libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/06_comp_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) 2016-2020 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 //  comp_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 <tr1/cmath>
  26 #if defined(__TEST_DEBUG)
  27 #  include <iostream>
  28 #  define VERIFY(A) \
  29   if (!(A)) \
  30     { \
  31       std::cout << "line " << __LINE__ \
  32         << "  max_abs_frac = " << max_abs_frac \
  33         << std::endl; \
  34     }
  35 #else
  36 #  include <testsuite_hooks.h>
  37 #endif
  38 #include <specfun_testcase.h>
  39
  40 // Test data for k=-0.90000000000000002.
  41 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 5
  42 // max(|f - f_Boost| / |f_Boost|): 1.2838262090802751e-16
  43 // mean(f - f_Boost): 4.4408920985006264e-17
  44 // variance(f - f_Boost): 2.4347558803117648e-34
  45 // stddev(f - f_Boost): 1.5603704304785339e-17
  46 const testcase_comp_ellint_3<double>
  47 data001[10] =
  48 {
  49   { 2.2805491384227703, -0.90000000000000002, 0.0000000000000000, 0.0 },
  50   { 2.4295011187834885, -0.90000000000000002, 0.10000000000000001, 0.0 },
  51   { 2.6076835743348412, -0.90000000000000002, 0.20000000000000001, 0.0 },
  52   { 2.8256506968858512, -0.90000000000000002, 0.30000000000000004, 0.0 },
  53   { 3.1000689868578619, -0.90000000000000002, 0.40000000000000002, 0.0 },
  54   { 3.4591069002104677, -0.90000000000000002, 0.50000000000000000, 0.0 },
  55   { 3.9549939883570229, -0.90000000000000002, 0.60000000000000009, 0.0 },
  56   { 4.6985482312992435, -0.90000000000000002, 0.70000000000000007, 0.0 },
  57   { 5.9820740813645710, -0.90000000000000002, 0.80000000000000004, 0.0 },
  58   { 8.9942562031858699, -0.90000000000000002, 0.90000000000000002, 0.0 },
  59 };
  60 const double toler001 = 2.5000000000000020e-13;
  61
  62 // Test data for k=-0.80000000000000004.
  63 // max(|f - f_Boost|): 1.7763568394002505e-15 at index 8
  64 // max(|f - f_Boost| / |f_Boost|): 4.1949393471095187e-16
  65 // mean(f - f_Boost): 9.5479180117763459e-16
  66 // variance(f - f_Boost): 5.4782007307014711e-34
  67 // stddev(f - f_Boost): 2.3405556457178006e-17
  68 const testcase_comp_ellint_3<double>
  69 data002[10] =
  70 {
  71   { 1.9953027776647294, -0.80000000000000004, 0.0000000000000000, 0.0 },
  72   { 2.1172616484005085, -0.80000000000000004, 0.10000000000000001, 0.0 },
  73   { 2.2624789434186798, -0.80000000000000004, 0.20000000000000001, 0.0 },
  74   { 2.4392042002725698, -0.80000000000000004, 0.30000000000000004, 0.0 },
  75   { 2.6604037035529728, -0.80000000000000004, 0.40000000000000002, 0.0 },
  76   { 2.9478781158239751, -0.80000000000000004, 0.50000000000000000, 0.0 },
  77   { 3.3418121892288055, -0.80000000000000004, 0.60000000000000009, 0.0 },
  78   { 3.9268876980046397, -0.80000000000000004, 0.70000000000000007, 0.0 },
  79   { 4.9246422058196071, -0.80000000000000004, 0.80000000000000004, 0.0 },
  80   { 7.2263259298637132, -0.80000000000000004, 0.90000000000000002, 0.0 },
  81 };
  82 const double toler002 = 2.5000000000000020e-13;
  83
  84 // Test data for k=-0.69999999999999996.
  85 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 3
  86 // max(|f - f_Boost| / |f_Boost|): 1.9832236886714888e-16
  87 // mean(f - f_Boost): -1.5543122344752191e-16
  88 // variance(f - f_Boost): 2.9825759533819119e-33
  89 // stddev(f - f_Boost): 5.4612965066748680e-17
  90 const testcase_comp_ellint_3<double>
  91 data003[10] =
  92 {
  93   { 1.8456939983747234, -0.69999999999999996, 0.0000000000000000, 0.0 },
  94   { 1.9541347343119564, -0.69999999999999996, 0.10000000000000001, 0.0 },
  95   { 2.0829290325820202, -0.69999999999999996, 0.20000000000000001, 0.0 },
  96   { 2.2392290510988535, -0.69999999999999996, 0.30000000000000004, 0.0 },
  97   { 2.4342502915307880, -0.69999999999999996, 0.40000000000000002, 0.0 },
  98   { 2.6868019968236996, -0.69999999999999996, 0.50000000000000000, 0.0 },
  99   { 3.0314573496746742, -0.69999999999999996, 0.60000000000000009, 0.0 },
 100   { 3.5408408771788564, -0.69999999999999996, 0.70000000000000007, 0.0 },
 101   { 4.4042405729076961, -0.69999999999999996, 0.80000000000000004, 0.0 },
 102   { 6.3796094177887754, -0.69999999999999996, 0.90000000000000002, 0.0 },
 103 };
 104 const double toler003 = 2.5000000000000020e-13;
 105
 106 // Test data for k=-0.59999999999999998.
 107 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 2
 108 // max(|f - f_Boost| / |f_Boost|): 2.2547200163366559e-16
 109 // mean(f - f_Boost): -1.9984014443252818e-16
 110 // variance(f - f_Boost): 4.9303806576313241e-33
 111 // stddev(f - f_Boost): 7.0216669371534022e-17
 112 const testcase_comp_ellint_3<double>
 113 data004[10] =
 114 {
 115   { 1.7507538029157526, -0.59999999999999998, 0.0000000000000000, 0.0 },
 116   { 1.8508766487100685, -0.59999999999999998, 0.10000000000000001, 0.0 },
 117   { 1.9695980282802217, -0.59999999999999998, 0.20000000000000001, 0.0 },
 118   { 2.1134154405060599, -0.59999999999999998, 0.30000000000000004, 0.0 },
 119   { 2.2925036420985130, -0.59999999999999998, 0.40000000000000002, 0.0 },
 120   { 2.5239007084492711, -0.59999999999999998, 0.50000000000000000, 0.0 },
 121   { 2.8388723099514972, -0.59999999999999998, 0.60000000000000009, 0.0 },
 122   { 3.3029735898397159, -0.59999999999999998, 0.70000000000000007, 0.0 },
 123   { 4.0867036409261832, -0.59999999999999998, 0.80000000000000004, 0.0 },
 124   { 5.8709993116265604, -0.59999999999999998, 0.90000000000000002, 0.0 },
 125 };
 126 const double toler004 = 2.5000000000000020e-13;
 127
 128 // Test data for k=-0.50000000000000000.
 129 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 3
 130 // max(|f - f_Boost| / |f_Boost|): 2.1900131385114407e-16
 131 // mean(f - f_Boost): 2.4424906541753446e-16
 132 // variance(f - f_Boost): 7.3651365379430888e-33
 133 // stddev(f - f_Boost): 8.5820373676319358e-17
 134 const testcase_comp_ellint_3<double>
 135 data005[10] =
 136 {
 137   { 1.6857503548125961, -0.50000000000000000, 0.0000000000000000, 0.0 },
 138   { 1.7803034946545482, -0.50000000000000000, 0.10000000000000001, 0.0 },
 139   { 1.8922947612264021, -0.50000000000000000, 0.20000000000000001, 0.0 },
 140   { 2.0277924458111314, -0.50000000000000000, 0.30000000000000004, 0.0 },
 141   { 2.1962905366178065, -0.50000000000000000, 0.40000000000000002, 0.0 },
 142   { 2.4136715042011945, -0.50000000000000000, 0.50000000000000000, 0.0 },
 143   { 2.7090491861753558, -0.50000000000000000, 0.60000000000000009, 0.0 },
 144   { 3.1433945297859229, -0.50000000000000000, 0.70000000000000007, 0.0 },
 145   { 3.8750701888108070, -0.50000000000000000, 0.80000000000000004, 0.0 },
 146   { 5.5355132096026463, -0.50000000000000000, 0.90000000000000002, 0.0 },
 147 };
 148 const double toler005 = 2.5000000000000020e-13;
 149
 150 // Test data for k=-0.39999999999999991.
 151 // max(|f - f_Boost|): 1.7763568394002505e-15 at index 9
 152 // max(|f - f_Boost| / |f_Boost|): 4.1718164615986397e-16
 153 // mean(f - f_Boost): 6.2172489379008762e-16
 154 // variance(f - f_Boost): 1.6458949750907531e-31
 155 // stddev(f - f_Boost): 4.0569631192441877e-16
 156 const testcase_comp_ellint_3<double>
 157 data006[10] =
 158 {
 159   { 1.6399998658645112, -0.39999999999999991, 0.0000000000000000, 0.0 },
 160   { 1.7306968836847190, -0.39999999999999991, 0.10000000000000001, 0.0 },
 161   { 1.8380358826317627, -0.39999999999999991, 0.20000000000000001, 0.0 },
 162   { 1.9677924132520139, -0.39999999999999991, 0.30000000000000004, 0.0 },
 163   { 2.1289968719280026, -0.39999999999999991, 0.40000000000000002, 0.0 },
 164   { 2.3367461373176512, -0.39999999999999991, 0.50000000000000000, 0.0 },
 165   { 2.6186940209850191, -0.39999999999999991, 0.60000000000000009, 0.0 },
 166   { 3.0327078743873246, -0.39999999999999991, 0.70000000000000007, 0.0 },
 167   { 3.7289548002199902, -0.39999999999999991, 0.80000000000000004, 0.0 },
 168   { 5.3055535102872513, -0.39999999999999991, 0.90000000000000002, 0.0 },
 169 };
 170 const double toler006 = 2.5000000000000020e-13;
 171
 172 // Test data for k=-0.29999999999999993.
 173 // max(|f - f_Boost|): 1.3322676295501878e-15 at index 8
 174 // max(|f - f_Boost| / |f_Boost|): 3.9274792319434433e-16
 175 // mean(f - f_Boost): 6.2172489379008762e-16
 176 // variance(f - f_Boost): 8.7651211691223537e-33
 177 // stddev(f - f_Boost): 9.3622225828712025e-17
 178 const testcase_comp_ellint_3<double>
 179 data007[10] =
 180 {
 181   { 1.6080486199305128, -0.29999999999999993, 0.0000000000000000, 0.0 },
 182   { 1.6960848815118226, -0.29999999999999993, 0.10000000000000001, 0.0 },
 183   { 1.8002173372290500, -0.29999999999999993, 0.20000000000000001, 0.0 },
 184   { 1.9260216862473254, -0.29999999999999993, 0.30000000000000004, 0.0 },
 185   { 2.0822121773175533, -0.29999999999999993, 0.40000000000000002, 0.0 },
 186   { 2.2833505881933971, -0.29999999999999993, 0.50000000000000000, 0.0 },
 187   { 2.5560975528589065, -0.29999999999999993, 0.60000000000000009, 0.0 },
 188   { 2.9562123549913877, -0.29999999999999993, 0.70000000000000007, 0.0 },
 189   { 3.6283050484567170, -0.29999999999999993, 0.80000000000000004, 0.0 },
 190   { 5.1479514944016795, -0.29999999999999993, 0.90000000000000002, 0.0 },
 191 };
 192 const double toler007 = 2.5000000000000020e-13;
 193
 194 // Test data for k=-0.19999999999999996.
 195 // max(|f - f_Boost|): 8.8817841970012523e-16 at index 9
 196 // max(|f - f_Boost| / |f_Boost|): 1.9753938705764407e-16
 197 // mean(f - f_Boost): 3.1086244689504381e-16
 198 // variance(f - f_Boost): 4.1147374377268827e-32
 199 // stddev(f - f_Boost): 2.0284815596220939e-16
 200 const testcase_comp_ellint_3<double>
 201 data008[10] =
 202 {
 203   { 1.5868678474541662, -0.19999999999999996, 0.0000000000000000, 0.0 },
 204   { 1.6731552050562593, -0.19999999999999996, 0.10000000000000001, 0.0 },
 205   { 1.7751816279738935, -0.19999999999999996, 0.20000000000000001, 0.0 },
 206   { 1.8983924169967101, -0.19999999999999996, 0.30000000000000004, 0.0 },
 207   { 2.0512956926676806, -0.19999999999999996, 0.40000000000000002, 0.0 },
 208   { 2.2481046259421302, -0.19999999999999996, 0.50000000000000000, 0.0 },
 209   { 2.5148333891629315, -0.19999999999999996, 0.60000000000000009, 0.0 },
 210   { 2.9058704854500967, -0.19999999999999996, 0.70000000000000007, 0.0 },
 211   { 3.5622166386422633, -0.19999999999999996, 0.80000000000000004, 0.0 },
 212   { 5.0448269356200370, -0.19999999999999996, 0.90000000000000002, 0.0 },
 213 };
 214 const double toler008 = 2.5000000000000020e-13;
 215
 216 // Test data for k=-0.099999999999999978.
 217 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 5
 218 // max(|f - f_Boost| / |f_Boost|): 1.9932308021417639e-16
 219 // mean(f - f_Boost): 0.0000000000000000
 220 // variance(f - f_Boost): 6.8368087769470551e-64
 221 // stddev(f - f_Boost): 2.6147291976315738e-32
 222 const testcase_comp_ellint_3<double>
 223 data009[10] =
 224 {
 225   { 1.5747455615173560, -0.099999999999999978, 0.0000000000000000, 0.0 },
 226   { 1.6600374067558428, -0.099999999999999978, 0.10000000000000001, 0.0 },
 227   { 1.7608656115083421, -0.099999999999999978, 0.20000000000000001, 0.0 },
 228   { 1.8826015946315438, -0.099999999999999978, 0.30000000000000004, 0.0 },
 229   { 2.0336367403076760, -0.099999999999999978, 0.40000000000000002, 0.0 },
 230   { 2.2279868912966849, -0.099999999999999978, 0.50000000000000000, 0.0 },
 231   { 2.4913004919173827, -0.099999999999999978, 0.60000000000000009, 0.0 },
 232   { 2.8771910188009744, -0.099999999999999978, 0.70000000000000007, 0.0 },
 233   { 3.5246199613295617, -0.099999999999999978, 0.80000000000000004, 0.0 },
 234   { 4.9862890417305508, -0.099999999999999978, 0.90000000000000002, 0.0 },
 235 };
 236 const double toler009 = 2.5000000000000020e-13;
 237
 238 // Test data for k=0.0000000000000000.
 239 // max(|f - f_Boost|): 8.8817841970012523e-16 at index 9
 240 // max(|f - f_Boost| / |f_Boost|): 2.1899085000907084e-16
 241 // mean(f - f_Boost): -2.2204460492503131e-16
 242 // variance(f - f_Boost): 5.4782007307014711e-32
 243 // stddev(f - f_Boost): 2.3405556457178008e-16
 244 const testcase_comp_ellint_3<double>
 245 data010[10] =
 246 {
 247   { 1.5707963267948966, 0.0000000000000000, 0.0000000000000000, 0.0 },
 248   { 1.6557647109660170, 0.0000000000000000, 0.10000000000000001, 0.0 },
 249   { 1.7562036827601817, 0.0000000000000000, 0.20000000000000001, 0.0 },
 250   { 1.8774607092226381, 0.0000000000000000, 0.30000000000000004, 0.0 },
 251   { 2.0278893379868062, 0.0000000000000000, 0.40000000000000002, 0.0 },
 252   { 2.2214414690791831, 0.0000000000000000, 0.50000000000000000, 0.0 },
 253   { 2.4836470664490258, 0.0000000000000000, 0.60000000000000009, 0.0 },
 254   { 2.8678686047727386, 0.0000000000000000, 0.70000000000000007, 0.0 },
 255   { 3.5124073655203634, 0.0000000000000000, 0.80000000000000004, 0.0 },
 256   { 4.9672941328980516, 0.0000000000000000, 0.90000000000000002, 0.0 },
 257 };
 258 const double toler010 = 2.5000000000000020e-13;
 259
 260 // Test data for k=0.10000000000000009.
 261 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 5
 262 // max(|f - f_Boost| / |f_Boost|): 1.9932308021417639e-16
 263 // mean(f - f_Boost): -2.2204460492503132e-17
 264 // variance(f - f_Boost): 6.0868897007794120e-35
 265 // stddev(f - f_Boost): 7.8018521523926693e-18
 266 const testcase_comp_ellint_3<double>
 267 data011[10] =
 268 {
 269   { 1.5747455615173560, 0.10000000000000009, 0.0000000000000000, 0.0 },
 270   { 1.6600374067558428, 0.10000000000000009, 0.10000000000000001, 0.0 },
 271   { 1.7608656115083421, 0.10000000000000009, 0.20000000000000001, 0.0 },
 272   { 1.8826015946315440, 0.10000000000000009, 0.30000000000000004, 0.0 },
 273   { 2.0336367403076760, 0.10000000000000009, 0.40000000000000002, 0.0 },
 274   { 2.2279868912966849, 0.10000000000000009, 0.50000000000000000, 0.0 },
 275   { 2.4913004919173827, 0.10000000000000009, 0.60000000000000009, 0.0 },
 276   { 2.8771910188009744, 0.10000000000000009, 0.70000000000000007, 0.0 },
 277   { 3.5246199613295617, 0.10000000000000009, 0.80000000000000004, 0.0 },
 278   { 4.9862890417305508, 0.10000000000000009, 0.90000000000000002, 0.0 },
 279 };
 280 const double toler011 = 2.5000000000000020e-13;
 281
 282 // Test data for k=0.20000000000000018.
 283 // max(|f - f_Boost|): 8.8817841970012523e-16 at index 9
 284 // max(|f - f_Boost| / |f_Boost|): 1.9753938705764407e-16
 285 // mean(f - f_Boost): 3.1086244689504381e-16
 286 // variance(f - f_Boost): 4.1147374377268827e-32
 287 // stddev(f - f_Boost): 2.0284815596220939e-16
 288 const testcase_comp_ellint_3<double>
 289 data012[10] =
 290 {
 291   { 1.5868678474541662, 0.20000000000000018, 0.0000000000000000, 0.0 },
 292   { 1.6731552050562593, 0.20000000000000018, 0.10000000000000001, 0.0 },
 293   { 1.7751816279738935, 0.20000000000000018, 0.20000000000000001, 0.0 },
 294   { 1.8983924169967101, 0.20000000000000018, 0.30000000000000004, 0.0 },
 295   { 2.0512956926676806, 0.20000000000000018, 0.40000000000000002, 0.0 },
 296   { 2.2481046259421302, 0.20000000000000018, 0.50000000000000000, 0.0 },
 297   { 2.5148333891629315, 0.20000000000000018, 0.60000000000000009, 0.0 },
 298   { 2.9058704854500967, 0.20000000000000018, 0.70000000000000007, 0.0 },
 299   { 3.5622166386422633, 0.20000000000000018, 0.80000000000000004, 0.0 },
 300   { 5.0448269356200370, 0.20000000000000018, 0.90000000000000002, 0.0 },
 301 };
 302 const double toler012 = 2.5000000000000020e-13;
 303
 304 // Test data for k=0.30000000000000004.
 305 // max(|f - f_Boost|): 8.8817841970012523e-16 at index 8
 306 // max(|f - f_Boost| / |f_Boost|): 3.4585997630846713e-16
 307 // mean(f - f_Boost): 5.1070259132757197e-16
 308 // variance(f - f_Boost): 1.7591111235252501e-32
 309 // stddev(f - f_Boost): 1.3263148659067538e-16
 310 const testcase_comp_ellint_3<double>
 311 data013[10] =
 312 {
 313   { 1.6080486199305128, 0.30000000000000004, 0.0000000000000000, 0.0 },
 314   { 1.6960848815118228, 0.30000000000000004, 0.10000000000000001, 0.0 },
 315   { 1.8002173372290500, 0.30000000000000004, 0.20000000000000001, 0.0 },
 316   { 1.9260216862473254, 0.30000000000000004, 0.30000000000000004, 0.0 },
 317   { 2.0822121773175533, 0.30000000000000004, 0.40000000000000002, 0.0 },
 318   { 2.2833505881933975, 0.30000000000000004, 0.50000000000000000, 0.0 },
 319   { 2.5560975528589065, 0.30000000000000004, 0.60000000000000009, 0.0 },
 320   { 2.9562123549913877, 0.30000000000000004, 0.70000000000000007, 0.0 },
 321   { 3.6283050484567174, 0.30000000000000004, 0.80000000000000004, 0.0 },
 322   { 5.1479514944016795, 0.30000000000000004, 0.90000000000000002, 0.0 },
 323 };
 324 const double toler013 = 2.5000000000000020e-13;
 325
 326 // Test data for k=0.40000000000000013.
 327 // max(|f - f_Boost|): 2.6645352591003757e-15 at index 9
 328 // max(|f - f_Boost| / |f_Boost|): 6.7696531428672557e-16
 329 // mean(f - f_Boost): 1.1990408665951691e-15
 330 // variance(f - f_Boost): 2.6514491536595121e-31
 331 // stddev(f - f_Boost): 5.1492224205791612e-16
 332 const testcase_comp_ellint_3<double>
 333 data014[10] =
 334 {
 335   { 1.6399998658645112, 0.40000000000000013, 0.0000000000000000, 0.0 },
 336   { 1.7306968836847190, 0.40000000000000013, 0.10000000000000001, 0.0 },
 337   { 1.8380358826317629, 0.40000000000000013, 0.20000000000000001, 0.0 },
 338   { 1.9677924132520141, 0.40000000000000013, 0.30000000000000004, 0.0 },
 339   { 2.1289968719280030, 0.40000000000000013, 0.40000000000000002, 0.0 },
 340   { 2.3367461373176512, 0.40000000000000013, 0.50000000000000000, 0.0 },
 341   { 2.6186940209850196, 0.40000000000000013, 0.60000000000000009, 0.0 },
 342   { 3.0327078743873246, 0.40000000000000013, 0.70000000000000007, 0.0 },
 343   { 3.7289548002199906, 0.40000000000000013, 0.80000000000000004, 0.0 },
 344   { 5.3055535102872522, 0.40000000000000013, 0.90000000000000002, 0.0 },
 345 };
 346 const double toler014 = 2.5000000000000020e-13;
 347
 348 // Test data for k=0.50000000000000000.
 349 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 3
 350 // max(|f - f_Boost| / |f_Boost|): 2.1900131385114407e-16
 351 // mean(f - f_Boost): 2.4424906541753446e-16
 352 // variance(f - f_Boost): 7.3651365379430888e-33
 353 // stddev(f - f_Boost): 8.5820373676319358e-17
 354 const testcase_comp_ellint_3<double>
 355 data015[10] =
 356 {
 357   { 1.6857503548125961, 0.50000000000000000, 0.0000000000000000, 0.0 },
 358   { 1.7803034946545482, 0.50000000000000000, 0.10000000000000001, 0.0 },
 359   { 1.8922947612264021, 0.50000000000000000, 0.20000000000000001, 0.0 },
 360   { 2.0277924458111314, 0.50000000000000000, 0.30000000000000004, 0.0 },
 361   { 2.1962905366178065, 0.50000000000000000, 0.40000000000000002, 0.0 },
 362   { 2.4136715042011945, 0.50000000000000000, 0.50000000000000000, 0.0 },
 363   { 2.7090491861753558, 0.50000000000000000, 0.60000000000000009, 0.0 },
 364   { 3.1433945297859229, 0.50000000000000000, 0.70000000000000007, 0.0 },
 365   { 3.8750701888108070, 0.50000000000000000, 0.80000000000000004, 0.0 },
 366   { 5.5355132096026463, 0.50000000000000000, 0.90000000000000002, 0.0 },
 367 };
 368 const double toler015 = 2.5000000000000020e-13;
 369
 370 // Test data for k=0.60000000000000009.
 371 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 2
 372 // max(|f - f_Boost| / |f_Boost|): 2.2547200163366559e-16
 373 // mean(f - f_Boost): -2.2204460492503131e-16
 374 // variance(f - f_Boost): 6.0868897007794117e-33
 375 // stddev(f - f_Boost): 7.8018521523926690e-17
 376 const testcase_comp_ellint_3<double>
 377 data016[10] =
 378 {
 379   { 1.7507538029157526, 0.60000000000000009, 0.0000000000000000, 0.0 },
 380   { 1.8508766487100687, 0.60000000000000009, 0.10000000000000001, 0.0 },
 381   { 1.9695980282802217, 0.60000000000000009, 0.20000000000000001, 0.0 },
 382   { 2.1134154405060599, 0.60000000000000009, 0.30000000000000004, 0.0 },
 383   { 2.2925036420985130, 0.60000000000000009, 0.40000000000000002, 0.0 },
 384   { 2.5239007084492711, 0.60000000000000009, 0.50000000000000000, 0.0 },
 385   { 2.8388723099514976, 0.60000000000000009, 0.60000000000000009, 0.0 },
 386   { 3.3029735898397159, 0.60000000000000009, 0.70000000000000007, 0.0 },
 387   { 4.0867036409261832, 0.60000000000000009, 0.80000000000000004, 0.0 },
 388   { 5.8709993116265613, 0.60000000000000009, 0.90000000000000002, 0.0 },
 389 };
 390 const double toler016 = 2.5000000000000020e-13;
 391
 392 // Test data for k=0.70000000000000018.
 393 // max(|f - f_Boost|): 1.7763568394002505e-15 at index 9
 394 // max(|f - f_Boost| / |f_Boost|): 2.9298727220933567e-16
 395 // mean(f - f_Boost): 4.8849813083506892e-16
 396 // variance(f - f_Boost): 2.0476296953421943e-31
 397 // stddev(f - f_Boost): 4.5250742483877478e-16
 398 const testcase_comp_ellint_3<double>
 399 data017[10] =
 400 {
 401   { 1.8456939983747238, 0.70000000000000018, 0.0000000000000000, 0.0 },
 402   { 1.9541347343119566, 0.70000000000000018, 0.10000000000000001, 0.0 },
 403   { 2.0829290325820207, 0.70000000000000018, 0.20000000000000001, 0.0 },
 404   { 2.2392290510988540, 0.70000000000000018, 0.30000000000000004, 0.0 },
 405   { 2.4342502915307880, 0.70000000000000018, 0.40000000000000002, 0.0 },
 406   { 2.6868019968237000, 0.70000000000000018, 0.50000000000000000, 0.0 },
 407   { 3.0314573496746746, 0.70000000000000018, 0.60000000000000009, 0.0 },
 408   { 3.5408408771788569, 0.70000000000000018, 0.70000000000000007, 0.0 },
 409   { 4.4042405729076970, 0.70000000000000018, 0.80000000000000004, 0.0 },
 410   { 6.3796094177887763, 0.70000000000000018, 0.90000000000000002, 0.0 },
 411 };
 412 const double toler017 = 2.5000000000000020e-13;
 413
 414 // Test data for k=0.80000000000000004.
 415 // max(|f - f_Boost|): 1.7763568394002505e-15 at index 8
 416 // max(|f - f_Boost| / |f_Boost|): 4.1949393471095187e-16
 417 // mean(f - f_Boost): 9.5479180117763459e-16
 418 // variance(f - f_Boost): 5.4782007307014711e-34
 419 // stddev(f - f_Boost): 2.3405556457178006e-17
 420 const testcase_comp_ellint_3<double>
 421 data018[10] =
 422 {
 423   { 1.9953027776647294, 0.80000000000000004, 0.0000000000000000, 0.0 },
 424   { 2.1172616484005085, 0.80000000000000004, 0.10000000000000001, 0.0 },
 425   { 2.2624789434186798, 0.80000000000000004, 0.20000000000000001, 0.0 },
 426   { 2.4392042002725698, 0.80000000000000004, 0.30000000000000004, 0.0 },
 427   { 2.6604037035529728, 0.80000000000000004, 0.40000000000000002, 0.0 },
 428   { 2.9478781158239751, 0.80000000000000004, 0.50000000000000000, 0.0 },
 429   { 3.3418121892288055, 0.80000000000000004, 0.60000000000000009, 0.0 },
 430   { 3.9268876980046397, 0.80000000000000004, 0.70000000000000007, 0.0 },
 431   { 4.9246422058196071, 0.80000000000000004, 0.80000000000000004, 0.0 },
 432   { 7.2263259298637132, 0.80000000000000004, 0.90000000000000002, 0.0 },
 433 };
 434 const double toler018 = 2.5000000000000020e-13;
 435
 436 // Test data for k=0.90000000000000013.
 437 // max(|f - f_Boost|): 4.4408920985006262e-16 at index 3
 438 // max(|f - f_Boost| / |f_Boost|): 1.5716352001310461e-16
 439 // mean(f - f_Boost): 4.4408920985006264e-17
 440 // variance(f - f_Boost): 2.4347558803117648e-34
 441 // stddev(f - f_Boost): 1.5603704304785339e-17
 442 const testcase_comp_ellint_3<double>
 443 data019[10] =
 444 {
 445   { 2.2805491384227707, 0.90000000000000013, 0.0000000000000000, 0.0 },
 446   { 2.4295011187834890, 0.90000000000000013, 0.10000000000000001, 0.0 },
 447   { 2.6076835743348421, 0.90000000000000013, 0.20000000000000001, 0.0 },
 448   { 2.8256506968858521, 0.90000000000000013, 0.30000000000000004, 0.0 },
 449   { 3.1000689868578628, 0.90000000000000013, 0.40000000000000002, 0.0 },
 450   { 3.4591069002104686, 0.90000000000000013, 0.50000000000000000, 0.0 },
 451   { 3.9549939883570242, 0.90000000000000013, 0.60000000000000009, 0.0 },
 452   { 4.6985482312992453, 0.90000000000000013, 0.70000000000000007, 0.0 },
 453   { 5.9820740813645727, 0.90000000000000013, 0.80000000000000004, 0.0 },
 454   { 8.9942562031858735, 0.90000000000000013, 0.90000000000000002, 0.0 },
 455 };
 456 const double toler019 = 2.5000000000000020e-13;
 457
 458 template<typename Ret, unsigned int Num>
 459   void
 460   test(const testcase_comp_ellint_3<Ret> (&data)[Num], Ret toler)
 461   {
 462     bool test __attribute__((unused)) = true;
 463     const Ret eps = std::numeric_limits<Ret>::epsilon();
 464     Ret max_abs_diff = -Ret(1);
 465     Ret max_abs_frac = -Ret(1);
 466     unsigned int num_datum = Num;
 467     for (unsigned int i = 0; i < num_datum; ++i)
 468       {
 469         const Ret f = std::tr1::comp_ellint_3(data[i].k, data[i].nu);
 470         const Ret f0 = data[i].f0;
 471         const Ret diff = f - f0;
 472         if (std::abs(diff) > max_abs_diff)
 473           max_abs_diff = std::abs(diff);
 474         if (std::abs(f0) > Ret(10) * eps
 475          && std::abs(f) > Ret(10) * eps)
 476           {
 477             const Ret frac = diff / f0;
 478             if (std::abs(frac) > max_abs_frac)
 479               max_abs_frac = std::abs(frac);
 480           }
 481       }
 482     VERIFY(max_abs_frac < toler);
 483   }
 484
 485 int
 486 main()
 487 {
 488   test(data001, toler001);
 489   test(data002, toler002);
 490   test(data003, toler003);
 491   test(data004, toler004);
 492   test(data005, toler005);
 493   test(data006, toler006);
 494   test(data007, toler007);
 495   test(data008, toler008);
 496   test(data009, toler009);
 497   test(data010, toler010);
 498   test(data011, toler011);
 499   test(data012, toler012);
 500   test(data013, toler013);
 501   test(data014, toler014);
 502   test(data015, toler015);
 503   test(data016, toler016);
 504   test(data017, toler017);
 505   test(data018, toler018);
 506   test(data019, toler019);
 507   return 0;
 508 }