits<Tp>::epsilon();
5556     Tp max_abs_diff = -Tp(1);
5557     Tp max_abs_frac = -Tp(1);
5558     unsigned int num_datum = Num;
5559     for (unsigned int i = 0; i < num_datum; ++i)
5560          {
5561         const Tp f = std::ellint_3(data[i].k, data[i].nu,
5562                      data[i].phi);
5563         const Tp f0 = data[i].f0;
5564         const Tp diff = f - f0;
5565         if (std::abs(diff) > max_abs_diff)
5566           max_abs_diff = std::abs(diff);
5567         if (std::abs(f0) > Tp(10) * eps
5568          && std::abs(f) > Tp(10) * eps)
5569           {
5570             const Tp frac = diff / f0;
5571             if (std::abs(frac) > max_abs_frac)
5572               max_abs_frac = std::abs(frac);
5573           }
5574       }
5575     VERIFY(max_abs_frac < toler);
5576   }
5577
5578 int
5579 main()
5580 {
5581   test(data001, toler001);
5582   test(data002, toler002);
5583   test(data003, toler003);
5584   test(data004, toler004);
5585   test(data005, toler005);
5586   test(data006, toler006);
5587   test(data007, toler007);
5588   test(data008, toler008);
5589   test(data009, toler009);
5590   test(data010, toler010);
5591   test(data011, toler011);
5592   test(data012, toler012);
5593   test(data013, toler013);
5594   test(data014, toler014);
5595   test(data015, toler015);
5596   test(data016, toler016);
5597   test(data017, toler017);
5598   test(data018, toler018);
5599   test(data019, toler019);
5600   test(data020, toler020);
5601   test(data021, toler021);
5602   test(data022, toler022);
5603   test(data023, toler023);
5604   test(data024, toler024);
5605   test(data025, toler025);
5606   test(data026, toler026);
5607   test(data027, toler027);
5608   test(data028, toler028);
5609   test(data029, toler029);
5610   test(data030, toler030);
5611   test(data031, toler031);
5612   test(data032, toler032);
5613   test(data033, toler033);
5614   test(data034, toler034);
5615   test(data035, toler035);
5616   test(data036, toler036);
5617   test(data037, toler037);
5618   test(data038, toler038);
5619   test(data039, toler039);
5620   test(data040, toler040);
5621   test(data041, toler041);
5622   test(data042, toler042);
5623   test(data043, toler043);
5624   test(data044, toler044);
5625   test(data045, toler045);
5626   test(data046, toler046);
5627   test(data047, toler047);
5628   test(data048, toler048);
5629   test(data049, toler049);
5630   test(data050, toler050);
5631   test(data051, toler051);
5632   test(data052, toler052);
5633   test(data053, toler053);
5634   test(data054, toler054);
5635   test(data055, toler055);
5636   test(data056, toler056);
5637   test(data057, toler057);
5638   test(data058, toler058);
5639   test(data059, toler059);
5640   test(data060, toler060);
5641   test(data061, toler061);
5642   test(data062, toler062);
5643   test(data063, toler063);
5644   test(data064, toler064);
5645   test(data065, toler065);
5646   test(data066, toler066);
5647   test(data067, toler067);
5648   test(data068, toler068);
5649   test(data069, toler069);
5650   test(data070, toler070);
5651   test(data071, toler071);
5652   test(data072, toler072);
5653   test(data073, toler073);
5654   test(data074, toler074);
5655   test(data075, toler075);
5656   test(data076, toler076);
5657   test(data077, toler077);
5658   test(data078, toler078);
5659   test(data079, toler079);
5660   test(data080, toler080);
5661   test(data081, toler081);
5662   test(data082, toler082);
5663   test(data083, toler083);
5664   test(data084, toler084);
5665   test(data085, toler085);
5666   test(data086, toler086);
5667   test(data087, toler087);
5668   test(data088, toler088);
5669   test(data089, toler089);
5670   test(data090, toler090);
5671   test(data091, toler091);
5672   test(data092, toler092);
5673   test(data093, toler093);
5674   test(data094, toler094);
5675   test(data095, toler095);
5676   test(data096, toler096);
5677   test(data097, toler097);
5678   test(data098, toler098);
5679   test(data099, toler099);
5680   test(data100, toler100);
5681   test(data101, toler101);
5682   test(data102, toler102);
5683   test(data103, toler103);
5684   test(data104, toler104);
5685   test(data105, toler105);
5686   test(data106, toler106);
5687   test(data107, toler107);
5688   test(data108, toler108);
5689   test(data109, toler109);
5690   test(data110, toler110);
5691   test(data111, toler111);
5692   test(data112, toler112);
5693   test(data113, toler113);
5694   test(data114, toler114);
5695   test(data115, toler115);
5696   test(data116, toler116);
5697   test(data117, toler117);
5698   test(data118, toler118);
5699   test(data119, toler119);
5700   test(data120, toler120);
5701   test(data121, toler121);
5702   test(data122, toler122);
5703   test(data123, toler123);
5704   test(data124, toler124);
5705   test(data125, toler125);
5706   test(data126, toler126);
5707   test(data127, toler127);
5708   test(data128, toler128);
5709   test(data129, toler129);
5710   test(data130, toler130);
5711   test(data131, toler131);
5712   test(data132, toler132);
5713   test(data133, toler133);
5714   test(data134, toler134);
5715   test(data135, toler135);
5716   test(data136, toler136);
5717   test(data137, toler137);
5718   test(data138, toler138);
5719   test(data139, toler139);
5720   test(data140, toler140);
5721   test(data141, toler141);
5722   test(data142, toler142);
5723   test(data143, toler143);
5724   test(data144, toler144);
5725   test(data145, toler145);
5726   test(data146, toler146);
5727   test(data147, toler147);
5728   test(data148, toler148);
5729   test(data149, toler149);
5730   test(data150, toler150);
5731   test(data151, toler151);
5732   test(data152, toler152);
5733   test(data153, toler153);
5734   test(data154, toler154);
5735   test(data155, toler155);
5736   test(data156, toler156);
5737   test(data157, toler157);
5738   test(data158, toler158);
5739   test(data159, toler159);
5740   test(data160, toler160);
5741   test(data161, toler161);
5742   test(data162, toler162);
5743   test(data163, toler163);
5744   test(data164, toler164);
5745   test(data165, toler165);
5746   test(data166, toler166);
5747   test(data167, toler167);
5748   test(data168, toler168);
5749   test(data169, toler169);
5750   test(data170, toler170);
5751   test(data171, toler171);
5752   test(data172, toler172);
5753   test(data173, toler173);
5754   test(data174, toler174);
5755   test(data175, toler175);
5756   test(data176, toler176);
5757   test(data177, toler177);
5758   test(data178, toler178);
5759   test(data179, toler179);
5760   test(data180, toler180);
5761   test(data181, toler181);
5762   test(data182, toler182);
5763   test(data183, toler183);
5764   test(data184, toler184);
5765   test(data185, toler185);
5766   test(data186, toler186);
5767   test(data187, toler187);
5768   test(data188, toler188);
5769   test(data189, toler189);
5770   test(data190, toler190);
5771   return 0;
5772 }