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

   1 // { dg-do run { target c++11 } }
   2 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
   3 //
   4 // Copyright (C) 2016-2017 Free Software Foundation, Inc.
   5 //
   6 // This file is part of the GNU ISO C++ Library.  This library is free
   7 // software; you can redistribute it and/or modify it under the
   8 // terms of the GNU General Public License as published by the
   9 // Free Software Foundation; either version 3, or (at your option)
  10 // any later version.
  11 //
  12 // This library is distributed in the hope that it will be useful,
  13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 // GNU General Public License for more details.
  16 //
  17 // You should have received a copy of the GNU General Public License along
  18 // with this library; see the file COPYING3.  If not see
  19 // <http://www.gnu.org/licenses/>.
  20
  21 //  ellint_3
  22 //  Compare against values generated by the GNU Scientific Library.
  23 //  The GSL can be found on the web: http://www.gnu.org/software/gsl/
  24 #include <limits>
  25 #include <cmath>
  26 #if defined(__TEST_DEBUG)
  27 #  include <iostream>
  28 #  define VERIFY(A) \
  29   if (!(A)) \
  30     { \
  31       std::cout << "line " << __LINE__ \
  32         << "  max_abs_frac = " << max_abs_frac \
  33         << std::endl; \
  34     }
  35 #else
  36 #  include <testsuite_hooks.h>
  37 #endif
  38 #include <specfun_testcase.h>
  39
  40
  41 // Test data for k=-0.90000000000000002, nu=0.0000000000000000.
  42 // max(|f - f_GSL|): 4.4408920985006262e-16
  43 // max(|f - f_GSL| / |f_GSL|): 2.9686139313362077e-16
  44 const testcase_ellint_3<double>
  45 data001[10] =
  46 {
  47   { 0.0000000000000000, -0.90000000000000002, 0.0000000000000000,
  48           0.0000000000000000 },
  49   { 0.17525427376115024, -0.90000000000000002, 0.0000000000000000,
  50           0.17453292519943295 },
  51   { 0.35492464591297446, -0.90000000000000002, 0.0000000000000000,
  52           0.34906585039886590 },
  53   { 0.54388221416157112, -0.90000000000000002, 0.0000000000000000,
  54           0.52359877559829882 },
  55   { 0.74797400423532490, -0.90000000000000002, 0.0000000000000000,
  56           0.69813170079773179 },
  57   { 0.97463898451966458, -0.90000000000000002, 0.0000000000000000,
  58           0.87266462599716477 },
  59   { 1.2334463254523440, -0.90000000000000002, 0.0000000000000000,
  60           1.0471975511965976 },
  61   { 1.5355247765594913, -0.90000000000000002, 0.0000000000000000,
  62           1.2217304763960306 },
  63   { 1.8882928567775121, -0.90000000000000002, 0.0000000000000000,
  64           1.3962634015954636 },
  65   { 2.2805491384227703, -0.90000000000000002, 0.0000000000000000,
  66           1.5707963267948966 },
  67 };
  68 const double toler001 = 2.5000000000000020e-13;
  69
  70 // Test data for k=-0.90000000000000002, nu=0.10000000000000001.
  71 // max(|f - f_GSL|): 4.4408920985006262e-16
  72 // max(|f - f_GSL| / |f_GSL|): 3.0141810743801079e-16
  73 const testcase_ellint_3<double>
  74 data002[10] =
  75 {
  76   { 0.0000000000000000, -0.90000000000000002, 0.10000000000000001,
  77           0.0000000000000000 },
  78   { 0.17507714233254656, -0.90000000000000002, 0.10000000000000001,
  79           0.17453292519943295 },
  80   { 0.35350932904326521, -0.90000000000000002, 0.10000000000000001,
  81           0.34906585039886590 },
  82   { 0.53911129989870976, -0.90000000000000002, 0.10000000000000001,
  83           0.52359877559829882 },
  84   { 0.73666644254508395, -0.90000000000000002, 0.10000000000000001,
  85           0.69813170079773179 },
  86   { 0.95250736612100195, -0.90000000000000002, 0.10000000000000001,
  87           0.87266462599716477 },
  88   { 1.1950199550905594, -0.90000000000000002, 0.10000000000000001,
  89           1.0471975511965976 },
  90   { 1.4741687286340850, -0.90000000000000002, 0.10000000000000001,
  91           1.2217304763960306 },
  92   { 1.7968678183506057, -0.90000000000000002, 0.10000000000000001,
  93           1.3962634015954636 },
  94   { 2.1537868513875287, -0.90000000000000002, 0.10000000000000001,
  95           1.5707963267948966 },
  96 };
  97 const double toler002 = 2.5000000000000020e-13;
  98
  99 // Test data for k=-0.90000000000000002, nu=0.20000000000000001.
 100 // max(|f - f_GSL|): 2.2204460492503131e-16
 101 // max(|f - f_GSL| / |f_GSL|): 3.0588292817405780e-16
 102 const testcase_ellint_3<double>
 103 data003[10] =
 104 {
 105   { 0.0000000000000000, -0.90000000000000002, 0.20000000000000001,
 106           0.0000000000000000 },
 107   { 0.17490065089140927, -0.90000000000000002, 0.20000000000000001,
 108           0.17453292519943295 },
 109   { 0.35211377590661436, -0.90000000000000002, 0.20000000000000001,
 110           0.34906585039886590 },
 111   { 0.53448220334204100, -0.90000000000000002, 0.20000000000000001,
 112           0.52359877559829882 },
 113   { 0.72591368943179579, -0.90000000000000002, 0.20000000000000001,
 114           0.69813170079773179 },
 115   { 0.93192539780038763, -0.90000000000000002, 0.20000000000000001,
 116           0.87266462599716477 },
 117   { 1.1600809679692683, -0.90000000000000002, 0.20000000000000001,
 118           1.0471975511965976 },
 119   { 1.4195407225882510, -0.90000000000000002, 0.20000000000000001,
 120           1.2217304763960306 },
 121   { 1.7168966476424525, -0.90000000000000002, 0.20000000000000001,
 122           1.3962634015954636 },
 123   { 2.0443194576468890, -0.90000000000000002, 0.20000000000000001,
 124           1.5707963267948966 },
 125 };
 126 const double toler003 = 2.5000000000000020e-13;
 127
 128 // Test data for k=-0.90000000000000002, nu=0.29999999999999999.
 129 // max(|f - f_GSL|): 4.4408920985006262e-16
 130 // max(|f - f_GSL| / |f_GSL|): 3.2403611223075570e-16
 131 const testcase_ellint_3<double>
 132 data004[10] =
 133 {
 134   { 0.0000000000000000, -0.90000000000000002, 0.29999999999999999,
 135           0.0000000000000000 },
 136   { 0.17472479532647531, -0.90000000000000002, 0.29999999999999999,
 137           0.17453292519943295 },
 138   { 0.35073750187374114, -0.90000000000000002, 0.29999999999999999,
 139           0.34906585039886590 },
 140   { 0.52998766129466957, -0.90000000000000002, 0.29999999999999999,
 141           0.52359877559829882 },
 142   { 0.71566993548699553, -0.90000000000000002, 0.29999999999999999,
 143           0.69813170079773179 },
 144   { 0.91271517762560195, -0.90000000000000002, 0.29999999999999999,
 145           0.87266462599716477 },
 146   { 1.1281241199843370, -0.90000000000000002, 0.29999999999999999,
 147           1.0471975511965976 },
 148   { 1.3704929576917451, -0.90000000000000002, 0.29999999999999999,
 149           1.2217304763960306 },
 150   { 1.6461981511487713, -0.90000000000000002, 0.29999999999999999,
 151           1.3962634015954636 },
 152   { 1.9486280260314426, -0.90000000000000002, 0.29999999999999999,
 153           1.5707963267948966 },
 154 };
 155 const double toler004 = 2.5000000000000020e-13;
 156
 157 // Test data for k=-0.90000000000000002, nu=0.40000000000000002.
 158 // max(|f - f_GSL|): 4.4408920985006262e-16
 159 // max(|f - f_GSL| / |f_GSL|): 3.3487482375512111e-16
 160 const testcase_ellint_3<double>
 161 data005[10] =
 162 {
 163   { 0.0000000000000000, -0.90000000000000002, 0.40000000000000002,
 164           0.0000000000000000 },
 165   { 0.17454957156468837, -0.90000000000000002, 0.40000000000000002,
 166           0.17453292519943295 },
 167   { 0.34938003933330430, -0.90000000000000002, 0.40000000000000002,
 168           0.34906585039886590 },
 169   { 0.52562093533067433, -0.90000000000000002, 0.40000000000000002,
 170           0.52359877559829882 },
 171   { 0.70589461324915670, -0.90000000000000002, 0.40000000000000002,
 172           0.69813170079773179 },
 173   { 0.89472658511942849, -0.90000000000000002, 0.40000000000000002,
 174           0.87266462599716477 },
 175   { 1.0987419542323440, -0.90000000000000002, 0.40000000000000002,
 176           1.0471975511965976 },
 177   { 1.3261349565496303, -0.90000000000000002, 0.40000000000000002,
 178           1.2217304763960306 },
 179   { 1.5831293909853765, -0.90000000000000002, 0.40000000000000002,
 180           1.3962634015954636 },
 181   { 1.8641114227238349, -0.90000000000000002, 0.40000000000000002,
 182           1.5707963267948966 },
 183 };
 184 const double toler005 = 2.5000000000000020e-13;
 185
 186 // Test data for k=-0.90000000000000002, nu=0.50000000000000000.
 187 // max(|f - f_GSL|): 4.4408920985006262e-16
 188 // max(|f - f_GSL| / |f_GSL|): 3.4538944656036724e-16
 189 const testcase_ellint_3<double>
 190 data006[10] =
 191 {
 192   { 0.0000000000000000, -0.90000000000000002, 0.50000000000000000,
 193           0.0000000000000000 },
 194   { 0.17437497557073334, -0.90000000000000002, 0.50000000000000000,
 195           0.17453292519943295 },
 196   { 0.34804093691586013, -0.90000000000000002, 0.50000000000000000,
 197           0.34906585039886590 },
 198   { 0.52137576320372891, -0.90000000000000002, 0.50000000000000000,
 199           0.52359877559829882 },
 200   { 0.69655163996912262, -0.90000000000000002, 0.50000000000000000,
 201           0.69813170079773179 },
 202   { 0.87783188683054236, -0.90000000000000002, 0.50000000000000000,
 203           0.87266462599716477 },
 204   { 1.0716015959755185, -0.90000000000000002, 0.50000000000000000,
 205           1.0471975511965976 },
 206   { 1.2857636916026749, -0.90000000000000002, 0.50000000000000000,
 207           1.2217304763960306 },
 208   { 1.5264263913252363, -0.90000000000000002, 0.50000000000000000,
 209           1.3962634015954636 },
 210   { 1.7888013241937861, -0.90000000000000002, 0.50000000000000000,
 211           1.5707963267948966 },
 212 };
 213 const double toler006 = 2.5000000000000020e-13;
 214
 215 // Test data for k=-0.90000000000000002, nu=0.59999999999999998.
 216 // max(|f - f_GSL|): 4.4408920985006262e-16
 217 // max(|f - f_GSL| / |f_GSL|): 3.5560830683344639e-16
 218 const testcase_ellint_3<double>
 219 data007[10] =
 220 {
 221   { 0.0000000000000000, -0.90000000000000002, 0.59999999999999998,
 222           0.0000000000000000 },
 223   { 0.17420100334657812, -0.90000000000000002, 0.59999999999999998,
 224           0.17453292519943295 },
 225   { 0.34671975876122157, -0.90000000000000002, 0.59999999999999998,
 226           0.34906585039886590 },
 227   { 0.51724631570707946, -0.90000000000000002, 0.59999999999999998,
 228           0.52359877559829882 },
 229   { 0.68760879113743023, -0.90000000000000002, 0.59999999999999998,
 230           0.69813170079773179 },
 231   { 0.86192157779698364, -0.90000000000000002, 0.59999999999999998,
 232           0.87266462599716477 },
 233   { 1.0464279696166354, -0.90000000000000002, 0.59999999999999998,
 234           1.0471975511965976 },
 235   { 1.2488156247094007, -0.90000000000000002, 0.59999999999999998,
 236           1.2217304763960306 },
 237   { 1.4750988777188472, -0.90000000000000002, 0.59999999999999998,
 238           1.3962634015954636 },
 239   { 1.7211781128919523, -0.90000000000000002, 0.59999999999999998,
 240           1.5707963267948966 },
 241 };
 242 const double toler007 = 2.5000000000000020e-13;
 243
 244 // Test data for k=-0.90000000000000002, nu=0.69999999999999996.
 245 // max(|f - f_GSL|): 6.6613381477509392e-16
 246 // max(|f - f_GSL| / |f_GSL|): 5.4833366769839281e-16
 247 const testcase_ellint_3<double>
 248 data008[10] =
 249 {
 250   { 0.0000000000000000, -0.90000000000000002, 0.69999999999999996,
 251           0.0000000000000000 },
 252   { 0.17402765093102207, -0.90000000000000002, 0.69999999999999996,
 253           0.17453292519943295 },
 254   { 0.34541608382635131, -0.90000000000000002, 0.69999999999999996,
 255           0.34906585039886590 },
 256   { 0.51322715827061682, -0.90000000000000002, 0.69999999999999996,
 257           0.52359877559829882 },
 258   { 0.67903717872440272, -0.90000000000000002, 0.69999999999999996,
 259           0.69813170079773179 },
 260   { 0.84690113601682671, -0.90000000000000002, 0.69999999999999996,
 261           0.87266462599716477 },
 262   { 1.0229914311548418, -0.90000000000000002, 0.69999999999999996,
 263           1.0471975511965976 },
 264   { 1.2148329639709381, -0.90000000000000002, 0.69999999999999996,
 265           1.2217304763960306 },
 266   { 1.4283586501307803, -0.90000000000000002, 0.69999999999999996,
 267           1.3962634015954636 },
 268   { 1.6600480747670940, -0.90000000000000002, 0.69999999999999996,
 269           1.5707963267948966 },
 270 };
 271 const double toler008 = 2.5000000000000020e-13;
 272
 273 // Test data for k=-0.90000000000000002, nu=0.80000000000000004.
 274 // max(|f - f_GSL|): 4.4408920985006262e-16
 275 // max(|f - f_GSL| / |f_GSL|): 3.7525301941362493e-16
 276 const testcase_ellint_3<double>
 277 data009[10] =
 278 {
 279   { 0.0000000000000000, -0.90000000000000002, 0.80000000000000004,
 280           0.0000000000000000 },
 281   { 0.17385491439925146, -0.90000000000000002, 0.80000000000000004,
 282           0.17453292519943295 },
 283   { 0.34412950523113928, -0.90000000000000002, 0.80000000000000004,
 284           0.34906585039886590 },
 285   { 0.50931321668729590, -0.90000000000000002, 0.80000000000000004,
 286           0.52359877559829882 },
 287   { 0.67081081392296327, -0.90000000000000002, 0.80000000000000004,
 288           0.69813170079773179 },
 289   { 0.83268846097293259, -0.90000000000000002, 0.80000000000000004,
 290           0.87266462599716477 },
 291   { 1.0010985015814027, -0.90000000000000002, 0.80000000000000004,
 292           1.0471975511965976 },
 293   { 1.1834394045489680, -0.90000000000000002, 0.80000000000000004,
 294           1.2217304763960306 },
 295   { 1.3855695891683186, -0.90000000000000002, 0.80000000000000004,
 296           1.3962634015954636 },
 297   { 1.6044591960982202, -0.90000000000000002, 0.80000000000000004,
 298           1.5707963267948966 },
 299 };
 300 const double toler009 = 2.5000000000000020e-13;
 301
 302 // Test data for k=-0.90000000000000002, nu=0.90000000000000002.
 303 // max(|f - f_GSL|): 4.4408920985006262e-16
 304 // max(|f - f_GSL| / |f_GSL|): 3.8471853989694167e-16
 305 const testcase_ellint_3<double>
 306 data010[10] =
 307 {
 308   { 0.0000000000000000, -0.90000000000000002, 0.90000000000000002,
 309           0.0000000000000000 },
 310   { 0.17368278986240135, -0.90000000000000002, 0.90000000000000002,
 311           0.17453292519943295 },
 312   { 0.34285962963961397, -0.90000000000000002, 0.90000000000000002,
 313           0.34906585039886590 },
 314   { 0.50549974644993312, -0.90000000000000002, 0.90000000000000002,
 315           0.52359877559829882 },
 316   { 0.66290623857720876, -0.90000000000000002, 0.90000000000000002,
 317           0.69813170079773179 },
 318   { 0.81921183128847175, -0.90000000000000002, 0.90000000000000002,
 319           0.87266462599716477 },
 320   { 0.98058481956066390, -0.90000000000000002, 0.90000000000000002,
 321           1.0471975511965976 },
 322   { 1.1543223520473569, -0.90000000000000002, 0.90000000000000002,
 323           1.2217304763960306 },
 324   { 1.3462119782292938, -0.90000000000000002, 0.90000000000000002,
 325           1.3962634015954636 },
 326   { 1.5536420236310946, -0.90000000000000002, 0.90000000000000002,
 327           1.5707963267948966 },
 328 };
 329 const double toler010 = 2.5000000000000020e-13;
 330
 331 // Test data for k=-0.80000000000000004, nu=0.0000000000000000.
 332 // max(|f - f_GSL|): 4.4408920985006262e-16
 333 // max(|f - f_GSL| / |f_GSL|): 4.1175183168766718e-16
 334 const testcase_ellint_3<double>
 335 data011[10] =
 336 {
 337   { 0.0000000000000000, -0.80000000000000004, 0.0000000000000000,
 338           0.0000000000000000 },
 339   { 0.17510154241338899, -0.80000000000000004, 0.0000000000000000,
 340           0.17453292519943295 },
 341   { 0.35365068839779390, -0.80000000000000004, 0.0000000000000000,
 342           0.34906585039886590 },
 343   { 0.53926804409084550, -0.80000000000000004, 0.0000000000000000,
 344           0.52359877559829882 },
 345   { 0.73587926028070361, -0.80000000000000004, 0.0000000000000000,
 346           0.69813170079773179 },
 347   { 0.94770942970071170, -0.80000000000000004, 0.0000000000000000,
 348           0.87266462599716477 },
 349   { 1.1789022995388236, -0.80000000000000004, 0.0000000000000000,
 350           1.0471975511965976 },
 351   { 1.4323027881876009, -0.80000000000000004, 0.0000000000000000,
 352           1.2217304763960306 },
 353   { 1.7069629739121674, -0.80000000000000004, 0.0000000000000000,
 354           1.3962634015954636 },
 355   { 1.9953027776647296, -0.80000000000000004, 0.0000000000000000,
 356           1.5707963267948966 },
 357 };
 358 const double toler011 = 2.5000000000000020e-13;
 359
 360 // Test data for k=-0.80000000000000004, nu=0.10000000000000001.
 361 // max(|f - f_GSL|): 4.4408920985006262e-16
 362 // max(|f - f_GSL| / |f_GSL|): 4.1537164503193145e-16
 363 const testcase_ellint_3<double>
 364 data012[10] =
 365 {
 366   { 0.0000000000000000, -0.80000000000000004, 0.10000000000000001,
 367           0.0000000000000000 },
 368   { 0.17492468824017163, -0.80000000000000004, 0.10000000000000001,
 369           0.17453292519943295 },
 370   { 0.35224443521476911, -0.80000000000000004, 0.10000000000000001,
 371           0.34906585039886590 },
 372   { 0.53456851853226950, -0.80000000000000004, 0.10000000000000001,
 373           0.52359877559829882 },
 374   { 0.72488875602364922, -0.80000000000000004, 0.10000000000000001,
 375           0.69813170079773179 },
 376   { 0.92661354274638952, -0.80000000000000004, 0.10000000000000001,
 377           0.87266462599716477 },
 378   { 1.1432651144499075, -0.80000000000000004, 0.10000000000000001,
 379           1.0471975511965976 },
 380   { 1.3774479927211429, -0.80000000000000004, 0.10000000000000001,
 381           1.2217304763960306 },
 382   { 1.6287092337196041, -0.80000000000000004, 0.10000000000000001,
 383           1.3962634015954636 },
 384   { 1.8910755418379521, -0.80000000000000004, 0.10000000000000001,
 385           1.5707963267948966 },
 386 };
 387 const double toler012 = 2.5000000000000020e-13;
 388
 389 // Test data for k=-0.80000000000000004, nu=0.20000000000000001.
 390 // max(|f - f_GSL|): 4.4408920985006262e-16
 391 // max(|f - f_GSL| / |f_GSL|): 4.1894552974436829e-16
 392 const testcase_ellint_3<double>
 393 data013[10] =
 394 {
 395   { 0.0000000000000000, -0.80000000000000004, 0.20000000000000001,
 396           0.0000000000000000 },
 397   { 0.17474847286224940, -0.80000000000000004, 0.20000000000000001,
 398           0.17453292519943295 },
 399   { 0.35085779529084682, -0.80000000000000004, 0.20000000000000001,
 400           0.34906585039886590 },
 401   { 0.53000829263059146, -0.80000000000000004, 0.20000000000000001,
 402           0.52359877559829882 },
 403   { 0.71443466027453384, -0.80000000000000004, 0.20000000000000001,
 404           0.69813170079773179 },
 405   { 0.90698196872715420, -0.80000000000000004, 0.20000000000000001,
 406           0.87266462599716477 },
 407   { 1.1108198200558579, -0.80000000000000004, 0.20000000000000001,
 408           1.0471975511965976 },
 409   { 1.3284988909963957, -0.80000000000000004, 0.20000000000000001,
 410           1.2217304763960306 },
 411   { 1.5600369318140328, -0.80000000000000004, 0.20000000000000001,
 412           1.3962634015954636 },
 413   { 1.8007226661734588, -0.80000000000000004, 0.20000000000000001,
 414           1.5707963267948966 },
 415 };
 416 const double toler013 = 2.5000000000000020e-13;
 417
 418 // Test data for k=-0.80000000000000004, nu=0.29999999999999999.
 419 // max(|f - f_GSL|): 4.4408920985006262e-16
 420 // max(|f - f_GSL| / |f_GSL|): 4.2247517409029886e-16
 421 const testcase_ellint_3<double>
 422 data014[10] =
 423 {
 424   { 0.0000000000000000, -0.80000000000000004, 0.29999999999999999,
 425           0.0000000000000000 },
 426   { 0.17457289217669889, -0.80000000000000004, 0.29999999999999999,
 427           0.17453292519943295 },
 428   { 0.34949028801501258, -0.80000000000000004, 0.29999999999999999,
 429           0.34906585039886590 },
 430   { 0.52558024362769307, -0.80000000000000004, 0.29999999999999999,
 431           0.52359877559829882 },
 432   { 0.70447281740094891, -0.80000000000000004, 0.29999999999999999,
 433           0.69813170079773179 },
 434   { 0.88864745641528986, -0.80000000000000004, 0.29999999999999999,
 435           0.87266462599716477 },
 436   { 1.0811075819341462, -0.80000000000000004, 0.29999999999999999,
 437           1.0471975511965976 },
 438   { 1.2844589654082377, -0.80000000000000004, 0.29999999999999999,
 439           1.2217304763960306 },
 440   { 1.4991461361277847, -0.80000000000000004, 0.29999999999999999,
 441           1.3962634015954636 },
 442   { 1.7214611048717301, -0.80000000000000004, 0.29999999999999999,
 443           1.5707963267948966 },
 444 };
 445 const double toler014 = 2.5000000000000020e-13;
 446
 447 // Test data for k=-0.80000000000000004, nu=0.40000000000000002.
 448 // max(|f - f_GSL|): 4.4408920985006262e-16
 449 // max(|f - f_GSL| / |f_GSL|): 4.2596216594752862e-16
 450 const testcase_ellint_3<double>
 451 data015[10] =
 452 {
 453   { 0.0000000000000000, -0.80000000000000004, 0.40000000000000002,
 454           0.0000000000000000 },
 455   { 0.17439794211872175, -0.80000000000000004, 0.40000000000000002,
 456           0.17453292519943295 },
 457   { 0.34814144964568972, -0.80000000000000004, 0.40000000000000002,
 458           0.34906585039886590 },
 459   { 0.52127776285273064, -0.80000000000000004, 0.40000000000000002,
 460           0.52359877559829882 },
 461   { 0.69496411438966588, -0.80000000000000004, 0.40000000000000002,
 462           0.69813170079773179 },
 463   { 0.87146878427509589, -0.80000000000000004, 0.40000000000000002,
 464           0.87266462599716477 },
 465   { 1.0537579024937762, -0.80000000000000004, 0.40000000000000002,
 466           1.0471975511965976 },
 467   { 1.2445534387922637, -0.80000000000000004, 0.40000000000000002,
 468           1.2217304763960306 },
 469   { 1.4446769766361993, -0.80000000000000004, 0.40000000000000002,
 470           1.3962634015954636 },
 471   { 1.6512267838651289, -0.80000000000000004, 0.40000000000000002,
 472           1.5707963267948966 },
 473 };
 474 const double toler015 = 2.5000000000000020e-13;
 475
 476 // Test data for k=-0.80000000000000004, nu=0.50000000000000000.
 477 // max(|f - f_GSL|): 4.4408920985006262e-16
 478 // max(|f - f_GSL| / |f_GSL|): 4.2940800093915668e-16
 479 const testcase_ellint_3<double>
 480 data016[10] =
 481 {
 482   { 0.0000000000000000, -0.80000000000000004, 0.50000000000000000,
 483           0.0000000000000000 },
 484   { 0.17422361866118044, -0.80000000000000004, 0.50000000000000000,
 485           0.17453292519943295 },
 486   { 0.34681083254170475, -0.80000000000000004, 0.50000000000000000,
 487           0.34906585039886590 },
 488   { 0.51709470815494440, -0.80000000000000004, 0.50000000000000000,
 489           0.52359877559829882 },
 490   { 0.68587375344080237, -0.80000000000000004, 0.50000000000000000,
 491           0.69813170079773179 },
 492   { 0.85532571852810624, -0.80000000000000004, 0.50000000000000000,
 493           0.87266462599716477 },
 494   { 1.0284677391874903, -0.80000000000000004, 0.50000000000000000,
 495           1.0471975511965976 },
 496   { 1.2081693942686225, -0.80000000000000004, 0.50000000000000000,
 497           1.2217304763960306 },
 498   { 1.3955803006426311, -0.80000000000000004, 0.50000000000000000,
 499           1.3962634015954636 },
 500   { 1.5884528947755532, -0.80000000000000004, 0.50000000000000000,
 501           1.5707963267948966 },
 502 };
 503 const double toler016 = 2.5000000000000020e-13;
 504
 505 // Test data for k=-0.80000000000000004, nu=0.59999999999999998.
 506 // max(|f - f_GSL|): 4.4408920985006262e-16
 507 // max(|f - f_GSL| / |f_GSL|): 4.3281408974056389e-16
 508 const testcase_ellint_3<double>
 509 data017[10] =
 510 {
 511   { 0.0000000000000000, -0.80000000000000004, 0.59999999999999998,
 512           0.0000000000000000 },
 513   { 0.17404991781414089, -0.80000000000000004, 0.59999999999999998,
 514           0.17453292519943295 },
 515   { 0.34549800443625167, -0.80000000000000004, 0.59999999999999998,
 516           0.34906585039886590 },
 517   { 0.51302536167001545, -0.80000000000000004, 0.59999999999999998,
 518           0.52359877559829882 },
 519   { 0.67717065003912236, -0.80000000000000004, 0.59999999999999998,
 520           0.69813170079773179 },
 521   { 0.84011512421134416, -0.80000000000000004, 0.59999999999999998,
 522           0.87266462599716477 },
 523   { 1.0049863847088740, -0.80000000000000004, 0.59999999999999998,
 524           1.0471975511965976 },
 525   { 1.1748145941898920, -0.80000000000000004, 0.59999999999999998,
 526           1.2217304763960306 },
 527   { 1.3510319699755071, -0.80000000000000004, 0.59999999999999998,
 528           1.3962634015954636 },
 529   { 1.5319262547427865, -0.80000000000000004, 0.59999999999999998,
 530           1.5707963267948966 },
 531 };
 532 const double toler017 = 2.5000000000000020e-13;
 533
 534 // Test data for k=-0.80000000000000004, nu=0.69999999999999996.
 535 // max(|f - f_GSL|): 2.2204460492503131e-16
 536 // max(|f - f_GSL| / |f_GSL|): 4.3618176466061808e-16
 537 const testcase_ellint_3<double>
 538 data018[10] =
 539 {
 540   { 0.0000000000000000, -0.80000000000000004, 0.69999999999999996,
 541           0.0000000000000000 },
 542   { 0.17387683562442199, -0.80000000000000004, 0.69999999999999996,
 543           0.17453292519943295 },
 544   { 0.34420254775101611, -0.80000000000000004, 0.69999999999999996,
 545           0.34906585039886590 },
 546   { 0.50906439222143673, -0.80000000000000004, 0.69999999999999996,
 547           0.52359877559829882 },
 548   { 0.66882693152688422, -0.80000000000000004, 0.69999999999999996,
 549           0.69813170079773179 },
 550   { 0.82574792844091316, -0.80000000000000004, 0.69999999999999996,
 551           0.87266462599716477 },
 552   { 0.98310431309490931, -0.80000000000000004, 0.69999999999999996,
 553           1.0471975511965976 },
 554   { 1.1440884535113258, -0.80000000000000004, 0.69999999999999996,
 555           1.2217304763960306 },
 556   { 1.3103743938952537, -0.80000000000000004, 0.69999999999999996,
 557           1.3962634015954636 },
 558   { 1.4806912324625332, -0.80000000000000004, 0.69999999999999996,
 559           1.5707963267948966 },
 560 };
 561 const double toler018 = 2.5000000000000020e-13;
 562
 563 // Test data for k=-0.80000000000000004, nu=0.80000000000000004.
 564 // max(|f - f_GSL|): 4.4408920985006262e-16
 565 // max(|f - f_GSL| / |f_GSL|): 4.3951228558314112e-16
 566 const testcase_ellint_3<double>
 567 data019[10] =
 568 {
 569   { 0.0000000000000000, -0.80000000000000004, 0.80000000000000004,
 570           0.0000000000000000 },
 571   { 0.17370436817515203, -0.80000000000000004, 0.80000000000000004,
 572           0.17453292519943295 },
 573   { 0.34292405894783395, -0.80000000000000004, 0.80000000000000004,
 574           0.34906585039886590 },
 575   { 0.50520682176250076, -0.80000000000000004, 0.80000000000000004,
 576           0.52359877559829882 },
 577   { 0.66081751679736178, -0.80000000000000004, 0.80000000000000004,
 578           0.69813170079773179 },
 579   { 0.81214672249355102, -0.80000000000000004, 0.80000000000000004,
 580           0.87266462599716477 },
 581   { 0.96264481387685552, -0.80000000000000004, 0.80000000000000004,
 582           1.0471975511965976 },
 583   { 1.1156611352656258, -0.80000000000000004, 0.80000000000000004,
 584           1.2217304763960306 },
 585   { 1.2730756225143889, -0.80000000000000004, 0.80000000000000004,
 586           1.3962634015954636 },
 587   { 1.4339837018309471, -0.80000000000000004, 0.80000000000000004,
 588           1.5707963267948966 },
 589 };
 590 const double toler019 = 2.5000000000000020e-13;
 591
 592 // Test data for k=-0.80000000000000004, nu=0.90000000000000002.
 593 // max(|f - f_GSL|): 3.3306690738754696e-16
 594 // max(|f - f_GSL| / |f_GSL|): 4.4280684534289690e-16
 595 const testcase_ellint_3<double>
 596 data020[10] =
 597 {
 598   { 0.0000000000000000, -0.80000000000000004, 0.90000000000000002,
 599           0.0000000000000000 },
 600   { 0.17353251158533151, -0.80000000000000004, 0.90000000000000002,
 601           0.17453292519943295 },
 602   { 0.34166214791545768, -0.80000000000000004, 0.90000000000000002,
 603           0.34906585039886590 },
 604   { 0.50144799535130569, -0.80000000000000004, 0.90000000000000002,
 605           0.52359877559829882 },
 606   { 0.65311976193814425, -0.80000000000000004, 0.90000000000000002,
 607           0.69813170079773179 },
 608   { 0.79924384892320866, -0.80000000000000004, 0.90000000000000002,
 609           0.87266462599716477 },
 610   { 0.94345762353365603, -0.80000000000000004, 0.90000000000000002,
 611           1.0471975511965976 },
 612   { 1.0892582069219161, -0.80000000000000004, 0.90000000000000002,
 613           1.2217304763960306 },
 614   { 1.2387000876610268, -0.80000000000000004, 0.90000000000000002,
 615           1.3962634015954636 },
 616   { 1.3911845406776222, -0.80000000000000004, 0.90000000000000002,
 617           1.5707963267948966 },
 618 };
 619 const double toler020 = 2.5000000000000020e-13;
 620
 621 // Test data for k=-0.69999999999999996, nu=0.0000000000000000.
 622 // max(|f - f_GSL|): 3.3306690738754696e-16
 623 // max(|f - f_GSL| / |f_GSL|): 3.5930208052157665e-16
 624 const testcase_ellint_3<double>
 625 data021[10] =
 626 {
 627   { 0.0000000000000000, -0.69999999999999996, 0.0000000000000000,
 628           0.0000000000000000 },
 629   { 0.17496737466916723, -0.69999999999999996, 0.0000000000000000,
 630           0.17453292519943295 },
 631   { 0.35254687535677925, -0.69999999999999996, 0.0000000000000000,
 632           0.34906585039886590 },
 633   { 0.53536740275997119, -0.69999999999999996, 0.0000000000000000,
 634           0.52359877559829882 },
 635   { 0.72603797651684454, -0.69999999999999996, 0.0000000000000000,
 636           0.69813170079773179 },
 637   { 0.92698296348313458, -0.69999999999999996, 0.0000000000000000,
 638           0.87266462599716477 },
 639   { 1.1400447527693316, -0.69999999999999996, 0.0000000000000000,
 640           1.0471975511965976 },
 641   { 1.3657668117194073, -0.69999999999999996, 0.0000000000000000,
 642           1.2217304763960306 },
 643   { 1.6024686895959159, -0.69999999999999996, 0.0000000000000000,
 644           1.3962634015954636 },
 645   { 1.8456939983747236, -0.69999999999999996, 0.0000000000000000,
 646           1.5707963267948966 },
 647 };
 648 const double toler021 = 2.5000000000000020e-13;
 649
 650 // Test data for k=-0.69999999999999996, nu=0.10000000000000001.
 651 // max(|f - f_GSL|): 3.3306690738754696e-16
 652 // max(|f - f_GSL| / |f_GSL|): 3.6735282577377367e-16
 653 const testcase_ellint_3<double>
 654 data022[10] =
 655 {
 656   { 0.0000000000000000, -0.69999999999999996, 0.10000000000000001,
 657           0.0000000000000000 },
 658   { 0.17479076384884684, -0.69999999999999996, 0.10000000000000001,
 659           0.17453292519943295 },
 660   { 0.35114844900396364, -0.69999999999999996, 0.10000000000000001,
 661           0.34906585039886590 },
 662   { 0.53072776947527001, -0.69999999999999996, 0.10000000000000001,
 663           0.52359877559829882 },
 664   { 0.71530198262386235, -0.69999999999999996, 0.10000000000000001,
 665           0.69813170079773179 },
 666   { 0.90666760677828306, -0.69999999999999996, 0.10000000000000001,
 667           0.87266462599716477 },
 668   { 1.1063366517438080, -0.69999999999999996, 0.10000000000000001,
 669           1.0471975511965976 },
 670   { 1.3149477243092149, -0.69999999999999996, 0.10000000000000001,
 671           1.2217304763960306 },
 672   { 1.5314886725038925, -0.69999999999999996, 0.10000000000000001,
 673           1.3962634015954636 },
 674   { 1.7528050171757608, -0.69999999999999996, 0.10000000000000001,
 675           1.5707963267948966 },
 676 };
 677 const double toler022 = 2.5000000000000020e-13;
 678
 679 // Test data for k=-0.69999999999999996, nu=0.20000000000000001.
 680 // max(|f - f_GSL|): 3.3306690738754696e-16
 681 // max(|f - f_GSL| / |f_GSL|): 3.7517969287516802e-16
 682 const testcase_ellint_3<double>
 683 data023[10] =
 684 {
 685   { 0.0000000000000000, -0.69999999999999996, 0.20000000000000001,
 686           0.0000000000000000 },
 687   { 0.17461479077791475, -0.69999999999999996, 0.20000000000000001,
 688           0.17453292519943295 },
 689   { 0.34976950621407538, -0.69999999999999996, 0.20000000000000001,
 690           0.34906585039886590 },
 691   { 0.52622533231350177, -0.69999999999999996, 0.20000000000000001,
 692           0.52359877559829882 },
 693   { 0.70508774017895215, -0.69999999999999996, 0.20000000000000001,
 694           0.69813170079773179 },
 695   { 0.88775302531730294, -0.69999999999999996, 0.20000000000000001,
 696           0.87266462599716477 },
 697   { 1.0756195476149006, -0.69999999999999996, 0.20000000000000001,
 698           1.0471975511965976 },
 699   { 1.2695349716654374, -0.69999999999999996, 0.20000000000000001,
 700           1.2217304763960306 },
 701   { 1.4690814617070540, -0.69999999999999996, 0.20000000000000001,
 702           1.3962634015954636 },
 703   { 1.6721098780092145, -0.69999999999999996, 0.20000000000000001,
 704           1.5707963267948966 },
 705 };
 706 const double toler023 = 2.5000000000000020e-13;
 707
 708 // Test data for k=-0.69999999999999996, nu=0.29999999999999999.
 709 // max(|f - f_GSL|): 4.4408920985006262e-16
 710 // max(|f - f_GSL| / |f_GSL|): 3.8280039841080712e-16
 711 const testcase_ellint_3<double>
 712 data024[10] =
 713 {
 714   { 0.0000000000000000, -0.69999999999999996, 0.29999999999999999,
 715           0.0000000000000000 },
 716   { 0.17443945136076175, -0.69999999999999996, 0.29999999999999999,
 717           0.17453292519943295 },
 718   { 0.34840956983535287, -0.69999999999999996, 0.29999999999999999,
 719           0.34906585039886590 },
 720   { 0.52185308551329168, -0.69999999999999996, 0.29999999999999999,
 721           0.52359877559829882 },
 722   { 0.69535240431168255, -0.69999999999999996, 0.29999999999999999,
 723           0.69813170079773179 },
 724   { 0.87007983473964923, -0.69999999999999996, 0.29999999999999999,
 725           0.87266462599716477 },
 726   { 1.0474657975577066, -0.69999999999999996, 0.29999999999999999,
 727           1.0471975511965976 },
 728   { 1.2286225419931891, -0.69999999999999996, 0.29999999999999999,
 729           1.2217304763960306 },
 730   { 1.4136490671013271, -0.69999999999999996, 0.29999999999999999,
 731           1.3962634015954636 },
 732   { 1.6011813647733213, -0.69999999999999996, 0.29999999999999999,
 733           1.5707963267948966 },
 734 };
 735 const double toler024 = 2.5000000000000020e-13;
 736
 737 // Test data for k=-0.69999999999999996, nu=0.40000000000000002.
 738 // max(|f - f_GSL|): 4.4408920985006262e-16
 739 // max(|f - f_GSL| / |f_GSL|): 4.3472957053482092e-16
 740 const testcase_ellint_3<double>
 741 data025[10] =
 742 {
 743   { 0.0000000000000000, -0.69999999999999996, 0.40000000000000002,
 744           0.0000000000000000 },
 745   { 0.17426474153983229, -0.69999999999999996, 0.40000000000000002,
 746           0.17453292519943295 },
 747   { 0.34706817945773732, -0.69999999999999996, 0.40000000000000002,
 748           0.34906585039886590 },
 749   { 0.51760452851738148, -0.69999999999999996, 0.40000000000000002,
 750           0.52359877559829882 },
 751   { 0.68605801534722755, -0.69999999999999996, 0.40000000000000002,
 752           0.69813170079773179 },
 753   { 0.85351339387296532, -0.69999999999999996, 0.40000000000000002,
 754           0.87266462599716477 },
 755   { 1.0215297967969539, -0.69999999999999996, 0.40000000000000002,
 756           1.0471975511965976 },
 757   { 1.1915051074460530, -0.69999999999999996, 0.40000000000000002,
 758           1.2217304763960306 },
 759   { 1.3639821911744707, -0.69999999999999996, 0.40000000000000002,
 760           1.3962634015954636 },
 761   { 1.5382162002954762, -0.69999999999999996, 0.40000000000000002,
 762           1.5707963267948966 },
 763 };
 764 const double toler025 = 2.5000000000000020e-13;
 765
 766 // Test data for k=-0.69999999999999996, nu=0.50000000000000000.
 767 // max(|f - f_GSL|): 3.3306690738754696e-16
 768 // max(|f - f_GSL| / |f_GSL|): 3.9748346743390620e-16
 769 const testcase_ellint_3<double>
 770 data026[10] =
 771 {
 772   { 0.0000000000000000, -0.69999999999999996, 0.50000000000000000,
 773           0.0000000000000000 },
 774   { 0.17409065729516096, -0.69999999999999996, 0.50000000000000000,
 775           0.17453292519943295 },
 776   { 0.34574489064986091, -0.69999999999999996, 0.50000000000000000,
 777           0.34906585039886590 },
 778   { 0.51347361925579782, -0.69999999999999996, 0.50000000000000000,
 779           0.52359877559829882 },
 780   { 0.67717079489579279, -0.69999999999999996, 0.50000000000000000,
 781           0.69813170079773179 },
 782   { 0.83793902055292280, -0.69999999999999996, 0.50000000000000000,
 783           0.87266462599716477 },
 784   { 0.99752863545289705, -0.69999999999999996, 0.50000000000000000,
 785           1.0471975511965976 },
 786   { 1.1576240080401501, -0.69999999999999996, 0.50000000000000000,
 787           1.2217304763960306 },
 788   { 1.3191464023923762, -0.69999999999999996, 0.50000000000000000,
 789           1.3962634015954636 },
 790   { 1.4818433192178544, -0.69999999999999996, 0.50000000000000000,
 791           1.5707963267948966 },
 792 };
 793 const double toler026 = 2.5000000000000020e-13;
 794
 795 // Test data for k=-0.69999999999999996, nu=0.59999999999999998.
 796 // max(|f - f_GSL|): 3.3306690738754696e-16
 797 // max(|f - f_GSL| / |f_GSL|): 4.0457157538295173e-16
 798 const testcase_ellint_3<double>
 799 data027[10] =
 800 {
 801   { 0.0000000000000000, -0.69999999999999996, 0.59999999999999998,
 802           0.0000000000000000 },
 803   { 0.17391719464391614, -0.69999999999999996, 0.59999999999999998,
 804           0.17453292519943295 },
 805   { 0.34443927423869031, -0.69999999999999996, 0.59999999999999998,
 806           0.34906585039886590 },
 807   { 0.50945473266486063, -0.69999999999999996, 0.59999999999999998,
 808           0.52359877559829882 },
 809   { 0.66866056326513812, -0.69999999999999996, 0.59999999999999998,
 810           0.69813170079773179 },
 811   { 0.82325830002337352, -0.69999999999999996, 0.59999999999999998,
 812           0.87266462599716477 },
 813   { 0.97522808245669368, -0.69999999999999996, 0.59999999999999998,
 814           1.0471975511965976 },
 815   { 1.1265300613705285, -0.69999999999999996, 0.59999999999999998,
 816           1.2217304763960306 },
 817   { 1.2784066076152001, -0.69999999999999996, 0.59999999999999998,
 818           1.3962634015954636 },
 819   { 1.4309994736080540, -0.69999999999999996, 0.59999999999999998,
 820           1.5707963267948966 },
 821 };
 822 const double toler027 = 2.5000000000000020e-13;
 823
 824 // Test data for k=-0.69999999999999996, nu=0.69999999999999996.
 825 // max(|f - f_GSL|): 4.4408920985006262e-16
 826 // max(|f - f_GSL| / |f_GSL|): 5.4867405596732161e-16
 827 const testcase_ellint_3<double>
 828 data028[10] =
 829 {
 830   { 0.0000000000000000, -0.69999999999999996, 0.69999999999999996,
 831           0.0000000000000000 },
 832   { 0.17374434963995031, -0.69999999999999996, 0.69999999999999996,
 833           0.17453292519943295 },
 834   { 0.34315091562900674, -0.69999999999999996, 0.69999999999999996,
 835           0.34906585039886590 },
 836   { 0.50554262375653347, -0.69999999999999996, 0.69999999999999996,
 837           0.52359877559829882 },
 838   { 0.66050025406305801, -0.69999999999999996, 0.69999999999999996,
 839           0.69813170079773179 },
 840   { 0.80938620118847404, -0.69999999999999996, 0.69999999999999996,
 841           0.87266462599716477 },
 842   { 0.95443223855852144, -0.69999999999999996, 0.69999999999999996,
 843           1.0471975511965976 },
 844   { 1.0978573207128304, -0.69999999999999996, 0.69999999999999996,
 845           1.2217304763960306 },
 846   { 1.2411754575007123, -0.69999999999999996, 0.69999999999999996,
 847           1.3962634015954636 },
 848   { 1.3848459188329196, -0.69999999999999996, 0.69999999999999996,
 849           1.5707963267948966 },
 850 };
 851 const double toler028 = 2.5000000000000020e-13;
 852
 853 // Test data for k=-0.69999999999999996, nu=0.80000000000000004.
 854 // max(|f - f_GSL|): 4.4408920985006262e-16
 855 // max(|f - f_GSL| / |f_GSL|): 4.1829502028913879e-16
 856 const testcase_ellint_3<double>
 857 data029[10] =
 858 {
 859   { 0.0000000000000000, -0.69999999999999996, 0.80000000000000004,
 860           0.0000000000000000 },
 861   { 0.17357211837335740, -0.69999999999999996, 0.80000000000000004,
 862           0.17453292519943295 },
 863   { 0.34187941416012108, -0.69999999999999996, 0.80000000000000004,
 864           0.34906585039886590 },
 865   { 0.50173239465478259, -0.69999999999999996, 0.80000000000000004,
 866           0.52359877559829882 },
 867   { 0.65266550725988315, -0.69999999999999996, 0.80000000000000004,
 868           0.69813170079773179 },
 869   { 0.79624879865249298, -0.69999999999999996, 0.80000000000000004,
 870           0.87266462599716477 },
 871   { 0.93497577043296920, -0.69999999999999996, 0.80000000000000004,
 872           1.0471975511965976 },
 873   { 1.0713041566930750, -0.69999999999999996, 0.80000000000000004,
 874           1.2217304763960306 },
 875   { 1.2069772023255654, -0.69999999999999996, 0.80000000000000004,
 876           1.3962634015954636 },
 877   { 1.3427110650397531, -0.69999999999999996, 0.80000000000000004,
 878           1.5707963267948966 },
 879 };
 880 const double toler029 = 2.5000000000000020e-13;
 881
 882 // Test data for k=-0.69999999999999996, nu=0.90000000000000002.
 883 // max(|f - f_GSL|): 3.3306690738754696e-16
 884 // max(|f - f_GSL| / |f_GSL|): 4.2494869624129105e-16
 885 const testcase_ellint_3<double>
 886 data030[10] =
 887 {
 888   { 0.0000000000000000, -0.69999999999999996, 0.90000000000000002,
 889           0.0000000000000000 },
 890   { 0.17340049697003637, -0.69999999999999996, 0.90000000000000002,
 891           0.17453292519943295 },
 892   { 0.34062438249741556, -0.69999999999999996, 0.90000000000000002,
 893           0.34906585039886590 },
 894   { 0.49801946510076867, -0.69999999999999996, 0.90000000000000002,
 895           0.52359877559829882 },
 896   { 0.64513432604750476, -0.69999999999999996, 0.90000000000000002,
 897           0.69813170079773179 },
 898   { 0.78378145487573758, -0.69999999999999996, 0.90000000000000002,
 899           0.87266462599716477 },
 900   { 0.91671799500854623, -0.69999999999999996, 0.90000000000000002,
 901           1.0471975511965976 },
 902   { 1.0466193579463123, -0.69999999999999996, 0.90000000000000002,
 903           1.2217304763960306 },
 904   { 1.1754218079199146, -0.69999999999999996, 0.90000000000000002,
 905           1.3962634015954636 },
 906   { 1.3040500499695913, -0.69999999999999996, 0.90000000000000002,
 907           1.5707963267948966 },
 908 };
 909 const double toler030 = 2.5000000000000020e-13;
 910
 911 // Test data for k=-0.59999999999999998, nu=0.0000000000000000.
 912 // max(|f - f_GSL|): 4.4408920985006262e-16
 913 // max(|f - f_GSL| / |f_GSL|): 2.8964816695821429e-16
 914 const testcase_ellint_3<double>
 915 data031[10] =
 916 {
 917   { 0.0000000000000000, -0.59999999999999998, 0.0000000000000000,
 918           0.0000000000000000 },
 919   { 0.17485154362988359, -0.59999999999999998, 0.0000000000000000,
 920           0.17453292519943295 },
 921   { 0.35160509865544326, -0.59999999999999998, 0.0000000000000000,
 922           0.34906585039886590 },
 923   { 0.53210652578446138, -0.59999999999999998, 0.0000000000000000,
 924           0.52359877559829882 },
 925   { 0.71805304664485659, -0.59999999999999998, 0.0000000000000000,
 926           0.69813170079773179 },
 927   { 0.91082759030195970, -0.59999999999999998, 0.0000000000000000,
 928           0.87266462599716477 },
 929   { 1.1112333229323361, -0.59999999999999998, 0.0000000000000000,
 930           1.0471975511965976 },
 931   { 1.3191461190365270, -0.59999999999999998, 0.0000000000000000,
 932           1.2217304763960306 },
 933   { 1.5332022105084773, -0.59999999999999998, 0.0000000000000000,
 934           1.3962634015954636 },
 935   { 1.7507538029157526, -0.59999999999999998, 0.0000000000000000,
 936           1.5707963267948966 },
 937 };
 938 const double toler031 = 2.5000000000000020e-13;
 939
 940 // Test data for k=-0.59999999999999998, nu=0.10000000000000001.
 941 // max(|f - f_GSL|): 4.4408920985006262e-16
 942 // max(|f - f_GSL| / |f_GSL|): 2.6674242225057385e-16
 943 const testcase_ellint_3<double>
 944 data032[10] =
 945 {
 946   { 0.0000000000000000, -0.59999999999999998, 0.10000000000000001,
 947           0.0000000000000000 },
 948   { 0.17467514275022011, -0.59999999999999998, 0.10000000000000001,
 949           0.17453292519943295 },
 950   { 0.35021333086258255, -0.59999999999999998, 0.10000000000000001,
 951           0.34906585039886590 },
 952   { 0.52751664092962691, -0.59999999999999998, 0.10000000000000001,
 953           0.52359877559829882 },
 954   { 0.70752126971957874, -0.59999999999999998, 0.10000000000000001,
 955           0.69813170079773179 },
 956   { 0.89111058756112871, -0.59999999999999998, 0.10000000000000001,
 957           0.87266462599716477 },
 958   { 1.0789241202877768, -0.59999999999999998, 0.10000000000000001,
 959           1.0471975511965976 },
 960   { 1.2710800210399946, -0.59999999999999998, 0.10000000000000001,
 961           1.2217304763960306 },
 962   { 1.4669060574440276, -0.59999999999999998, 0.10000000000000001,
 963           1.3962634015954636 },
 964   { 1.6648615773343014, -0.59999999999999998, 0.10000000000000001,
 965           1.5707963267948966 },
 966 };
 967 const double toler032 = 2.5000000000000020e-13;
 968
 969 // Test data for k=-0.59999999999999998, nu=0.20000000000000001.
 970 // max(|f - f_GSL|): 6.6613381477509392e-16
 971 // max(|f - f_GSL| / |f_GSL|): 4.1891472451898755e-16
 972 const testcase_ellint_3<double>
 973 data033[10] =
 974 {
 975   { 0.0000000000000000, -0.59999999999999998, 0.20000000000000001,
 976           0.0000000000000000 },
 977   { 0.17449937871800650, -0.59999999999999998, 0.20000000000000001,
 978           0.17453292519943295 },
 979   { 0.34884093647346553, -0.59999999999999998, 0.20000000000000001,
 980           0.34906585039886590 },
 981   { 0.52306221119844087, -0.59999999999999998, 0.20000000000000001,
 982           0.52359877559829882 },
 983   { 0.69749955678982223, -0.59999999999999998, 0.20000000000000001,
 984           0.69813170079773179 },
 985   { 0.87274610682416853, -0.59999999999999998, 0.20000000000000001,
 986           0.87266462599716477 },
 987   { 1.0494620540750792, -0.59999999999999998, 0.20000000000000001,
 988           1.0471975511965976 },
 989   { 1.2280847305507339, -0.59999999999999998, 0.20000000000000001,
 990           1.2217304763960306 },
 991   { 1.4085436279696886, -0.59999999999999998, 0.20000000000000001,
 992           1.3962634015954636 },
 993   { 1.5901418016279374, -0.59999999999999998, 0.20000000000000001,
 994           1.5707963267948966 },
 995 };
 996 const double toler033 = 2.5000000000000020e-13;
 997
 998 // Test data for k=-0.59999999999999998, nu=0.29999999999999999.
 999 // max(|f - f_GSL|): 4.4408920985006262e-16
1000 // max(|f - f_GSL| / |f_GSL|): 2.9132420715478757e-16
1001 const testcase_ellint_3<double>
1002 data034[10] =
1003 {
1004   { 0.0000000000000000, -0.59999999999999998, 0.29999999999999999,
1005           0.0000000000000000 },
1006   { 0.17432424744393932, -0.59999999999999998, 0.29999999999999999,
1007           0.17453292519943295 },
1008   { 0.34748744127146447, -0.59999999999999998, 0.29999999999999999,
1009           0.34906585039886590 },
1010   { 0.51873632743924825, -0.59999999999999998, 0.29999999999999999,
1011           0.52359877559829882 },
1012   { 0.68794610396313116, -0.59999999999999998, 0.29999999999999999,
1013           0.69813170079773179 },
1014   { 0.85558070175468726, -0.59999999999999998, 0.29999999999999999,
1015           0.87266462599716477 },
1016   { 1.0224416343605653, -0.59999999999999998, 0.29999999999999999,
1017           1.0471975511965976 },
1018   { 1.1893144457936788, -0.59999999999999998, 0.29999999999999999,
1019           1.2217304763960306 },
1020   { 1.3566435377982575, -0.59999999999999998, 0.29999999999999999,
1021           1.3962634015954636 },
1022   { 1.5243814243493585, -0.59999999999999998, 0.29999999999999999,
1023           1.5707963267948966 },
1024 };
1025 const double toler034 = 2.5000000000000020e-13;
1026
1027 // Test data for k=-0.59999999999999998, nu=0.40000000000000002.
1028 // max(|f - f_GSL|): 4.4408920985006262e-16
1029 // max(|f - f_GSL| / |f_GSL|): 3.3897581541285558e-16
1030 const testcase_ellint_3<double>
1031 data035[10] =
1032 {
1033   { 0.0000000000000000, -0.59999999999999998, 0.40000000000000002,
1034           0.0000000000000000 },
1035   { 0.17414974487670717, -0.59999999999999998, 0.40000000000000002,
1036           0.17453292519943295 },
1037   { 0.34615238767335027, -0.59999999999999998, 0.40000000000000002,
1038           0.34906585039886590 },
1039   { 0.51453257838108557, -0.59999999999999998, 0.40000000000000002,
1040           0.52359877559829882 },
1041   { 0.67882386787534399, -0.59999999999999998, 0.40000000000000002,
1042           0.69813170079773179 },
1043   { 0.83948470233173578, -0.59999999999999998, 0.40000000000000002,
1044           0.87266462599716477 },
1045   { 0.99753496200073977, -0.59999999999999998, 0.40000000000000002,
1046           1.0471975511965976 },
1047   { 1.1541101404388487, -0.59999999999999998, 0.40000000000000002,
1048           1.2217304763960306 },
1049   { 1.3100911323398814, -0.59999999999999998, 0.40000000000000002,
1050           1.3962634015954636 },
1051   { 1.4659345278069984, -0.59999999999999998, 0.40000000000000002,
1052           1.5707963267948966 },
1053 };
1054 const double toler035 = 2.5000000000000020e-13;
1055
1056 // Test data for k=-0.59999999999999998, nu=0.50000000000000000.
1057 // max(|f - f_GSL|): 4.4408920985006262e-16
1058 // max(|f - f_GSL| / |f_GSL|): 3.5022138270566200e-16
1059 const testcase_ellint_3<double>
1060 data036[10] =
1061 {
1062   { 0.0000000000000000, -0.59999999999999998, 0.50000000000000000,
1063           0.0000000000000000 },
1064   { 0.17397586700252807, -0.59999999999999998, 0.50000000000000000,
1065           0.17453292519943295 },
1066   { 0.34483533397138516, -0.59999999999999998, 0.50000000000000000,
1067           0.34906585039886590 },
1068   { 0.51044500461706477, -0.59999999999999998, 0.50000000000000000,
1069           0.52359877559829882 },
1070   { 0.67009988034712664, -0.59999999999999998, 0.50000000000000000,
1071           0.69813170079773179 },
1072   { 0.82434762375735193, -0.59999999999999998, 0.50000000000000000,
1073           0.87266462599716477 },
1074   { 0.97447346702798998, -0.59999999999999998, 0.50000000000000000,
1075           1.0471975511965976 },
1076   { 1.1219494000522143, -0.59999999999999998, 0.50000000000000000,
1077           1.2217304763960306 },
1078   { 1.2680242605954484, -0.59999999999999998, 0.50000000000000000,
1079           1.3962634015954636 },
1080   { 1.4135484285693078, -0.59999999999999998, 0.50000000000000000,
1081           1.5707963267948966 },
1082 };
1083 const double toler036 = 2.5000000000000020e-13;
1084
1085 // Test data for k=-0.59999999999999998, nu=0.59999999999999998.
1086 // max(|f - f_GSL|): 4.4408920985006262e-16
1087 // max(|f - f_GSL| / |f_GSL|): 3.2504224329684343e-16
1088 const testcase_ellint_3<double>
1089 data037[10] =
1090 {
1091   { 0.0000000000000000, -0.59999999999999998, 0.59999999999999998,
1092           0.0000000000000000 },
1093   { 0.17380260984469353, -0.59999999999999998, 0.59999999999999998,
1094           0.17453292519943295 },
1095   { 0.34353585361777839, -0.59999999999999998, 0.59999999999999998,
1096           0.34906585039886590 },
1097   { 0.50646805774321380, -0.59999999999999998, 0.59999999999999998,
1098           0.52359877559829882 },
1099   { 0.66174468108625506, -0.59999999999999998, 0.59999999999999998,
1100           0.69813170079773179 },
1101   { 0.81007462280278408, -0.59999999999999998, 0.59999999999999998,
1102           0.87266462599716477 },
1103   { 0.95303466945718729, -0.59999999999999998, 0.59999999999999998,
1104           1.0471975511965976 },
1105   { 1.0924118588677505, -0.59999999999999998, 0.59999999999999998,
1106           1.2217304763960306 },
1107   { 1.2297640574847937, -0.59999999999999998, 0.59999999999999998,
1108           1.3962634015954636 },
1109   { 1.3662507535812816, -0.59999999999999998, 0.59999999999999998,
1110           1.5707963267948966 },
1111 };
1112 const double toler037 = 2.5000000000000020e-13;
1113
1114 // Test data for k=-0.59999999999999998, nu=0.69999999999999996.
1115 // max(|f - f_GSL|): 4.4408920985006262e-16
1116 // max(|f - f_GSL| / |f_GSL|): 3.3559889697529752e-16
1117 const testcase_ellint_3<double>
1118 data038[10] =
1119 {
1120   { 0.0000000000000000, -0.59999999999999998, 0.69999999999999996,
1121           0.0000000000000000 },
1122   { 0.17362996946312007, -0.59999999999999998, 0.69999999999999996,
1123           0.17453292519943295 },
1124   { 0.34225353454870588, -0.59999999999999998, 0.69999999999999996,
1125           0.34906585039886590 },
1126   { 0.50259656397799524, -0.59999999999999998, 0.69999999999999996,
1127           0.52359877559829882 },
1128   { 0.65373184496628933, -0.59999999999999998, 0.69999999999999996,
1129           0.69813170079773179 },
1130   { 0.79658372884056439, -0.59999999999999998, 0.69999999999999996,
1131           0.87266462599716477 },
1132   { 0.93303240100245421, -0.59999999999999998, 0.69999999999999996,
1133           1.0471975511965976 },
1134   { 1.0651547944716557, -0.59999999999999998, 0.69999999999999996,
1135           1.2217304763960306 },
1136   { 1.1947676204853441, -0.59999999999999998, 0.69999999999999996,
1137           1.3962634015954636 },
1138   { 1.3232737468822813, -0.59999999999999998, 0.69999999999999996,
1139           1.5707963267948966 },
1140 };
1141 const double toler038 = 2.5000000000000020e-13;
1142
1143 // Test data for k=-0.59999999999999998, nu=0.80000000000000004.
1144 // max(|f - f_GSL|): 6.6613381477509392e-16
1145 // max(|f - f_GSL| / |f_GSL|): 5.1879494682720725e-16
1146 const testcase_ellint_3<double>
1147 data039[10] =
1148 {
1149   { 0.0000000000000000, -0.59999999999999998, 0.80000000000000004,
1150           0.0000000000000000 },
1151   { 0.17345794195390685, -0.59999999999999998, 0.80000000000000004,
1152           0.17453292519943295 },
1153   { 0.34098797854531027, -0.59999999999999998, 0.80000000000000004,
1154           0.34906585039886590 },
1155   { 0.49882569168826213, -0.59999999999999998, 0.80000000000000004,
1156           0.52359877559829882 },
1157   { 0.64603758566475511, -0.59999999999999998, 0.80000000000000004,
1158           0.69813170079773179 },
1159   { 0.78380365594769730, -0.59999999999999998, 0.80000000000000004,
1160           0.87266462599716477 },
1161   { 0.91430946255611190, -0.59999999999999998, 0.80000000000000004,
1162           1.0471975511965976 },
1163   { 1.0398955217270607, -0.59999999999999998, 0.80000000000000004,
1164           1.2217304763960306 },
1165   { 1.1625948314277679, -0.59999999999999998, 0.80000000000000004,
1166           1.3962634015954636 },
1167   { 1.2840021261752192, -0.59999999999999998, 0.80000000000000004,
1168           1.5707963267948966 },
1169 };
1170 const double toler039 = 2.5000000000000020e-13;
1171
1172 // Test data for k=-0.59999999999999998, nu=0.90000000000000002.
1173 // max(|f - f_GSL|): 2.2204460492503131e-16
1174 // max(|f - f_GSL| / |f_GSL|): 3.4768329326726447e-16
1175 const testcase_ellint_3<double>
1176 data040[10] =
1177 {
1178   { 0.0000000000000000, -0.59999999999999998, 0.90000000000000002,
1179           0.0000000000000000 },
1180   { 0.17328652344890030, -0.59999999999999998, 0.90000000000000002,
1181           0.17453292519943295 },
1182   { 0.33973880062929018, -0.59999999999999998, 0.90000000000000002,
1183           0.34906585039886590 },
1184   { 0.49515092233122743, -0.59999999999999998, 0.90000000000000002,
1185           0.52359877559829882 },
1186   { 0.63864042139737043, -0.59999999999999998, 0.90000000000000002,
1187           0.69813170079773179 },
1188   { 0.77167205646538850, -0.59999999999999998, 0.90000000000000002,
1189           0.87266462599716477 },
1190   { 0.89673202848034383, -0.59999999999999998, 0.90000000000000002,
1191           1.0471975511965976 },
1192   { 1.0163984492661304, -0.59999999999999998, 0.90000000000000002,
1193           1.2217304763960306 },
1194   { 1.1328845785162431, -0.59999999999999998, 0.90000000000000002,
1195           1.3962634015954636 },
1196   { 1.2479362973851875, -0.59999999999999998, 0.90000000000000002,
1197           1.5707963267948966 },
1198 };
1199 const double toler040 = 2.5000000000000020e-13;
1200
1201 // Test data for k=-0.50000000000000000, nu=0.0000000000000000.
1202 // max(|f - f_GSL|): 2.2204460492503131e-16
1203 // max(|f - f_GSL| / |f_GSL|): 3.1201497220602069e-16
1204 const testcase_ellint_3<double>
1205 data041[10] =
1206 {
1207   { 0.0000000000000000, -0.50000000000000000, 0.0000000000000000,
1208           0.0000000000000000 },
1209   { 0.17475385514035785, -0.50000000000000000, 0.0000000000000000,
1210           0.17453292519943295 },
1211   { 0.35081868470101585, -0.50000000000000000, 0.0000000000000000,
1212           0.34906585039886590 },
1213   { 0.52942862705190574, -0.50000000000000000, 0.0000000000000000,
1214           0.52359877559829882 },
1215   { 0.71164727562630314, -0.50000000000000000, 0.0000000000000000,
1216           0.69813170079773179 },
1217   { 0.89824523594227768, -0.50000000000000000, 0.0000000000000000,
1218           0.87266462599716477 },
1219   { 1.0895506700518851, -0.50000000000000000, 0.0000000000000000,
1220           1.0471975511965976 },
1221   { 1.2853005857432931, -0.50000000000000000, 0.0000000000000000,
1222           1.2217304763960306 },
1223   { 1.4845545520549484, -0.50000000000000000, 0.0000000000000000,
1224           1.3962634015954636 },
1225   { 1.6857503548125963, -0.50000000000000000, 0.0000000000000000,
1226           1.5707963267948966 },
1227 };
1228 const double toler041 = 2.5000000000000020e-13;
1229
1230 // Test data for k=-0.50000000000000000, nu=0.10000000000000001.
1231 // max(|f - f_GSL|): 2.2204460492503131e-16
1232 // max(|f - f_GSL| / |f_GSL|): 3.1662857256911530e-16
1233 const testcase_ellint_3<double>
1234 data042[10] =
1235 {
1236   { 0.0000000000000000, -0.50000000000000000, 0.10000000000000001,
1237           0.0000000000000000 },
1238   { 0.17457763120814676, -0.50000000000000000, 0.10000000000000001,
1239           0.17453292519943295 },
1240   { 0.34943246340849154, -0.50000000000000000, 0.10000000000000001,
1241           0.34906585039886590 },
1242   { 0.52487937869610790, -0.50000000000000000, 0.10000000000000001,
1243           0.52359877559829882 },
1244   { 0.70127785096388384, -0.50000000000000000, 0.10000000000000001,
1245           0.69813170079773179 },
1246   { 0.87898815988624479, -0.50000000000000000, 0.10000000000000001,
1247           0.87266462599716477 },
1248   { 1.0582764576094172, -0.50000000000000000, 0.10000000000000001,
1249           1.0471975511965976 },
1250   { 1.2391936844060205, -0.50000000000000000, 0.10000000000000001,
1251           1.2217304763960306 },
1252   { 1.4214793542995841, -0.50000000000000000, 0.10000000000000001,
1253           1.3962634015954636 },
1254   { 1.6045524936084892, -0.50000000000000000, 0.10000000000000001,
1255           1.5707963267948966 },
1256 };
1257 const double toler042 = 2.5000000000000020e-13;
1258
1259 // Test data for k=-0.50000000000000000, nu=0.20000000000000001.
1260 // max(|f - f_GSL|): 2.2204460492503131e-16
1261 // max(|f - f_GSL| / |f_GSL|): 3.2114786773102175e-16
1262 const testcase_ellint_3<double>
1263 data043[10] =
1264 {
1265   { 0.0000000000000000, -0.50000000000000000, 0.20000000000000001,
1266           0.0000000000000000 },
1267   { 0.17440204336345433, -0.50000000000000000, 0.20000000000000001,
1268           0.17453292519943295 },
1269   { 0.34806552388338824, -0.50000000000000000, 0.20000000000000001,
1270           0.34906585039886590 },
1271   { 0.52046416757129810, -0.50000000000000000, 0.20000000000000001,
1272           0.52359877559829882 },
1273   { 0.69140924550993865, -0.50000000000000000, 0.20000000000000001,
1274           0.69813170079773179 },
1275   { 0.86104678636125520, -0.50000000000000000, 0.20000000000000001,
1276           0.87266462599716477 },
1277   { 1.0297439459053981, -0.50000000000000000, 0.20000000000000001,
1278           1.0471975511965976 },
1279   { 1.1979214112912033, -0.50000000000000000, 0.20000000000000001,
1280           1.2217304763960306 },
1281   { 1.3659033858648930, -0.50000000000000000, 0.20000000000000001,
1282           1.3962634015954636 },
1283   { 1.5338490483665983, -0.50000000000000000, 0.20000000000000001,
1284           1.5707963267948966 },
1285 };
1286 const double toler043 = 2.5000000000000020e-13;
1287
1288 // Test data for k=-0.50000000000000000, nu=0.29999999999999999.
1289 // max(|f - f_GSL|): 2.2204460492503131e-16
1290 // max(|f - f_GSL| / |f_GSL|): 3.2557837230041312e-16
1291 const testcase_ellint_3<double>
1292 data044[10] =
1293 {
1294   { 0.0000000000000000, -0.50000000000000000, 0.29999999999999999,
1295           0.0000000000000000 },
1296   { 0.17422708752228896, -0.50000000000000000, 0.29999999999999999,
1297           0.17453292519943295 },
1298   { 0.34671739434855858, -0.50000000000000000, 0.29999999999999999,
1299           0.34906585039886590 },
1300   { 0.51617616305641878, -0.50000000000000000, 0.29999999999999999,
1301           0.52359877559829882 },
1302   { 0.68200047612545167, -0.50000000000000000, 0.29999999999999999,
1303           0.69813170079773179 },
1304   { 0.84427217869498372, -0.50000000000000000, 0.29999999999999999,
1305           0.87266462599716477 },
1306   { 1.0035637821389782, -0.50000000000000000, 0.29999999999999999,
1307           1.0471975511965976 },
1308   { 1.1606800483933111, -0.50000000000000000, 0.29999999999999999,
1309           1.2217304763960306 },
1310   { 1.3164407134643459, -0.50000000000000000, 0.29999999999999999,
1311           1.3962634015954636 },
1312   { 1.4715681939859637, -0.50000000000000000, 0.29999999999999999,
1313           1.5707963267948966 },
1314 };
1315 const double toler044 = 2.5000000000000020e-13;
1316
1317 // Test data for k=-0.50000000000000000, nu=0.40000000000000002.
1318 // max(|f - f_GSL|): 2.2204460492503131e-16
1319 // max(|f - f_GSL| / |f_GSL|): 3.2992508582900068e-16
1320 const testcase_ellint_3<double>
1321 data045[10] =
1322 {
1323   { 0.0000000000000000, -0.50000000000000000, 0.40000000000000002,
1324           0.0000000000000000 },
1325   { 0.17405275963859917, -0.50000000000000000, 0.40000000000000002,
1326           0.17453292519943295 },
1327   { 0.34538761957029329, -0.50000000000000000, 0.40000000000000002,
1328           0.34906585039886590 },
1329   { 0.51200902646603907, -0.50000000000000000, 0.40000000000000002,
1330           0.52359877559829882 },
1331   { 0.67301522212868792, -0.50000000000000000, 0.40000000000000002,
1332           0.69813170079773179 },
1333   { 0.82853844466313320, -0.50000000000000000, 0.40000000000000002,
1334           0.87266462599716477 },
1335   { 0.97942097862681488, -0.50000000000000000, 0.40000000000000002,
1336           1.0471975511965976 },
1337   { 1.1268429801220614, -0.50000000000000000, 0.40000000000000002,
1338           1.2217304763960306 },
1339   { 1.2720406704533922, -0.50000000000000000, 0.40000000000000002,
1340           1.3962634015954636 },
1341   { 1.4161679518465340, -0.50000000000000000, 0.40000000000000002,
1342           1.5707963267948966 },
1343 };
1344 const double toler045 = 2.5000000000000020e-13;
1345
1346 // Test data for k=-0.50000000000000000, nu=0.50000000000000000.
1347 // max(|f - f_GSL|): 2.2204460492503131e-16
1348 // max(|f - f_GSL| / |f_GSL|): 3.3419255755184137e-16
1349 const testcase_ellint_3<double>
1350 data046[10] =
1351 {
1352   { 0.0000000000000000, -0.50000000000000000, 0.50000000000000000,
1353           0.0000000000000000 },
1354   { 0.17387905570381157, -0.50000000000000000, 0.50000000000000000,
1355           0.17453292519943295 },
1356   { 0.34407576010465207, -0.50000000000000000, 0.50000000000000000,
1357           0.34906585039886590 },
1358   { 0.50795686560160824, -0.50000000000000000, 0.50000000000000000,
1359           0.52359877559829882 },
1360   { 0.66442115453330164, -0.50000000000000000, 0.50000000000000000,
1361           0.69813170079773179 },
1362   { 0.81373829119355345, -0.50000000000000000, 0.50000000000000000,
1363           0.87266462599716477 },
1364   { 0.95705743313235825, -0.50000000000000000, 0.50000000000000000,
1365           1.0471975511965976 },
1366   { 1.0959131991362554, -0.50000000000000000, 0.50000000000000000,
1367           1.2217304763960306 },
1368   { 1.2318900529754597, -0.50000000000000000, 0.50000000000000000,
1369           1.3962634015954636 },
1370   { 1.3664739530045971, -0.50000000000000000, 0.50000000000000000,
1371           1.5707963267948966 },
1372 };
1373 const double toler046 = 2.5000000000000020e-13;
1374
1375 // Test data for k=-0.50000000000000000, nu=0.59999999999999998.
1376 // max(|f - f_GSL|): 2.2204460492503131e-16
1377 // max(|f - f_GSL| / |f_GSL|): 3.3838494104749599e-16
1378 const testcase_ellint_3<double>
1379 data047[10] =
1380 {
1381   { 0.0000000000000000, -0.50000000000000000, 0.59999999999999998,
1382           0.0000000000000000 },
1383   { 0.17370597174637581, -0.50000000000000000, 0.59999999999999998,
1384           0.17453292519943295 },
1385   { 0.34278139158591414, -0.50000000000000000, 0.59999999999999998,
1386           0.34906585039886590 },
1387   { 0.50401419439302708, -0.50000000000000000, 0.59999999999999998,
1388           0.52359877559829882 },
1389   { 0.65618938076167210, -0.50000000000000000, 0.59999999999999998,
1390           0.69813170079773179 },
1391   { 0.79977959248855424, -0.50000000000000000, 0.59999999999999998,
1392           0.87266462599716477 },
1393   { 0.93625925190753545, -0.50000000000000000, 0.59999999999999998,
1394           1.0471975511965976 },
1395   { 1.0674905658379708, -0.50000000000000000, 0.59999999999999998,
1396           1.2217304763960306 },
1397   { 1.1953481298023050, -0.50000000000000000, 0.59999999999999998,
1398           1.3962634015954636 },
1399   { 1.3215740290190876, -0.50000000000000000, 0.59999999999999998,
1400           1.5707963267948966 },
1401 };
1402 const double toler047 = 2.5000000000000020e-13;
1403
1404 // Test data for k=-0.50000000000000000, nu=0.69999999999999996.
1405 // max(|f - f_GSL|): 2.2204460492503131e-16
1406 // max(|f - f_GSL| / |f_GSL|): 3.4250604066951477e-16
1407 const testcase_ellint_3<double>
1408 data048[10] =
1409 {
1410   { 0.0000000000000000, -0.50000000000000000, 0.69999999999999996,
1411           0.0000000000000000 },
1412   { 0.17353350383131641, -0.50000000000000000, 0.69999999999999996,
1413           0.17453292519943295 },
1414   { 0.34150410405436771, -0.50000000000000000, 0.69999999999999996,
1415           0.34906585039886590 },
1416   { 0.50017589696443487, -0.50000000000000000, 0.69999999999999996,
1417           0.52359877559829882 },
1418   { 0.64829398188419951, -0.50000000000000000, 0.69999999999999996,
1419           0.69813170079773179 },
1420   { 0.78658270782402073, -0.50000000000000000, 0.69999999999999996,
1421           0.87266462599716477 },
1422   { 0.91684738336675053, -0.50000000000000000, 0.69999999999999996,
1423           1.0471975511965976 },
1424   { 1.0412486789555935, -0.50000000000000000, 0.69999999999999996,
1425           1.2217304763960306 },
1426   { 1.1619021847612001, -0.50000000000000000, 0.69999999999999996,
1427           1.3962634015954636 },
1428   { 1.2807475181182502, -0.50000000000000000, 0.69999999999999996,
1429           1.5707963267948966 },
1430 };
1431 const double toler048 = 2.5000000000000020e-13;
1432
1433 // Test data for k=-0.50000000000000000, nu=0.80000000000000004.
1434 // max(|f - f_GSL|): 4.4408920985006262e-16
1435 // max(|f - f_GSL| / |f_GSL|): 3.5715240651179632e-16
1436 const testcase_ellint_3<double>
1437 data049[10] =
1438 {
1439   { 0.0000000000000000, -0.50000000000000000, 0.80000000000000004,
1440           0.0000000000000000 },
1441   { 0.17336164805979126, -0.50000000000000000, 0.80000000000000004,
1442           0.17453292519943295 },
1443   { 0.34024350132086773, -0.50000000000000000, 0.80000000000000004,
1444           0.34906585039886590 },
1445   { 0.49643719555734073, -0.50000000000000000, 0.80000000000000004,
1446           0.52359877559829882 },
1447   { 0.64071162456976150, -0.50000000000000000, 0.80000000000000004,
1448           0.69813170079773179 },
1449   { 0.77407836177211908, -0.50000000000000000, 0.80000000000000004,
1450           0.87266462599716477 },
1451   { 0.89867058251905652, -0.50000000000000000, 0.80000000000000004,
1452           1.0471975511965976 },
1453   { 1.0169181822134910, -0.50000000000000000, 0.80000000000000004,
1454           1.2217304763960306 },
1455   { 1.1311363312779448, -0.50000000000000000, 0.80000000000000004,
1456           1.3962634015954636 },
1457   { 1.2434165408189539, -0.50000000000000000, 0.80000000000000004,
1458           1.5707963267948966 },
1459 };
1460 const double toler049 = 2.5000000000000020e-13;
1461
1462 // Test data for k=-0.50000000000000000, nu=0.90000000000000002.
1463 // max(|f - f_GSL|): 4.4408920985006262e-16
1464 // max(|f - f_GSL| / |f_GSL|): 4.4664649039489274e-16
1465 const testcase_ellint_3<double>
1466 data050[10] =
1467 {
1468   { 0.0000000000000000, -0.50000000000000000, 0.90000000000000002,
1469           0.0000000000000000 },
1470   { 0.17319040056865681, -0.50000000000000000, 0.90000000000000002,
1471           0.17453292519943295 },
1472   { 0.33899920036578557, -0.50000000000000000, 0.90000000000000002,
1473           0.34906585039886590 },
1474   { 0.49279362182695174, -0.50000000000000000, 0.90000000000000002,
1475           0.52359877559829882 },
1476   { 0.63342123379746151, -0.50000000000000000, 0.90000000000000002,
1477           0.69813170079773179 },
1478   { 0.76220595179550321, -0.50000000000000000, 0.90000000000000002,
1479           0.87266462599716477 },
1480   { 0.88160004743532294, -0.50000000000000000, 0.90000000000000002,
1481           1.0471975511965976 },
1482   { 0.99427448642310123, -0.50000000000000000, 0.90000000000000002,
1483           1.2217304763960306 },
1484   { 1.1027091512470095, -0.50000000000000000, 0.90000000000000002,
1485           1.3962634015954636 },
1486   { 1.2091116095504744, -0.50000000000000000, 0.90000000000000002,
1487           1.5707963267948966 },
1488 };
1489 const double toler050 = 2.5000000000000020e-13;
1490
1491 // Test data for k=-0.40000000000000002, nu=0.0000000000000000.
1492 // max(|f - f_GSL|): 6.6613381477509392e-16
1493 // max(|f - f_GSL| / |f_GSL|): 4.0617918857203532e-16
1494 const testcase_ellint_3<double>
1495 data051[10] =
1496 {
1497   { 0.0000000000000000, -0.40000000000000002, 0.0000000000000000,
1498           0.0000000000000000 },
1499   { 0.17467414669441528, -0.40000000000000002, 0.0000000000000000,
1500           0.17453292519943295 },
1501   { 0.35018222772483443, -0.40000000000000002, 0.0000000000000000,
1502           0.34906585039886590 },
1503   { 0.52729015917508737, -0.40000000000000002, 0.0000000000000000,
1504           0.52359877559829882 },
1505   { 0.70662374407341244, -0.40000000000000002, 0.0000000000000000,
1506           0.69813170079773179 },
1507   { 0.88859210497602170, -0.40000000000000002, 0.0000000000000000,
1508           0.87266462599716477 },
1509   { 1.0733136290471379, -0.40000000000000002, 0.0000000000000000,
1510           1.0471975511965976 },
1511   { 1.2605612170157061, -0.40000000000000002, 0.0000000000000000,
1512           1.2217304763960306 },
1513   { 1.4497513956433439, -0.40000000000000002, 0.0000000000000000,
1514           1.3962634015954636 },
1515   { 1.6399998658645112, -0.40000000000000002, 0.0000000000000000,
1516           1.5707963267948966 },
1517 };
1518 const double toler051 = 2.5000000000000020e-13;
1519
1520 // Test data for k=-0.40000000000000002, nu=0.10000000000000001.
1521 // max(|f - f_GSL|): 6.6613381477509392e-16
1522 // max(|f - f_GSL| / |f_GSL|): 4.2644663257577874e-16
1523 const testcase_ellint_3<double>
1524 data052[10] =
1525 {
1526   { 0.0000000000000000, -0.40000000000000002, 0.10000000000000001,
1527           0.0000000000000000 },
1528   { 0.17449806706684670, -0.40000000000000002, 0.10000000000000001,
1529           0.17453292519943295 },
1530   { 0.34880048623856075, -0.40000000000000002, 0.10000000000000001,
1531           0.34906585039886590 },
1532   { 0.52277322065757392, -0.40000000000000002, 0.10000000000000001,
1533           0.52359877559829882 },
1534   { 0.69638072056918365, -0.40000000000000002, 0.10000000000000001,
1535           0.69813170079773179 },
1536   { 0.86968426619831540, -0.40000000000000002, 0.10000000000000001,
1537           0.87266462599716477 },
1538   { 1.0428044206578095, -0.40000000000000002, 0.10000000000000001,
1539           1.0471975511965976 },
1540   { 1.2158651158274378, -0.40000000000000002, 0.10000000000000001,
1541           1.2217304763960306 },
1542   { 1.3889447129893324, -0.40000000000000002, 0.10000000000000001,
1543           1.3962634015954636 },
1544   { 1.5620566886683604, -0.40000000000000002, 0.10000000000000001,
1545           1.5707963267948966 },
1546 };
1547 const double toler052 = 2.5000000000000020e-13;
1548
1549 // Test data for k=-0.40000000000000002, nu=0.20000000000000001.
1550 // max(|f - f_GSL|): 6.6613381477509392e-16
1551 // max(|f - f_GSL| / |f_GSL|): 4.4583049464169287e-16
1552 const testcase_ellint_3<double>
1553 data053[10] =
1554 {
1555   { 0.0000000000000000, -0.40000000000000002, 0.20000000000000001,
1556           0.0000000000000000 },
1557   { 0.17432262290723397, -0.40000000000000002, 0.20000000000000001,
1558           0.17453292519943295 },
1559   { 0.34743795258968596, -0.40000000000000002, 0.20000000000000001,
1560           0.34906585039886590 },
1561   { 0.51838919472805101, -0.40000000000000002, 0.20000000000000001,
1562           0.52359877559829882 },
1563   { 0.68663134739057907, -0.40000000000000002, 0.20000000000000001,
1564           0.69813170079773179 },
1565   { 0.85206432981833979, -0.40000000000000002, 0.20000000000000001,
1566           0.87266462599716477 },
1567   { 1.0149595349004430, -0.40000000000000002, 0.20000000000000001,
1568           1.0471975511965976 },
1569   { 1.1758349405464676, -0.40000000000000002, 0.20000000000000001,
1570           1.2217304763960306 },
1571   { 1.3353337673882637, -0.40000000000000002, 0.20000000000000001,
1572           1.3962634015954636 },
1573   { 1.4941414344266770, -0.40000000000000002, 0.20000000000000001,
1574           1.5707963267948966 },
1575 };
1576 const double toler053 = 2.5000000000000020e-13;
1577
1578 // Test data for k=-0.40000000000000002, nu=0.29999999999999999.
1579 // max(|f - f_GSL|): 8.8817841970012523e-16
1580 // max(|f - f_GSL| / |f_GSL|): 6.1925080711125793e-16
1581 const testcase_ellint_3<double>
1582 data054[10] =
1583 {
1584   { 0.0000000000000000, -0.40000000000000002, 0.29999999999999999,
1585           0.0000000000000000 },
1586   { 0.17414781013591540, -0.40000000000000002, 0.29999999999999999,
1587           0.17453292519943295 },
1588   { 0.34609415696777285, -0.40000000000000002, 0.29999999999999999,
1589           0.34906585039886590 },
1590   { 0.51413131295862535, -0.40000000000000002, 0.29999999999999999,
1591           0.52359877559829882 },
1592   { 0.67733527622935630, -0.40000000000000002, 0.29999999999999999,
1593           0.69813170079773179 },
1594   { 0.83558675182733266, -0.40000000000000002, 0.29999999999999999,
1595           0.87266462599716477 },
1596   { 0.98940140808865906, -0.40000000000000002, 0.29999999999999999,
1597           1.0471975511965976 },
1598   { 1.1396968797728058, -0.40000000000000002, 0.29999999999999999,
1599           1.2217304763960306 },
1600   { 1.2875920037865090, -0.40000000000000002, 0.29999999999999999,
1601           1.3962634015954636 },
1602   { 1.4342789859950078, -0.40000000000000002, 0.29999999999999999,
1603           1.5707963267948966 },
1604 };
1605 const double toler054 = 2.5000000000000020e-13;
1606
1607 // Test data for k=-0.40000000000000002, nu=0.40000000000000002.
1608 // max(|f - f_GSL|): 6.6613381477509392e-16
1609 // max(|f - f_GSL| / |f_GSL|): 4.8235661108581362e-16
1610 const testcase_ellint_3<double>
1611 data055[10] =
1612 {
1613   { 0.0000000000000000, -0.40000000000000002, 0.40000000000000002,
1614           0.0000000000000000 },
1615   { 0.17397362471112707, -0.40000000000000002, 0.40000000000000002,
1616           0.17453292519943295 },
1617   { 0.34476864603333196, -0.40000000000000002, 0.40000000000000002,
1618           0.34906585039886590 },
1619   { 0.50999329415379346, -0.40000000000000002, 0.40000000000000002,
1620           0.52359877559829882 },
1621   { 0.66845674551396006, -0.40000000000000002, 0.40000000000000002,
1622           0.69813170079773179 },
1623   { 0.82012848346231748, -0.40000000000000002, 0.40000000000000002,
1624           0.87266462599716477 },
1625   { 0.96582449258349057, -0.40000000000000002, 0.40000000000000002,
1626           1.0471975511965976 },
1627   { 1.1068473749476286, -0.40000000000000002, 0.40000000000000002,
1628           1.2217304763960306 },
1629   { 1.2447132729159989, -0.40000000000000002, 0.40000000000000002,
1630           1.3962634015954636 },
1631   { 1.3809986210732901, -0.40000000000000002, 0.40000000000000002,
1632           1.5707963267948966 },
1633 };
1634 const double toler055 = 2.5000000000000020e-13;
1635
1636 // Test data for k=-0.40000000000000002, nu=0.50000000000000000.
1637 // max(|f - f_GSL|): 6.6613381477509392e-16
1638 // max(|f - f_GSL| / |f_GSL|): 4.9965792755639576e-16
1639 const testcase_ellint_3<double>
1640 data056[10] =
1641 {
1642   { 0.0000000000000000, -0.40000000000000002, 0.50000000000000000,
1643           0.0000000000000000 },
1644   { 0.17380006262854136, -0.40000000000000002, 0.50000000000000000,
1645           0.17453292519943295 },
1646   { 0.34346098216756610, -0.40000000000000002, 0.50000000000000000,
1647           0.34906585039886590 },
1648   { 0.50596929935059420, -0.40000000000000002, 0.50000000000000000,
1649           0.52359877559829882 },
1650   { 0.65996392089131251, -0.40000000000000002, 0.50000000000000000,
1651           0.69813170079773179 },
1652   { 0.80558463511364786, -0.40000000000000002, 0.50000000000000000,
1653           0.87266462599716477 },
1654   { 0.94397834522857704, -0.40000000000000002, 0.50000000000000000,
1655           1.0471975511965976 },
1656   { 1.0768075114108115, -0.40000000000000002, 0.50000000000000000,
1657           1.2217304763960306 },
1658   { 1.2059184624251333, -0.40000000000000002, 0.50000000000000000,
1659           1.3962634015954636 },
1660   { 1.3331797176377398, -0.40000000000000002, 0.50000000000000000,
1661           1.5707963267948966 },
1662 };
1663 const double toler056 = 2.5000000000000020e-13;
1664
1665 // Test data for k=-0.40000000000000002, nu=0.59999999999999998.
1666 // max(|f - f_GSL|): 6.6613381477509392e-16
1667 // max(|f - f_GSL| / |f_GSL|): 5.1640223038298069e-16
1668 const testcase_ellint_3<double>
1669 data057[10] =
1670 {
1671   { 0.0000000000000000, -0.40000000000000002, 0.59999999999999998,
1672           0.0000000000000000 },
1673   { 0.17362711992081245, -0.40000000000000002, 0.59999999999999998,
1674           0.17453292519943295 },
1675   { 0.34217074276403953, -0.40000000000000002, 0.59999999999999998,
1676           0.34906585039886590 },
1677   { 0.50205389185761606, -0.40000000000000002, 0.59999999999999998,
1678           0.52359877559829882 },
1679   { 0.65182834920372734, -0.40000000000000002, 0.59999999999999998,
1680           0.69813170079773179 },
1681   { 0.79186512820565136, -0.40000000000000002, 0.59999999999999998,
1682           0.87266462599716477 },
1683   { 0.92365535916287134, -0.40000000000000002, 0.59999999999999998,
1684           1.0471975511965976 },
1685   { 1.0491915663957907, -0.40000000000000002, 0.59999999999999998,
1686           1.2217304763960306 },
1687   { 1.1705934291745106, -0.40000000000000002, 0.59999999999999998,
1688           1.3962634015954636 },
1689   { 1.2899514672527024, -0.40000000000000002, 0.59999999999999998,
1690           1.5707963267948966 },
1691 };
1692 const double toler057 = 2.5000000000000020e-13;
1693
1694 // Test data for k=-0.40000000000000002, nu=0.69999999999999996.
1695 // max(|f - f_GSL|): 6.6613381477509392e-16
1696 // max(|f - f_GSL| / |f_GSL|): 5.3264047918332349e-16
1697 const testcase_ellint_3<double>
1698 data058[10] =
1699 {
1700   { 0.0000000000000000, -0.40000000000000002, 0.69999999999999996,
1701           0.0000000000000000 },
1702   { 0.17345479265712868, -0.40000000000000002, 0.69999999999999996,
1703           0.17453292519943295 },
1704   { 0.34089751955950354, -0.40000000000000002, 0.69999999999999996,
1705           0.34906585039886590 },
1706   { 0.49824200167361332, -0.40000000000000002, 0.69999999999999996,
1707           0.52359877559829882 },
1708   { 0.64402450341199402, -0.40000000000000002, 0.69999999999999996,
1709           0.69813170079773179 },
1710   { 0.77889207804122873, -0.40000000000000002, 0.69999999999999996,
1711           0.87266462599716477 },
1712   { 0.90468169720957992, -0.40000000000000002, 0.69999999999999996,
1713           1.0471975511965976 },
1714   { 1.0236847823692916, -0.40000000000000002, 0.69999999999999996,
1715           1.2217304763960306 },
1716   { 1.1382465247425166, -0.40000000000000002, 0.69999999999999996,
1717           1.3962634015954636 },
1718   { 1.2506255923253344, -0.40000000000000002, 0.69999999999999996,
1719           1.5707963267948966 },
1720 };
1721 const double toler058 = 2.5000000000000020e-13;
1722
1723 // Test data for k=-0.40000000000000002, nu=0.80000000000000004.
1724 // max(|f - f_GSL|): 6.6613381477509392e-16
1725 // max(|f - f_GSL| / |f_GSL|): 6.6611561645571024e-16
1726 const testcase_ellint_3<double>
1727 data059[10] =
1728 {
1729   { 0.0000000000000000, -0.40000000000000002, 0.80000000000000004,
1730           0.0000000000000000 },
1731   { 0.17328307694277154, -0.40000000000000002, 0.80000000000000004,
1732           0.17453292519943295 },
1733   { 0.33964091800132007, -0.40000000000000002, 0.80000000000000004,
1734           0.34906585039886590 },
1735   { 0.49452889372467440, -0.40000000000000002, 0.80000000000000004,
1736           0.52359877559829882 },
1737   { 0.63652940095937316, -0.40000000000000002, 0.80000000000000004,
1738           0.69813170079773179 },
1739   { 0.76659772511159097, -0.40000000000000002, 0.80000000000000004,
1740           0.87266462599716477 },
1741   { 0.88691047977338111, -0.40000000000000002, 0.80000000000000004,
1742           1.0471975511965976 },
1743   { 1.0000273200611638, -0.40000000000000002, 0.80000000000000004,
1744           1.2217304763960306 },
1745   { 1.1084787902188009, -0.40000000000000002, 0.80000000000000004,
1746           1.3962634015954636 },
1747   { 1.2146499565727209, -0.40000000000000002, 0.80000000000000004,
1748           1.5707963267948966 },
1749 };
1750 const double toler059 = 2.5000000000000020e-13;
1751
1752 // Test data for k=-0.40000000000000002, nu=0.90000000000000002.
1753 // max(|f - f_GSL|): 6.6613381477509392e-16
1754 // max(|f - f_GSL| / |f_GSL|): 5.6376730823308004e-16
1755 const testcase_ellint_3<double>
1756 data060[10] =
1757 {
1758   { 0.0000000000000000, -0.40000000000000002, 0.90000000000000002,
1759           0.0000000000000000 },
1760   { 0.17311196891868127, -0.40000000000000002, 0.90000000000000002,
1761           0.17453292519943295 },
1762   { 0.33840055664911906, -0.40000000000000002, 0.90000000000000002,
1763           0.34906585039886590 },
1764   { 0.49091013944075329, -0.40000000000000002, 0.90000000000000002,
1765           0.52359877559829882 },
1766   { 0.62932228186809580, -0.40000000000000002, 0.90000000000000002,
1767           0.69813170079773179 },
1768   { 0.75492278323019801, -0.40000000000000002, 0.90000000000000002,
1769           0.87266462599716477 },
1770   { 0.87021659043854294, -0.40000000000000002, 0.90000000000000002,
1771           1.0471975511965976 },
1772   { 0.97800245228239246, -0.40000000000000002, 0.90000000000000002,
1773           1.2217304763960306 },
1774   { 1.0809625773173697, -0.40000000000000002, 0.90000000000000002,
1775           1.3962634015954636 },
1776   { 1.1815758115929846, -0.40000000000000002, 0.90000000000000002,
1777           1.5707963267948966 },
1778 };
1779 const double toler060 = 2.5000000000000020e-13;
1780
1781 // Test data for k=-0.30000000000000004, nu=0.0000000000000000.
1782 // max(|f - f_GSL|): 8.8817841970012523e-16
1783 // max(|f - f_GSL| / |f_GSL|): 6.3361874537309281e-16
1784 const testcase_ellint_3<double>
1785 data061[10] =
1786 {
1787   { 0.0000000000000000, -0.30000000000000004, 0.0000000000000000,
1788           0.0000000000000000 },
1789   { 0.17461228653000099, -0.30000000000000004, 0.0000000000000000,
1790           0.17453292519943295 },
1791   { 0.34969146102798415, -0.30000000000000004, 0.0000000000000000,
1792           0.34906585039886590 },
1793   { 0.52565822873726320, -0.30000000000000004, 0.0000000000000000,
1794           0.52359877559829882 },
1795   { 0.70284226512408532, -0.30000000000000004, 0.0000000000000000,
1796           0.69813170079773179 },
1797   { 0.88144139195111182, -0.30000000000000004, 0.0000000000000000,
1798           0.87266462599716477 },
1799   { 1.0614897067260520, -0.30000000000000004, 0.0000000000000000,
1800           1.0471975511965976 },
1801   { 1.2428416824174218, -0.30000000000000004, 0.0000000000000000,
1802           1.2217304763960306 },
1803   { 1.4251795877015927, -0.30000000000000004, 0.0000000000000000,
1804           1.3962634015954636 },
1805   { 1.6080486199305128, -0.30000000000000004, 0.0000000000000000,
1806           1.5707963267948966 },
1807 };
1808 const double toler061 = 2.5000000000000020e-13;
1809
1810 // Test data for k=-0.30000000000000004, nu=0.10000000000000001.
1811 // max(|f - f_GSL|): 8.8817841970012523e-16
1812 // max(|f - f_GSL| / |f_GSL|): 6.3908043711907203e-16
1813 const testcase_ellint_3<double>
1814 data062[10] =
1815 {
1816   { 0.0000000000000000, -0.30000000000000004, 0.10000000000000001,
1817           0.0000000000000000 },
1818   { 0.17443631884814376, -0.30000000000000004, 0.10000000000000001,
1819           0.17453292519943295 },
1820   { 0.34831316835124926, -0.30000000000000004, 0.10000000000000001,
1821           0.34906585039886590 },
1822   { 0.52116586276523857, -0.30000000000000004, 0.10000000000000001,
1823           0.52359877559829882 },
1824   { 0.69269385837910036, -0.30000000000000004, 0.10000000000000001,
1825           0.69813170079773179 },
1826   { 0.86279023163070856, -0.30000000000000004, 0.10000000000000001,
1827           0.87266462599716477 },
1828   { 1.0315321461438263, -0.30000000000000004, 0.10000000000000001,
1829           1.0471975511965976 },
1830   { 1.1991449111869024, -0.30000000000000004, 0.10000000000000001,
1831           1.2217304763960306 },
1832   { 1.3659561780923213, -0.30000000000000004, 0.10000000000000001,
1833           1.3962634015954636 },
1834   { 1.5323534693557528, -0.30000000000000004, 0.10000000000000001,
1835           1.5707963267948966 },
1836 };
1837 const double toler062 = 2.5000000000000020e-13;
1838
1839 // Test data for k=-0.30000000000000004, nu=0.20000000000000001.
1840 // max(|f - f_GSL|): 8.8817841970012523e-16
1841 // max(|f - f_GSL| / |f_GSL|): 6.4447238179454079e-16
1842 const testcase_ellint_3<double>
1843 data063[10] =
1844 {
1845   { 0.0000000000000000, -0.30000000000000004, 0.20000000000000001,
1846           0.0000000000000000 },
1847   { 0.17426098615372088, -0.30000000000000004, 0.20000000000000001,
1848           0.17453292519943295 },
1849   { 0.34695402664689923, -0.30000000000000004, 0.20000000000000001,
1850           0.34906585039886590 },
1851   { 0.51680555567038933, -0.30000000000000004, 0.20000000000000001,
1852           0.52359877559829882 },
1853   { 0.68303375225260210, -0.30000000000000004, 0.20000000000000001,
1854           0.69813170079773179 },
1855   { 0.84540662891295026, -0.30000000000000004, 0.20000000000000001,
1856           0.87266462599716477 },
1857   { 1.0041834051646927, -0.30000000000000004, 0.20000000000000001,
1858           1.0471975511965976 },
1859   { 1.1599952702345711, -0.30000000000000004, 0.20000000000000001,
1860           1.2217304763960306 },
1861   { 1.3137179520499165, -0.30000000000000004, 0.20000000000000001,
1862           1.3962634015954636 },
1863   { 1.4663658145259877, -0.30000000000000004, 0.20000000000000001,
1864           1.5707963267948966 },
1865 };
1866 const double toler063 = 2.5000000000000020e-13;
1867
1868 // Test data for k=-0.30000000000000004, nu=0.29999999999999999.
1869 // max(|f - f_GSL|): 8.8817841970012523e-16
1870 // max(|f - f_GSL| / |f_GSL|): 6.4979715256503266e-16
1871 const testcase_ellint_3<double>
1872 data064[10] =
1873 {
1874   { 0.0000000000000000, -0.30000000000000004, 0.29999999999999999,
1875           0.0000000000000000 },
1876   { 0.17408628437042842, -0.30000000000000004, 0.29999999999999999,
1877           0.17453292519943295 },
1878   { 0.34561356761638401, -0.30000000000000004, 0.29999999999999999,
1879           0.34906585039886590 },
1880   { 0.51257058617875850, -0.30000000000000004, 0.29999999999999999,
1881           0.52359877559829882 },
1882   { 0.67382207124602878, -0.30000000000000004, 0.29999999999999999,
1883           0.69813170079773179 },
1884   { 0.82914751587825131, -0.30000000000000004, 0.29999999999999999,
1885           0.87266462599716477 },
1886   { 0.97907434814374938, -0.30000000000000004, 0.29999999999999999,
1887           1.0471975511965976 },
1888   { 1.1246399297351584, -0.30000000000000004, 0.29999999999999999,
1889           1.2217304763960306 },
1890   { 1.2671793970398149, -0.30000000000000004, 0.29999999999999999,
1891           1.3962634015954636 },
1892   { 1.4081767433479091, -0.30000000000000004, 0.29999999999999999,
1893           1.5707963267948966 },
1894 };
1895 const double toler064 = 2.5000000000000020e-13;
1896
1897 // Test data for k=-0.30000000000000004, nu=0.40000000000000002.
1898 // max(|f - f_GSL|): 8.8817841970012523e-16
1899 // max(|f - f_GSL| / |f_GSL|): 6.5505716921759864e-16
1900 const testcase_ellint_3<double>
1901 data065[10] =
1902 {
1903   { 0.0000000000000000, -0.30000000000000004, 0.40000000000000002,
1904           0.0000000000000000 },
1905   { 0.17391220945982727, -0.30000000000000004, 0.40000000000000002,
1906           0.17453292519943295 },
1907   { 0.34429133937639689, -0.30000000000000004, 0.40000000000000002,
1908           0.34906585039886590 },
1909   { 0.50845471668581632, -0.30000000000000004, 0.40000000000000002,
1910           0.52359877559829882 },
1911   { 0.66502347027873854, -0.30000000000000004, 0.40000000000000002,
1912           0.69813170079773179 },
1913   { 0.81389191978012254, -0.30000000000000004, 0.40000000000000002,
1914           0.87266462599716477 },
1915   { 0.95590618002140570, -0.30000000000000004, 0.40000000000000002,
1916           1.0471975511965976 },
1917   { 1.0924915195213121, -0.30000000000000004, 0.40000000000000002,
1918           1.2217304763960306 },
1919   { 1.2253651604038061, -0.30000000000000004, 0.40000000000000002,
1920           1.3962634015954636 },
1921   { 1.3563643538969763, -0.30000000000000004, 0.40000000000000002,
1922           1.5707963267948966 },
1923 };
1924 const double toler065 = 2.5000000000000020e-13;
1925
1926 // Test data for k=-0.30000000000000004, nu=0.50000000000000000.
1927 // max(|f - f_GSL|): 8.8817841970012523e-16
1928 // max(|f - f_GSL| / |f_GSL|): 6.7807908859023716e-16
1929 const testcase_ellint_3<double>
1930 data066[10] =
1931 {
1932   { 0.0000000000000000, -0.30000000000000004, 0.50000000000000000,
1933           0.0000000000000000 },
1934   { 0.17373875742088232, -0.30000000000000004, 0.50000000000000000,
1935           0.17453292519943295 },
1936   { 0.34298690571124157, -0.30000000000000004, 0.50000000000000000,
1937           0.34906585039886590 },
1938   { 0.50445214859646936, -0.30000000000000004, 0.50000000000000000,
1939           0.52359877559829882 },
1940   { 0.65660648352418516, -0.30000000000000004, 0.50000000000000000,
1941           0.69813170079773179 },
1942   { 0.79953670639287289, -0.30000000000000004, 0.50000000000000000,
1943           0.87266462599716477 },
1944   { 0.93443393926588536, -0.30000000000000004, 0.50000000000000000,
1945           1.0471975511965976 },
1946   { 1.0630838369016911, -0.30000000000000004, 0.50000000000000000,
1947           1.2217304763960306 },
1948   { 1.1875197325653029, -0.30000000000000004, 0.50000000000000000,
1949           1.3962634015954636 },
1950   { 1.3098448759814962, -0.30000000000000004, 0.50000000000000000,
1951           1.5707963267948966 },
1952 };
1953 const double toler066 = 2.5000000000000020e-13;
1954
1955 // Test data for k=-0.30000000000000004, nu=0.59999999999999998.
1956 // max(|f - f_GSL|): 8.8817841970012523e-16
1957 // max(|f - f_GSL| / |f_GSL|): 7.0057999499931649e-16
1958 const testcase_ellint_3<double>
1959 data067[10] =
1960 {
1961   { 0.0000000000000000, -0.30000000000000004, 0.59999999999999998,
1962           0.0000000000000000 },
1963   { 0.17356592428950823, -0.30000000000000004, 0.59999999999999998,
1964           0.17453292519943295 },
1965   { 0.34169984536697379, -0.30000000000000004, 0.59999999999999998,
1966           0.34906585039886590 },
1967   { 0.50055748266498457, -0.30000000000000004, 0.59999999999999998,
1968           0.52359877559829882 },
1969   { 0.64854298527106768, -0.30000000000000004, 0.59999999999999998,
1970           0.69813170079773179 },
1971   { 0.78599329284207431, -0.30000000000000004, 0.59999999999999998,
1972           0.87266462599716477 },
1973   { 0.91445452089128199, -0.30000000000000004, 0.59999999999999998,
1974           1.0471975511965976 },
1975   { 1.0360412952290587, -0.30000000000000004, 0.59999999999999998,
1976           1.2217304763960306 },
1977   { 1.1530473919778641, -0.30000000000000004, 0.59999999999999998,
1978           1.3962634015954636 },
1979   { 1.2677758800420669, -0.30000000000000004, 0.59999999999999998,
1980           1.5707963267948966 },
1981 };
1982 const double toler067 = 2.5000000000000020e-13;
1983
1984 // Test data for k=-0.30000000000000004, nu=0.69999999999999996.
1985 // max(|f - f_GSL|): 8.8817841970012523e-16
1986 // max(|f - f_GSL| / |f_GSL|): 7.2239502844122443e-16
1987 const testcase_ellint_3<double>
1988 data068[10] =
1989 {
1990   { 0.0000000000000000, -0.30000000000000004, 0.69999999999999996,
1991           0.0000000000000000 },
1992   { 0.17339370613812224, -0.30000000000000004, 0.69999999999999996,
1993           0.17453292519943295 },
1994   { 0.34042975138455933, -0.30000000000000004, 0.69999999999999996,
1995           0.34906585039886590 },
1996   { 0.49676568368075985, -0.30000000000000004, 0.69999999999999996,
1997           0.52359877559829882 },
1998   { 0.64080774055753720, -0.30000000000000004, 0.69999999999999996,
1999           0.69813170079773179 },
2000   { 0.77318507779667278, -0.30000000000000004, 0.69999999999999996,
2001           0.87266462599716477 },
2002   { 0.89579782346548609, -0.30000000000000004, 0.69999999999999996,
2003           1.0471975511965976 },
2004   { 1.0110573286052202, -0.30000000000000004, 0.69999999999999996,
2005           1.2217304763960306 },
2006   { 1.1214710972949635, -0.30000000000000004, 0.69999999999999996,
2007           1.3962634015954636 },
2008   { 1.2294913236274982, -0.30000000000000004, 0.69999999999999996,
2009           1.5707963267948966 },
2010 };
2011 const double toler068 = 2.5000000000000020e-13;
2012
2013 // Test data for k=-0.30000000000000004, nu=0.80000000000000004.
2014 // max(|f - f_GSL|): 8.8817841970012523e-16
2015 // max(|f - f_GSL| / |f_GSL|): 7.4358357000101250e-16
2016 const testcase_ellint_3<double>
2017 data069[10] =
2018 {
2019   { 0.0000000000000000, -0.30000000000000004, 0.80000000000000004,
2020           0.0000000000000000 },
2021   { 0.17322209907520358, -0.30000000000000004, 0.80000000000000004,
2022           0.17453292519943295 },
2023   { 0.33917623046949996, -0.30000000000000004, 0.80000000000000004,
2024           0.34906585039886590 },
2025   { 0.49307204894329176, -0.30000000000000004, 0.80000000000000004,
2026           0.52359877559829882 },
2027   { 0.63337802830291734, -0.30000000000000004, 0.80000000000000004,
2028           0.69813170079773179 },
2029   { 0.76104540997689407, -0.30000000000000004, 0.80000000000000004,
2030           0.87266462599716477 },
2031   { 0.87832009635450714, -0.30000000000000004, 0.80000000000000004,
2032           1.0471975511965976 },
2033   { 0.98787879723171790, -0.30000000000000004, 0.80000000000000004,
2034           1.2217304763960306 },
2035   { 1.0924036340069339, -0.30000000000000004, 0.80000000000000004,
2036           1.3962634015954636 },
2037   { 1.1944567571590048, -0.30000000000000004, 0.80000000000000004,
2038           1.5707963267948966 },
2039 };
2040 const double toler069 = 2.5000000000000020e-13;
2041
2042 // Test data for k=-0.30000000000000004, nu=0.90000000000000002.
2043 // max(|f - f_GSL|): 8.8817841970012523e-16
2044 // max(|f - f_GSL| / |f_GSL|): 7.6419688299804087e-16
2045 const testcase_ellint_3<double>
2046 data070[10] =
2047 {
2048   { 0.0000000000000000, -0.30000000000000004, 0.90000000000000002,
2049           0.0000000000000000 },
2050   { 0.17305109924485945, -0.30000000000000004, 0.90000000000000002,
2051           0.17453292519943295 },
2052   { 0.33793890239556984, -0.30000000000000004, 0.90000000000000002,
2053           0.34906585039886590 },
2054   { 0.48947218005089738, -0.30000000000000004, 0.90000000000000002,
2055           0.52359877559829882 },
2056   { 0.62623332340775151, -0.30000000000000004, 0.90000000000000002,
2057           0.69813170079773179 },
2058   { 0.74951596581511148, -0.30000000000000004, 0.90000000000000002,
2059           0.87266462599716477 },
2060   { 0.86189886597755994, -0.30000000000000004, 0.90000000000000002,
2061           1.0471975511965976 },
2062   { 0.96629451153092005, -0.30000000000000004, 0.90000000000000002,
2063           1.2217304763960306 },
2064   { 1.0655269133492682, -0.30000000000000004, 0.90000000000000002,
2065           1.3962634015954636 },
2066   { 1.1622376896064914, -0.30000000000000004, 0.90000000000000002,
2067           1.5707963267948966 },
2068 };
2069 const double toler070 = 2.5000000000000020e-13;
2070
2071 // Test data for k=-0.19999999999999996, nu=0.0000000000000000.
2072 // max(|f - f_GSL|): 4.4408920985006262e-16
2073 // max(|f - f_GSL| / |f_GSL|): 4.2156475739151676e-16
2074 const testcase_ellint_3<double>
2075 data071[10] =
2076 {
2077   { 0.0000000000000000, -0.19999999999999996, 0.0000000000000000,
2078           0.0000000000000000 },
2079   { 0.17456817290292809, -0.19999999999999996, 0.0000000000000000,
2080           0.17453292519943295 },
2081   { 0.34934315932086801, -0.19999999999999996, 0.0000000000000000,
2082           0.34906585039886590 },
2083   { 0.52450880529443988, -0.19999999999999996, 0.0000000000000000,
2084           0.52359877559829882 },
2085   { 0.70020491009844876, -0.19999999999999996, 0.0000000000000000,
2086           0.69813170079773179 },
2087   { 0.87651006649967955, -0.19999999999999996, 0.0000000000000000,
2088           0.87266462599716477 },
2089   { 1.0534305870298994, -0.19999999999999996, 0.0000000000000000,
2090           1.0471975511965976 },
2091   { 1.2308975521670784, -0.19999999999999996, 0.0000000000000000,
2092           1.2217304763960306 },
2093   { 1.4087733584990738, -0.19999999999999996, 0.0000000000000000,
2094           1.3962634015954636 },
2095   { 1.5868678474541660, -0.19999999999999996, 0.0000000000000000,
2096           1.5707963267948966 },
2097 };
2098 const double toler071 = 2.5000000000000020e-13;
2099
2100 // Test data for k=-0.19999999999999996, nu=0.10000000000000001.
2101 // max(|f - f_GSL|): 4.4408920985006262e-16
2102 // max(|f - f_GSL| / |f_GSL|): 4.3374593253183472e-16
2103 const testcase_ellint_3<double>
2104 data072[10] =
2105 {
2106   { 0.0000000000000000, -0.19999999999999996, 0.10000000000000001,
2107           0.0000000000000000 },
2108   { 0.17439228502691748, -0.19999999999999996, 0.10000000000000001,
2109           0.17453292519943295 },
2110   { 0.34796731137565740, -0.19999999999999996, 0.10000000000000001,
2111           0.34906585039886590 },
2112   { 0.52003370294544848, -0.19999999999999996, 0.10000000000000001,
2113           0.52359877559829882 },
2114   { 0.69012222258631462, -0.19999999999999996, 0.10000000000000001,
2115           0.69813170079773179 },
2116   { 0.85803491465566772, -0.19999999999999996, 0.10000000000000001,
2117           0.87266462599716477 },
2118   { 1.0238463961099364, -0.19999999999999996, 0.10000000000000001,
2119           1.0471975511965976 },
2120   { 1.1878691059202153, -0.19999999999999996, 0.10000000000000001,
2121           1.2217304763960306 },
2122   { 1.3505985031831940, -0.19999999999999996, 0.10000000000000001,
2123           1.3962634015954636 },
2124   { 1.5126513474261087, -0.19999999999999996, 0.10000000000000001,
2125           1.5707963267948966 },
2126 };
2127 const double toler072 = 2.5000000000000020e-13;
2128
2129 // Test data for k=-0.19999999999999996, nu=0.20000000000000001.
2130 // max(|f - f_GSL|): 4.4408920985006262e-16
2131 // max(|f - f_GSL| / |f_GSL|): 4.4549984059502760e-16
2132 const testcase_ellint_3<double>
2133 data073[10] =
2134 {
2135   { 0.0000000000000000, -0.19999999999999996, 0.20000000000000001,
2136           0.0000000000000000 },
2137   { 0.17421703179583747, -0.19999999999999996, 0.20000000000000001,
2138           0.17453292519943295 },
2139   { 0.34661057411998791, -0.19999999999999996, 0.20000000000000001,
2140           0.34906585039886590 },
2141   { 0.51569006052647393, -0.19999999999999996, 0.20000000000000001,
2142           0.52359877559829882 },
2143   { 0.68052412821107244, -0.19999999999999996, 0.20000000000000001,
2144           0.69813170079773179 },
2145   { 0.84081341263313825, -0.19999999999999996, 0.20000000000000001,
2146           0.87266462599716477 },
2147   { 0.99683359988842890, -0.19999999999999996, 0.20000000000000001,
2148           1.0471975511965976 },
2149   { 1.1493086715118852, -0.19999999999999996, 0.20000000000000001,
2150           1.2217304763960306 },
2151   { 1.2992699693957541, -0.19999999999999996, 0.20000000000000001,
2152           1.3962634015954636 },
2153   { 1.4479323932249564, -0.19999999999999996, 0.20000000000000001,
2154           1.5707963267948966 },
2155 };
2156 const double toler073 = 2.5000000000000020e-13;
2157
2158 // Test data for k=-0.19999999999999996, nu=0.29999999999999999.
2159 // max(|f - f_GSL|): 6.6613381477509392e-16
2160 // max(|f - f_GSL| / |f_GSL|): 5.3140668101543467e-16
2161 const testcase_ellint_3<double>
2162 data074[10] =
2163 {
2164   { 0.0000000000000000, -0.19999999999999996, 0.29999999999999999,
2165           0.0000000000000000 },
2166   { 0.17404240913577704, -0.19999999999999996, 0.29999999999999999,
2167           0.17453292519943295 },
2168   { 0.34527248032587193, -0.19999999999999996, 0.29999999999999999,
2169           0.34906585039886590 },
2170   { 0.51147118981668416, -0.19999999999999996, 0.29999999999999999,
2171           0.52359877559829882 },
2172   { 0.67137107867777601, -0.19999999999999996, 0.29999999999999999,
2173           0.69813170079773179 },
2174   { 0.82470418188668893, -0.19999999999999996, 0.29999999999999999,
2175           0.87266462599716477 },
2176   { 0.97202873223594299, -0.19999999999999996, 0.29999999999999999,
2177           1.0471975511965976 },
2178   { 1.1144773569375266, -0.19999999999999996, 0.29999999999999999,
2179           1.2217304763960306 },
2180   { 1.2535292433701000, -0.19999999999999996, 0.29999999999999999,
2181           1.3962634015954636 },
2182   { 1.3908453514752477, -0.19999999999999996, 0.29999999999999999,
2183           1.5707963267948966 },
2184 };
2185 const double toler074 = 2.5000000000000020e-13;
2186
2187 // Test data for k=-0.19999999999999996, nu=0.40000000000000002.
2188 // max(|f - f_GSL|): 4.4408920985006262e-16
2189 // max(|f - f_GSL| / |f_GSL|): 4.6788709752760483e-16
2190 const testcase_ellint_3<double>
2191 data075[10] =
2192 {
2193   { 0.0000000000000000, -0.19999999999999996, 0.40000000000000002,
2194           0.0000000000000000 },
2195   { 0.17386841301066674, -0.19999999999999996, 0.40000000000000002,
2196           0.17453292519943295 },
2197   { 0.34395257914113253, -0.19999999999999996, 0.40000000000000002,
2198           0.34906585039886590 },
2199   { 0.50737088376869466, -0.19999999999999996, 0.40000000000000002,
2200           0.52359877559829882 },
2201   { 0.66262801717277631, -0.19999999999999996, 0.40000000000000002,
2202           0.69813170079773179 },
2203   { 0.80958766645079094, -0.19999999999999996, 0.40000000000000002,
2204           0.87266462599716477 },
2205   { 0.94913754236162040, -0.19999999999999996, 0.40000000000000002,
2206           1.0471975511965976 },
2207   { 1.0827985514222997, -0.19999999999999996, 0.40000000000000002,
2208           1.2217304763960306 },
2209   { 1.2124212429050478, -0.19999999999999996, 0.40000000000000002,
2210           1.3962634015954636 },
2211   { 1.3400002519661005, -0.19999999999999996, 0.40000000000000002,
2212           1.5707963267948966 },
2213 };
2214 const double toler075 = 2.5000000000000020e-13;
2215
2216 // Test data for k=-0.19999999999999996, nu=0.50000000000000000.
2217 // max(|f - f_GSL|): 4.4408920985006262e-16
2218 // max(|f - f_GSL| / |f_GSL|): 3.7788201301356829e-16
2219 const testcase_ellint_3<double>
2220 data076[10] =
2221 {
2222   { 0.0000000000000000, -0.19999999999999996, 0.50000000000000000,
2223           0.0000000000000000 },
2224   { 0.17369503942181799, -0.19999999999999996, 0.50000000000000000,
2225           0.17453292519943295 },
2226   { 0.34265043534362660, -0.19999999999999996, 0.50000000000000000,
2227           0.34906585039886590 },
2228   { 0.50338337208655415, -0.19999999999999996, 0.50000000000000000,
2229           0.52359877559829882 },
2230   { 0.65426373297163609, -0.19999999999999996, 0.50000000000000000,
2231           0.69813170079773179 },
2232   { 0.79536193036145808, -0.19999999999999996, 0.50000000000000000,
2233           0.87266462599716477 },
2234   { 0.92791875910061605, -0.19999999999999996, 0.50000000000000000,
2235           1.0471975511965976 },
2236   { 1.0538145052725829, -0.19999999999999996, 0.50000000000000000,
2237           1.2217304763960306 },
2238   { 1.1752060022875899, -0.19999999999999996, 0.50000000000000000,
2239           1.3962634015954636 },
2240   { 1.2943374404397372, -0.19999999999999996, 0.50000000000000000,
2241           1.5707963267948966 },
2242 };
2243 const double toler076 = 2.5000000000000020e-13;
2244
2245 // Test data for k=-0.19999999999999996, nu=0.59999999999999998.
2246 // max(|f - f_GSL|): 4.4408920985006262e-16
2247 // max(|f - f_GSL| / |f_GSL|): 4.8899223779598256e-16
2248 const testcase_ellint_3<double>
2249 data077[10] =
2250 {
2251   { 0.0000000000000000, -0.19999999999999996, 0.59999999999999998,
2252           0.0000000000000000 },
2253   { 0.17352228440746925, -0.19999999999999996, 0.59999999999999998,
2254           0.17453292519943295 },
2255   { 0.34136562863713626, -0.19999999999999996, 0.59999999999999998,
2256           0.34906585039886590 },
2257   { 0.49950328177638481, -0.19999999999999996, 0.59999999999999998,
2258           0.52359877559829882 },
2259   { 0.64625032705690799, -0.19999999999999996, 0.59999999999999998,
2260           0.69813170079773179 },
2261   { 0.78193941198403083, -0.19999999999999996, 0.59999999999999998,
2262           0.87266462599716477 },
2263   { 0.90817230934317128, -0.19999999999999996, 0.59999999999999998,
2264           1.0471975511965976 },
2265   { 1.0271563751276462, -0.19999999999999996, 0.59999999999999998,
2266           1.2217304763960306 },
2267   { 1.1412999379040518, -0.19999999999999996, 0.59999999999999998,
2268           1.3962634015954636 },
2269   { 1.2530330675914556, -0.19999999999999996, 0.59999999999999998,
2270           1.5707963267948966 },
2271 };
2272 const double toler077 = 2.5000000000000020e-13;
2273
2274 // Test data for k=-0.19999999999999996, nu=0.69999999999999996.
2275 // max(|f - f_GSL|): 6.6613381477509392e-16
2276 // max(|f - f_GSL| / |f_GSL|): 5.9999318361775115e-16
2277 const testcase_ellint_3<double>
2278 data078[10] =
2279 {
2280   { 0.0000000000000000, -0.19999999999999996, 0.69999999999999996,
2281           0.0000000000000000 },
2282   { 0.17335014404233895, -0.19999999999999996, 0.69999999999999996,
2283           0.17453292519943295 },
2284   { 0.34009775298617811, -0.19999999999999996, 0.69999999999999996,
2285           0.34906585039886590 },
2286   { 0.49572560201923810, -0.19999999999999996, 0.69999999999999996,
2287           0.52359877559829882 },
2288   { 0.63856276669886503, -0.19999999999999996, 0.69999999999999996,
2289           0.69813170079773179 },
2290   { 0.76924438644867565, -0.19999999999999996, 0.69999999999999996,
2291           0.87266462599716477 },
2292   { 0.88973060843856466, -0.19999999999999996, 0.69999999999999996,
2293           1.0471975511965976 },
2294   { 1.0025230471636377, -0.19999999999999996, 0.69999999999999996,
2295           1.2217304763960306 },
2296   { 1.1102356376093103, -0.19999999999999996, 0.69999999999999996,
2297           1.3962634015954636 },
2298   { 1.2154356555075863, -0.19999999999999996, 0.69999999999999996,
2299           1.5707963267948966 },
2300 };
2301 const double toler078 = 2.5000000000000020e-13;
2302
2303 // Test data for k=-0.19999999999999996, nu=0.80000000000000004.
2304 // max(|f - f_GSL|): 4.4408920985006262e-16
2305 // max(|f - f_GSL| / |f_GSL|): 5.0901276230707249e-16
2306 const testcase_ellint_3<double>
2307 data079[10] =
2308 {
2309   { 0.0000000000000000, -0.19999999999999996, 0.80000000000000004,
2310           0.0000000000000000 },
2311   { 0.17317861443718538, -0.19999999999999996, 0.80000000000000004,
2312           0.17453292519943295 },
2313   { 0.33884641598718701, -0.19999999999999996, 0.80000000000000004,
2314           0.34906585039886590 },
2315   { 0.49204565281259494, -0.19999999999999996, 0.80000000000000004,
2316           0.52359877559829882 },
2317   { 0.63117851188220320, -0.19999999999999996, 0.80000000000000004,
2318           0.69813170079773179 },
2319   { 0.75721095949544170, -0.19999999999999996, 0.80000000000000004,
2320           0.87266462599716477 },
2321   { 0.87245201443919118, -0.19999999999999996, 0.80000000000000004,
2322           1.0471975511965976 },
2323   { 0.97966584238831089, -0.19999999999999996, 0.80000000000000004,
2324           1.2217304763960306 },
2325   { 1.0816336325174360, -0.19999999999999996, 0.80000000000000004,
2326           1.3962634015954636 },
2327   { 1.1810223448909909, -0.19999999999999996, 0.80000000000000004,
2328           1.5707963267948966 },
2329 };
2330 const double toler079 = 2.5000000000000020e-13;
2331
2332 // Test data for k=-0.19999999999999996, nu=0.90000000000000002.
2333 // max(|f - f_GSL|): 6.6613381477509392e-16
2334 // max(|f - f_GSL| / |f_GSL|): 6.4833128442756722e-16
2335 const testcase_ellint_3<double>
2336 data080[10] =
2337 {
2338   { 0.0000000000000000, -0.19999999999999996, 0.90000000000000002,
2339           0.0000000000000000 },
2340   { 0.17300769173837277, -0.19999999999999996, 0.90000000000000002,
2341           0.17453292519943295 },
2342   { 0.33761123827372508, -0.19999999999999996, 0.90000000000000002,
2343           0.34906585039886590 },
2344   { 0.48845905690769426, -0.19999999999999996, 0.90000000000000002,
2345           0.52359877559829882 },
2346   { 0.62407720017324952, -0.19999999999999996, 0.90000000000000002,
2347           0.69813170079773179 },
2348   { 0.74578146525124289, -0.19999999999999996, 0.90000000000000002,
2349           0.87266462599716477 },
2350   { 0.85621583540073076, -0.19999999999999996, 0.90000000000000002,
2351           1.0471975511965976 },
2352   { 0.95837725988001199, -0.19999999999999996, 0.90000000000000002,
2353           1.2217304763960306 },
2354   { 1.0551821412633928, -0.19999999999999996, 0.90000000000000002,
2355           1.3962634015954636 },
2356   { 1.1493679916141861, -0.19999999999999996, 0.90000000000000002,
2357           1.5707963267948966 },
2358 };
2359 const double toler080 = 2.5000000000000020e-13;
2360
2361 // Test data for k=-0.099999999999999978, nu=0.0000000000000000.
2362 // max(|f - f_GSL|): 4.4408920985006262e-16
2363 // max(|f - f_GSL| / |f_GSL|): 3.1735566504509650e-16
2364 const testcase_ellint_3<double>
2365 data081[10] =
2366 {
2367   { 0.0000000000000000, -0.099999999999999978, 0.0000000000000000,
2368           0.0000000000000000 },
2369   { 0.17454173353063659, -0.099999999999999978, 0.0000000000000000,
2370           0.17453292519943295 },
2371   { 0.34913506721468091, -0.099999999999999978, 0.0000000000000000,
2372           0.34906585039886590 },
2373   { 0.52382550016538942, -0.099999999999999978, 0.0000000000000000,
2374           0.52359877559829882 },
2375   { 0.69864700854177020, -0.099999999999999978, 0.0000000000000000,
2376           0.69813170079773179 },
2377   { 0.87361792586964870, -0.099999999999999978, 0.0000000000000000,
2378           0.87266462599716477 },
2379   { 1.0487386319621683, -0.099999999999999978, 0.0000000000000000,
2380           1.0471975511965976 },
2381   { 1.2239913752078757, -0.099999999999999978, 0.0000000000000000,
2382           1.2217304763960306 },
2383   { 1.3993423113684049, -0.099999999999999978, 0.0000000000000000,
2384           1.3962634015954636 },
2385   { 1.5747455615173562, -0.099999999999999978, 0.0000000000000000,
2386           1.5707963267948966 },
2387 };
2388 const double toler081 = 2.5000000000000020e-13;
2389
2390 // Test data for k=-0.099999999999999978, nu=0.10000000000000001.
2391 // max(|f - f_GSL|): 4.4408920985006262e-16
2392 // max(|f - f_GSL| / |f_GSL|): 3.3097339877269682e-16
2393 const testcase_ellint_3<double>
2394 data082[10] =
2395 {
2396   { 0.0000000000000000, -0.099999999999999978, 0.10000000000000001,
2397           0.0000000000000000 },
2398   { 0.17436589347616613, -0.099999999999999978, 0.10000000000000001,
2399           0.17453292519943295 },
2400   { 0.34776067871237359, -0.099999999999999978, 0.10000000000000001,
2401           0.34906585039886590 },
2402   { 0.51936064354727796, -0.099999999999999978, 0.10000000000000001,
2403           0.52359877559829882 },
2404   { 0.68860303749364349, -0.099999999999999978, 0.10000000000000001,
2405           0.69813170079773179 },
2406   { 0.85524561882332051, -0.099999999999999978, 0.10000000000000001,
2407           0.87266462599716477 },
2408   { 1.0193708301908335, -0.099999999999999978, 0.10000000000000001,
2409           1.0471975511965976 },
2410   { 1.1813474067123044, -0.099999999999999978, 0.10000000000000001,
2411           1.2217304763960306 },
2412   { 1.3417670770424983, -0.099999999999999978, 0.10000000000000001,
2413           1.3962634015954636 },
2414   { 1.5013711111199950, -0.099999999999999978, 0.10000000000000001,
2415           1.5707963267948966 },
2416 };
2417 const double toler082 = 2.5000000000000020e-13;
2418
2419 // Test data for k=-0.099999999999999978, nu=0.20000000000000001.
2420 // max(|f - f_GSL|): 4.4408920985006262e-16
2421 // max(|f - f_GSL| / |f_GSL|): 3.4399947764827574e-16
2422 const testcase_ellint_3<double>
2423 data083[10] =
2424 {
2425   { 0.0000000000000000, -0.099999999999999978, 0.20000000000000001,
2426           0.0000000000000000 },
2427   { 0.17419068786141340, -0.099999999999999978, 0.20000000000000001,
2428           0.17453292519943295 },
2429   { 0.34640537686230133, -0.099999999999999978, 0.20000000000000001,
2430           0.34906585039886590 },
2431   { 0.51502689171753946, -0.099999999999999978, 0.20000000000000001,
2432           0.52359877559829882 },
2433   { 0.67904147863672715, -0.099999999999999978, 0.20000000000000001,
2434           0.69813170079773179 },
2435   { 0.83811885126105179, -0.099999999999999978, 0.20000000000000001,
2436           0.87266462599716477 },
2437   { 0.99255278555742787, -0.099999999999999978, 0.20000000000000001,
2438           1.0471975511965976 },
2439   { 1.1431260546194930, -0.099999999999999978, 0.20000000000000001,
2440           1.2217304763960306 },
2441   { 1.2909589656532101, -0.099999999999999978, 0.20000000000000001,
2442           1.3962634015954636 },
2443   { 1.4373749386463430, -0.099999999999999978, 0.20000000000000001,
2444           1.5707963267948966 },
2445 };
2446 const double toler083 = 2.5000000000000020e-13;
2447
2448 // Test data for k=-0.099999999999999978, nu=0.29999999999999999.
2449 // max(|f - f_GSL|): 4.4408920985006262e-16
2450 // max(|f - f_GSL| / |f_GSL|): 3.5650492137236872e-16
2451 const testcase_ellint_3<double>
2452 data084[10] =
2453 {
2454   { 0.0000000000000000, -0.099999999999999978, 0.29999999999999999,
2455           0.0000000000000000 },
2456   { 0.17401611261390104, -0.099999999999999978, 0.29999999999999999,
2457           0.17453292519943295 },
2458   { 0.34506869507511773, -0.099999999999999978, 0.29999999999999999,
2459           0.34906585039886590 },
2460   { 0.51081757604259859, -0.099999999999999978, 0.29999999999999999,
2461           0.52359877559829882 },
2462   { 0.66992297597712303, -0.099999999999999978, 0.29999999999999999,
2463           0.69813170079773179 },
2464   { 0.82209722856174228, -0.099999999999999978, 0.29999999999999999,
2465           0.87266462599716477 },
2466   { 0.96792430487669590, -0.099999999999999978, 0.29999999999999999,
2467           1.0471975511965976 },
2468   { 1.1085964108954092, -0.099999999999999978, 0.29999999999999999,
2469           1.2217304763960306 },
2470   { 1.2456748370836999, -0.099999999999999978, 0.29999999999999999,
2471           1.3962634015954636 },
2472   { 1.3809159606704959, -0.099999999999999978, 0.29999999999999999,
2473           1.5707963267948966 },
2474 };
2475 const double toler084 = 2.5000000000000020e-13;
2476
2477 // Test data for k=-0.099999999999999978, nu=0.40000000000000002.
2478 // max(|f - f_GSL|): 4.4408920985006262e-16
2479 // max(|f - f_GSL| / |f_GSL|): 3.6854758534459740e-16
2480 const testcase_ellint_3<double>
2481 data085[10] =
2482 {
2483   { 0.0000000000000000, -0.099999999999999978, 0.40000000000000002,
2484           0.0000000000000000 },
2485   { 0.17384216369897931, -0.099999999999999978, 0.40000000000000002,
2486           0.17453292519943295 },
2487   { 0.34375018311376787, -0.099999999999999978, 0.40000000000000002,
2488           0.34906585039886590 },
2489   { 0.50672650758380455, -0.099999999999999978, 0.40000000000000002,
2490           0.52359877559829882 },
2491   { 0.66121264213337616, -0.099999999999999978, 0.40000000000000002,
2492           0.69813170079773179 },
2493   { 0.80706202005774441, -0.099999999999999978, 0.40000000000000002,
2494           0.87266462599716477 },
2495   { 0.94519376138245870, -0.099999999999999978, 0.40000000000000002,
2496           1.0471975511965976 },
2497   { 1.0771880300759584, -0.099999999999999978, 0.40000000000000002,
2498           1.2217304763960306 },
2499   { 1.2049711557188272, -0.099999999999999978, 0.40000000000000002,
2500           1.3962634015954636 },
2501   { 1.3306223265207477, -0.099999999999999978, 0.40000000000000002,
2502           1.5707963267948966 },
2503 };
2504 const double toler085 = 2.5000000000000020e-13;
2505
2506 // Test data for k=-0.099999999999999978, nu=0.50000000000000000.
2507 // max(|f - f_GSL|): 4.4408920985006262e-16
2508 // max(|f - f_GSL| / |f_GSL|): 3.8017534281650347e-16
2509 const testcase_ellint_3<double>
2510 data086[10] =
2511 {
2512   { 0.0000000000000000, -0.099999999999999978, 0.50000000000000000,
2513           0.0000000000000000 },
2514   { 0.17366883711936548, -0.099999999999999978, 0.50000000000000000,
2515           0.17453292519943295 },
2516   { 0.34244940634881882, -0.099999999999999978, 0.50000000000000000,
2517           0.34906585039886590 },
2518   { 0.50274793281634367, -0.099999999999999978, 0.50000000000000000,
2519           0.52359877559829882 },
2520   { 0.65287941633275082, -0.099999999999999978, 0.50000000000000000,
2521           0.69813170079773179 },
2522   { 0.79291198790315398, -0.099999999999999978, 0.50000000000000000,
2523           0.87266462599716477 },
2524   { 0.92412201537880323, -0.099999999999999978, 0.50000000000000000,
2525           1.0471975511965976 },
2526   { 1.0484480076799372, -0.099999999999999978, 0.50000000000000000,
2527           1.2217304763960306 },
2528   { 1.1681168130475206, -0.099999999999999978, 0.50000000000000000,
2529           1.3962634015954636 },
2530   { 1.2854480708580160, -0.099999999999999978, 0.50000000000000000,
2531           1.5707963267948966 },
2532 };
2533 const double toler086 = 2.5000000000000020e-13;
2534
2535 // Test data for k=-0.099999999999999978, nu=0.59999999999999998.
2536 // max(|f - f_GSL|): 4.4408920985006262e-16
2537 // max(|f - f_GSL| / |f_GSL|): 3.9142834151672032e-16
2538 const testcase_ellint_3<double>
2539 data087[10] =
2540 {
2541   { 0.0000000000000000, -0.099999999999999978, 0.59999999999999998,
2542           0.0000000000000000 },
2543   { 0.17349612891469013, -0.099999999999999978, 0.59999999999999998,
2544           0.17453292519943295 },
2545   { 0.34116594505539444, -0.099999999999999978, 0.59999999999999998,
2546           0.34906585039886590 },
2547   { 0.49887649430466674, -0.099999999999999978, 0.59999999999999998,
2548           0.52359877559829882 },
2549   { 0.64489553282165146, -0.099999999999999978, 0.59999999999999998,
2550           0.69813170079773179 },
2551   { 0.77956016553782437, -0.099999999999999978, 0.59999999999999998,
2552           0.87266462599716477 },
2553   { 0.90451074530096287, -0.099999999999999978, 0.59999999999999998,
2554           1.0471975511965976 },
2555   { 1.0220113666961632, -0.099999999999999978, 0.59999999999999998,
2556           1.2217304763960306 },
2557   { 1.1345351441065563, -0.099999999999999978, 0.59999999999999998,
2558           1.3962634015954636 },
2559   { 1.2445798942989255, -0.099999999999999978, 0.59999999999999998,
2560           1.5707963267948966 },
2561 };
2562 const double toler087 = 2.5000000000000020e-13;
2563
2564 // Test data for k=-0.099999999999999978, nu=0.69999999999999996.
2565 // max(|f - f_GSL|): 6.6613381477509392e-16
2566 // max(|f - f_GSL| / |f_GSL|): 5.5172091551439012e-16
2567 const testcase_ellint_3<double>
2568 data088[10] =
2569 {
2570   { 0.0000000000000000, -0.099999999999999978, 0.69999999999999996,
2571           0.0000000000000000 },
2572   { 0.17332403516105047, -0.099999999999999978, 0.69999999999999996,
2573           0.17453292519943295 },
2574   { 0.33989939374896883, -0.099999999999999978, 0.69999999999999996,
2575           0.34906585039886590 },
2576   { 0.49510719568614070, -0.099999999999999978, 0.69999999999999996,
2577           0.52359877559829882 },
2578   { 0.63723607776354974, -0.099999999999999978, 0.69999999999999996,
2579           0.69813170079773179 },
2580   { 0.76693133887935327, -0.099999999999999978, 0.69999999999999996,
2581           0.87266462599716477 },
2582   { 0.88619382078823805, -0.099999999999999978, 0.69999999999999996,
2583           1.0471975511965976 },
2584   { 0.99758012018676490, -0.099999999999999978, 0.69999999999999996,
2585           1.2217304763960306 },
2586   { 1.1037642270814410, -0.099999999999999978, 0.69999999999999996,
2587           1.3962634015954636 },
2588   { 1.2073745911083185, -0.099999999999999978, 0.69999999999999996,
2589           1.5707963267948966 },
2590 };
2591 const double toler088 = 2.5000000000000020e-13;
2592
2593 // Test data for k=-0.099999999999999978, nu=0.80000000000000004.
2594 // max(|f - f_GSL|): 4.4408920985006262e-16
2595 // max(|f - f_GSL| / |f_GSL|): 4.1294144515772258e-16
2596 const testcase_ellint_3<double>
2597 data089[10] =
2598 {
2599   { 0.0000000000000000, -0.099999999999999978, 0.80000000000000004,
2600           0.0000000000000000 },
2601   { 0.17315255197057014, -0.099999999999999978, 0.80000000000000004,
2602           0.17453292519943295 },
2603   { 0.33864936055747991, -0.099999999999999978, 0.80000000000000004,
2604           0.34906585039886590 },
2605   { 0.49143537041117613, -0.099999999999999978, 0.80000000000000004,
2606           0.52359877559829882 },
2607   { 0.62987861760047492, -0.099999999999999978, 0.80000000000000004,
2608           0.69813170079773179 },
2609   { 0.75496005490917517, -0.099999999999999978, 0.80000000000000004,
2610           0.87266462599716477 },
2611   { 0.86903081862701881, -0.099999999999999978, 0.80000000000000004,
2612           1.0471975511965976 },
2613   { 0.97490814820725591, -0.099999999999999978, 0.80000000000000004,
2614           1.2217304763960306 },
2615   { 1.0754290107171083, -0.099999999999999978, 0.80000000000000004,
2616           1.3962634015954636 },
2617   { 1.1733158866987732, -0.099999999999999978, 0.80000000000000004,
2618           1.5707963267948966 },
2619 };
2620 const double toler089 = 2.5000000000000020e-13;
2621
2622 // Test data for k=-0.099999999999999978, nu=0.90000000000000002.
2623 // max(|f - f_GSL|): 4.4408920985006262e-16
2624 // max(|f - f_GSL| / |f_GSL|): 4.2325599449457852e-16
2625 const testcase_ellint_3<double>
2626 data090[10] =
2627 {
2628   { 0.0000000000000000, -0.099999999999999978, 0.90000000000000002,
2629           0.0000000000000000 },
2630   { 0.17298167549096563, -0.099999999999999978, 0.90000000000000002,
2631           0.17453292519943295 },
2632   { 0.33741546662741589, -0.099999999999999978, 0.90000000000000002,
2633           0.34906585039886590 },
2634   { 0.48785665376856868, -0.099999999999999978, 0.90000000000000002,
2635           0.52359877559829882 },
2636   { 0.62280288554518959, -0.099999999999999978, 0.90000000000000002,
2637           0.69813170079773179 },
2638   { 0.74358903115455188, -0.099999999999999978, 0.90000000000000002,
2639           0.87266462599716477 },
2640   { 0.85290207679298335, -0.099999999999999978, 0.90000000000000002,
2641           1.0471975511965976 },
2642   { 0.95379006645397379, -0.099999999999999978, 0.90000000000000002,
2643           1.2217304763960306 },
2644   { 1.0492213119872327, -0.099999999999999978, 0.90000000000000002,
2645           1.3962634015954636 },
2646   { 1.1419839485283374, -0.099999999999999978, 0.90000000000000002,
2647           1.5707963267948966 },
2648 };
2649 const double toler090 = 2.5000000000000020e-13;
2650
2651 // Test data for k=0.0000000000000000, nu=0.0000000000000000.
2652 // max(|f - f_GSL|): 2.2204460492503131e-16
2653 // max(|f - f_GSL| / |f_GSL|): 2.1203697876423452e-16
2654 const testcase_ellint_3<double>
2655 data091[10] =
2656 {
2657   { 0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
2658           0.0000000000000000 },
2659   { 0.17453292519943292, 0.0000000000000000, 0.0000000000000000,
2660           0.17453292519943295 },
2661   { 0.34906585039886584, 0.0000000000000000, 0.0000000000000000,
2662           0.34906585039886590 },
2663   { 0.52359877559829870, 0.0000000000000000, 0.0000000000000000,
2664           0.52359877559829882 },
2665   { 0.69813170079773168, 0.0000000000000000, 0.0000000000000000,
2666           0.69813170079773179 },
2667   { 0.87266462599716477, 0.0000000000000000, 0.0000000000000000,
2668           0.87266462599716477 },
2669   { 1.0471975511965974, 0.0000000000000000, 0.0000000000000000,
2670           1.0471975511965976 },
2671   { 1.2217304763960304, 0.0000000000000000, 0.0000000000000000,
2672           1.2217304763960306 },
2673   { 1.3962634015954631, 0.0000000000000000, 0.0000000000000000,
2674           1.3962634015954636 },
2675   { 1.5707963267948966, 0.0000000000000000, 0.0000000000000000,
2676           1.5707963267948966 },
2677 };
2678 const double toler091 = 2.5000000000000020e-13;
2679
2680 // Test data for k=0.0000000000000000, nu=0.10000000000000001.
2681 // max(|f - f_GSL|): 2.2204460492503131e-16
2682 // max(|f - f_GSL| / |f_GSL|): 2.1813975824747021e-16
2683 const testcase_ellint_3<double>
2684 data092[10] =
2685 {
2686   { 0.0000000000000000, 0.0000000000000000, 0.10000000000000001,
2687           0.0000000000000000 },
2688   { 0.17435710107516605, 0.0000000000000000, 0.10000000000000001,
2689           0.17453292519943295 },
2690   { 0.34769194715329604, 0.0000000000000000, 0.10000000000000001,
2691           0.34906585039886590 },
2692   { 0.51913731575866107, 0.0000000000000000, 0.10000000000000001,
2693           0.52359877559829882 },
2694   { 0.68810051897078450, 0.0000000000000000, 0.10000000000000001,
2695           0.69813170079773179 },
2696   { 0.85432615661706823, 0.0000000000000000, 0.10000000000000001,
2697           0.87266462599716477 },
2698   { 1.0179006647340794, 0.0000000000000000, 0.10000000000000001,
2699           1.0471975511965976 },
2700   { 1.1792120640746322, 0.0000000000000000, 0.10000000000000001,
2701           1.2217304763960306 },
2702   { 1.3388834245070498, 0.0000000000000000, 0.10000000000000001,
2703           1.3962634015954636 },
2704   { 1.4976955329233277, 0.0000000000000000, 0.10000000000000001,
2705           1.5707963267948966 },
2706 };
2707 const double toler092 = 2.5000000000000020e-13;
2708
2709 // Test data for k=0.0000000000000000, nu=0.20000000000000001.
2710 // max(|f - f_GSL|): 2.2204460492503131e-16
2711 // max(|f - f_GSL| / |f_GSL|): 2.2402804784409065e-16
2712 const testcase_ellint_3<double>
2713 data093[10] =
2714 {
2715   { 0.0000000000000000, 0.0000000000000000, 0.20000000000000001,
2716           0.0000000000000000 },
2717   { 0.17418191132226074, 0.0000000000000000, 0.20000000000000001,
2718           0.17453292519943295 },
2719   { 0.34633712256943405, 0.0000000000000000, 0.20000000000000001,
2720           0.34906585039886590 },
2721   { 0.51480684302043700, 0.0000000000000000, 0.20000000000000001,
2722           0.52359877559829882 },
2723   { 0.67855102942481937, 0.0000000000000000, 0.20000000000000001,
2724           0.69813170079773179 },
2725   { 0.83723056090326253, 0.0000000000000000, 0.20000000000000001,
2726           0.87266462599716477 },
2727   { 0.99114645269578161, 0.0000000000000000, 0.20000000000000001,
2728           1.0471975511965976 },
2729   { 1.1411014627915537, 0.0000000000000000, 0.20000000000000001,
2730           1.2217304763960306 },
2731   { 1.2882448138013969, 0.0000000000000000, 0.20000000000000001,
2732           1.3962634015954636 },
2733   { 1.4339343023863691, 0.0000000000000000, 0.20000000000000001,
2734           1.5707963267948966 },
2735 };
2736 const double toler093 = 2.5000000000000020e-13;
2737
2738 // Test data for k=0.0000000000000000, nu=0.29999999999999999.
2739 // max(|f - f_GSL|): 2.2204460492503131e-16
2740 // max(|f - f_GSL| / |f_GSL|): 2.2972291118632678e-16
2741 const testcase_ellint_3<double>
2742 data094[10] =
2743 {
2744   { 0.0000000000000000, 0.0000000000000000, 0.29999999999999999,
2745           0.0000000000000000 },
2746   { 0.17400735186871724, 0.0000000000000000, 0.29999999999999999,
2747           0.17453292519943295 },
2748   { 0.34500091027020219, 0.0000000000000000, 0.29999999999999999,
2749           0.34906585039886590 },
2750   { 0.51060069523901530, 0.0000000000000000, 0.29999999999999999,
2751           0.52359877559829882 },
2752   { 0.66944393961375448, 0.0000000000000000, 0.29999999999999999,
2753           0.69813170079773179 },
2754   { 0.82123776744538157, 0.0000000000000000, 0.29999999999999999,
2755           0.87266462599716477 },
2756   { 0.96657579245516501, 0.0000000000000000, 0.29999999999999999,
2757           1.0471975511965976 },
2758   { 1.1066703663542414, 0.0000000000000000, 0.29999999999999999,
2759           1.2217304763960306 },
2760   { 1.2431094251944901, 0.0000000000000000, 0.29999999999999999,
2761           1.3962634015954636 },
2762   { 1.3776795151134889, 0.0000000000000000, 0.29999999999999999,
2763           1.5707963267948966 },
2764 };
2765 const double toler094 = 2.5000000000000020e-13;
2766
2767 // Test data for k=0.0000000000000000, nu=0.40000000000000002.
2768 // max(|f - f_GSL|): 2.2204460492503131e-16
2769 // max(|f - f_GSL| / |f_GSL|): 2.3524218164111537e-16
2770 const testcase_ellint_3<double>
2771 data095[10] =
2772 {
2773   { 0.0000000000000000, 0.0000000000000000, 0.40000000000000002,
2774           0.0000000000000000 },
2775   { 0.17383341868035862, 0.0000000000000000, 0.40000000000000002,
2776           0.17453292519943295 },
2777   { 0.34368286022299821, 0.0000000000000000, 0.40000000000000002,
2778           0.34906585039886590 },
2779   { 0.50651268947499395, 0.0000000000000000, 0.40000000000000002,
2780           0.52359877559829882 },
2781   { 0.66074441806097539, 0.0000000000000000, 0.40000000000000002,
2782           0.69813170079773179 },
2783   { 0.80622931670113474, 0.0000000000000000, 0.40000000000000002,
2784           0.87266462599716477 },
2785   { 0.94389791565435210, 0.0000000000000000, 0.40000000000000002,
2786           1.0471975511965976 },
2787   { 1.0753503387899728, 0.0000000000000000, 0.40000000000000002,
2788           1.2217304763960306 },
2789   { 1.2025374759127518, 0.0000000000000000, 0.40000000000000002,
2790           1.3962634015954636 },
2791   { 1.3275651989026320, 0.0000000000000000, 0.40000000000000002,
2792           1.5707963267948966 },
2793 };
2794 const double toler095 = 2.5000000000000020e-13;
2795
2796 // Test data for k=0.0000000000000000, nu=0.50000000000000000.
2797 // max(|f - f_GSL|): 3.3306690738754696e-16
2798 // max(|f - f_GSL| / |f_GSL|): 3.6090167266677240e-16
2799 const testcase_ellint_3<double>
2800 data096[10] =
2801 {
2802   { 0.0000000000000000, 0.0000000000000000, 0.50000000000000000,
2803           0.0000000000000000 },
2804   { 0.17366010776037044, 0.0000000000000000, 0.50000000000000000,
2805           0.17453292519943295 },
2806   { 0.34238253799539309, 0.0000000000000000, 0.50000000000000000,
2807           0.34906585039886590 },
2808   { 0.50253707775976397, 0.0000000000000000, 0.50000000000000000,
2809           0.52359877559829882 },
2810   { 0.65242145347295766, 0.0000000000000000, 0.50000000000000000,
2811           0.69813170079773179 },
2812   { 0.79210420018698058, 0.0000000000000000, 0.50000000000000000,
2813           0.87266462599716477 },
2814   { 0.92287437995632171, 0.0000000000000000, 0.50000000000000000,
2815           1.0471975511965976 },
2816   { 1.0466900550798659, 0.0000000000000000, 0.50000000000000000,
2817           1.2217304763960306 },
2818   { 1.1658007366618623, 0.0000000000000000, 0.50000000000000000,
2819           1.3962634015954636 },
2820   { 1.2825498301618641, 0.0000000000000000, 0.50000000000000000,
2821           1.5707963267948966 },
2822 };
2823 const double toler096 = 2.5000000000000020e-13;
2824
2825 // Test data for k=0.0000000000000000, nu=0.59999999999999998.
2826 // max(|f - f_GSL|): 2.2204460492503131e-16
2827 // max(|f - f_GSL| / |f_GSL|): 2.4581288258006758e-16
2828 const testcase_ellint_3<double>
2829 data097[10] =
2830 {
2831   { 0.0000000000000000, 0.0000000000000000, 0.59999999999999998,
2832           0.0000000000000000 },
2833   { 0.17348741514884700, 0.0000000000000000, 0.59999999999999998,
2834           0.17453292519943295 },
2835   { 0.34109952405241289, 0.0000000000000000, 0.59999999999999998,
2836           0.34906585039886590 },
2837   { 0.49866850781226285, 0.0000000000000000, 0.59999999999999998,
2838           0.52359877559829882 },
2839   { 0.64444732407062499, 0.0000000000000000, 0.59999999999999998,
2840           0.69813170079773179 },
2841   { 0.77877564686544720, 0.0000000000000000, 0.59999999999999998,
2842           0.87266462599716477 },
2843   { 0.90330743691883475, 0.0000000000000000, 0.59999999999999998,
2844           1.0471975511965976 },
2845   { 1.0203257987604104, 0.0000000000000000, 0.59999999999999998,
2846           1.2217304763960306 },
2847   { 1.1323247918768629, 0.0000000000000000, 0.59999999999999998,
2848           1.3962634015954636 },
2849   { 1.2418235332245127, 0.0000000000000000, 0.59999999999999998,
2850           1.5707963267948966 },
2851 };
2852 const double toler097 = 2.5000000000000020e-13;
2853
2854 // Test data for k=0.0000000000000000, nu=0.69999999999999996.
2855 // max(|f - f_GSL|): 2.2204460492503131e-16
2856 // max(|f - f_GSL| / |f_GSL|): 2.5088894797856263e-16
2857 const testcase_ellint_3<double>
2858 data098[10] =
2859 {
2860   { 0.0000000000000000, 0.0000000000000000, 0.69999999999999996,
2861           0.0000000000000000 },
2862   { 0.17331533692234474, 0.0000000000000000, 0.69999999999999996,
2863           0.17453292519943295 },
2864   { 0.33983341309265935, 0.0000000000000000, 0.69999999999999996,
2865           0.34906585039886590 },
2866   { 0.49490198805931979, 0.0000000000000000, 0.69999999999999996,
2867           0.52359877559829882 },
2868   { 0.63679715525145297, 0.0000000000000000, 0.69999999999999996,
2869           0.69813170079773179 },
2870   { 0.76616861049481944, 0.0000000000000000, 0.69999999999999996,
2871           0.87266462599716477 },
2872   { 0.88503143209004198, 0.0000000000000000, 0.69999999999999996,
2873           1.0471975511965976 },
2874   { 0.99596060249112173, 0.0000000000000000, 0.69999999999999996,
2875           1.2217304763960306 },
2876   { 1.1016495050260424, 0.0000000000000000, 0.69999999999999996,
2877           1.3962634015954636 },
2878   { 1.2047457872617382, 0.0000000000000000, 0.69999999999999996,
2879           1.5707963267948966 },
2880 };
2881 const double toler098 = 2.5000000000000020e-13;
2882
2883 // Test data for k=0.0000000000000000, nu=0.80000000000000004.
2884 // max(|f - f_GSL|): 3.3306690738754696e-16
2885 // max(|f - f_GSL| / |f_GSL|): 3.8375904358197891e-16
2886 const testcase_ellint_3<double>
2887 data099[10] =
2888 {
2889   { 0.0000000000000000, 0.0000000000000000, 0.80000000000000004,
2890           0.0000000000000000 },
2891   { 0.17314386919344210, 0.0000000000000000, 0.80000000000000004,
2892           0.17453292519943295 },
2893   { 0.33858381342073240, 0.0000000000000000, 0.80000000000000004,
2894           0.34906585039886590 },
2895   { 0.49123285640844727, 0.0000000000000000, 0.80000000000000004,
2896           0.52359877559829882 },
2897   { 0.62944854858904509, 0.0000000000000000, 0.80000000000000004,
2898           0.69813170079773179 },
2899   { 0.75421778305499343, 0.0000000000000000, 0.80000000000000004,
2900           0.87266462599716477 },
2901   { 0.86790634112156617, 0.0000000000000000, 0.80000000000000004,
2902           1.0471975511965976 },
2903   { 0.97334918087427558, 0.0000000000000000, 0.80000000000000004,
2904           1.2217304763960306 },
2905   { 1.0734012615283985, 0.0000000000000000, 0.80000000000000004,
2906           1.3962634015954636 },
2907   { 1.1708024551734544, 0.0000000000000000, 0.80000000000000004,
2908           1.5707963267948966 },
2909 };
2910 const double toler099 = 2.5000000000000020e-13;
2911
2912 // Test data for k=0.0000000000000000, nu=0.90000000000000002.
2913 // max(|f - f_GSL|): 1.1102230246251565e-16
2914 // max(|f - f_GSL| / |f_GSL|): 1.7838310376154469e-16
2915 const testcase_ellint_3<double>
2916 data100[10] =
2917 {
2918   { 0.0000000000000000, 0.0000000000000000, 0.90000000000000002,
2919           0.0000000000000000 },
2920   { 0.17297300811030597, 0.0000000000000000, 0.90000000000000002,
2921           0.17453292519943295 },
2922   { 0.33735034635360817, 0.0000000000000000, 0.90000000000000002,
2923           0.34906585039886590 },
2924   { 0.48765675230233130, 0.0000000000000000, 0.90000000000000002,
2925           0.52359877559829882 },
2926   { 0.62238126886123568, 0.0000000000000000, 0.90000000000000002,
2927           0.69813170079773179 },
2928   { 0.74286600807269243, 0.0000000000000000, 0.90000000000000002,
2929           0.87266462599716477 },
2930   { 0.85181283909264949, 0.0000000000000000, 0.90000000000000002,
2931           1.0471975511965976 },
2932   { 0.95228683995371133, 0.0000000000000000, 0.90000000000000002,
2933           1.2217304763960306 },
2934   { 1.0472730487412552, 0.0000000000000000, 0.90000000000000002,
2935           1.3962634015954636 },
2936   { 1.1395754288497419, 0.0000000000000000, 0.90000000000000002,
2937           1.5707963267948966 },
2938 };
2939 const double toler100 = 2.5000000000000020e-13;
2940
2941 // Test data for k=0.10000000000000009, nu=0.0000000000000000.
2942 // max(|f - f_GSL|): 4.4408920985006262e-16
2943 // max(|f - f_GSL| / |f_GSL|): 3.1735566504509650e-16
2944 const testcase_ellint_3<double>
2945 data101[10] =
2946 {
2947   { 0.0000000000000000, 0.10000000000000009, 0.0000000000000000,
2948           0.0000000000000000 },
2949   { 0.17454173353063659, 0.10000000000000009, 0.0000000000000000,
2950           0.17453292519943295 },
2951   { 0.34913506721468091, 0.10000000000000009, 0.0000000000000000,
2952           0.34906585039886590 },
2953   { 0.52382550016538942, 0.10000000000000009, 0.0000000000000000,
2954           0.52359877559829882 },
2955   { 0.69864700854177020, 0.10000000000000009, 0.0000000000000000,
2956           0.69813170079773179 },
2957   { 0.87361792586964870, 0.10000000000000009, 0.0000000000000000,
2958           0.87266462599716477 },
2959   { 1.0487386319621683, 0.10000000000000009, 0.0000000000000000,
2960           1.0471975511965976 },
2961   { 1.2239913752078757, 0.10000000000000009, 0.0000000000000000,
2962           1.2217304763960306 },
2963   { 1.3993423113684049, 0.10000000000000009, 0.0000000000000000,
2964           1.3962634015954636 },
2965   { 1.5747455615173562, 0.10000000000000009, 0.0000000000000000,
2966           1.5707963267948966 },
2967 };
2968 const double toler101 = 2.5000000000000020e-13;
2969
2970 // Test data for k=0.10000000000000009, nu=0.10000000000000001.
2971 // max(|f - f_GSL|): 4.4408920985006262e-16
2972 // max(|f - f_GSL| / |f_GSL|): 3.3097339877269682e-16
2973 const testcase_ellint_3<double>
2974 data102[10] =
2975 {
2976   { 0.0000000000000000, 0.10000000000000009, 0.10000000000000001,
2977           0.0000000000000000 },
2978   { 0.17436589347616613, 0.10000000000000009, 0.10000000000000001,
2979           0.17453292519943295 },
2980   { 0.34776067871237359, 0.10000000000000009, 0.10000000000000001,
2981           0.34906585039886590 },
2982   { 0.51936064354727796, 0.10000000000000009, 0.10000000000000001,
2983           0.52359877559829882 },
2984   { 0.68860303749364349, 0.10000000000000009, 0.10000000000000001,
2985           0.69813170079773179 },
2986   { 0.85524561882332051, 0.10000000000000009, 0.10000000000000001,
2987           0.87266462599716477 },
2988   { 1.0193708301908335, 0.10000000000000009, 0.10000000000000001,
2989           1.0471975511965976 },
2990   { 1.1813474067123044, 0.10000000000000009, 0.10000000000000001,
2991           1.2217304763960306 },
2992   { 1.3417670770424983, 0.10000000000000009, 0.10000000000000001,
2993           1.3962634015954636 },
2994   { 1.5013711111199950, 0.10000000000000009, 0.10000000000000001,
2995           1.5707963267948966 },
2996 };
2997 const double toler102 = 2.5000000000000020e-13;
2998
2999 // Test data for k=0.10000000000000009, nu=0.20000000000000001.
3000 // max(|f - f_GSL|): 4.4408920985006262e-16
3001 // max(|f - f_GSL| / |f_GSL|): 3.4399947764827574e-16
3002 const testcase_ellint_3<double>
3003 data103[10] =
3004 {
3005   { 0.0000000000000000, 0.10000000000000009, 0.20000000000000001,
3006           0.0000000000000000 },
3007   { 0.17419068786141340, 0.10000000000000009, 0.20000000000000001,
3008           0.17453292519943295 },
3009   { 0.34640537686230133, 0.10000000000000009, 0.20000000000000001,
3010           0.34906585039886590 },
3011   { 0.51502689171753946, 0.10000000000000009, 0.20000000000000001,
3012           0.52359877559829882 },
3013   { 0.67904147863672715, 0.10000000000000009, 0.20000000000000001,
3014           0.69813170079773179 },
3015   { 0.83811885126105179, 0.10000000000000009, 0.20000000000000001,
3016           0.87266462599716477 },
3017   { 0.99255278555742787, 0.10000000000000009, 0.20000000000000001,
3018           1.0471975511965976 },
3019   { 1.1431260546194930, 0.10000000000000009, 0.20000000000000001,
3020           1.2217304763960306 },
3021   { 1.2909589656532101, 0.10000000000000009, 0.20000000000000001,
3022           1.3962634015954636 },
3023   { 1.4373749386463430, 0.10000000000000009, 0.20000000000000001,
3024           1.5707963267948966 },
3025 };
3026 const double toler103 = 2.5000000000000020e-13;
3027
3028 // Test data for k=0.10000000000000009, nu=0.29999999999999999.
3029 // max(|f - f_GSL|): 4.4408920985006262e-16
3030 // max(|f - f_GSL| / |f_GSL|): 3.5650492137236872e-16
3031 const testcase_ellint_3<double>
3032 data104[10] =
3033 {
3034   { 0.0000000000000000, 0.10000000000000009, 0.29999999999999999,
3035           0.0000000000000000 },
3036   { 0.17401611261390104, 0.10000000000000009, 0.29999999999999999,
3037           0.17453292519943295 },
3038   { 0.34506869507511773, 0.10000000000000009, 0.29999999999999999,
3039           0.34906585039886590 },
3040   { 0.51081757604259859, 0.10000000000000009, 0.29999999999999999,
3041           0.52359877559829882 },
3042   { 0.66992297597712303, 0.10000000000000009, 0.29999999999999999,
3043           0.69813170079773179 },
3044   { 0.82209722856174228, 0.10000000000000009, 0.29999999999999999,
3045           0.87266462599716477 },
3046   { 0.96792430487669590, 0.10000000000000009, 0.29999999999999999,
3047           1.0471975511965976 },
3048   { 1.1085964108954092, 0.10000000000000009, 0.29999999999999999,
3049           1.2217304763960306 },
3050   { 1.2456748370836999, 0.10000000000000009, 0.29999999999999999,
3051           1.3962634015954636 },
3052   { 1.3809159606704959, 0.10000000000000009, 0.29999999999999999,
3053           1.5707963267948966 },
3054 };
3055 const double toler104 = 2.5000000000000020e-13;
3056
3057 // Test data for k=0.10000000000000009, nu=0.40000000000000002.
3058 // max(|f - f_GSL|): 4.4408920985006262e-16
3059 // max(|f - f_GSL| / |f_GSL|): 3.6854758534459740e-16
3060 const testcase_ellint_3<double>
3061 data105[10] =
3062 {
3063   { 0.0000000000000000, 0.10000000000000009, 0.40000000000000002,
3064           0.0000000000000000 },
3065   { 0.17384216369897931, 0.10000000000000009, 0.40000000000000002,
3066           0.17453292519943295 },
3067   { 0.34375018311376787, 0.10000000000000009, 0.40000000000000002,
3068           0.34906585039886590 },
3069   { 0.50672650758380455, 0.10000000000000009, 0.40000000000000002,
3070           0.52359877559829882 },
3071   { 0.66121264213337616, 0.10000000000000009, 0.40000000000000002,
3072           0.69813170079773179 },
3073   { 0.80706202005774441, 0.10000000000000009, 0.40000000000000002,
3074           0.87266462599716477 },
3075   { 0.94519376138245870, 0.10000000000000009, 0.40000000000000002,
3076           1.0471975511965976 },
3077   { 1.0771880300759584, 0.10000000000000009, 0.40000000000000002,
3078           1.2217304763960306 },
3079   { 1.2049711557188272, 0.10000000000000009, 0.40000000000000002,
3080           1.3962634015954636 },
3081   { 1.3306223265207477, 0.10000000000000009, 0.40000000000000002,
3082           1.5707963267948966 },
3083 };
3084 const double toler105 = 2.5000000000000020e-13;
3085
3086 // Test data for k=0.10000000000000009, nu=0.50000000000000000.
3087 // max(|f - f_GSL|): 4.4408920985006262e-16
3088 // max(|f - f_GSL| / |f_GSL|): 3.8017534281650347e-16
3089 const testcase_ellint_3<double>
3090 data106[10] =
3091 {
3092   { 0.0000000000000000, 0.10000000000000009, 0.50000000000000000,
3093           0.0000000000000000 },
3094   { 0.17366883711936548, 0.10000000000000009, 0.50000000000000000,
3095           0.17453292519943295 },
3096   { 0.34244940634881882, 0.10000000000000009, 0.50000000000000000,
3097           0.34906585039886590 },
3098   { 0.50274793281634367, 0.10000000000000009, 0.50000000000000000,
3099           0.52359877559829882 },
3100   { 0.65287941633275082, 0.10000000000000009, 0.50000000000000000,
3101           0.69813170079773179 },
3102   { 0.79291198790315398, 0.10000000000000009, 0.50000000000000000,
3103           0.87266462599716477 },
3104   { 0.92412201537880323, 0.10000000000000009, 0.50000000000000000,
3105           1.0471975511965976 },
3106   { 1.0484480076799372, 0.10000000000000009, 0.50000000000000000,
3107           1.2217304763960306 },
3108   { 1.1681168130475206, 0.10000000000000009, 0.50000000000000000,
3109           1.3962634015954636 },
3110   { 1.2854480708580160, 0.10000000000000009, 0.50000000000000000,
3111           1.5707963267948966 },
3112 };
3113 const double toler106 = 2.5000000000000020e-13;
3114
3115 // Test data for k=0.10000000000000009, nu=0.59999999999999998.
3116 // max(|f - f_GSL|): 4.4408920985006262e-16
3117 // max(|f - f_GSL| / |f_GSL|): 3.9142834151672032e-16
3118 const testcase_ellint_3<double>
3119 data107[10] =
3120 {
3121   { 0.0000000000000000, 0.10000000000000009, 0.59999999999999998,
3122           0.0000000000000000 },
3123   { 0.17349612891469013, 0.10000000000000009, 0.59999999999999998,
3124           0.17453292519943295 },
3125   { 0.34116594505539444, 0.10000000000000009, 0.59999999999999998,
3126           0.34906585039886590 },
3127   { 0.49887649430466674, 0.10000000000000009, 0.59999999999999998,
3128           0.52359877559829882 },
3129   { 0.64489553282165146, 0.10000000000000009, 0.59999999999999998,
3130           0.69813170079773179 },
3131   { 0.77956016553782437, 0.10000000000000009, 0.59999999999999998,
3132           0.87266462599716477 },
3133   { 0.90451074530096287, 0.10000000000000009, 0.59999999999999998,
3134           1.0471975511965976 },
3135   { 1.0220113666961632, 0.10000000000000009, 0.59999999999999998,
3136           1.2217304763960306 },
3137   { 1.1345351441065563, 0.10000000000000009, 0.59999999999999998,
3138           1.3962634015954636 },
3139   { 1.2445798942989255, 0.10000000000000009, 0.59999999999999998,
3140           1.5707963267948966 },
3141 };
3142 const double toler107 = 2.5000000000000020e-13;
3143
3144 // Test data for k=0.10000000000000009, nu=0.69999999999999996.
3145 // max(|f - f_GSL|): 6.6613381477509392e-16
3146 // max(|f - f_GSL| / |f_GSL|): 5.5172091551439012e-16
3147 const testcase_ellint_3<double>
3148 data108[10] =
3149 {
3150   { 0.0000000000000000, 0.10000000000000009, 0.69999999999999996,
3151           0.0000000000000000 },
3152   { 0.17332403516105047, 0.10000000000000009, 0.69999999999999996,
3153           0.17453292519943295 },
3154   { 0.33989939374896883, 0.10000000000000009, 0.69999999999999996,
3155           0.34906585039886590 },
3156   { 0.49510719568614070, 0.10000000000000009, 0.69999999999999996,
3157           0.52359877559829882 },
3158   { 0.63723607776354974, 0.10000000000000009, 0.69999999999999996,
3159           0.69813170079773179 },
3160   { 0.76693133887935327, 0.10000000000000009, 0.69999999999999996,
3161           0.87266462599716477 },
3162   { 0.88619382078823805, 0.10000000000000009, 0.69999999999999996,
3163           1.0471975511965976 },
3164   { 0.99758012018676490, 0.10000000000000009, 0.69999999999999996,
3165           1.2217304763960306 },
3166   { 1.1037642270814410, 0.10000000000000009, 0.69999999999999996,
3167           1.3962634015954636 },
3168   { 1.2073745911083185, 0.10000000000000009, 0.69999999999999996,
3169           1.5707963267948966 },
3170 };
3171 const double toler108 = 2.5000000000000020e-13;
3172
3173 // Test data for k=0.10000000000000009, nu=0.80000000000000004.
3174 // max(|f - f_GSL|): 4.4408920985006262e-16
3175 // max(|f - f_GSL| / |f_GSL|): 4.1294144515772258e-16
3176 const testcase_ellint_3<double>
3177 data109[10] =
3178 {
3179   { 0.0000000000000000, 0.10000000000000009, 0.80000000000000004,
3180           0.0000000000000000 },
3181   { 0.17315255197057014, 0.10000000000000009, 0.80000000000000004,
3182           0.17453292519943295 },
3183   { 0.33864936055747991, 0.10000000000000009, 0.80000000000000004,
3184           0.34906585039886590 },
3185   { 0.49143537041117613, 0.10000000000000009, 0.80000000000000004,
3186           0.52359877559829882 },
3187   { 0.62987861760047492, 0.10000000000000009, 0.80000000000000004,
3188           0.69813170079773179 },
3189   { 0.75496005490917517, 0.10000000000000009, 0.80000000000000004,
3190           0.87266462599716477 },
3191   { 0.86903081862701881, 0.10000000000000009, 0.80000000000000004,
3192           1.0471975511965976 },
3193   { 0.97490814820725591, 0.10000000000000009, 0.80000000000000004,
3194           1.2217304763960306 },
3195   { 1.0754290107171083, 0.10000000000000009, 0.80000000000000004,
3196           1.3962634015954636 },
3197   { 1.1733158866987732, 0.10000000000000009, 0.80000000000000004,
3198           1.5707963267948966 },
3199 };
3200 const double toler109 = 2.5000000000000020e-13;
3201
3202 // Test data for k=0.10000000000000009, nu=0.90000000000000002.
3203 // max(|f - f_GSL|): 4.4408920985006262e-16
3204 // max(|f - f_GSL| / |f_GSL|): 4.2325599449457852e-16
3205 const testcase_ellint_3<double>
3206 data110[10] =
3207 {
3208   { 0.0000000000000000, 0.10000000000000009, 0.90000000000000002,
3209           0.0000000000000000 },
3210   { 0.17298167549096563, 0.10000000000000009, 0.90000000000000002,
3211           0.17453292519943295 },
3212   { 0.33741546662741589, 0.10000000000000009, 0.90000000000000002,
3213           0.34906585039886590 },
3214   { 0.48785665376856868, 0.10000000000000009, 0.90000000000000002,
3215           0.52359877559829882 },
3216   { 0.62280288554518959, 0.10000000000000009, 0.90000000000000002,
3217           0.69813170079773179 },
3218   { 0.74358903115455188, 0.10000000000000009, 0.90000000000000002,
3219           0.87266462599716477 },
3220   { 0.85290207679298335, 0.10000000000000009, 0.90000000000000002,
3221           1.0471975511965976 },
3222   { 0.95379006645397379, 0.10000000000000009, 0.90000000000000002,
3223           1.2217304763960306 },
3224   { 1.0492213119872327, 0.10000000000000009, 0.90000000000000002,
3225           1.3962634015954636 },
3226   { 1.1419839485283374, 0.10000000000000009, 0.90000000000000002,
3227           1.5707963267948966 },
3228 };
3229 const double toler110 = 2.5000000000000020e-13;
3230
3231 // Test data for k=0.19999999999999996, nu=0.0000000000000000.
3232 // max(|f - f_GSL|): 4.4408920985006262e-16
3233 // max(|f - f_GSL| / |f_GSL|): 4.2156475739151676e-16
3234 const testcase_ellint_3<double>
3235 data111[10] =
3236 {
3237   { 0.0000000000000000, 0.19999999999999996, 0.0000000000000000,
3238           0.0000000000000000 },
3239   { 0.17456817290292809, 0.19999999999999996, 0.0000000000000000,
3240           0.17453292519943295 },
3241   { 0.34934315932086801, 0.19999999999999996, 0.0000000000000000,
3242           0.34906585039886590 },
3243   { 0.52450880529443988, 0.19999999999999996, 0.0000000000000000,
3244           0.52359877559829882 },
3245   { 0.70020491009844876, 0.19999999999999996, 0.0000000000000000,
3246           0.69813170079773179 },
3247   { 0.87651006649967955, 0.19999999999999996, 0.0000000000000000,
3248           0.87266462599716477 },
3249   { 1.0534305870298994, 0.19999999999999996, 0.0000000000000000,
3250           1.0471975511965976 },
3251   { 1.2308975521670784, 0.19999999999999996, 0.0000000000000000,
3252           1.2217304763960306 },
3253   { 1.4087733584990738, 0.19999999999999996, 0.0000000000000000,
3254           1.3962634015954636 },
3255   { 1.5868678474541660, 0.19999999999999996, 0.0000000000000000,
3256           1.5707963267948966 },
3257 };
3258 const double toler111 = 2.5000000000000020e-13;
3259
3260 // Test data for k=0.19999999999999996, nu=0.10000000000000001.
3261 // max(|f - f_GSL|): 4.4408920985006262e-16
3262 // max(|f - f_GSL| / |f_GSL|): 4.3374593253183472e-16
3263 const testcase_ellint_3<double>
3264 data112[10] =
3265 {
3266   { 0.0000000000000000, 0.19999999999999996, 0.10000000000000001,
3267           0.0000000000000000 },
3268   { 0.17439228502691748, 0.19999999999999996, 0.10000000000000001,
3269           0.17453292519943295 },
3270   { 0.34796731137565740, 0.19999999999999996, 0.10000000000000001,
3271           0.34906585039886590 },
3272   { 0.52003370294544848, 0.19999999999999996, 0.10000000000000001,
3273           0.52359877559829882 },
3274   { 0.69012222258631462, 0.19999999999999996, 0.10000000000000001,
3275           0.69813170079773179 },
3276   { 0.85803491465566772, 0.19999999999999996, 0.10000000000000001,
3277           0.87266462599716477 },
3278   { 1.0238463961099364, 0.19999999999999996, 0.10000000000000001,
3279           1.0471975511965976 },
3280   { 1.1878691059202153, 0.19999999999999996, 0.10000000000000001,
3281           1.2217304763960306 },
3282   { 1.3505985031831940, 0.19999999999999996, 0.10000000000000001,
3283           1.3962634015954636 },
3284   { 1.5126513474261087, 0.19999999999999996, 0.10000000000000001,
3285           1.5707963267948966 },
3286 };
3287 const double toler112 = 2.5000000000000020e-13;
3288
3289 // Test data for k=0.19999999999999996, nu=0.20000000000000001.
3290 // max(|f - f_GSL|): 4.4408920985006262e-16
3291 // max(|f - f_GSL| / |f_GSL|): 4.4549984059502760e-16
3292 const testcase_ellint_3<double>
3293 data113[10] =
3294 {
3295   { 0.0000000000000000, 0.19999999999999996, 0.20000000000000001,
3296           0.0000000000000000 },
3297   { 0.17421703179583747, 0.19999999999999996, 0.20000000000000001,
3298           0.17453292519943295 },
3299   { 0.34661057411998791, 0.19999999999999996, 0.20000000000000001,
3300           0.34906585039886590 },
3301   { 0.51569006052647393, 0.19999999999999996, 0.20000000000000001,
3302           0.52359877559829882 },
3303   { 0.68052412821107244, 0.19999999999999996, 0.20000000000000001,
3304           0.69813170079773179 },
3305   { 0.84081341263313825, 0.19999999999999996, 0.20000000000000001,
3306           0.87266462599716477 },
3307   { 0.99683359988842890, 0.19999999999999996, 0.20000000000000001,
3308           1.0471975511965976 },
3309   { 1.1493086715118852, 0.19999999999999996, 0.20000000000000001,
3310           1.2217304763960306 },
3311   { 1.2992699693957541, 0.19999999999999996, 0.20000000000000001,
3312           1.3962634015954636 },
3313   { 1.4479323932249564, 0.19999999999999996, 0.20000000000000001,
3314           1.5707963267948966 },
3315 };
3316 const double toler113 = 2.5000000000000020e-13;
3317
3318 // Test data for k=0.19999999999999996, nu=0.29999999999999999.
3319 // max(|f - f_GSL|): 6.6613381477509392e-16
3320 // max(|f - f_GSL| / |f_GSL|): 5.3140668101543467e-16
3321 const testcase_ellint_3<double>
3322 data114[10] =
3323 {
3324   { 0.0000000000000000, 0.19999999999999996, 0.29999999999999999,
3325           0.0000000000000000 },
3326   { 0.17404240913577704, 0.19999999999999996, 0.29999999999999999,
3327           0.17453292519943295 },
3328   { 0.34527248032587193, 0.19999999999999996, 0.29999999999999999,
3329           0.34906585039886590 },
3330   { 0.51147118981668416, 0.19999999999999996, 0.29999999999999999,
3331           0.52359877559829882 },
3332   { 0.67137107867777601, 0.19999999999999996, 0.29999999999999999,
3333           0.69813170079773179 },
3334   { 0.82470418188668893, 0.19999999999999996, 0.29999999999999999,
3335           0.87266462599716477 },
3336   { 0.97202873223594299, 0.19999999999999996, 0.29999999999999999,
3337           1.0471975511965976 },
3338   { 1.1144773569375266, 0.19999999999999996, 0.29999999999999999,
3339           1.2217304763960306 },
3340   { 1.2535292433701000, 0.19999999999999996, 0.29999999999999999,
3341           1.3962634015954636 },
3342   { 1.3908453514752477, 0.19999999999999996, 0.29999999999999999,
3343           1.5707963267948966 },
3344 };
3345 const double toler114 = 2.5000000000000020e-13;
3346
3347 // Test data for k=0.19999999999999996, nu=0.40000000000000002.
3348 // max(|f - f_GSL|): 4.4408920985006262e-16
3349 // max(|f - f_GSL| / |f_GSL|): 4.6788709752760483e-16
3350 const testcase_ellint_3<double>
3351 data115[10] =
3352 {
3353   { 0.0000000000000000, 0.19999999999999996, 0.40000000000000002,
3354           0.0000000000000000 },
3355   { 0.17386841301066674, 0.19999999999999996, 0.40000000000000002,
3356           0.17453292519943295 },
3357   { 0.34395257914113253, 0.19999999999999996, 0.40000000000000002,
3358           0.34906585039886590 },
3359   { 0.50737088376869466, 0.19999999999999996, 0.40000000000000002,
3360           0.52359877559829882 },
3361   { 0.66262801717277631, 0.19999999999999996, 0.40000000000000002,
3362           0.69813170079773179 },
3363   { 0.80958766645079094, 0.19999999999999996, 0.40000000000000002,
3364           0.87266462599716477 },
3365   { 0.94913754236162040, 0.19999999999999996, 0.40000000000000002,
3366           1.0471975511965976 },
3367   { 1.0827985514222997, 0.19999999999999996, 0.40000000000000002,
3368           1.2217304763960306 },
3369   { 1.2124212429050478, 0.19999999999999996, 0.40000000000000002,
3370           1.3962634015954636 },
3371   { 1.3400002519661005, 0.19999999999999996, 0.40000000000000002,
3372           1.5707963267948966 },
3373 };
3374 const double toler115 = 2.5000000000000020e-13;
3375
3376 // Test data for k=0.19999999999999996, nu=0.50000000000000000.
3377 // max(|f - f_GSL|): 4.4408920985006262e-16
3378 // max(|f - f_GSL| / |f_GSL|): 3.7788201301356829e-16
3379 const testcase_ellint_3<double>
3380 data116[10] =
3381 {
3382   { 0.0000000000000000, 0.19999999999999996, 0.50000000000000000,
3383           0.0000000000000000 },
3384   { 0.17369503942181799, 0.19999999999999996, 0.50000000000000000,
3385           0.17453292519943295 },
3386   { 0.34265043534362660, 0.19999999999999996, 0.50000000000000000,
3387           0.34906585039886590 },
3388   { 0.50338337208655415, 0.19999999999999996, 0.50000000000000000,
3389           0.52359877559829882 },
3390   { 0.65426373297163609, 0.19999999999999996, 0.50000000000000000,
3391           0.69813170079773179 },
3392   { 0.79536193036145808, 0.19999999999999996, 0.50000000000000000,
3393           0.87266462599716477 },
3394   { 0.92791875910061605, 0.19999999999999996, 0.50000000000000000,
3395           1.0471975511965976 },
3396   { 1.0538145052725829, 0.19999999999999996, 0.50000000000000000,
3397           1.2217304763960306 },
3398   { 1.1752060022875899, 0.19999999999999996, 0.50000000000000000,
3399           1.3962634015954636 },
3400   { 1.2943374404397372, 0.19999999999999996, 0.50000000000000000,
3401           1.5707963267948966 },
3402 };
3403 const double toler116 = 2.5000000000000020e-13;
3404
3405 // Test data for k=0.19999999999999996, nu=0.59999999999999998.
3406 // max(|f - f_GSL|): 4.4408920985006262e-16
3407 // max(|f - f_GSL| / |f_GSL|): 4.8899223779598256e-16
3408 const testcase_ellint_3<double>
3409 data117[10] =
3410 {
3411   { 0.0000000000000000, 0.19999999999999996, 0.59999999999999998,
3412           0.0000000000000000 },
3413   { 0.17352228440746925, 0.19999999999999996, 0.59999999999999998,
3414           0.17453292519943295 },
3415   { 0.34136562863713626, 0.19999999999999996, 0.59999999999999998,
3416           0.34906585039886590 },
3417   { 0.49950328177638481, 0.19999999999999996, 0.59999999999999998,
3418           0.52359877559829882 },
3419   { 0.64625032705690799, 0.19999999999999996, 0.59999999999999998,
3420           0.69813170079773179 },
3421   { 0.78193941198403083, 0.19999999999999996, 0.59999999999999998,
3422           0.87266462599716477 },
3423   { 0.90817230934317128, 0.19999999999999996, 0.59999999999999998,
3424           1.0471975511965976 },
3425   { 1.0271563751276462, 0.19999999999999996, 0.59999999999999998,
3426           1.2217304763960306 },
3427   { 1.1412999379040518, 0.19999999999999996, 0.59999999999999998,
3428           1.3962634015954636 },
3429   { 1.2530330675914556, 0.19999999999999996, 0.59999999999999998,
3430           1.5707963267948966 },
3431 };
3432 const double toler117 = 2.5000000000000020e-13;
3433
3434 // Test data for k=0.19999999999999996, nu=0.69999999999999996.
3435 // max(|f - f_GSL|): 6.6613381477509392e-16
3436 // max(|f - f_GSL| / |f_GSL|): 5.9999318361775115e-16
3437 const testcase_ellint_3<double>
3438 data118[10] =
3439 {
3440   { 0.0000000000000000, 0.19999999999999996, 0.69999999999999996,
3441           0.0000000000000000 },
3442   { 0.17335014404233895, 0.19999999999999996, 0.69999999999999996,
3443           0.17453292519943295 },
3444   { 0.34009775298617811, 0.19999999999999996, 0.69999999999999996,
3445           0.34906585039886590 },
3446   { 0.49572560201923810, 0.19999999999999996, 0.69999999999999996,
3447           0.52359877559829882 },
3448   { 0.63856276669886503, 0.19999999999999996, 0.69999999999999996,
3449           0.69813170079773179 },
3450   { 0.76924438644867565, 0.19999999999999996, 0.69999999999999996,
3451           0.87266462599716477 },
3452   { 0.88973060843856466, 0.19999999999999996, 0.69999999999999996,
3453           1.0471975511965976 },
3454   { 1.0025230471636377, 0.19999999999999996, 0.69999999999999996,
3455           1.2217304763960306 },
3456   { 1.1102356376093103, 0.19999999999999996, 0.69999999999999996,
3457           1.3962634015954636 },
3458   { 1.2154356555075863, 0.19999999999999996, 0.69999999999999996,
3459           1.5707963267948966 },
3460 };
3461 const double toler118 = 2.5000000000000020e-13;
3462
3463 // Test data for k=0.19999999999999996, nu=0.80000000000000004.
3464 // max(|f - f_GSL|): 4.4408920985006262e-16
3465 // max(|f - f_GSL| / |f_GSL|): 5.0901276230707249e-16
3466 const testcase_ellint_3<double>
3467 data119[10] =
3468 {
3469   { 0.0000000000000000, 0.19999999999999996, 0.80000000000000004,
3470           0.0000000000000000 },
3471   { 0.17317861443718538, 0.19999999999999996, 0.80000000000000004,
3472           0.17453292519943295 },
3473   { 0.33884641598718701, 0.19999999999999996, 0.80000000000000004,
3474           0.34906585039886590 },
3475   { 0.49204565281259494, 0.19999999999999996, 0.80000000000000004,
3476           0.52359877559829882 },
3477   { 0.63117851188220320, 0.19999999999999996, 0.80000000000000004,
3478           0.69813170079773179 },
3479   { 0.75721095949544170, 0.19999999999999996, 0.80000000000000004,
3480           0.87266462599716477 },
3481   { 0.87245201443919118, 0.19999999999999996, 0.80000000000000004,
3482           1.0471975511965976 },
3483   { 0.97966584238831089, 0.19999999999999996, 0.80000000000000004,
3484           1.2217304763960306 },
3485   { 1.0816336325174360, 0.19999999999999996, 0.80000000000000004,
3486           1.3962634015954636 },
3487   { 1.1810223448909909, 0.19999999999999996, 0.80000000000000004,
3488           1.5707963267948966 },
3489 };
3490 const double toler119 = 2.5000000000000020e-13;
3491
3492 // Test data for k=0.19999999999999996, nu=0.90000000000000002.
3493 // max(|f - f_GSL|): 6.6613381477509392e-16
3494 // max(|f - f_GSL| / |f_GSL|): 6.4833128442756722e-16
3495 const testcase_ellint_3<double>
3496 data120[10] =
3497 {
3498   { 0.0000000000000000, 0.19999999999999996, 0.90000000000000002,
3499           0.0000000000000000 },
3500   { 0.17300769173837277, 0.19999999999999996, 0.90000000000000002,
3501           0.17453292519943295 },
3502   { 0.33761123827372508, 0.19999999999999996, 0.90000000000000002,
3503           0.34906585039886590 },
3504   { 0.48845905690769426, 0.19999999999999996, 0.90000000000000002,
3505           0.52359877559829882 },
3506   { 0.62407720017324952, 0.19999999999999996, 0.90000000000000002,
3507           0.69813170079773179 },
3508   { 0.74578146525124289, 0.19999999999999996, 0.90000000000000002,
3509           0.87266462599716477 },
3510   { 0.85621583540073076, 0.19999999999999996, 0.90000000000000002,
3511           1.0471975511965976 },
3512   { 0.95837725988001199, 0.19999999999999996, 0.90000000000000002,
3513           1.2217304763960306 },
3514   { 1.0551821412633928, 0.19999999999999996, 0.90000000000000002,
3515           1.3962634015954636 },
3516   { 1.1493679916141861, 0.19999999999999996, 0.90000000000000002,
3517           1.5707963267948966 },
3518 };
3519 const double toler120 = 2.5000000000000020e-13;
3520
3521 // Test data for k=0.30000000000000004, nu=0.0000000000000000.
3522 // max(|f - f_GSL|): 8.8817841970012523e-16
3523 // max(|f - f_GSL| / |f_GSL|): 6.3361874537309281e-16
3524 const testcase_ellint_3<double>
3525 data121[10] =
3526 {
3527   { 0.0000000000000000, 0.30000000000000004, 0.0000000000000000,
3528           0.0000000000000000 },
3529   { 0.17461228653000099, 0.30000000000000004, 0.0000000000000000,
3530           0.17453292519943295 },
3531   { 0.34969146102798415, 0.30000000000000004, 0.0000000000000000,
3532           0.34906585039886590 },
3533   { 0.52565822873726320, 0.30000000000000004, 0.0000000000000000,
3534           0.52359877559829882 },
3535   { 0.70284226512408532, 0.30000000000000004, 0.0000000000000000,
3536           0.69813170079773179 },
3537   { 0.88144139195111182, 0.30000000000000004, 0.0000000000000000,
3538           0.87266462599716477 },
3539   { 1.0614897067260520, 0.30000000000000004, 0.0000000000000000,
3540           1.0471975511965976 },
3541   { 1.2428416824174218, 0.30000000000000004, 0.0000000000000000,
3542           1.2217304763960306 },
3543   { 1.4251795877015927, 0.30000000000000004, 0.0000000000000000,
3544           1.3962634015954636 },
3545   { 1.6080486199305128, 0.30000000000000004, 0.0000000000000000,
3546           1.5707963267948966 },
3547 };
3548 const double toler121 = 2.5000000000000020e-13;
3549
3550 // Test data for k=0.30000000000000004, nu=0.10000000000000001.
3551 // max(|f - f_GSL|): 8.8817841970012523e-16
3552 // max(|f - f_GSL| / |f_GSL|): 6.3908043711907203e-16
3553 const testcase_ellint_3<double>
3554 data122[10] =
3555 {
3556   { 0.0000000000000000, 0.30000000000000004, 0.10000000000000001,
3557           0.0000000000000000 },
3558   { 0.17443631884814376, 0.30000000000000004, 0.10000000000000001,
3559           0.17453292519943295 },
3560   { 0.34831316835124926, 0.30000000000000004, 0.10000000000000001,
3561           0.34906585039886590 },
3562   { 0.52116586276523857, 0.30000000000000004, 0.10000000000000001,
3563           0.52359877559829882 },
3564   { 0.69269385837910036, 0.30000000000000004, 0.10000000000000001,
3565           0.69813170079773179 },
3566   { 0.86279023163070856, 0.30000000000000004, 0.10000000000000001,
3567           0.87266462599716477 },
3568   { 1.0315321461438263, 0.30000000000000004, 0.10000000000000001,
3569           1.0471975511965976 },
3570   { 1.1991449111869024, 0.30000000000000004, 0.10000000000000001,
3571           1.2217304763960306 },
3572   { 1.3659561780923213, 0.30000000000000004, 0.10000000000000001,
3573           1.3962634015954636 },
3574   { 1.5323534693557528, 0.30000000000000004, 0.10000000000000001,
3575           1.5707963267948966 },
3576 };
3577 const double toler122 = 2.5000000000000020e-13;
3578
3579 // Test data for k=0.30000000000000004, nu=0.20000000000000001.
3580 // max(|f - f_GSL|): 8.8817841970012523e-16
3581 // max(|f - f_GSL| / |f_GSL|): 6.4447238179454079e-16
3582 const testcase_ellint_3<double>
3583 data123[10] =
3584 {
3585   { 0.0000000000000000, 0.30000000000000004, 0.20000000000000001,
3586           0.0000000000000000 },
3587   { 0.17426098615372088, 0.30000000000000004, 0.20000000000000001,
3588           0.17453292519943295 },
3589   { 0.34695402664689923, 0.30000000000000004, 0.20000000000000001,
3590           0.34906585039886590 },
3591   { 0.51680555567038933, 0.30000000000000004, 0.20000000000000001,
3592           0.52359877559829882 },
3593   { 0.68303375225260210, 0.30000000000000004, 0.20000000000000001,
3594           0.69813170079773179 },
3595   { 0.84540662891295026, 0.30000000000000004, 0.20000000000000001,
3596           0.87266462599716477 },
3597   { 1.0041834051646927, 0.30000000000000004, 0.20000000000000001,
3598           1.0471975511965976 },
3599   { 1.1599952702345711, 0.30000000000000004, 0.20000000000000001,
3600           1.2217304763960306 },
3601   { 1.3137179520499165, 0.30000000000000004, 0.20000000000000001,
3602           1.3962634015954636 },
3603   { 1.4663658145259877, 0.30000000000000004, 0.20000000000000001,
3604           1.5707963267948966 },
3605 };
3606 const double toler123 = 2.5000000000000020e-13;
3607
3608 // Test data for k=0.30000000000000004, nu=0.29999999999999999.
3609 // max(|f - f_GSL|): 8.8817841970012523e-16
3610 // max(|f - f_GSL| / |f_GSL|): 6.4979715256503266e-16
3611 const testcase_ellint_3<double>
3612 data124[10] =
3613 {
3614   { 0.0000000000000000, 0.30000000000000004, 0.29999999999999999,
3615           0.0000000000000000 },
3616   { 0.17408628437042842, 0.30000000000000004, 0.29999999999999999,
3617           0.17453292519943295 },
3618   { 0.34561356761638401, 0.30000000000000004, 0.29999999999999999,
3619           0.34906585039886590 },
3620   { 0.51257058617875850, 0.30000000000000004, 0.29999999999999999,
3621           0.52359877559829882 },
3622   { 0.67382207124602878, 0.30000000000000004, 0.29999999999999999,
3623           0.69813170079773179 },
3624   { 0.82914751587825131, 0.30000000000000004, 0.29999999999999999,
3625           0.87266462599716477 },
3626   { 0.97907434814374938, 0.30000000000000004, 0.29999999999999999,
3627           1.0471975511965976 },
3628   { 1.1246399297351584, 0.30000000000000004, 0.29999999999999999,
3629           1.2217304763960306 },
3630   { 1.2671793970398149, 0.30000000000000004, 0.29999999999999999,
3631           1.3962634015954636 },
3632   { 1.4081767433479091, 0.30000000000000004, 0.29999999999999999,
3633           1.5707963267948966 },
3634 };
3635 const double toler124 = 2.5000000000000020e-13;
3636
3637 // Test data for k=0.30000000000000004, nu=0.40000000000000002.
3638 // max(|f - f_GSL|): 8.8817841970012523e-16
3639 // max(|f - f_GSL| / |f_GSL|): 6.5505716921759864e-16
3640 const testcase_ellint_3<double>
3641 data125[10] =
3642 {
3643   { 0.0000000000000000, 0.30000000000000004, 0.40000000000000002,
3644           0.0000000000000000 },
3645   { 0.17391220945982727, 0.30000000000000004, 0.40000000000000002,
3646           0.17453292519943295 },
3647   { 0.34429133937639689, 0.30000000000000004, 0.40000000000000002,
3648           0.34906585039886590 },
3649   { 0.50845471668581632, 0.30000000000000004, 0.40000000000000002,
3650           0.52359877559829882 },
3651   { 0.66502347027873854, 0.30000000000000004, 0.40000000000000002,
3652           0.69813170079773179 },
3653   { 0.81389191978012254, 0.30000000000000004, 0.40000000000000002,
3654           0.87266462599716477 },
3655   { 0.95590618002140570, 0.30000000000000004, 0.40000000000000002,
3656           1.0471975511965976 },
3657   { 1.0924915195213121, 0.30000000000000004, 0.40000000000000002,
3658           1.2217304763960306 },
3659   { 1.2253651604038061, 0.30000000000000004, 0.40000000000000002,
3660           1.3962634015954636 },
3661   { 1.3563643538969763, 0.30000000000000004, 0.40000000000000002,
3662           1.5707963267948966 },
3663 };
3664 const double toler125 = 2.5000000000000020e-13;
3665
3666 // Test data for k=0.30000000000000004, nu=0.50000000000000000.
3667 // max(|f - f_GSL|): 8.8817841970012523e-16
3668 // max(|f - f_GSL| / |f_GSL|): 6.7807908859023716e-16
3669 const testcase_ellint_3<double>
3670 data126[10] =
3671 {
3672   { 0.0000000000000000, 0.30000000000000004, 0.50000000000000000,
3673           0.0000000000000000 },
3674   { 0.17373875742088232, 0.30000000000000004, 0.50000000000000000,
3675           0.17453292519943295 },
3676   { 0.34298690571124157, 0.30000000000000004, 0.50000000000000000,
3677           0.34906585039886590 },
3678   { 0.50445214859646936, 0.30000000000000004, 0.50000000000000000,
3679           0.52359877559829882 },
3680   { 0.65660648352418516, 0.30000000000000004, 0.50000000000000000,
3681           0.69813170079773179 },
3682   { 0.79953670639287289, 0.30000000000000004, 0.50000000000000000,
3683           0.87266462599716477 },
3684   { 0.93443393926588536, 0.30000000000000004, 0.50000000000000000,
3685           1.0471975511965976 },
3686   { 1.0630838369016911, 0.30000000000000004, 0.50000000000000000,
3687           1.2217304763960306 },
3688   { 1.1875197325653029, 0.30000000000000004, 0.50000000000000000,
3689           1.3962634015954636 },
3690   { 1.3098448759814962, 0.30000000000000004, 0.50000000000000000,
3691           1.5707963267948966 },
3692 };
3693 const double toler126 = 2.5000000000000020e-13;
3694
3695 // Test data for k=0.30000000000000004, nu=0.59999999999999998.
3696 // max(|f - f_GSL|): 8.8817841970012523e-16
3697 // max(|f - f_GSL| / |f_GSL|): 7.0057999499931649e-16
3698 const testcase_ellint_3<double>
3699 data127[10] =
3700 {
3701   { 0.0000000000000000, 0.30000000000000004, 0.59999999999999998,
3702           0.0000000000000000 },
3703   { 0.17356592428950823, 0.30000000000000004, 0.59999999999999998,
3704           0.17453292519943295 },
3705   { 0.34169984536697379, 0.30000000000000004, 0.59999999999999998,
3706           0.34906585039886590 },
3707   { 0.50055748266498457, 0.30000000000000004, 0.59999999999999998,
3708           0.52359877559829882 },
3709   { 0.64854298527106768, 0.30000000000000004, 0.59999999999999998,
3710           0.69813170079773179 },
3711   { 0.78599329284207431, 0.30000000000000004, 0.59999999999999998,
3712           0.87266462599716477 },
3713   { 0.91445452089128199, 0.30000000000000004, 0.59999999999999998,
3714           1.0471975511965976 },
3715   { 1.0360412952290587, 0.30000000000000004, 0.59999999999999998,
3716           1.2217304763960306 },
3717   { 1.1530473919778641, 0.30000000000000004, 0.59999999999999998,
3718           1.3962634015954636 },
3719   { 1.2677758800420669, 0.30000000000000004, 0.59999999999999998,
3720           1.5707963267948966 },
3721 };
3722 const double toler127 = 2.5000000000000020e-13;
3723
3724 // Test data for k=0.30000000000000004, nu=0.69999999999999996.
3725 // max(|f - f_GSL|): 8.8817841970012523e-16
3726 // max(|f - f_GSL| / |f_GSL|): 7.2239502844122443e-16
3727 const testcase_ellint_3<double>
3728 data128[10] =
3729 {
3730   { 0.0000000000000000, 0.30000000000000004, 0.69999999999999996,
3731           0.0000000000000000 },
3732   { 0.17339370613812224, 0.30000000000000004, 0.69999999999999996,
3733           0.17453292519943295 },
3734   { 0.34042975138455933, 0.30000000000000004, 0.69999999999999996,
3735           0.34906585039886590 },
3736   { 0.49676568368075985, 0.30000000000000004, 0.69999999999999996,
3737           0.52359877559829882 },
3738   { 0.64080774055753720, 0.30000000000000004, 0.69999999999999996,
3739           0.69813170079773179 },
3740   { 0.77318507779667278, 0.30000000000000004, 0.69999999999999996,
3741           0.87266462599716477 },
3742   { 0.89579782346548609, 0.30000000000000004, 0.69999999999999996,
3743           1.0471975511965976 },
3744   { 1.0110573286052202, 0.30000000000000004, 0.69999999999999996,
3745           1.2217304763960306 },
3746   { 1.1214710972949635, 0.30000000000000004, 0.69999999999999996,
3747           1.3962634015954636 },
3748   { 1.2294913236274982, 0.30000000000000004, 0.69999999999999996,
3749           1.5707963267948966 },
3750 };
3751 const double toler128 = 2.5000000000000020e-13;
3752
3753 // Test data for k=0.30000000000000004, nu=0.80000000000000004.
3754 // max(|f - f_GSL|): 8.8817841970012523e-16
3755 // max(|f - f_GSL| / |f_GSL|): 7.4358357000101250e-16
3756 const testcase_ellint_3<double>
3757 data129[10] =
3758 {
3759   { 0.0000000000000000, 0.30000000000000004, 0.80000000000000004,
3760           0.0000000000000000 },
3761   { 0.17322209907520358, 0.30000000000000004, 0.80000000000000004,
3762           0.17453292519943295 },
3763   { 0.33917623046949996, 0.30000000000000004, 0.80000000000000004,
3764           0.34906585039886590 },
3765   { 0.49307204894329176, 0.30000000000000004, 0.80000000000000004,
3766           0.52359877559829882 },
3767   { 0.63337802830291734, 0.30000000000000004, 0.80000000000000004,
3768           0.69813170079773179 },
3769   { 0.76104540997689407, 0.30000000000000004, 0.80000000000000004,
3770           0.87266462599716477 },
3771   { 0.87832009635450714, 0.30000000000000004, 0.80000000000000004,
3772           1.0471975511965976 },
3773   { 0.98787879723171790, 0.30000000000000004, 0.80000000000000004,
3774           1.2217304763960306 },
3775   { 1.0924036340069339, 0.30000000000000004, 0.80000000000000004,
3776           1.3962634015954636 },
3777   { 1.1944567571590048, 0.30000000000000004, 0.80000000000000004,
3778           1.5707963267948966 },
3779 };
3780 const double toler129 = 2.5000000000000020e-13;
3781
3782 // Test data for k=0.30000000000000004, nu=0.90000000000000002.
3783 // max(|f - f_GSL|): 8.8817841970012523e-16
3784 // max(|f - f_GSL| / |f_GSL|): 7.6419688299804087e-16
3785 const testcase_ellint_3<double>
3786 data130[10] =
3787 {
3788   { 0.0000000000000000, 0.30000000000000004, 0.90000000000000002,
3789           0.0000000000000000 },
3790   { 0.17305109924485945, 0.30000000000000004, 0.90000000000000002,
3791           0.17453292519943295 },
3792   { 0.33793890239556984, 0.30000000000000004, 0.90000000000000002,
3793           0.34906585039886590 },
3794   { 0.48947218005089738, 0.30000000000000004, 0.90000000000000002,
3795           0.52359877559829882 },
3796   { 0.62623332340775151, 0.30000000000000004, 0.90000000000000002,
3797           0.69813170079773179 },
3798   { 0.74951596581511148, 0.30000000000000004, 0.90000000000000002,
3799           0.87266462599716477 },
3800   { 0.86189886597755994, 0.30000000000000004, 0.90000000000000002,
3801           1.0471975511965976 },
3802   { 0.96629451153092005, 0.30000000000000004, 0.90000000000000002,
3803           1.2217304763960306 },
3804   { 1.0655269133492682, 0.30000000000000004, 0.90000000000000002,
3805           1.3962634015954636 },
3806   { 1.1622376896064914, 0.30000000000000004, 0.90000000000000002,
3807           1.5707963267948966 },
3808 };
3809 const double toler130 = 2.5000000000000020e-13;
3810
3811 // Test data for k=0.39999999999999991, nu=0.0000000000000000.
3812 // max(|f - f_GSL|): 8.8817841970012523e-16
3813 // max(|f - f_GSL| / |f_GSL|): 5.4157225142938039e-16
3814 const testcase_ellint_3<double>
3815 data131[10] =
3816 {
3817   { 0.0000000000000000, 0.39999999999999991, 0.0000000000000000,
3818           0.0000000000000000 },
3819   { 0.17467414669441528, 0.39999999999999991, 0.0000000000000000,
3820           0.17453292519943295 },
3821   { 0.35018222772483443, 0.39999999999999991, 0.0000000000000000,
3822           0.34906585039886590 },
3823   { 0.52729015917508737, 0.39999999999999991, 0.0000000000000000,
3824           0.52359877559829882 },
3825   { 0.70662374407341244, 0.39999999999999991, 0.0000000000000000,
3826           0.69813170079773179 },
3827   { 0.88859210497602170, 0.39999999999999991, 0.0000000000000000,
3828           0.87266462599716477 },
3829   { 1.0733136290471379, 0.39999999999999991, 0.0000000000000000,
3830           1.0471975511965976 },
3831   { 1.2605612170157061, 0.39999999999999991, 0.0000000000000000,
3832           1.2217304763960306 },
3833   { 1.4497513956433439, 0.39999999999999991, 0.0000000000000000,
3834           1.3962634015954636 },
3835   { 1.6399998658645112, 0.39999999999999991, 0.0000000000000000,
3836           1.5707963267948966 },
3837 };
3838 const double toler131 = 2.5000000000000020e-13;
3839
3840 // Test data for k=0.39999999999999991, nu=0.10000000000000001.
3841 // max(|f - f_GSL|): 8.8817841970012523e-16
3842 // max(|f - f_GSL| / |f_GSL|): 5.6859551010103832e-16
3843 const testcase_ellint_3<double>
3844 data132[10] =
3845 {
3846   { 0.0000000000000000, 0.39999999999999991, 0.10000000000000001,
3847           0.0000000000000000 },
3848   { 0.17449806706684670, 0.39999999999999991, 0.10000000000000001,
3849           0.17453292519943295 },
3850   { 0.34880048623856075, 0.39999999999999991, 0.10000000000000001,
3851           0.34906585039886590 },
3852   { 0.52277322065757392, 0.39999999999999991, 0.10000000000000001,
3853           0.52359877559829882 },
3854   { 0.69638072056918365, 0.39999999999999991, 0.10000000000000001,
3855           0.69813170079773179 },
3856   { 0.86968426619831540, 0.39999999999999991, 0.10000000000000001,
3857           0.87266462599716477 },
3858   { 1.0428044206578095, 0.39999999999999991, 0.10000000000000001,
3859           1.0471975511965976 },
3860   { 1.2158651158274378, 0.39999999999999991, 0.10000000000000001,
3861           1.2217304763960306 },
3862   { 1.3889447129893324, 0.39999999999999991, 0.10000000000000001,
3863           1.3962634015954636 },
3864   { 1.5620566886683604, 0.39999999999999991, 0.10000000000000001,
3865           1.5707963267948966 },
3866 };
3867 const double toler132 = 2.5000000000000020e-13;
3868
3869 // Test data for k=0.39999999999999991, nu=0.20000000000000001.
3870 // max(|f - f_GSL|): 8.8817841970012523e-16
3871 // max(|f - f_GSL| / |f_GSL|): 5.9444065952225719e-16
3872 const testcase_ellint_3<double>
3873 data133[10] =
3874 {
3875   { 0.0000000000000000, 0.39999999999999991, 0.20000000000000001,
3876           0.0000000000000000 },
3877   { 0.17432262290723397, 0.39999999999999991, 0.20000000000000001,
3878           0.17453292519943295 },
3879   { 0.34743795258968596, 0.39999999999999991, 0.20000000000000001,
3880           0.34906585039886590 },
3881   { 0.51838919472805112, 0.39999999999999991, 0.20000000000000001,
3882           0.52359877559829882 },
3883   { 0.68663134739057907, 0.39999999999999991, 0.20000000000000001,
3884           0.69813170079773179 },
3885   { 0.85206432981833979, 0.39999999999999991, 0.20000000000000001,
3886           0.87266462599716477 },
3887   { 1.0149595349004430, 0.39999999999999991, 0.20000000000000001,
3888           1.0471975511965976 },
3889   { 1.1758349405464676, 0.39999999999999991, 0.20000000000000001,
3890           1.2217304763960306 },
3891   { 1.3353337673882637, 0.39999999999999991, 0.20000000000000001,
3892           1.3962634015954636 },
3893   { 1.4941414344266770, 0.39999999999999991, 0.20000000000000001,
3894           1.5707963267948966 },
3895 };
3896 const double toler133 = 2.5000000000000020e-13;
3897
3898 // Test data for k=0.39999999999999991, nu=0.29999999999999999.
3899 // max(|f - f_GSL|): 1.1102230246251565e-15
3900 // max(|f - f_GSL| / |f_GSL|): 7.7406350888907249e-16
3901 const testcase_ellint_3<double>
3902 data134[10] =
3903 {
3904   { 0.0000000000000000, 0.39999999999999991, 0.29999999999999999,
3905           0.0000000000000000 },
3906   { 0.17414781013591540, 0.39999999999999991, 0.29999999999999999,
3907           0.17453292519943295 },
3908   { 0.34609415696777285, 0.39999999999999991, 0.29999999999999999,
3909           0.34906585039886590 },
3910   { 0.51413131295862535, 0.39999999999999991, 0.29999999999999999,
3911           0.52359877559829882 },
3912   { 0.67733527622935630, 0.39999999999999991, 0.29999999999999999,
3913           0.69813170079773179 },
3914   { 0.83558675182733266, 0.39999999999999991, 0.29999999999999999,
3915           0.87266462599716477 },
3916   { 0.98940140808865906, 0.39999999999999991, 0.29999999999999999,
3917           1.0471975511965976 },
3918   { 1.1396968797728058, 0.39999999999999991, 0.29999999999999999,
3919           1.2217304763960306 },
3920   { 1.2875920037865090, 0.39999999999999991, 0.29999999999999999,
3921           1.3962634015954636 },
3922   { 1.4342789859950078, 0.39999999999999991, 0.29999999999999999,
3923           1.5707963267948966 },
3924 };
3925 const double toler134 = 2.5000000000000020e-13;
3926
3927 // Test data for k=0.39999999999999991, nu=0.40000000000000002.
3928 // max(|f - f_GSL|): 8.8817841970012523e-16
3929 // max(|f - f_GSL| / |f_GSL|): 6.4314214811441816e-16
3930 const testcase_ellint_3<double>
3931 data135[10] =
3932 {
3933   { 0.0000000000000000, 0.39999999999999991, 0.40000000000000002,
3934           0.0000000000000000 },
3935   { 0.17397362471112707, 0.39999999999999991, 0.40000000000000002,
3936           0.17453292519943295 },
3937   { 0.34476864603333196, 0.39999999999999991, 0.40000000000000002,
3938           0.34906585039886590 },
3939   { 0.50999329415379346, 0.39999999999999991, 0.40000000000000002,
3940           0.52359877559829882 },
3941   { 0.66845674551396006, 0.39999999999999991, 0.40000000000000002,
3942           0.69813170079773179 },
3943   { 0.82012848346231748, 0.39999999999999991, 0.40000000000000002,
3944           0.87266462599716477 },
3945   { 0.96582449258349057, 0.39999999999999991, 0.40000000000000002,
3946           1.0471975511965976 },
3947   { 1.1068473749476286, 0.39999999999999991, 0.40000000000000002,
3948           1.2217304763960306 },
3949   { 1.2447132729159989, 0.39999999999999991, 0.40000000000000002,
3950           1.3962634015954636 },
3951   { 1.3809986210732901, 0.39999999999999991, 0.40000000000000002,
3952           1.5707963267948966 },
3953 };
3954 const double toler135 = 2.5000000000000020e-13;
3955
3956 // Test data for k=0.39999999999999991, nu=0.50000000000000000.
3957 // max(|f - f_GSL|): 8.8817841970012523e-16
3958 // max(|f - f_GSL| / |f_GSL|): 6.6621057007519435e-16
3959 const testcase_ellint_3<double>
3960 data136[10] =
3961 {
3962   { 0.0000000000000000, 0.39999999999999991, 0.50000000000000000,
3963           0.0000000000000000 },
3964   { 0.17380006262854136, 0.39999999999999991, 0.50000000000000000,
3965           0.17453292519943295 },
3966   { 0.34346098216756610, 0.39999999999999991, 0.50000000000000000,
3967           0.34906585039886590 },
3968   { 0.50596929935059420, 0.39999999999999991, 0.50000000000000000,
3969           0.52359877559829882 },
3970   { 0.65996392089131251, 0.39999999999999991, 0.50000000000000000,
3971           0.69813170079773179 },
3972   { 0.80558463511364786, 0.39999999999999991, 0.50000000000000000,
3973           0.87266462599716477 },
3974   { 0.94397834522857704, 0.39999999999999991, 0.50000000000000000,
3975           1.0471975511965976 },
3976   { 1.0768075114108115, 0.39999999999999991, 0.50000000000000000,
3977           1.2217304763960306 },
3978   { 1.2059184624251333, 0.39999999999999991, 0.50000000000000000,
3979           1.3962634015954636 },
3980   { 1.3331797176377398, 0.39999999999999991, 0.50000000000000000,
3981           1.5707963267948966 },
3982 };
3983 const double toler136 = 2.5000000000000020e-13;
3984
3985 // Test data for k=0.39999999999999991, nu=0.59999999999999998.
3986 // max(|f - f_GSL|): 8.8817841970012523e-16
3987 // max(|f - f_GSL| / |f_GSL|): 6.8853630717730749e-16
3988 const testcase_ellint_3<double>
3989 data137[10] =
3990 {
3991   { 0.0000000000000000, 0.39999999999999991, 0.59999999999999998,
3992           0.0000000000000000 },
3993   { 0.17362711992081245, 0.39999999999999991, 0.59999999999999998,
3994           0.17453292519943295 },
3995   { 0.34217074276403953, 0.39999999999999991, 0.59999999999999998,
3996           0.34906585039886590 },
3997   { 0.50205389185761606, 0.39999999999999991, 0.59999999999999998,
3998           0.52359877559829882 },
3999   { 0.65182834920372734, 0.39999999999999991, 0.59999999999999998,
4000           0.69813170079773179 },
4001   { 0.79186512820565136, 0.39999999999999991, 0.59999999999999998,
4002           0.87266462599716477 },
4003   { 0.92365535916287134, 0.39999999999999991, 0.59999999999999998,
4004           1.0471975511965976 },
4005   { 1.0491915663957907, 0.39999999999999991, 0.59999999999999998,
4006           1.2217304763960306 },
4007   { 1.1705934291745106, 0.39999999999999991, 0.59999999999999998,
4008           1.3962634015954636 },
4009   { 1.2899514672527024, 0.39999999999999991, 0.59999999999999998,
4010           1.5707963267948966 },
4011 };
4012 const double toler137 = 2.5000000000000020e-13;
4013
4014 // Test data for k=0.39999999999999991, nu=0.69999999999999996.
4015 // max(|f - f_GSL|): 8.8817841970012523e-16
4016 // max(|f - f_GSL| / |f_GSL|): 7.1018730557776469e-16
4017 const testcase_ellint_3<double>
4018 data138[10] =
4019 {
4020   { 0.0000000000000000, 0.39999999999999991, 0.69999999999999996,
4021           0.0000000000000000 },
4022   { 0.17345479265712868, 0.39999999999999991, 0.69999999999999996,
4023           0.17453292519943295 },
4024   { 0.34089751955950354, 0.39999999999999991, 0.69999999999999996,
4025           0.34906585039886590 },
4026   { 0.49824200167361332, 0.39999999999999991, 0.69999999999999996,
4027           0.52359877559829882 },
4028   { 0.64402450341199402, 0.39999999999999991, 0.69999999999999996,
4029           0.69813170079773179 },
4030   { 0.77889207804122873, 0.39999999999999991, 0.69999999999999996,
4031           0.87266462599716477 },
4032   { 0.90468169720957992, 0.39999999999999991, 0.69999999999999996,
4033           1.0471975511965976 },
4034   { 1.0236847823692916, 0.39999999999999991, 0.69999999999999996,
4035           1.2217304763960306 },
4036   { 1.1382465247425166, 0.39999999999999991, 0.69999999999999996,
4037           1.3962634015954636 },
4038   { 1.2506255923253344, 0.39999999999999991, 0.69999999999999996,
4039           1.5707963267948966 },
4040 };
4041 const double toler138 = 2.5000000000000020e-13;
4042
4043 // Test data for k=0.39999999999999991, nu=0.80000000000000004.
4044 // max(|f - f_GSL|): 8.8817841970012523e-16
4045 // max(|f - f_GSL| / |f_GSL|): 7.3122171115555478e-16
4046 const testcase_ellint_3<double>
4047 data139[10] =
4048 {
4049   { 0.0000000000000000, 0.39999999999999991, 0.80000000000000004,
4050           0.0000000000000000 },
4051   { 0.17328307694277154, 0.39999999999999991, 0.80000000000000004,
4052           0.17453292519943295 },
4053   { 0.33964091800132007, 0.39999999999999991, 0.80000000000000004,
4054           0.34906585039886590 },
4055   { 0.49452889372467440, 0.39999999999999991, 0.80000000000000004,
4056           0.52359877559829882 },
4057   { 0.63652940095937316, 0.39999999999999991, 0.80000000000000004,
4058           0.69813170079773179 },
4059   { 0.76659772511159097, 0.39999999999999991, 0.80000000000000004,
4060           0.87266462599716477 },
4061   { 0.88691047977338111, 0.39999999999999991, 0.80000000000000004,
4062           1.0471975511965976 },
4063   { 1.0000273200611638, 0.39999999999999991, 0.80000000000000004,
4064           1.2217304763960306 },
4065   { 1.1084787902188009, 0.39999999999999991, 0.80000000000000004,
4066           1.3962634015954636 },
4067   { 1.2146499565727209, 0.39999999999999991, 0.80000000000000004,
4068           1.5707963267948966 },
4069 };
4070 const double toler139 = 2.5000000000000020e-13;
4071
4072 // Test data for k=0.39999999999999991, nu=0.90000000000000002.
4073 // max(|f - f_GSL|): 8.8817841970012523e-16
4074 // max(|f - f_GSL| / |f_GSL|): 7.5168974431077345e-16
4075 const testcase_ellint_3<double>
4076 data140[10] =
4077 {
4078   { 0.0000000000000000, 0.39999999999999991, 0.90000000000000002,
4079           0.0000000000000000 },
4080   { 0.17311196891868127, 0.39999999999999991, 0.90000000000000002,
4081           0.17453292519943295 },
4082   { 0.33840055664911906, 0.39999999999999991, 0.90000000000000002,
4083           0.34906585039886590 },
4084   { 0.49091013944075329, 0.39999999999999991, 0.90000000000000002,
4085           0.52359877559829882 },
4086   { 0.62932228186809580, 0.39999999999999991, 0.90000000000000002,
4087           0.69813170079773179 },
4088   { 0.75492278323019801, 0.39999999999999991, 0.90000000000000002,
4089           0.87266462599716477 },
4090   { 0.87021659043854294, 0.39999999999999991, 0.90000000000000002,
4091           1.0471975511965976 },
4092   { 0.97800245228239246, 0.39999999999999991, 0.90000000000000002,
4093           1.2217304763960306 },
4094   { 1.0809625773173697, 0.39999999999999991, 0.90000000000000002,
4095           1.3962634015954636 },
4096   { 1.1815758115929846, 0.39999999999999991, 0.90000000000000002,
4097           1.5707963267948966 },
4098 };
4099 const double toler140 = 2.5000000000000020e-13;
4100
4101 // Test data for k=0.50000000000000000, nu=0.0000000000000000.
4102 // max(|f - f_GSL|): 2.2204460492503131e-16
4103 // max(|f - f_GSL| / |f_GSL|): 3.1201497220602069e-16
4104 const testcase_ellint_3<double>
4105 data141[10] =
4106 {
4107   { 0.0000000000000000, 0.50000000000000000, 0.0000000000000000,
4108           0.0000000000000000 },
4109   { 0.17475385514035785, 0.50000000000000000, 0.0000000000000000,
4110           0.17453292519943295 },
4111   { 0.35081868470101585, 0.50000000000000000, 0.0000000000000000,
4112           0.34906585039886590 },
4113   { 0.52942862705190574, 0.50000000000000000, 0.0000000000000000,
4114           0.52359877559829882 },
4115   { 0.71164727562630314, 0.50000000000000000, 0.0000000000000000,
4116           0.69813170079773179 },
4117   { 0.89824523594227768, 0.50000000000000000, 0.0000000000000000,
4118           0.87266462599716477 },
4119   { 1.0895506700518851, 0.50000000000000000, 0.0000000000000000,
4120           1.0471975511965976 },
4121   { 1.2853005857432931, 0.50000000000000000, 0.0000000000000000,
4122           1.2217304763960306 },
4123   { 1.4845545520549484, 0.50000000000000000, 0.0000000000000000,
4124           1.3962634015954636 },
4125   { 1.6857503548125963, 0.50000000000000000, 0.0000000000000000,
4126           1.5707963267948966 },
4127 };
4128 const double toler141 = 2.5000000000000020e-13;
4129
4130 // Test data for k=0.50000000000000000, nu=0.10000000000000001.
4131 // max(|f - f_GSL|): 2.2204460492503131e-16
4132 // max(|f - f_GSL| / |f_GSL|): 3.1662857256911530e-16
4133 const testcase_ellint_3<double>
4134 data142[10] =
4135 {
4136   { 0.0000000000000000, 0.50000000000000000, 0.10000000000000001,
4137           0.0000000000000000 },
4138   { 0.17457763120814676, 0.50000000000000000, 0.10000000000000001,
4139           0.17453292519943295 },
4140   { 0.34943246340849154, 0.50000000000000000, 0.10000000000000001,
4141           0.34906585039886590 },
4142   { 0.52487937869610790, 0.50000000000000000, 0.10000000000000001,
4143           0.52359877559829882 },
4144   { 0.70127785096388384, 0.50000000000000000, 0.10000000000000001,
4145           0.69813170079773179 },
4146   { 0.87898815988624479, 0.50000000000000000, 0.10000000000000001,
4147           0.87266462599716477 },
4148   { 1.0582764576094172, 0.50000000000000000, 0.10000000000000001,
4149           1.0471975511965976 },
4150   { 1.2391936844060205, 0.50000000000000000, 0.10000000000000001,
4151           1.2217304763960306 },
4152   { 1.4214793542995841, 0.50000000000000000, 0.10000000000000001,
4153           1.3962634015954636 },
4154   { 1.6045524936084892, 0.50000000000000000, 0.10000000000000001,
4155           1.5707963267948966 },
4156 };
4157 const double toler142 = 2.5000000000000020e-13;
4158
4159 // Test data for k=0.50000000000000000, nu=0.20000000000000001.
4160 // max(|f - f_GSL|): 2.2204460492503131e-16
4161 // max(|f - f_GSL| / |f_GSL|): 3.2114786773102175e-16
4162 const testcase_ellint_3<double>
4163 data143[10] =
4164 {
4165   { 0.0000000000000000, 0.50000000000000000, 0.20000000000000001,
4166           0.0000000000000000 },
4167   { 0.17440204336345433, 0.50000000000000000, 0.20000000000000001,
4168           0.17453292519943295 },
4169   { 0.34806552388338824, 0.50000000000000000, 0.20000000000000001,
4170           0.34906585039886590 },
4171   { 0.52046416757129810, 0.50000000000000000, 0.20000000000000001,
4172           0.52359877559829882 },
4173   { 0.69140924550993865, 0.50000000000000000, 0.20000000000000001,
4174           0.69813170079773179 },
4175   { 0.86104678636125520, 0.50000000000000000, 0.20000000000000001,
4176           0.87266462599716477 },
4177   { 1.0297439459053981, 0.50000000000000000, 0.20000000000000001,
4178           1.0471975511965976 },
4179   { 1.1979214112912033, 0.50000000000000000, 0.20000000000000001,
4180           1.2217304763960306 },
4181   { 1.3659033858648930, 0.50000000000000000, 0.20000000000000001,
4182           1.3962634015954636 },
4183   { 1.5338490483665983, 0.50000000000000000, 0.20000000000000001,
4184           1.5707963267948966 },
4185 };
4186 const double toler143 = 2.5000000000000020e-13;
4187
4188 // Test data for k=0.50000000000000000, nu=0.29999999999999999.
4189 // max(|f - f_GSL|): 2.2204460492503131e-16
4190 // max(|f - f_GSL| / |f_GSL|): 3.2557837230041312e-16
4191 const testcase_ellint_3<double>
4192 data144[10] =
4193 {
4194   { 0.0000000000000000, 0.50000000000000000, 0.29999999999999999,
4195           0.0000000000000000 },
4196   { 0.17422708752228896, 0.50000000000000000, 0.29999999999999999,
4197           0.17453292519943295 },
4198   { 0.34671739434855858, 0.50000000000000000, 0.29999999999999999,
4199           0.34906585039886590 },
4200   { 0.51617616305641878, 0.50000000000000000, 0.29999999999999999,
4201           0.52359877559829882 },
4202   { 0.68200047612545167, 0.50000000000000000, 0.29999999999999999,
4203           0.69813170079773179 },
4204   { 0.84427217869498372, 0.50000000000000000, 0.29999999999999999,
4205           0.87266462599716477 },
4206   { 1.0035637821389782, 0.50000000000000000, 0.29999999999999999,
4207           1.0471975511965976 },
4208   { 1.1606800483933111, 0.50000000000000000, 0.29999999999999999,
4209           1.2217304763960306 },
4210   { 1.3164407134643459, 0.50000000000000000, 0.29999999999999999,
4211           1.3962634015954636 },
4212   { 1.4715681939859637, 0.50000000000000000, 0.29999999999999999,
4213           1.5707963267948966 },
4214 };
4215 const double toler144 = 2.5000000000000020e-13;
4216
4217 // Test data for k=0.50000000000000000, nu=0.40000000000000002.
4218 // max(|f - f_GSL|): 2.2204460492503131e-16
4219 // max(|f - f_GSL| / |f_GSL|): 3.2992508582900068e-16
4220 const testcase_ellint_3<double>
4221 data145[10] =
4222 {
4223   { 0.0000000000000000, 0.50000000000000000, 0.40000000000000002,
4224           0.0000000000000000 },
4225   { 0.17405275963859917, 0.50000000000000000, 0.40000000000000002,
4226           0.17453292519943295 },
4227   { 0.34538761957029329, 0.50000000000000000, 0.40000000000000002,
4228           0.34906585039886590 },
4229   { 0.51200902646603907, 0.50000000000000000, 0.40000000000000002,
4230           0.52359877559829882 },
4231   { 0.67301522212868792, 0.50000000000000000, 0.40000000000000002,
4232           0.69813170079773179 },
4233   { 0.82853844466313320, 0.50000000000000000, 0.40000000000000002,
4234           0.87266462599716477 },
4235   { 0.97942097862681488, 0.50000000000000000, 0.40000000000000002,
4236           1.0471975511965976 },
4237   { 1.1268429801220614, 0.50000000000000000, 0.40000000000000002,
4238           1.2217304763960306 },
4239   { 1.2720406704533922, 0.50000000000000000, 0.40000000000000002,
4240           1.3962634015954636 },
4241   { 1.4161679518465340, 0.50000000000000000, 0.40000000000000002,
4242           1.5707963267948966 },
4243 };
4244 const double toler145 = 2.5000000000000020e-13;
4245
4246 // Test data for k=0.50000000000000000, nu=0.50000000000000000.
4247 // max(|f - f_GSL|): 2.2204460492503131e-16
4248 // max(|f - f_GSL| / |f_GSL|): 3.3419255755184137e-16
4249 const testcase_ellint_3<double>
4250 data146[10] =
4251 {
4252   { 0.0000000000000000, 0.50000000000000000, 0.50000000000000000,
4253           0.0000000000000000 },
4254   { 0.17387905570381157, 0.50000000000000000, 0.50000000000000000,
4255           0.17453292519943295 },
4256   { 0.34407576010465207, 0.50000000000000000, 0.50000000000000000,
4257           0.34906585039886590 },
4258   { 0.50795686560160824, 0.50000000000000000, 0.50000000000000000,
4259           0.52359877559829882 },
4260   { 0.66442115453330164, 0.50000000000000000, 0.50000000000000000,
4261           0.69813170079773179 },
4262   { 0.81373829119355345, 0.50000000000000000, 0.50000000000000000,
4263           0.87266462599716477 },
4264   { 0.95705743313235825, 0.50000000000000000, 0.50000000000000000,
4265           1.0471975511965976 },
4266   { 1.0959131991362554, 0.50000000000000000, 0.50000000000000000,
4267           1.2217304763960306 },
4268   { 1.2318900529754597, 0.50000000000000000, 0.50000000000000000,
4269           1.3962634015954636 },
4270   { 1.3664739530045971, 0.50000000000000000, 0.50000000000000000,
4271           1.5707963267948966 },
4272 };
4273 const double toler146 = 2.5000000000000020e-13;
4274
4275 // Test data for k=0.50000000000000000, nu=0.59999999999999998.
4276 // max(|f - f_GSL|): 2.2204460492503131e-16
4277 // max(|f - f_GSL| / |f_GSL|): 3.3838494104749599e-16
4278 const testcase_ellint_3<double>
4279 data147[10] =
4280 {
4281   { 0.0000000000000000, 0.50000000000000000, 0.59999999999999998,
4282           0.0000000000000000 },
4283   { 0.17370597174637581, 0.50000000000000000, 0.59999999999999998,
4284           0.17453292519943295 },
4285   { 0.34278139158591414, 0.50000000000000000, 0.59999999999999998,
4286           0.34906585039886590 },
4287   { 0.50401419439302708, 0.50000000000000000, 0.59999999999999998,
4288           0.52359877559829882 },
4289   { 0.65618938076167210, 0.50000000000000000, 0.59999999999999998,
4290           0.69813170079773179 },
4291   { 0.79977959248855424, 0.50000000000000000, 0.59999999999999998,
4292           0.87266462599716477 },
4293   { 0.93625925190753545, 0.50000000000000000, 0.59999999999999998,
4294           1.0471975511965976 },
4295   { 1.0674905658379708, 0.50000000000000000, 0.59999999999999998,
4296           1.2217304763960306 },
4297   { 1.1953481298023050, 0.50000000000000000, 0.59999999999999998,
4298           1.3962634015954636 },
4299   { 1.3215740290190876, 0.50000000000000000, 0.59999999999999998,
4300           1.5707963267948966 },
4301 };
4302 const double toler147 = 2.5000000000000020e-13;
4303
4304 // Test data for k=0.50000000000000000, nu=0.69999999999999996.
4305 // max(|f - f_GSL|): 2.2204460492503131e-16
4306 // max(|f - f_GSL| / |f_GSL|): 3.4250604066951477e-16
4307 const testcase_ellint_3<double>
4308 data148[10] =
4309 {
4310   { 0.0000000000000000, 0.50000000000000000, 0.69999999999999996,
4311           0.0000000000000000 },
4312   { 0.17353350383131641, 0.50000000000000000, 0.69999999999999996,
4313           0.17453292519943295 },
4314   { 0.34150410405436771, 0.50000000000000000, 0.69999999999999996,
4315           0.34906585039886590 },
4316   { 0.50017589696443487, 0.50000000000000000, 0.69999999999999996,
4317           0.52359877559829882 },
4318   { 0.64829398188419951, 0.50000000000000000, 0.69999999999999996,
4319           0.69813170079773179 },
4320   { 0.78658270782402073, 0.50000000000000000, 0.69999999999999996,
4321           0.87266462599716477 },
4322   { 0.91684738336675053, 0.50000000000000000, 0.69999999999999996,
4323           1.0471975511965976 },
4324   { 1.0412486789555935, 0.50000000000000000, 0.69999999999999996,
4325           1.2217304763960306 },
4326   { 1.1619021847612001, 0.50000000000000000, 0.69999999999999996,
4327           1.3962634015954636 },
4328   { 1.2807475181182502, 0.50000000000000000, 0.69999999999999996,
4329           1.5707963267948966 },
4330 };
4331 const double toler148 = 2.5000000000000020e-13;
4332
4333 // Test data for k=0.50000000000000000, nu=0.80000000000000004.
4334 // max(|f - f_GSL|): 4.4408920985006262e-16
4335 // max(|f - f_GSL| / |f_GSL|): 3.5715240651179632e-16
4336 const testcase_ellint_3<double>
4337 data149[10] =
4338 {
4339   { 0.0000000000000000, 0.50000000000000000, 0.80000000000000004,
4340           0.0000000000000000 },
4341   { 0.17336164805979126, 0.50000000000000000, 0.80000000000000004,
4342           0.17453292519943295 },
4343   { 0.34024350132086773, 0.50000000000000000, 0.80000000000000004,
4344           0.34906585039886590 },
4345   { 0.49643719555734073, 0.50000000000000000, 0.80000000000000004,
4346           0.52359877559829882 },
4347   { 0.64071162456976150, 0.50000000000000000, 0.80000000000000004,
4348           0.69813170079773179 },
4349   { 0.77407836177211908, 0.50000000000000000, 0.80000000000000004,
4350           0.87266462599716477 },
4351   { 0.89867058251905652, 0.50000000000000000, 0.80000000000000004,
4352           1.0471975511965976 },
4353   { 1.0169181822134910, 0.50000000000000000, 0.80000000000000004,
4354           1.2217304763960306 },
4355   { 1.1311363312779448, 0.50000000000000000, 0.80000000000000004,
4356           1.3962634015954636 },
4357   { 1.2434165408189539, 0.50000000000000000, 0.80000000000000004,
4358           1.5707963267948966 },
4359 };
4360 const double toler149 = 2.5000000000000020e-13;
4361
4362 // Test data for k=0.50000000000000000, nu=0.90000000000000002.
4363 // max(|f - f_GSL|): 4.4408920985006262e-16
4364 // max(|f - f_GSL| / |f_GSL|): 4.4664649039489274e-16
4365 const testcase_ellint_3<double>
4366 data150[10] =
4367 {
4368   { 0.0000000000000000, 0.50000000000000000, 0.90000000000000002,
4369           0.0000000000000000 },
4370   { 0.17319040056865681, 0.50000000000000000, 0.90000000000000002,
4371           0.17453292519943295 },
4372   { 0.33899920036578557, 0.50000000000000000, 0.90000000000000002,
4373           0.34906585039886590 },
4374   { 0.49279362182695174, 0.50000000000000000, 0.90000000000000002,
4375           0.52359877559829882 },
4376   { 0.63342123379746151, 0.50000000000000000, 0.90000000000000002,
4377           0.69813170079773179 },
4378   { 0.76220595179550321, 0.50000000000000000, 0.90000000000000002,
4379           0.87266462599716477 },
4380   { 0.88160004743532294, 0.50000000000000000, 0.90000000000000002,
4381           1.0471975511965976 },
4382   { 0.99427448642310123, 0.50000000000000000, 0.90000000000000002,
4383           1.2217304763960306 },
4384   { 1.1027091512470095, 0.50000000000000000, 0.90000000000000002,
4385           1.3962634015954636 },
4386   { 1.2091116095504744, 0.50000000000000000, 0.90000000000000002,
4387           1.5707963267948966 },
4388 };
4389 const double toler150 = 2.5000000000000020e-13;
4390
4391 // Test data for k=0.60000000000000009, nu=0.0000000000000000.
4392 // max(|f - f_GSL|): 4.4408920985006262e-16
4393 // max(|f - f_GSL| / |f_GSL|): 3.3664899092028927e-16
4394 const testcase_ellint_3<double>
4395 data151[10] =
4396 {
4397   { 0.0000000000000000, 0.60000000000000009, 0.0000000000000000,
4398           0.0000000000000000 },
4399   { 0.17485154362988359, 0.60000000000000009, 0.0000000000000000,
4400           0.17453292519943295 },
4401   { 0.35160509865544326, 0.60000000000000009, 0.0000000000000000,
4402           0.34906585039886590 },
4403   { 0.53210652578446138, 0.60000000000000009, 0.0000000000000000,
4404           0.52359877559829882 },
4405   { 0.71805304664485659, 0.60000000000000009, 0.0000000000000000,
4406           0.69813170079773179 },
4407   { 0.91082759030195970, 0.60000000000000009, 0.0000000000000000,
4408           0.87266462599716477 },
4409   { 1.1112333229323361, 0.60000000000000009, 0.0000000000000000,
4410           1.0471975511965976 },
4411   { 1.3191461190365270, 0.60000000000000009, 0.0000000000000000,
4412           1.2217304763960306 },
4413   { 1.5332022105084775, 0.60000000000000009, 0.0000000000000000,
4414           1.3962634015954636 },
4415   { 1.7507538029157526, 0.60000000000000009, 0.0000000000000000,
4416           1.5707963267948966 },
4417 };
4418 const double toler151 = 2.5000000000000020e-13;
4419
4420 // Test data for k=0.60000000000000009, nu=0.10000000000000001.
4421 // max(|f - f_GSL|): 4.4408920985006262e-16
4422 // max(|f - f_GSL| / |f_GSL|): 3.4937942733669112e-16
4423 const testcase_ellint_3<double>
4424 data152[10] =
4425 {
4426   { 0.0000000000000000, 0.60000000000000009, 0.10000000000000001,
4427           0.0000000000000000 },
4428   { 0.17467514275022011, 0.60000000000000009, 0.10000000000000001,
4429           0.17453292519943295 },
4430   { 0.35021333086258255, 0.60000000000000009, 0.10000000000000001,
4431           0.34906585039886590 },
4432   { 0.52751664092962691, 0.60000000000000009, 0.10000000000000001,
4433           0.52359877559829882 },
4434   { 0.70752126971957874, 0.60000000000000009, 0.10000000000000001,
4435           0.69813170079773179 },
4436   { 0.89111058756112871, 0.60000000000000009, 0.10000000000000001,
4437           0.87266462599716477 },
4438   { 1.0789241202877768, 0.60000000000000009, 0.10000000000000001,
4439           1.0471975511965976 },
4440   { 1.2710800210399946, 0.60000000000000009, 0.10000000000000001,
4441           1.2217304763960306 },
4442   { 1.4669060574440276, 0.60000000000000009, 0.10000000000000001,
4443           1.3962634015954636 },
4444   { 1.6648615773343014, 0.60000000000000009, 0.10000000000000001,
4445           1.5707963267948966 },
4446 };
4447 const double toler152 = 2.5000000000000020e-13;
4448
4449 // Test data for k=0.60000000000000009, nu=0.20000000000000001.
4450 // max(|f - f_GSL|): 6.6613381477509392e-16
4451 // max(|f - f_GSL| / |f_GSL|): 4.1891472451898755e-16
4452 const testcase_ellint_3<double>
4453 data153[10] =
4454 {
4455   { 0.0000000000000000, 0.60000000000000009, 0.20000000000000001,
4456           0.0000000000000000 },
4457   { 0.17449937871800650, 0.60000000000000009, 0.20000000000000001,
4458           0.17453292519943295 },
4459   { 0.34884093647346553, 0.60000000000000009, 0.20000000000000001,
4460           0.34906585039886590 },
4461   { 0.52306221119844087, 0.60000000000000009, 0.20000000000000001,
4462           0.52359877559829882 },
4463   { 0.69749955678982223, 0.60000000000000009, 0.20000000000000001,
4464           0.69813170079773179 },
4465   { 0.87274610682416853, 0.60000000000000009, 0.20000000000000001,
4466           0.87266462599716477 },
4467   { 1.0494620540750792, 0.60000000000000009, 0.20000000000000001,
4468           1.0471975511965976 },
4469   { 1.2280847305507339, 0.60000000000000009, 0.20000000000000001,
4470           1.2217304763960306 },
4471   { 1.4085436279696888, 0.60000000000000009, 0.20000000000000001,
4472           1.3962634015954636 },
4473   { 1.5901418016279374, 0.60000000000000009, 0.20000000000000001,
4474           1.5707963267948966 },
4475 };
4476 const double toler153 = 2.5000000000000020e-13;
4477
4478 // Test data for k=0.60000000000000009, nu=0.29999999999999999.
4479 // max(|f - f_GSL|): 4.4408920985006262e-16
4480 // max(|f - f_GSL| / |f_GSL|): 3.7339932380431439e-16
4481 const testcase_ellint_3<double>
4482 data154[10] =
4483 {
4484   { 0.0000000000000000, 0.60000000000000009, 0.29999999999999999,
4485           0.0000000000000000 },
4486   { 0.17432424744393932, 0.60000000000000009, 0.29999999999999999,
4487           0.17453292519943295 },
4488   { 0.34748744127146447, 0.60000000000000009, 0.29999999999999999,
4489           0.34906585039886590 },
4490   { 0.51873632743924825, 0.60000000000000009, 0.29999999999999999,
4491           0.52359877559829882 },
4492   { 0.68794610396313116, 0.60000000000000009, 0.29999999999999999,
4493           0.69813170079773179 },
4494   { 0.85558070175468726, 0.60000000000000009, 0.29999999999999999,
4495           0.87266462599716477 },
4496   { 1.0224416343605653, 0.60000000000000009, 0.29999999999999999,
4497           1.0471975511965976 },
4498   { 1.1893144457936788, 0.60000000000000009, 0.29999999999999999,
4499           1.2217304763960306 },
4500   { 1.3566435377982575, 0.60000000000000009, 0.29999999999999999,
4501           1.3962634015954636 },
4502   { 1.5243814243493585, 0.60000000000000009, 0.29999999999999999,
4503           1.5707963267948966 },
4504 };
4505 const double toler154 = 2.5000000000000020e-13;
4506
4507 // Test data for k=0.60000000000000009, nu=0.40000000000000002.
4508 // max(|f - f_GSL|): 6.6613381477509392e-16
4509 // max(|f - f_GSL| / |f_GSL|): 4.5440898085101625e-16
4510 const testcase_ellint_3<double>
4511 data155[10] =
4512 {
4513   { 0.0000000000000000, 0.60000000000000009, 0.40000000000000002,
4514           0.0000000000000000 },
4515   { 0.17414974487670717, 0.60000000000000009, 0.40000000000000002,
4516           0.17453292519943295 },
4517   { 0.34615238767335027, 0.60000000000000009, 0.40000000000000002,
4518           0.34906585039886590 },
4519   { 0.51453257838108557, 0.60000000000000009, 0.40000000000000002,
4520           0.52359877559829882 },
4521   { 0.67882386787534399, 0.60000000000000009, 0.40000000000000002,
4522           0.69813170079773179 },
4523   { 0.83948470233173578, 0.60000000000000009, 0.40000000000000002,
4524           0.87266462599716477 },
4525   { 0.99753496200073977, 0.60000000000000009, 0.40000000000000002,
4526           1.0471975511965976 },
4527   { 1.1541101404388487, 0.60000000000000009, 0.40000000000000002,
4528           1.2217304763960306 },
4529   { 1.3100911323398816, 0.60000000000000009, 0.40000000000000002,
4530           1.3962634015954636 },
4531   { 1.4659345278069984, 0.60000000000000009, 0.40000000000000002,
4532           1.5707963267948966 },
4533 };
4534 const double toler155 = 2.5000000000000020e-13;
4535
4536 // Test data for k=0.60000000000000009, nu=0.50000000000000000.
4537 // max(|f - f_GSL|): 6.6613381477509392e-16
4538 // max(|f - f_GSL| / |f_GSL|): 4.7124937590522226e-16
4539 const testcase_ellint_3<double>
4540 data156[10] =
4541 {
4542   { 0.0000000000000000, 0.60000000000000009, 0.50000000000000000,
4543           0.0000000000000000 },
4544   { 0.17397586700252807, 0.60000000000000009, 0.50000000000000000,
4545           0.17453292519943295 },
4546   { 0.34483533397138516, 0.60000000000000009, 0.50000000000000000,
4547           0.34906585039886590 },
4548   { 0.51044500461706477, 0.60000000000000009, 0.50000000000000000,
4549           0.52359877559829882 },
4550   { 0.67009988034712664, 0.60000000000000009, 0.50000000000000000,
4551           0.69813170079773179 },
4552   { 0.82434762375735193, 0.60000000000000009, 0.50000000000000000,
4553           0.87266462599716477 },
4554   { 0.97447346702798998, 0.60000000000000009, 0.50000000000000000,
4555           1.0471975511965976 },
4556   { 1.1219494000522143, 0.60000000000000009, 0.50000000000000000,
4557           1.2217304763960306 },
4558   { 1.2680242605954486, 0.60000000000000009, 0.50000000000000000,
4559           1.3962634015954636 },
4560   { 1.4135484285693078, 0.60000000000000009, 0.50000000000000000,
4561           1.5707963267948966 },
4562 };
4563 const double toler156 = 2.5000000000000020e-13;
4564
4565 // Test data for k=0.60000000000000009, nu=0.59999999999999998.
4566 // max(|f - f_GSL|): 4.4408920985006262e-16
4567 // max(|f - f_GSL| / |f_GSL|): 4.0652177678695900e-16
4568 const testcase_ellint_3<double>
4569 data157[10] =
4570 {
4571   { 0.0000000000000000, 0.60000000000000009, 0.59999999999999998,
4572           0.0000000000000000 },
4573   { 0.17380260984469353, 0.60000000000000009, 0.59999999999999998,
4574           0.17453292519943295 },
4575   { 0.34353585361777839, 0.60000000000000009, 0.59999999999999998,
4576           0.34906585039886590 },
4577   { 0.50646805774321380, 0.60000000000000009, 0.59999999999999998,
4578           0.52359877559829882 },
4579   { 0.66174468108625506, 0.60000000000000009, 0.59999999999999998,
4580           0.69813170079773179 },
4581   { 0.81007462280278408, 0.60000000000000009, 0.59999999999999998,
4582           0.87266462599716477 },
4583   { 0.95303466945718729, 0.60000000000000009, 0.59999999999999998,
4584           1.0471975511965976 },
4585   { 1.0924118588677505, 0.60000000000000009, 0.59999999999999998,
4586           1.2217304763960306 },
4587   { 1.2297640574847937, 0.60000000000000009, 0.59999999999999998,
4588           1.3962634015954636 },
4589   { 1.3662507535812816, 0.60000000000000009, 0.59999999999999998,
4590           1.5707963267948966 },
4591 };
4592 const double toler157 = 2.5000000000000020e-13;
4593
4594 // Test data for k=0.60000000000000009, nu=0.69999999999999996.
4595 // max(|f - f_GSL|): 4.4408920985006262e-16
4596 // max(|f - f_GSL| / |f_GSL|): 4.1692457486457856e-16
4597 const testcase_ellint_3<double>
4598 data158[10] =
4599 {
4600   { 0.0000000000000000, 0.60000000000000009, 0.69999999999999996,
4601           0.0000000000000000 },
4602   { 0.17362996946312007, 0.60000000000000009, 0.69999999999999996,
4603           0.17453292519943295 },
4604   { 0.34225353454870588, 0.60000000000000009, 0.69999999999999996,
4605           0.34906585039886590 },
4606   { 0.50259656397799524, 0.60000000000000009, 0.69999999999999996,
4607           0.52359877559829882 },
4608   { 0.65373184496628933, 0.60000000000000009, 0.69999999999999996,
4609           0.69813170079773179 },
4610   { 0.79658372884056439, 0.60000000000000009, 0.69999999999999996,
4611           0.87266462599716477 },
4612   { 0.93303240100245421, 0.60000000000000009, 0.69999999999999996,
4613           1.0471975511965976 },
4614   { 1.0651547944716557, 0.60000000000000009, 0.69999999999999996,
4615           1.2217304763960306 },
4616   { 1.1947676204853441, 0.60000000000000009, 0.69999999999999996,
4617           1.3962634015954636 },
4618   { 1.3232737468822813, 0.60000000000000009, 0.69999999999999996,
4619           1.5707963267948966 },
4620 };
4621 const double toler158 = 2.5000000000000020e-13;
4622
4623 // Test data for k=0.60000000000000009, nu=0.80000000000000004.
4624 // max(|f - f_GSL|): 4.4408920985006262e-16
4625 // max(|f - f_GSL| / |f_GSL|): 4.2705175719241326e-16
4626 const testcase_ellint_3<double>
4627 data159[10] =
4628 {
4629   { 0.0000000000000000, 0.60000000000000009, 0.80000000000000004,
4630           0.0000000000000000 },
4631   { 0.17345794195390685, 0.60000000000000009, 0.80000000000000004,
4632           0.17453292519943295 },
4633   { 0.34098797854531027, 0.60000000000000009, 0.80000000000000004,
4634           0.34906585039886590 },
4635   { 0.49882569168826213, 0.60000000000000009, 0.80000000000000004,
4636           0.52359877559829882 },
4637   { 0.64603758566475511, 0.60000000000000009, 0.80000000000000004,
4638           0.69813170079773179 },
4639   { 0.78380365594769730, 0.60000000000000009, 0.80000000000000004,
4640           0.87266462599716477 },
4641   { 0.91430946255611190, 0.60000000000000009, 0.80000000000000004,
4642           1.0471975511965976 },
4643   { 1.0398955217270607, 0.60000000000000009, 0.80000000000000004,
4644           1.2217304763960306 },
4645   { 1.1625948314277679, 0.60000000000000009, 0.80000000000000004,
4646           1.3962634015954636 },
4647   { 1.2840021261752192, 0.60000000000000009, 0.80000000000000004,
4648           1.5707963267948966 },
4649 };
4650 const double toler159 = 2.5000000000000020e-13;
4651
4652 // Test data for k=0.60000000000000009, nu=0.90000000000000002.
4653 // max(|f - f_GSL|): 4.4408920985006262e-16
4654 // max(|f - f_GSL| / |f_GSL|): 3.5585887739668036e-16
4655 const testcase_ellint_3<double>
4656 data160[10] =
4657 {
4658   { 0.0000000000000000, 0.60000000000000009, 0.90000000000000002,
4659           0.0000000000000000 },
4660   { 0.17328652344890030, 0.60000000000000009, 0.90000000000000002,
4661           0.17453292519943295 },
4662   { 0.33973880062929018, 0.60000000000000009, 0.90000000000000002,
4663           0.34906585039886590 },
4664   { 0.49515092233122743, 0.60000000000000009, 0.90000000000000002,
4665           0.52359877559829882 },
4666   { 0.63864042139737043, 0.60000000000000009, 0.90000000000000002,
4667           0.69813170079773179 },
4668   { 0.77167205646538850, 0.60000000000000009, 0.90000000000000002,
4669           0.87266462599716477 },
4670   { 0.89673202848034383, 0.60000000000000009, 0.90000000000000002,
4671           1.0471975511965976 },
4672   { 1.0163984492661304, 0.60000000000000009, 0.90000000000000002,
4673           1.2217304763960306 },
4674   { 1.1328845785162431, 0.60000000000000009, 0.90000000000000002,
4675           1.3962634015954636 },
4676   { 1.2479362973851873, 0.60000000000000009, 0.90000000000000002,
4677           1.5707963267948966 },
4678 };
4679 const double toler160 = 2.5000000000000020e-13;
4680
4681 // Test data for k=0.69999999999999996, nu=0.0000000000000000.
4682 // max(|f - f_GSL|): 3.3306690738754696e-16
4683 // max(|f - f_GSL| / |f_GSL|): 3.5930208052157665e-16
4684 const testcase_ellint_3<double>
4685 data161[10] =
4686 {
4687   { 0.0000000000000000, 0.69999999999999996, 0.0000000000000000,
4688           0.0000000000000000 },
4689   { 0.17496737466916723, 0.69999999999999996, 0.0000000000000000,
4690           0.17453292519943295 },
4691   { 0.35254687535677925, 0.69999999999999996, 0.0000000000000000,
4692           0.34906585039886590 },
4693   { 0.53536740275997119, 0.69999999999999996, 0.0000000000000000,
4694           0.52359877559829882 },
4695   { 0.72603797651684454, 0.69999999999999996, 0.0000000000000000,
4696           0.69813170079773179 },
4697   { 0.92698296348313458, 0.69999999999999996, 0.0000000000000000,
4698           0.87266462599716477 },
4699   { 1.1400447527693316, 0.69999999999999996, 0.0000000000000000,
4700           1.0471975511965976 },
4701   { 1.3657668117194073, 0.69999999999999996, 0.0000000000000000,
4702           1.2217304763960306 },
4703   { 1.6024686895959159, 0.69999999999999996, 0.0000000000000000,
4704           1.3962634015954636 },
4705   { 1.8456939983747236, 0.69999999999999996, 0.0000000000000000,
4706           1.5707963267948966 },
4707 };
4708 const double toler161 = 2.5000000000000020e-13;
4709
4710 // Test data for k=0.69999999999999996, nu=0.10000000000000001.
4711 // max(|f - f_GSL|): 3.3306690738754696e-16
4712 // max(|f - f_GSL| / |f_GSL|): 3.6735282577377367e-16
4713 const testcase_ellint_3<double>
4714 data162[10] =
4715 {
4716   { 0.0000000000000000, 0.69999999999999996, 0.10000000000000001,
4717           0.0000000000000000 },
4718   { 0.17479076384884684, 0.69999999999999996, 0.10000000000000001,
4719           0.17453292519943295 },
4720   { 0.35114844900396364, 0.69999999999999996, 0.10000000000000001,
4721           0.34906585039886590 },
4722   { 0.53072776947527001, 0.69999999999999996, 0.10000000000000001,
4723           0.52359877559829882 },
4724   { 0.71530198262386235, 0.69999999999999996, 0.10000000000000001,
4725           0.69813170079773179 },
4726   { 0.90666760677828306, 0.69999999999999996, 0.10000000000000001,
4727           0.87266462599716477 },
4728   { 1.1063366517438080, 0.69999999999999996, 0.10000000000000001,
4729           1.0471975511965976 },
4730   { 1.3149477243092149, 0.69999999999999996, 0.10000000000000001,
4731           1.2217304763960306 },
4732   { 1.5314886725038925, 0.69999999999999996, 0.10000000000000001,
4733           1.3962634015954636 },
4734   { 1.7528050171757608, 0.69999999999999996, 0.10000000000000001,
4735           1.5707963267948966 },
4736 };
4737 const double toler162 = 2.5000000000000020e-13;
4738
4739 // Test data for k=0.69999999999999996, nu=0.20000000000000001.
4740 // max(|f - f_GSL|): 3.3306690738754696e-16
4741 // max(|f - f_GSL| / |f_GSL|): 3.7517969287516802e-16
4742 const testcase_ellint_3<double>
4743 data163[10] =
4744 {
4745   { 0.0000000000000000, 0.69999999999999996, 0.20000000000000001,
4746           0.0000000000000000 },
4747   { 0.17461479077791475, 0.69999999999999996, 0.20000000000000001,
4748           0.17453292519943295 },
4749   { 0.34976950621407538, 0.69999999999999996, 0.20000000000000001,
4750           0.34906585039886590 },
4751   { 0.52622533231350177, 0.69999999999999996, 0.20000000000000001,
4752           0.52359877559829882 },
4753   { 0.70508774017895215, 0.69999999999999996, 0.20000000000000001,
4754           0.69813170079773179 },
4755   { 0.88775302531730294, 0.69999999999999996, 0.20000000000000001,
4756           0.87266462599716477 },
4757   { 1.0756195476149006, 0.69999999999999996, 0.20000000000000001,
4758           1.0471975511965976 },
4759   { 1.2695349716654374, 0.69999999999999996, 0.20000000000000001,
4760           1.2217304763960306 },
4761   { 1.4690814617070540, 0.69999999999999996, 0.20000000000000001,
4762           1.3962634015954636 },
4763   { 1.6721098780092145, 0.69999999999999996, 0.20000000000000001,
4764           1.5707963267948966 },
4765 };
4766 const double toler163 = 2.5000000000000020e-13;
4767
4768 // Test data for k=0.69999999999999996, nu=0.29999999999999999.
4769 // max(|f - f_GSL|): 4.4408920985006262e-16
4770 // max(|f - f_GSL| / |f_GSL|): 3.8280039841080712e-16
4771 const testcase_ellint_3<double>
4772 data164[10] =
4773 {
4774   { 0.0000000000000000, 0.69999999999999996, 0.29999999999999999,
4775           0.0000000000000000 },
4776   { 0.17443945136076175, 0.69999999999999996, 0.29999999999999999,
4777           0.17453292519943295 },
4778   { 0.34840956983535287, 0.69999999999999996, 0.29999999999999999,
4779           0.34906585039886590 },
4780   { 0.52185308551329168, 0.69999999999999996, 0.29999999999999999,
4781           0.52359877559829882 },
4782   { 0.69535240431168255, 0.69999999999999996, 0.29999999999999999,
4783           0.69813170079773179 },
4784   { 0.87007983473964923, 0.69999999999999996, 0.29999999999999999,
4785           0.87266462599716477 },
4786   { 1.0474657975577066, 0.69999999999999996, 0.29999999999999999,
4787           1.0471975511965976 },
4788   { 1.2286225419931891, 0.69999999999999996, 0.29999999999999999,
4789           1.2217304763960306 },
4790   { 1.4136490671013271, 0.69999999999999996, 0.29999999999999999,
4791           1.3962634015954636 },
4792   { 1.6011813647733213, 0.69999999999999996, 0.29999999999999999,
4793           1.5707963267948966 },
4794 };
4795 const double toler164 = 2.5000000000000020e-13;
4796
4797 // Test data for k=0.69999999999999996, nu=0.40000000000000002.
4798 // max(|f - f_GSL|): 4.4408920985006262e-16
4799 // max(|f - f_GSL| / |f_GSL|): 4.3472957053482092e-16
4800 const testcase_ellint_3<double>
4801 data165[10] =
4802 {
4803   { 0.0000000000000000, 0.69999999999999996, 0.40000000000000002,
4804           0.0000000000000000 },
4805   { 0.17426474153983229, 0.69999999999999996, 0.40000000000000002,
4806           0.17453292519943295 },
4807   { 0.34706817945773732, 0.69999999999999996, 0.40000000000000002,
4808           0.34906585039886590 },
4809   { 0.51760452851738148, 0.69999999999999996, 0.40000000000000002,
4810           0.52359877559829882 },
4811   { 0.68605801534722755, 0.69999999999999996, 0.40000000000000002,
4812           0.69813170079773179 },
4813   { 0.85351339387296532, 0.69999999999999996, 0.40000000000000002,
4814           0.87266462599716477 },
4815   { 1.0215297967969539, 0.69999999999999996, 0.40000000000000002,
4816           1.0471975511965976 },
4817   { 1.1915051074460530, 0.69999999999999996, 0.40000000000000002,
4818           1.2217304763960306 },
4819   { 1.3639821911744707, 0.69999999999999996, 0.40000000000000002,
4820           1.3962634015954636 },
4821   { 1.5382162002954762, 0.69999999999999996, 0.40000000000000002,
4822           1.5707963267948966 },
4823 };
4824 const double toler165 = 2.5000000000000020e-13;
4825
4826 // Test data for k=0.69999999999999996, nu=0.50000000000000000.
4827 // max(|f - f_GSL|): 3.3306690738754696e-16
4828 // max(|f - f_GSL| / |f_GSL|): 3.9748346743390620e-16
4829 const testcase_ellint_3<double>
4830 data166[10] =
4831 {
4832   { 0.0000000000000000, 0.69999999999999996, 0.50000000000000000,
4833           0.0000000000000000 },
4834   { 0.17409065729516096, 0.69999999999999996, 0.50000000000000000,
4835           0.17453292519943295 },
4836   { 0.34574489064986091, 0.69999999999999996, 0.50000000000000000,
4837           0.34906585039886590 },
4838   { 0.51347361925579782, 0.69999999999999996, 0.50000000000000000,
4839           0.52359877559829882 },
4840   { 0.67717079489579279, 0.69999999999999996, 0.50000000000000000,
4841           0.69813170079773179 },
4842   { 0.83793902055292280, 0.69999999999999996, 0.50000000000000000,
4843           0.87266462599716477 },
4844   { 0.99752863545289705, 0.69999999999999996, 0.50000000000000000,
4845           1.0471975511965976 },
4846   { 1.1576240080401501, 0.69999999999999996, 0.50000000000000000,
4847           1.2217304763960306 },
4848   { 1.3191464023923762, 0.69999999999999996, 0.50000000000000000,
4849           1.3962634015954636 },
4850   { 1.4818433192178544, 0.69999999999999996, 0.50000000000000000,
4851           1.5707963267948966 },
4852 };
4853 const double toler166 = 2.5000000000000020e-13;
4854
4855 // Test data for k=0.69999999999999996, nu=0.59999999999999998.
4856 // max(|f - f_GSL|): 3.3306690738754696e-16
4857 // max(|f - f_GSL| / |f_GSL|): 4.0457157538295173e-16
4858 const testcase_ellint_3<double>
4859 data167[10] =
4860 {
4861   { 0.0000000000000000, 0.69999999999999996, 0.59999999999999998,
4862           0.0000000000000000 },
4863   { 0.17391719464391614, 0.69999999999999996, 0.59999999999999998,
4864           0.17453292519943295 },
4865   { 0.34443927423869031, 0.69999999999999996, 0.59999999999999998,
4866           0.34906585039886590 },
4867   { 0.50945473266486063, 0.69999999999999996, 0.59999999999999998,
4868           0.52359877559829882 },
4869   { 0.66866056326513812, 0.69999999999999996, 0.59999999999999998,
4870           0.69813170079773179 },
4871   { 0.82325830002337352, 0.69999999999999996, 0.59999999999999998,
4872           0.87266462599716477 },
4873   { 0.97522808245669368, 0.69999999999999996, 0.59999999999999998,
4874           1.0471975511965976 },
4875   { 1.1265300613705285, 0.69999999999999996, 0.59999999999999998,
4876           1.2217304763960306 },
4877   { 1.2784066076152001, 0.69999999999999996, 0.59999999999999998,
4878           1.3962634015954636 },
4879   { 1.4309994736080540, 0.69999999999999996, 0.59999999999999998,
4880           1.5707963267948966 },
4881 };
4882 const double toler167 = 2.5000000000000020e-13;
4883
4884 // Test data for k=0.69999999999999996, nu=0.69999999999999996.
4885 // max(|f - f_GSL|): 4.4408920985006262e-16
4886 // max(|f - f_GSL| / |f_GSL|): 5.4867405596732161e-16
4887 const testcase_ellint_3<double>
4888 data168[10] =
4889 {
4890   { 0.0000000000000000, 0.69999999999999996, 0.69999999999999996,
4891           0.0000000000000000 },
4892   { 0.17374434963995031, 0.69999999999999996, 0.69999999999999996,
4893           0.17453292519943295 },
4894   { 0.34315091562900674, 0.69999999999999996, 0.69999999999999996,
4895           0.34906585039886590 },
4896   { 0.50554262375653347, 0.69999999999999996, 0.69999999999999996,
4897           0.52359877559829882 },
4898   { 0.66050025406305801, 0.69999999999999996, 0.69999999999999996,
4899           0.69813170079773179 },
4900   { 0.80938620118847404, 0.69999999999999996, 0.69999999999999996,
4901           0.87266462599716477 },
4902   { 0.95443223855852144, 0.69999999999999996, 0.69999999999999996,
4903           1.0471975511965976 },
4904   { 1.0978573207128304, 0.69999999999999996, 0.69999999999999996,
4905           1.2217304763960306 },
4906   { 1.2411754575007123, 0.69999999999999996, 0.69999999999999996,
4907           1.3962634015954636 },
4908   { 1.3848459188329196, 0.69999999999999996, 0.69999999999999996,
4909           1.5707963267948966 },
4910 };
4911 const double toler168 = 2.5000000000000020e-13;
4912
4913 // Test data for k=0.69999999999999996, nu=0.80000000000000004.
4914 // max(|f - f_GSL|): 4.4408920985006262e-16
4915 // max(|f - f_GSL| / |f_GSL|): 4.1829502028913879e-16
4916 const testcase_ellint_3<double>
4917 data169[10] =
4918 {
4919   { 0.0000000000000000, 0.69999999999999996, 0.80000000000000004,
4920           0.0000000000000000 },
4921   { 0.17357211837335740, 0.69999999999999996, 0.80000000000000004,
4922           0.17453292519943295 },
4923   { 0.34187941416012108, 0.69999999999999996, 0.80000000000000004,
4924           0.34906585039886590 },
4925   { 0.50173239465478259, 0.69999999999999996, 0.80000000000000004,
4926           0.52359877559829882 },
4927   { 0.65266550725988315, 0.69999999999999996, 0.80000000000000004,
4928           0.69813170079773179 },
4929   { 0.79624879865249298, 0.69999999999999996, 0.80000000000000004,
4930           0.87266462599716477 },
4931   { 0.93497577043296920, 0.69999999999999996, 0.80000000000000004,
4932           1.0471975511965976 },
4933   { 1.0713041566930750, 0.69999999999999996, 0.80000000000000004,
4934           1.2217304763960306 },
4935   { 1.2069772023255654, 0.69999999999999996, 0.80000000000000004,
4936           1.3962634015954636 },
4937   { 1.3427110650397531, 0.69999999999999996, 0.80000000000000004,
4938           1.5707963267948966 },
4939 };
4940 const double toler169 = 2.5000000000000020e-13;
4941
4942 // Test data for k=0.69999999999999996, nu=0.90000000000000002.
4943 // max(|f - f_GSL|): 3.3306690738754696e-16
4944 // max(|f - f_GSL| / |f_GSL|): 4.2494869624129105e-16
4945 const testcase_ellint_3<double>
4946 data170[10] =
4947 {
4948   { 0.0000000000000000, 0.69999999999999996, 0.90000000000000002,
4949           0.0000000000000000 },
4950   { 0.17340049697003637, 0.69999999999999996, 0.90000000000000002,
4951           0.17453292519943295 },
4952   { 0.34062438249741556, 0.69999999999999996, 0.90000000000000002,
4953           0.34906585039886590 },
4954   { 0.49801946510076867, 0.69999999999999996, 0.90000000000000002,
4955           0.52359877559829882 },
4956   { 0.64513432604750476, 0.69999999999999996, 0.90000000000000002,
4957           0.69813170079773179 },
4958   { 0.78378145487573758, 0.69999999999999996, 0.90000000000000002,
4959           0.87266462599716477 },
4960   { 0.91671799500854623, 0.69999999999999996, 0.90000000000000002,
4961           1.0471975511965976 },
4962   { 1.0466193579463123, 0.69999999999999996, 0.90000000000000002,
4963           1.2217304763960306 },
4964   { 1.1754218079199146, 0.69999999999999996, 0.90000000000000002,
4965           1.3962634015954636 },
4966   { 1.3040500499695913, 0.69999999999999996, 0.90000000000000002,
4967           1.5707963267948966 },
4968 };
4969 const double toler170 = 2.5000000000000020e-13;
4970
4971 // Test data for k=0.80000000000000004, nu=0.0000000000000000.
4972 // max(|f - f_GSL|): 4.4408920985006262e-16
4973 // max(|f - f_GSL| / |f_GSL|): 4.1175183168766718e-16
4974 const testcase_ellint_3<double>
4975 data171[10] =
4976 {
4977   { 0.0000000000000000, 0.80000000000000004, 0.0000000000000000,
4978           0.0000000000000000 },
4979   { 0.17510154241338899, 0.80000000000000004, 0.0000000000000000,
4980           0.17453292519943295 },
4981   { 0.35365068839779390, 0.80000000000000004, 0.0000000000000000,
4982           0.34906585039886590 },
4983   { 0.53926804409084550, 0.80000000000000004, 0.0000000000000000,
4984           0.52359877559829882 },
4985   { 0.73587926028070361, 0.80000000000000004, 0.0000000000000000,
4986           0.69813170079773179 },
4987   { 0.94770942970071170, 0.80000000000000004, 0.0000000000000000,
4988           0.87266462599716477 },
4989   { 1.1789022995388236, 0.80000000000000004, 0.0000000000000000,
4990           1.0471975511965976 },
4991   { 1.4323027881876009, 0.80000000000000004, 0.0000000000000000,
4992           1.2217304763960306 },
4993   { 1.7069629739121674, 0.80000000000000004, 0.0000000000000000,
4994           1.3962634015954636 },
4995   { 1.9953027776647296, 0.80000000000000004, 0.0000000000000000,
4996           1.5707963267948966 },
4997 };
4998 const double toler171 = 2.5000000000000020e-13;
4999
5000 // Test data for k=0.80000000000000004, nu=0.10000000000000001.
5001 // max(|f - f_GSL|): 4.4408920985006262e-16
5002 // max(|f - f_GSL| / |f_GSL|): 4.1537164503193145e-16
5003 const testcase_ellint_3<double>
5004 data172[10] =
5005 {
5006   { 0.0000000000000000, 0.80000000000000004, 0.10000000000000001,
5007           0.0000000000000000 },
5008   { 0.17492468824017163, 0.80000000000000004, 0.10000000000000001,
5009           0.17453292519943295 },
5010   { 0.35224443521476911, 0.80000000000000004, 0.10000000000000001,
5011           0.34906585039886590 },
5012   { 0.53456851853226950, 0.80000000000000004, 0.10000000000000001,
5013           0.52359877559829882 },
5014   { 0.72488875602364922, 0.80000000000000004, 0.10000000000000001,
5015           0.69813170079773179 },
5016   { 0.92661354274638952, 0.80000000000000004, 0.10000000000000001,
5017           0.87266462599716477 },
5018   { 1.1432651144499075, 0.80000000000000004, 0.10000000000000001,
5019           1.0471975511965976 },
5020   { 1.3774479927211429, 0.80000000000000004, 0.10000000000000001,
5021           1.2217304763960306 },
5022   { 1.6287092337196041, 0.80000000000000004, 0.10000000000000001,
5023           1.3962634015954636 },
5024   { 1.8910755418379521, 0.80000000000000004, 0.10000000000000001,
5025           1.5707963267948966 },
5026 };
5027 const double toler172 = 2.5000000000000020e-13;
5028
5029 // Test data for k=0.80000000000000004, nu=0.20000000000000001.
5030 // max(|f - f_GSL|): 4.4408920985006262e-16
5031 // max(|f - f_GSL| / |f_GSL|): 4.1894552974436829e-16
5032 const testcase_ellint_3<double>
5033 data173[10] =
5034 {
5035   { 0.0000000000000000, 0.80000000000000004, 0.20000000000000001,
5036           0.0000000000000000 },
5037   { 0.17474847286224940, 0.80000000000000004, 0.20000000000000001,
5038           0.17453292519943295 },
5039   { 0.35085779529084682, 0.80000000000000004, 0.20000000000000001,
5040           0.34906585039886590 },
5041   { 0.53000829263059146, 0.80000000000000004, 0.20000000000000001,
5042           0.52359877559829882 },
5043   { 0.71443466027453384, 0.80000000000000004, 0.20000000000000001,
5044           0.69813170079773179 },
5045   { 0.90698196872715420, 0.80000000000000004, 0.20000000000000001,
5046           0.87266462599716477 },
5047   { 1.1108198200558579, 0.80000000000000004, 0.20000000000000001,
5048           1.0471975511965976 },
5049   { 1.3284988909963957, 0.80000000000000004, 0.20000000000000001,
5050           1.2217304763960306 },
5051   { 1.5600369318140328, 0.80000000000000004, 0.20000000000000001,
5052           1.3962634015954636 },
5053   { 1.8007226661734588, 0.80000000000000004, 0.20000000000000001,
5054           1.5707963267948966 },
5055 };
5056 const double toler173 = 2.5000000000000020e-13;
5057
5058 // Test data for k=0.80000000000000004, nu=0.29999999999999999.
5059 // max(|f - f_GSL|): 4.4408920985006262e-16
5060 // max(|f - f_GSL| / |f_GSL|): 4.2247517409029886e-16
5061 const testcase_ellint_3<double>
5062 data174[10] =
5063 {
5064   { 0.0000000000000000, 0.80000000000000004, 0.29999999999999999,
5065           0.0000000000000000 },
5066   { 0.17457289217669889, 0.80000000000000004, 0.29999999999999999,
5067           0.17453292519943295 },
5068   { 0.34949028801501258, 0.80000000000000004, 0.29999999999999999,
5069           0.34906585039886590 },
5070   { 0.52558024362769307, 0.80000000000000004, 0.29999999999999999,
5071           0.52359877559829882 },
5072   { 0.70447281740094891, 0.80000000000000004, 0.29999999999999999,
5073           0.69813170079773179 },
5074   { 0.88864745641528986, 0.80000000000000004, 0.29999999999999999,
5075           0.87266462599716477 },
5076   { 1.0811075819341462, 0.80000000000000004, 0.29999999999999999,
5077           1.0471975511965976 },
5078   { 1.2844589654082377, 0.80000000000000004, 0.29999999999999999,
5079           1.2217304763960306 },
5080   { 1.4991461361277847, 0.80000000000000004, 0.29999999999999999,
5081           1.3962634015954636 },
5082   { 1.7214611048717301, 0.80000000000000004, 0.29999999999999999,
5083           1.5707963267948966 },
5084 };
5085 const double toler174 = 2.5000000000000020e-13;
5086
5087 // Test data for k=0.80000000000000004, nu=0.40000000000000002.
5088 // max(|f - f_GSL|): 4.4408920985006262e-16
5089 // max(|f - f_GSL| / |f_GSL|): 4.2596216594752862e-16
5090 const testcase_ellint_3<double>
5091 data175[10] =
5092 {
5093   { 0.0000000000000000, 0.80000000000000004, 0.40000000000000002,
5094           0.0000000000000000 },
5095   { 0.17439794211872175, 0.80000000000000004, 0.40000000000000002,
5096           0.17453292519943295 },
5097   { 0.34814144964568972, 0.80000000000000004, 0.40000000000000002,
5098           0.34906585039886590 },
5099   { 0.52127776285273064, 0.80000000000000004, 0.40000000000000002,
5100           0.52359877559829882 },
5101   { 0.69496411438966588, 0.80000000000000004, 0.40000000000000002,
5102           0.69813170079773179 },
5103   { 0.87146878427509589, 0.80000000000000004, 0.40000000000000002,
5104           0.87266462599716477 },
5105   { 1.0537579024937762, 0.80000000000000004, 0.40000000000000002,
5106           1.0471975511965976 },
5107   { 1.2445534387922637, 0.80000000000000004, 0.40000000000000002,
5108           1.2217304763960306 },
5109   { 1.4446769766361993, 0.80000000000000004, 0.40000000000000002,
5110           1.3962634015954636 },
5111   { 1.6512267838651289, 0.80000000000000004, 0.40000000000000002,
5112           1.5707963267948966 },
5113 };
5114 const double toler175 = 2.5000000000000020e-13;
5115
5116 // Test data for k=0.80000000000000004, nu=0.50000000000000000.
5117 // max(|f - f_GSL|): 4.4408920985006262e-16
5118 // max(|f - f_GSL| / |f_GSL|): 4.2940800093915668e-16
5119 const testcase_ellint_3<double>
5120 data176[10] =
5121 {
5122   { 0.0000000000000000, 0.80000000000000004, 0.50000000000000000,
5123           0.0000000000000000 },
5124   { 0.17422361866118044, 0.80000000000000004, 0.50000000000000000,
5125           0.17453292519943295 },
5126   { 0.34681083254170475, 0.80000000000000004, 0.50000000000000000,
5127           0.34906585039886590 },
5128   { 0.51709470815494440, 0.80000000000000004, 0.50000000000000000,
5129           0.52359877559829882 },
5130   { 0.68587375344080237, 0.80000000000000004, 0.50000000000000000,
5131           0.69813170079773179 },
5132   { 0.85532571852810624, 0.80000000000000004, 0.50000000000000000,
5133           0.87266462599716477 },
5134   { 1.0284677391874903, 0.80000000000000004, 0.50000000000000000,
5135           1.0471975511965976 },
5136   { 1.2081693942686225, 0.80000000000000004, 0.50000000000000000,
5137           1.2217304763960306 },
5138   { 1.3955803006426311, 0.80000000000000004, 0.50000000000000000,
5139           1.3962634015954636 },
5140   { 1.5884528947755532, 0.80000000000000004, 0.50000000000000000,
5141           1.5707963267948966 },
5142 };
5143 const double toler176 = 2.5000000000000020e-13;
5144
5145 // Test data for k=0.80000000000000004, nu=0.59999999999999998.
5146 // max(|f - f_GSL|): 4.4408920985006262e-16
5147 // max(|f - f_GSL| / |f_GSL|): 4.3281408974056389e-16
5148 const testcase_ellint_3<double>
5149 data177[10] =
5150 {
5151   { 0.0000000000000000, 0.80000000000000004, 0.59999999999999998,
5152           0.0000000000000000 },
5153   { 0.17404991781414089, 0.80000000000000004, 0.59999999999999998,
5154           0.17453292519943295 },
5155   { 0.34549800443625167, 0.80000000000000004, 0.59999999999999998,
5156           0.34906585039886590 },
5157   { 0.51302536167001545, 0.80000000000000004, 0.59999999999999998,
5158           0.52359877559829882 },
5159   { 0.67717065003912236, 0.80000000000000004, 0.59999999999999998,
5160           0.69813170079773179 },
5161   { 0.84011512421134416, 0.80000000000000004, 0.59999999999999998,
5162           0.87266462599716477 },
5163   { 1.0049863847088740, 0.80000000000000004, 0.59999999999999998,
5164           1.0471975511965976 },
5165   { 1.1748145941898920, 0.80000000000000004, 0.59999999999999998,
5166           1.2217304763960306 },
5167   { 1.3510319699755071, 0.80000000000000004, 0.59999999999999998,
5168           1.3962634015954636 },
5169   { 1.5319262547427865, 0.80000000000000004, 0.59999999999999998,
5170           1.5707963267948966 },
5171 };
5172 const double toler177 = 2.5000000000000020e-13;
5173
5174 // Test data for k=0.80000000000000004, nu=0.69999999999999996.
5175 // max(|f - f_GSL|): 2.2204460492503131e-16
5176 // max(|f - f_GSL| / |f_GSL|): 4.3618176466061808e-16
5177 const testcase_ellint_3<double>
5178 data178[10] =
5179 {
5180   { 0.0000000000000000, 0.80000000000000004, 0.69999999999999996,
5181           0.0000000000000000 },
5182   { 0.17387683562442199, 0.80000000000000004, 0.69999999999999996,
5183           0.17453292519943295 },
5184   { 0.34420254775101611, 0.80000000000000004, 0.69999999999999996,
5185           0.34906585039886590 },
5186   { 0.50906439222143673, 0.80000000000000004, 0.69999999999999996,
5187           0.52359877559829882 },
5188   { 0.66882693152688422, 0.80000000000000004, 0.69999999999999996,
5189           0.69813170079773179 },
5190   { 0.82574792844091316, 0.80000000000000004, 0.69999999999999996,
5191           0.87266462599716477 },
5192   { 0.98310431309490931, 0.80000000000000004, 0.69999999999999996,
5193           1.0471975511965976 },
5194   { 1.1440884535113258, 0.80000000000000004, 0.69999999999999996,
5195           1.2217304763960306 },
5196   { 1.3103743938952537, 0.80000000000000004, 0.69999999999999996,
5197           1.3962634015954636 },
5198   { 1.4806912324625332, 0.80000000000000004, 0.69999999999999996,
5199           1.5707963267948966 },
5200 };
5201 const double toler178 = 2.5000000000000020e-13;
5202
5203 // Test data for k=0.80000000000000004, nu=0.80000000000000004.
5204 // max(|f - f_GSL|): 4.4408920985006262e-16
5205 // max(|f - f_GSL| / |f_GSL|): 4.3951228558314112e-16
5206 const testcase_ellint_3<double>
5207 data179[10] =
5208 {
5209   { 0.0000000000000000, 0.80000000000000004, 0.80000000000000004,
5210           0.0000000000000000 },
5211   { 0.17370436817515203, 0.80000000000000004, 0.80000000000000004,
5212           0.17453292519943295 },
5213   { 0.34292405894783395, 0.80000000000000004, 0.80000000000000004,
5214           0.34906585039886590 },
5215   { 0.50520682176250076, 0.80000000000000004, 0.80000000000000004,
5216           0.52359877559829882 },
5217   { 0.66081751679736178, 0.80000000000000004, 0.80000000000000004,
5218           0.69813170079773179 },
5219   { 0.81214672249355102, 0.80000000000000004, 0.80000000000000004,
5220           0.87266462599716477 },
5221   { 0.96264481387685552, 0.80000000000000004, 0.80000000000000004,
5222           1.0471975511965976 },
5223   { 1.1156611352656258, 0.80000000000000004, 0.80000000000000004,
5224           1.2217304763960306 },
5225   { 1.2730756225143889, 0.80000000000000004, 0.80000000000000004,
5226           1.3962634015954636 },
5227   { 1.4339837018309471, 0.80000000000000004, 0.80000000000000004,
5228           1.5707963267948966 },
5229 };
5230 const double toler179 = 2.5000000000000020e-13;
5231
5232 // Test data for k=0.80000000000000004, nu=0.90000000000000002.
5233 // max(|f - f_GSL|): 3.3306690738754696e-16
5234 // max(|f - f_GSL| / |f_GSL|): 4.4280684534289690e-16
5235 const testcase_ellint_3<double>
5236 data180[10] =
5237 {
5238   { 0.0000000000000000, 0.80000000000000004, 0.90000000000000002,
5239           0.0000000000000000 },
5240   { 0.17353251158533151, 0.80000000000000004, 0.90000000000000002,
5241           0.17453292519943295 },
5242   { 0.34166214791545768, 0.80000000000000004, 0.90000000000000002,
5243           0.34906585039886590 },
5244   { 0.50144799535130569, 0.80000000000000004, 0.90000000000000002,
5245           0.52359877559829882 },
5246   { 0.65311976193814425, 0.80000000000000004, 0.90000000000000002,
5247           0.69813170079773179 },
5248   { 0.79924384892320866, 0.80000000000000004, 0.90000000000000002,
5249           0.87266462599716477 },
5250   { 0.94345762353365603, 0.80000000000000004, 0.90000000000000002,
5251           1.0471975511965976 },
5252   { 1.0892582069219161, 0.80000000000000004, 0.90000000000000002,
5253           1.2217304763960306 },
5254   { 1.2387000876610268, 0.80000000000000004, 0.90000000000000002,
5255           1.3962634015954636 },
5256   { 1.3911845406776222, 0.80000000000000004, 0.90000000000000002,
5257           1.5707963267948966 },
5258 };
5259 const double toler180 = 2.5000000000000020e-13;
5260
5261 // Test data for k=0.89999999999999991, nu=0.0000000000000000.
5262 // max(|f - f_GSL|): 8.8817841970012523e-16
5263 // max(|f - f_GSL| / |f_GSL|): 3.8945813740035884e-16
5264 const testcase_ellint_3<double>
5265 data181[10] =
5266 {
5267   { 0.0000000000000000, 0.89999999999999991, 0.0000000000000000,
5268           0.0000000000000000 },
5269   { 0.17525427376115024, 0.89999999999999991, 0.0000000000000000,
5270           0.17453292519943295 },
5271   { 0.35492464591297446, 0.89999999999999991, 0.0000000000000000,
5272           0.34906585039886590 },
5273   { 0.54388221416157112, 0.89999999999999991, 0.0000000000000000,
5274           0.52359877559829882 },
5275   { 0.74797400423532490, 0.89999999999999991, 0.0000000000000000,
5276           0.69813170079773179 },
5277   { 0.97463898451966458, 0.89999999999999991, 0.0000000000000000,
5278           0.87266462599716477 },
5279   { 1.2334463254523440, 0.89999999999999991, 0.0000000000000000,
5280           1.0471975511965976 },
5281   { 1.5355247765594910, 0.89999999999999991, 0.0000000000000000,
5282           1.2217304763960306 },
5283   { 1.8882928567775117, 0.89999999999999991, 0.0000000000000000,
5284           1.3962634015954636 },
5285   { 2.2805491384227703, 0.89999999999999991, 0.0000000000000000,
5286           1.5707963267948966 },
5287 };
5288 const double toler181 = 2.5000000000000020e-13;
5289
5290 // Test data for k=0.89999999999999991, nu=0.10000000000000001.
5291 // max(|f - f_GSL|): 8.8817841970012523e-16
5292 // max(|f - f_GSL| / |f_GSL|): 4.1237990617685137e-16
5293 const testcase_ellint_3<double>
5294 data182[10] =
5295 {
5296   { 0.0000000000000000, 0.89999999999999991, 0.10000000000000001,
5297           0.0000000000000000 },
5298   { 0.17507714233254656, 0.89999999999999991, 0.10000000000000001,
5299           0.17453292519943295 },
5300   { 0.35350932904326521, 0.89999999999999991, 0.10000000000000001,
5301           0.34906585039886590 },
5302   { 0.53911129989870976, 0.89999999999999991, 0.10000000000000001,
5303           0.52359877559829882 },
5304   { 0.73666644254508395, 0.89999999999999991, 0.10000000000000001,
5305           0.69813170079773179 },
5306   { 0.95250736612100195, 0.89999999999999991, 0.10000000000000001,
5307           0.87266462599716477 },
5308   { 1.1950199550905594, 0.89999999999999991, 0.10000000000000001,
5309           1.0471975511965976 },
5310   { 1.4741687286340848, 0.89999999999999991, 0.10000000000000001,
5311           1.2217304763960306 },
5312   { 1.7968678183506053, 0.89999999999999991, 0.10000000000000001,
5313           1.3962634015954636 },
5314   { 2.1537868513875287, 0.89999999999999991, 0.10000000000000001,
5315           1.5707963267948966 },
5316 };
5317 const double toler182 = 2.5000000000000020e-13;
5318
5319 // Test data for k=0.89999999999999991, nu=0.20000000000000001.
5320 // max(|f - f_GSL|): 8.8817841970012523e-16
5321 // max(|f - f_GSL| / |f_GSL|): 4.3446165733924066e-16
5322 const testcase_ellint_3<double>
5323 data183[10] =
5324 {
5325   { 0.0000000000000000, 0.89999999999999991, 0.20000000000000001,
5326           0.0000000000000000 },
5327   { 0.17490065089140927, 0.89999999999999991, 0.20000000000000001,
5328           0.17453292519943295 },
5329   { 0.35211377590661436, 0.89999999999999991, 0.20000000000000001,
5330           0.34906585039886590 },
5331   { 0.53448220334204100, 0.89999999999999991, 0.20000000000000001,
5332           0.52359877559829882 },
5333   { 0.72591368943179579, 0.89999999999999991, 0.20000000000000001,
5334           0.69813170079773179 },
5335   { 0.93192539780038763, 0.89999999999999991, 0.20000000000000001,
5336           0.87266462599716477 },
5337   { 1.1600809679692683, 0.89999999999999991, 0.20000000000000001,
5338           1.0471975511965976 },
5339   { 1.4195407225882508, 0.89999999999999991, 0.20000000000000001,
5340           1.2217304763960306 },
5341   { 1.7168966476424521, 0.89999999999999991, 0.20000000000000001,
5342           1.3962634015954636 },
5343   { 2.0443194576468895, 0.89999999999999991, 0.20000000000000001,
5344           1.5707963267948966 },
5345 };
5346 const double toler183 = 2.5000000000000020e-13;
5347
5348 // Test data for k=0.89999999999999991, nu=0.29999999999999999.
5349 // max(|f - f_GSL|): 1.1102230246251565e-15
5350 // max(|f - f_GSL| / |f_GSL|): 5.6974600067013622e-16
5351 const testcase_ellint_3<double>
5352 data184[10] =
5353 {
5354   { 0.0000000000000000, 0.89999999999999991, 0.29999999999999999,
5355           0.0000000000000000 },
5356   { 0.17472479532647531, 0.89999999999999991, 0.29999999999999999,
5357           0.17453292519943295 },
5358   { 0.35073750187374114, 0.89999999999999991, 0.29999999999999999,
5359           0.34906585039886590 },
5360   { 0.52998766129466957, 0.89999999999999991, 0.29999999999999999,
5361           0.52359877559829882 },
5362   { 0.71566993548699553, 0.89999999999999991, 0.29999999999999999,
5363           0.69813170079773179 },
5364   { 0.91271517762560195, 0.89999999999999991, 0.29999999999999999,
5365           0.87266462599716477 },
5366   { 1.1281241199843370, 0.89999999999999991, 0.29999999999999999,
5367           1.0471975511965976 },
5368   { 1.3704929576917448, 0.89999999999999991, 0.29999999999999999,
5369           1.2217304763960306 },
5370   { 1.6461981511487711, 0.89999999999999991, 0.29999999999999999,
5371           1.3962634015954636 },
5372   { 1.9486280260314426, 0.89999999999999991, 0.29999999999999999,
5373           1.5707963267948966 },
5374 };
5375 const double toler184 = 2.5000000000000020e-13;
5376
5377 // Test data for k=0.89999999999999991, nu=0.40000000000000002.
5378 // max(|f - f_GSL|): 8.8817841970012523e-16
5379 // max(|f - f_GSL| / |f_GSL|): 4.7646208744449464e-16
5380 const testcase_ellint_3<double>
5381 data185[10] =
5382 {
5383   { 0.0000000000000000, 0.89999999999999991, 0.40000000000000002,
5384           0.0000000000000000 },
5385   { 0.17454957156468837, 0.89999999999999991, 0.40000000000000002,
5386           0.17453292519943295 },
5387   { 0.34938003933330430, 0.89999999999999991, 0.40000000000000002,
5388           0.34906585039886590 },
5389   { 0.52562093533067433, 0.89999999999999991, 0.40000000000000002,
5390           0.52359877559829882 },
5391   { 0.70589461324915670, 0.89999999999999991, 0.40000000000000002,
5392           0.69813170079773179 },
5393   { 0.89472658511942849, 0.89999999999999991, 0.40000000000000002,
5394           0.87266462599716477 },
5395   { 1.0987419542323440, 0.89999999999999991, 0.40000000000000002,
5396           1.0471975511965976 },
5397   { 1.3261349565496301, 0.89999999999999991, 0.40000000000000002,
5398           1.2217304763960306 },
5399   { 1.5831293909853763, 0.89999999999999991, 0.40000000000000002,
5400           1.3962634015954636 },
5401   { 1.8641114227238351, 0.89999999999999991, 0.40000000000000002,
5402           1.5707963267948966 },
5403 };
5404 const double toler185 = 2.5000000000000020e-13;
5405
5406 // Test data for k=0.89999999999999991, nu=0.50000000000000000.
5407 // max(|f - f_GSL|): 8.8817841970012523e-16
5408 // max(|f - f_GSL| / |f_GSL|): 4.9652155758573562e-16
5409 const testcase_ellint_3<double>
5410 data186[10] =
5411 {
5412   { 0.0000000000000000, 0.89999999999999991, 0.50000000000000000,
5413           0.0000000000000000 },
5414   { 0.17437497557073334, 0.89999999999999991, 0.50000000000000000,
5415           0.17453292519943295 },
5416   { 0.34804093691586013, 0.89999999999999991, 0.50000000000000000,
5417           0.34906585039886590 },
5418   { 0.52137576320372891, 0.89999999999999991, 0.50000000000000000,
5419           0.52359877559829882 },
5420   { 0.69655163996912262, 0.89999999999999991, 0.50000000000000000,
5421           0.69813170079773179 },
5422   { 0.87783188683054236, 0.89999999999999991, 0.50000000000000000,
5423           0.87266462599716477 },
5424   { 1.0716015959755185, 0.89999999999999991, 0.50000000000000000,
5425           1.0471975511965976 },
5426   { 1.2857636916026749, 0.89999999999999991, 0.50000000000000000,
5427           1.2217304763960306 },
5428   { 1.5264263913252358, 0.89999999999999991, 0.50000000000000000,
5429           1.3962634015954636 },
5430   { 1.7888013241937863, 0.89999999999999991, 0.50000000000000000,
5431           1.5707963267948966 },
5432 };
5433 const double toler186 = 2.5000000000000020e-13;
5434
5435 // Test data for k=0.89999999999999991, nu=0.59999999999999998.
5436 // max(|f - f_GSL|): 6.6613381477509392e-16
5437 // max(|f - f_GSL| / |f_GSL|): 3.8702201113622378e-16
5438 const testcase_ellint_3<double>
5439 data187[10] =
5440 {
5441   { 0.0000000000000000, 0.89999999999999991, 0.59999999999999998,
5442           0.0000000000000000 },
5443   { 0.17420100334657812, 0.89999999999999991, 0.59999999999999998,
5444           0.17453292519943295 },
5445   { 0.34671975876122157, 0.89999999999999991, 0.59999999999999998,
5446           0.34906585039886590 },
5447   { 0.51724631570707946, 0.89999999999999991, 0.59999999999999998,
5448           0.52359877559829882 },
5449   { 0.68760879113743023, 0.89999999999999991, 0.59999999999999998,
5450           0.69813170079773179 },
5451   { 0.86192157779698364, 0.89999999999999991, 0.59999999999999998,
5452           0.87266462599716477 },
5453   { 1.0464279696166354, 0.89999999999999991, 0.59999999999999998,
5454           1.0471975511965976 },
5455   { 1.2488156247094004, 0.89999999999999991, 0.59999999999999998,
5456           1.2217304763960306 },
5457   { 1.4750988777188470, 0.89999999999999991, 0.59999999999999998,
5458           1.3962634015954636 },
5459   { 1.7211781128919525, 0.89999999999999991, 0.59999999999999998,
5460           1.5707963267948966 },
5461 };
5462 const double toler187 = 2.5000000000000020e-13;
5463
5464 // Test data for k=0.89999999999999991, nu=0.69999999999999996.
5465 // max(|f - f_GSL|): 4.4408920985006262e-16
5466 // max(|f - f_GSL| / |f_GSL|): 4.3410843563834748e-16
5467 const testcase_ellint_3<double>
5468 data188[10] =
5469 {
5470   { 0.0000000000000000, 0.89999999999999991, 0.69999999999999996,
5471           0.0000000000000000 },
5472   { 0.17402765093102207, 0.89999999999999991, 0.69999999999999996,
5473           0.17453292519943295 },
5474   { 0.34541608382635131, 0.89999999999999991, 0.69999999999999996,
5475           0.34906585039886590 },
5476   { 0.51322715827061682, 0.89999999999999991, 0.69999999999999996,
5477           0.52359877559829882 },
5478   { 0.67903717872440272, 0.89999999999999991, 0.69999999999999996,
5479           0.69813170079773179 },
5480   { 0.84690113601682671, 0.89999999999999991, 0.69999999999999996,
5481           0.87266462599716477 },
5482   { 1.0229914311548418, 0.89999999999999991, 0.69999999999999996,
5483           1.0471975511965976 },
5484   { 1.2148329639709381, 0.89999999999999991, 0.69999999999999996,
5485           1.2217304763960306 },
5486   { 1.4283586501307799, 0.89999999999999991, 0.69999999999999996,
5487           1.3962634015954636 },
5488   { 1.6600480747670940, 0.89999999999999991, 0.69999999999999996,
5489           1.5707963267948966 },
5490 };
5491 const double toler188 = 2.5000000000000020e-13;
5492
5493 // Test data for k=0.89999999999999991, nu=0.80000000000000004.
5494 // max(|f - f_GSL|): 4.4408920985006262e-16
5495 // max(|f - f_GSL| / |f_GSL|): 3.3100928058463168e-16
5496 const testcase_ellint_3<double>
5497 data189[10] =
5498 {
5499   { 0.0000000000000000, 0.89999999999999991, 0.80000000000000004,
5500           0.0000000000000000 },
5501   { 0.17385491439925146, 0.89999999999999991, 0.80000000000000004,
5502           0.17453292519943295 },
5503   { 0.34412950523113928, 0.89999999999999991, 0.80000000000000004,
5504           0.34906585039886590 },
5505   { 0.50931321668729590, 0.89999999999999991, 0.80000000000000004,
5506           0.52359877559829882 },
5507   { 0.67081081392296327, 0.89999999999999991, 0.80000000000000004,
5508           0.69813170079773179 },
5509   { 0.83268846097293259, 0.89999999999999991, 0.80000000000000004,
5510           0.87266462599716477 },
5511   { 1.0010985015814027, 0.89999999999999991, 0.80000000000000004,
5512           1.0471975511965976 },
5513   { 1.1834394045489678, 0.89999999999999991, 0.80000000000000004,
5514           1.2217304763960306 },
5515   { 1.3855695891683182, 0.89999999999999991, 0.80000000000000004,
5516           1.3962634015954636 },
5517   { 1.6044591960982202, 0.89999999999999991, 0.80000000000000004,
5518           1.5707963267948966 },
5519 };
5520 const double toler189 = 2.5000000000000020e-13;
5521
5522 // Test data for k=0.89999999999999991, nu=0.90000000000000002.
5523 // max(|f - f_GSL|): 8.8817841970012523e-16
5524 // max(|f - f_GSL| / |f_GSL|): 5.7167507456081732e-16
5525 const testcase_ellint_3<double>
5526 data190[10] =
5527 {
5528   { 0.0000000000000000, 0.89999999999999991, 0.90000000000000002,
5529           0.0000000000000000 },
5530   { 0.17368278986240135, 0.89999999999999991, 0.90000000000000002,
5531           0.17453292519943295 },
5532   { 0.34285962963961397, 0.89999999999999991, 0.90000000000000002,
5533           0.34906585039886590 },
5534   { 0.50549974644993312, 0.89999999999999991, 0.90000000000000002,
5535           0.52359877559829882 },
5536   { 0.66290623857720876, 0.89999999999999991, 0.90000000000000002,
5537           0.69813170079773179 },
5538   { 0.81921183128847175, 0.89999999999999991, 0.90000000000000002,
5539           0.87266462599716477 },
5540   { 0.98058481956066390, 0.89999999999999991, 0.90000000000000002,
5541           1.0471975511965976 },
5542   { 1.1543223520473569, 0.89999999999999991, 0.90000000000000002,
5543           1.2217304763960306 },
5544   { 1.3462119782292934, 0.89999999999999991, 0.90000000000000002,
5545           1.3962634015954636 },
5546   { 1.5536420236310948, 0.89999999999999991, 0.90000000000000002,
5547           1.5707963267948966 },
5548 };
5549 const double toler190 = 2.5000000000000020e-13;
5550
5551 template<typename Tp, unsigned int Num>
5552   void
5553   test(const testcase_ellint_3<Tp> (&data)[Num], Tp toler)
5554   {
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 }