libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/06_comp_ellint_3/check_value.cc

   1 // 2007-02-04  Edward Smith-Rowland <3dw4rd@verizon.net>
   2 //
   3 // Copyright (C) 2007, 2009 Free Software Foundation, Inc.
   4 //
   5 // This file is part of the GNU ISO C++ Library.  This library is free
   6 // software; you can redistribute it and/or modify it under the
   7 // terms of the GNU General Public License as published by the
   8 // Free Software Foundation; either version 3, or (at your option)
   9 // any later version.
  10 //
  11 // This library is distributed in the hope that it will be useful,
  12 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14 // GNU General Public License for more details.
  15 //
  16 // You should have received a copy of the GNU General Public License along
  17 // with this library; see the file COPYING3.  If not see
  18 // <http://www.gnu.org/licenses/>.
  19
  20 //  comp_ellint_3
  21
  22
  23 //  Compare against values generated by the GNU Scientific Library.
  24 //  The GSL can be found on the web: http://www.gnu.org/software/gsl/
  25
  26 #include <tr1/cmath>
  27 #if defined(__TEST_DEBUG)
  28 #include <iostream>
  29 #define VERIFY(A) \
  30 if (!(A)) \
  31   { \
  32     std::cout << "line " << __LINE__ \
  33       << "  max_abs_frac = " << max_abs_frac \
  34       << std::endl; \
  35   }
  36 #else
  37 #include <testsuite_hooks.h>
  38 #endif
  39 #include "../testcase.h"
  40
  41
  42 // Test data for k=-0.90000000000000002.
  43 testcase_comp_ellint_3<double> data001[] = {
  44   { 2.2805491384227703, -0.90000000000000002, 0.0000000000000000 },
  45   { 2.1537868513875287, -0.90000000000000002, 0.10000000000000001 },
  46   { 2.0443194576468890, -0.90000000000000002, 0.20000000000000001 },
  47   { 1.9486280260314426, -0.90000000000000002, 0.29999999999999999 },
  48   { 1.8641114227238349, -0.90000000000000002, 0.40000000000000002 },
  49   { 1.7888013241937861, -0.90000000000000002, 0.50000000000000000 },
  50   { 1.7211781128919523, -0.90000000000000002, 0.59999999999999998 },
  51   { 1.6600480747670938, -0.90000000000000002, 0.69999999999999996 },
  52   { 1.6044591960982204, -0.90000000000000002, 0.80000000000000004 },
  53   { 1.5536420236310946, -0.90000000000000002, 0.90000000000000002 },
  54 };
  55
  56 // Test function for k=-0.90000000000000002.
  57 template <typename Tp>
  58 void test001()
  59 {
  60   const Tp eps = std::numeric_limits<Tp>::epsilon();
  61   Tp max_abs_diff = -Tp(1);
  62   Tp max_abs_frac = -Tp(1);
  63   unsigned int num_datum = sizeof(data001)
  64                          / sizeof(testcase_comp_ellint_3<double>);
  65   for (unsigned int i = 0; i < num_datum; ++i)
  66     {
  67       const Tp f = std::tr1::comp_ellint_3(Tp(data001[i].k), Tp(data001[i].nu));
  68       const Tp f0 = data001[i].f0;
  69       const Tp diff = f - f0;
  70       if (std::abs(diff) > max_abs_diff)
  71         max_abs_diff = std::abs(diff);
  72       if (std::abs(f0) > Tp(10) * eps
  73        && std::abs(f) > Tp(10) * eps)
  74         {
  75           const Tp frac = diff / f0;
  76           if (std::abs(frac) > max_abs_frac)
  77             max_abs_frac = std::abs(frac);
  78         }
  79     }
  80   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
  81 }
  82
  83 // Test data for k=-0.80000000000000004.
  84 testcase_comp_ellint_3<double> data002[] = {
  85   { 1.9953027776647296, -0.80000000000000004, 0.0000000000000000 },
  86   { 1.8910755418379521, -0.80000000000000004, 0.10000000000000001 },
  87   { 1.8007226661734588, -0.80000000000000004, 0.20000000000000001 },
  88   { 1.7214611048717301, -0.80000000000000004, 0.29999999999999999 },
  89   { 1.6512267838651289, -0.80000000000000004, 0.40000000000000002 },
  90   { 1.5884528947755532, -0.80000000000000004, 0.50000000000000000 },
  91   { 1.5319262547427865, -0.80000000000000004, 0.59999999999999998 },
  92   { 1.4806912324625332, -0.80000000000000004, 0.69999999999999996 },
  93   { 1.4339837018309474, -0.80000000000000004, 0.80000000000000004 },
  94   { 1.3911845406776222, -0.80000000000000004, 0.90000000000000002 },
  95 };
  96
  97 // Test function for k=-0.80000000000000004.
  98 template <typename Tp>
  99 void test002()
 100 {
 101   const Tp eps = std::numeric_limits<Tp>::epsilon();
 102   Tp max_abs_diff = -Tp(1);
 103   Tp max_abs_frac = -Tp(1);
 104   unsigned int num_datum = sizeof(data002)
 105                          / sizeof(testcase_comp_ellint_3<double>);
 106   for (unsigned int i = 0; i < num_datum; ++i)
 107     {
 108       const Tp f = std::tr1::comp_ellint_3(Tp(data002[i].k), Tp(data002[i].nu));
 109       const Tp f0 = data002[i].f0;
 110       const Tp diff = f - f0;
 111       if (std::abs(diff) > max_abs_diff)
 112         max_abs_diff = std::abs(diff);
 113       if (std::abs(f0) > Tp(10) * eps
 114        && std::abs(f) > Tp(10) * eps)
 115         {
 116           const Tp frac = diff / f0;
 117           if (std::abs(frac) > max_abs_frac)
 118             max_abs_frac = std::abs(frac);
 119         }
 120     }
 121   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 122 }
 123
 124 // Test data for k=-0.69999999999999996.
 125 testcase_comp_ellint_3<double> data003[] = {
 126   { 1.8456939983747236, -0.69999999999999996, 0.0000000000000000 },
 127   { 1.7528050171757608, -0.69999999999999996, 0.10000000000000001 },
 128   { 1.6721098780092147, -0.69999999999999996, 0.20000000000000001 },
 129   { 1.6011813647733213, -0.69999999999999996, 0.29999999999999999 },
 130   { 1.5382162002954762, -0.69999999999999996, 0.40000000000000002 },
 131   { 1.4818433192178544, -0.69999999999999996, 0.50000000000000000 },
 132   { 1.4309994736080540, -0.69999999999999996, 0.59999999999999998 },
 133   { 1.3848459188329196, -0.69999999999999996, 0.69999999999999996 },
 134   { 1.3427110650397533, -0.69999999999999996, 0.80000000000000004 },
 135   { 1.3040500499695911, -0.69999999999999996, 0.90000000000000002 },
 136 };
 137
 138 // Test function for k=-0.69999999999999996.
 139 template <typename Tp>
 140 void test003()
 141 {
 142   const Tp eps = std::numeric_limits<Tp>::epsilon();
 143   Tp max_abs_diff = -Tp(1);
 144   Tp max_abs_frac = -Tp(1);
 145   unsigned int num_datum = sizeof(data003)
 146                          / sizeof(testcase_comp_ellint_3<double>);
 147   for (unsigned int i = 0; i < num_datum; ++i)
 148     {
 149       const Tp f = std::tr1::comp_ellint_3(Tp(data003[i].k), Tp(data003[i].nu));
 150       const Tp f0 = data003[i].f0;
 151       const Tp diff = f - f0;
 152       if (std::abs(diff) > max_abs_diff)
 153         max_abs_diff = std::abs(diff);
 154       if (std::abs(f0) > Tp(10) * eps
 155        && std::abs(f) > Tp(10) * eps)
 156         {
 157           const Tp frac = diff / f0;
 158           if (std::abs(frac) > max_abs_frac)
 159             max_abs_frac = std::abs(frac);
 160         }
 161     }
 162   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 163 }
 164
 165 // Test data for k=-0.59999999999999998.
 166 testcase_comp_ellint_3<double> data004[] = {
 167   { 1.7507538029157526, -0.59999999999999998, 0.0000000000000000 },
 168   { 1.6648615773343014, -0.59999999999999998, 0.10000000000000001 },
 169   { 1.5901418016279374, -0.59999999999999998, 0.20000000000000001 },
 170   { 1.5243814243493585, -0.59999999999999998, 0.29999999999999999 },
 171   { 1.4659345278069984, -0.59999999999999998, 0.40000000000000002 },
 172   { 1.4135484285693078, -0.59999999999999998, 0.50000000000000000 },
 173   { 1.3662507535812816, -0.59999999999999998, 0.59999999999999998 },
 174   { 1.3232737468822811, -0.59999999999999998, 0.69999999999999996 },
 175   { 1.2840021261752192, -0.59999999999999998, 0.80000000000000004 },
 176   { 1.2479362973851875, -0.59999999999999998, 0.90000000000000002 },
 177 };
 178
 179 // Test function for k=-0.59999999999999998.
 180 template <typename Tp>
 181 void test004()
 182 {
 183   const Tp eps = std::numeric_limits<Tp>::epsilon();
 184   Tp max_abs_diff = -Tp(1);
 185   Tp max_abs_frac = -Tp(1);
 186   unsigned int num_datum = sizeof(data004)
 187                          / sizeof(testcase_comp_ellint_3<double>);
 188   for (unsigned int i = 0; i < num_datum; ++i)
 189     {
 190       const Tp f = std::tr1::comp_ellint_3(Tp(data004[i].k), Tp(data004[i].nu));
 191       const Tp f0 = data004[i].f0;
 192       const Tp diff = f - f0;
 193       if (std::abs(diff) > max_abs_diff)
 194         max_abs_diff = std::abs(diff);
 195       if (std::abs(f0) > Tp(10) * eps
 196        && std::abs(f) > Tp(10) * eps)
 197         {
 198           const Tp frac = diff / f0;
 199           if (std::abs(frac) > max_abs_frac)
 200             max_abs_frac = std::abs(frac);
 201         }
 202     }
 203   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 204 }
 205
 206 // Test data for k=-0.50000000000000000.
 207 testcase_comp_ellint_3<double> data005[] = {
 208   { 1.6857503548125963, -0.50000000000000000, 0.0000000000000000 },
 209   { 1.6045524936084892, -0.50000000000000000, 0.10000000000000001 },
 210   { 1.5338490483665983, -0.50000000000000000, 0.20000000000000001 },
 211   { 1.4715681939859637, -0.50000000000000000, 0.29999999999999999 },
 212   { 1.4161679518465340, -0.50000000000000000, 0.40000000000000002 },
 213   { 1.3664739530045971, -0.50000000000000000, 0.50000000000000000 },
 214   { 1.3215740290190876, -0.50000000000000000, 0.59999999999999998 },
 215   { 1.2807475181182502, -0.50000000000000000, 0.69999999999999996 },
 216   { 1.2434165408189539, -0.50000000000000000, 0.80000000000000004 },
 217   { 1.2091116095504744, -0.50000000000000000, 0.90000000000000002 },
 218 };
 219
 220 // Test function for k=-0.50000000000000000.
 221 template <typename Tp>
 222 void test005()
 223 {
 224   const Tp eps = std::numeric_limits<Tp>::epsilon();
 225   Tp max_abs_diff = -Tp(1);
 226   Tp max_abs_frac = -Tp(1);
 227   unsigned int num_datum = sizeof(data005)
 228                          / sizeof(testcase_comp_ellint_3<double>);
 229   for (unsigned int i = 0; i < num_datum; ++i)
 230     {
 231       const Tp f = std::tr1::comp_ellint_3(Tp(data005[i].k), Tp(data005[i].nu));
 232       const Tp f0 = data005[i].f0;
 233       const Tp diff = f - f0;
 234       if (std::abs(diff) > max_abs_diff)
 235         max_abs_diff = std::abs(diff);
 236       if (std::abs(f0) > Tp(10) * eps
 237        && std::abs(f) > Tp(10) * eps)
 238         {
 239           const Tp frac = diff / f0;
 240           if (std::abs(frac) > max_abs_frac)
 241             max_abs_frac = std::abs(frac);
 242         }
 243     }
 244   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 245 }
 246
 247 // Test data for k=-0.40000000000000002.
 248 testcase_comp_ellint_3<double> data006[] = {
 249   { 1.6399998658645112, -0.40000000000000002, 0.0000000000000000 },
 250   { 1.5620566886683604, -0.40000000000000002, 0.10000000000000001 },
 251   { 1.4941414344266770, -0.40000000000000002, 0.20000000000000001 },
 252   { 1.4342789859950078, -0.40000000000000002, 0.29999999999999999 },
 253   { 1.3809986210732901, -0.40000000000000002, 0.40000000000000002 },
 254   { 1.3331797176377398, -0.40000000000000002, 0.50000000000000000 },
 255   { 1.2899514672527024, -0.40000000000000002, 0.59999999999999998 },
 256   { 1.2506255923253344, -0.40000000000000002, 0.69999999999999996 },
 257   { 1.2146499565727209, -0.40000000000000002, 0.80000000000000004 },
 258   { 1.1815758115929846, -0.40000000000000002, 0.90000000000000002 },
 259 };
 260
 261 // Test function for k=-0.40000000000000002.
 262 template <typename Tp>
 263 void test006()
 264 {
 265   const Tp eps = std::numeric_limits<Tp>::epsilon();
 266   Tp max_abs_diff = -Tp(1);
 267   Tp max_abs_frac = -Tp(1);
 268   unsigned int num_datum = sizeof(data006)
 269                          / sizeof(testcase_comp_ellint_3<double>);
 270   for (unsigned int i = 0; i < num_datum; ++i)
 271     {
 272       const Tp f = std::tr1::comp_ellint_3(Tp(data006[i].k), Tp(data006[i].nu));
 273       const Tp f0 = data006[i].f0;
 274       const Tp diff = f - f0;
 275       if (std::abs(diff) > max_abs_diff)
 276         max_abs_diff = std::abs(diff);
 277       if (std::abs(f0) > Tp(10) * eps
 278        && std::abs(f) > Tp(10) * eps)
 279         {
 280           const Tp frac = diff / f0;
 281           if (std::abs(frac) > max_abs_frac)
 282             max_abs_frac = std::abs(frac);
 283         }
 284     }
 285   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 286 }
 287
 288 // Test data for k=-0.30000000000000004.
 289 testcase_comp_ellint_3<double> data007[] = {
 290   { 1.6080486199305126, -0.30000000000000004, 0.0000000000000000 },
 291   { 1.5323534693557526, -0.30000000000000004, 0.10000000000000001 },
 292   { 1.4663658145259875, -0.30000000000000004, 0.20000000000000001 },
 293   { 1.4081767433479089, -0.30000000000000004, 0.29999999999999999 },
 294   { 1.3563643538969761, -0.30000000000000004, 0.40000000000000002 },
 295   { 1.3098448759814960, -0.30000000000000004, 0.50000000000000000 },
 296   { 1.2677758800420666, -0.30000000000000004, 0.59999999999999998 },
 297   { 1.2294913236274980, -0.30000000000000004, 0.69999999999999996 },
 298   { 1.1944567571590046, -0.30000000000000004, 0.80000000000000004 },
 299   { 1.1622376896064912, -0.30000000000000004, 0.90000000000000002 },
 300 };
 301
 302 // Test function for k=-0.30000000000000004.
 303 template <typename Tp>
 304 void test007()
 305 {
 306   const Tp eps = std::numeric_limits<Tp>::epsilon();
 307   Tp max_abs_diff = -Tp(1);
 308   Tp max_abs_frac = -Tp(1);
 309   unsigned int num_datum = sizeof(data007)
 310                          / sizeof(testcase_comp_ellint_3<double>);
 311   for (unsigned int i = 0; i < num_datum; ++i)
 312     {
 313       const Tp f = std::tr1::comp_ellint_3(Tp(data007[i].k), Tp(data007[i].nu));
 314       const Tp f0 = data007[i].f0;
 315       const Tp diff = f - f0;
 316       if (std::abs(diff) > max_abs_diff)
 317         max_abs_diff = std::abs(diff);
 318       if (std::abs(f0) > Tp(10) * eps
 319        && std::abs(f) > Tp(10) * eps)
 320         {
 321           const Tp frac = diff / f0;
 322           if (std::abs(frac) > max_abs_frac)
 323             max_abs_frac = std::abs(frac);
 324         }
 325     }
 326   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 327 }
 328
 329 // Test data for k=-0.19999999999999996.
 330 testcase_comp_ellint_3<double> data008[] = {
 331   { 1.5868678474541664, -0.19999999999999996, 0.0000000000000000 },
 332   { 1.5126513474261092, -0.19999999999999996, 0.10000000000000001 },
 333   { 1.4479323932249568, -0.19999999999999996, 0.20000000000000001 },
 334   { 1.3908453514752481, -0.19999999999999996, 0.29999999999999999 },
 335   { 1.3400002519661010, -0.19999999999999996, 0.40000000000000002 },
 336   { 1.2943374404397376, -0.19999999999999996, 0.50000000000000000 },
 337   { 1.2530330675914561, -0.19999999999999996, 0.59999999999999998 },
 338   { 1.2154356555075867, -0.19999999999999996, 0.69999999999999996 },
 339   { 1.1810223448909913, -0.19999999999999996, 0.80000000000000004 },
 340   { 1.1493679916141863, -0.19999999999999996, 0.90000000000000002 },
 341 };
 342
 343 // Test function for k=-0.19999999999999996.
 344 template <typename Tp>
 345 void test008()
 346 {
 347   const Tp eps = std::numeric_limits<Tp>::epsilon();
 348   Tp max_abs_diff = -Tp(1);
 349   Tp max_abs_frac = -Tp(1);
 350   unsigned int num_datum = sizeof(data008)
 351                          / sizeof(testcase_comp_ellint_3<double>);
 352   for (unsigned int i = 0; i < num_datum; ++i)
 353     {
 354       const Tp f = std::tr1::comp_ellint_3(Tp(data008[i].k), Tp(data008[i].nu));
 355       const Tp f0 = data008[i].f0;
 356       const Tp diff = f - f0;
 357       if (std::abs(diff) > max_abs_diff)
 358         max_abs_diff = std::abs(diff);
 359       if (std::abs(f0) > Tp(10) * eps
 360        && std::abs(f) > Tp(10) * eps)
 361         {
 362           const Tp frac = diff / f0;
 363           if (std::abs(frac) > max_abs_frac)
 364             max_abs_frac = std::abs(frac);
 365         }
 366     }
 367   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 368 }
 369
 370 // Test data for k=-0.099999999999999978.
 371 testcase_comp_ellint_3<double> data009[] = {
 372   { 1.5747455615173562, -0.099999999999999978, 0.0000000000000000 },
 373   { 1.5013711111199950, -0.099999999999999978, 0.10000000000000001 },
 374   { 1.4373749386463430, -0.099999999999999978, 0.20000000000000001 },
 375   { 1.3809159606704959, -0.099999999999999978, 0.29999999999999999 },
 376   { 1.3306223265207477, -0.099999999999999978, 0.40000000000000002 },
 377   { 1.2854480708580160, -0.099999999999999978, 0.50000000000000000 },
 378   { 1.2445798942989255, -0.099999999999999978, 0.59999999999999998 },
 379   { 1.2073745911083187, -0.099999999999999978, 0.69999999999999996 },
 380   { 1.1733158866987732, -0.099999999999999978, 0.80000000000000004 },
 381   { 1.1419839485283374, -0.099999999999999978, 0.90000000000000002 },
 382 };
 383
 384 // Test function for k=-0.099999999999999978.
 385 template <typename Tp>
 386 void test009()
 387 {
 388   const Tp eps = std::numeric_limits<Tp>::epsilon();
 389   Tp max_abs_diff = -Tp(1);
 390   Tp max_abs_frac = -Tp(1);
 391   unsigned int num_datum = sizeof(data009)
 392                          / sizeof(testcase_comp_ellint_3<double>);
 393   for (unsigned int i = 0; i < num_datum; ++i)
 394     {
 395       const Tp f = std::tr1::comp_ellint_3(Tp(data009[i].k), Tp(data009[i].nu));
 396       const Tp f0 = data009[i].f0;
 397       const Tp diff = f - f0;
 398       if (std::abs(diff) > max_abs_diff)
 399         max_abs_diff = std::abs(diff);
 400       if (std::abs(f0) > Tp(10) * eps
 401        && std::abs(f) > Tp(10) * eps)
 402         {
 403           const Tp frac = diff / f0;
 404           if (std::abs(frac) > max_abs_frac)
 405             max_abs_frac = std::abs(frac);
 406         }
 407     }
 408   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 409 }
 410
 411 // Test data for k=0.0000000000000000.
 412 testcase_comp_ellint_3<double> data010[] = {
 413   { 1.5707963267948966, 0.0000000000000000, 0.0000000000000000 },
 414   { 1.4976955329233277, 0.0000000000000000, 0.10000000000000001 },
 415   { 1.4339343023863691, 0.0000000000000000, 0.20000000000000001 },
 416   { 1.3776795151134889, 0.0000000000000000, 0.29999999999999999 },
 417   { 1.3275651989026322, 0.0000000000000000, 0.40000000000000002 },
 418   { 1.2825498301618641, 0.0000000000000000, 0.50000000000000000 },
 419   { 1.2418235332245127, 0.0000000000000000, 0.59999999999999998 },
 420   { 1.2047457872617382, 0.0000000000000000, 0.69999999999999996 },
 421   { 1.1708024551734544, 0.0000000000000000, 0.80000000000000004 },
 422   { 1.1395754288497419, 0.0000000000000000, 0.90000000000000002 },
 423 };
 424
 425 // Test function for k=0.0000000000000000.
 426 template <typename Tp>
 427 void test010()
 428 {
 429   const Tp eps = std::numeric_limits<Tp>::epsilon();
 430   Tp max_abs_diff = -Tp(1);
 431   Tp max_abs_frac = -Tp(1);
 432   unsigned int num_datum = sizeof(data010)
 433                          / sizeof(testcase_comp_ellint_3<double>);
 434   for (unsigned int i = 0; i < num_datum; ++i)
 435     {
 436       const Tp f = std::tr1::comp_ellint_3(Tp(data010[i].k), Tp(data010[i].nu));
 437       const Tp f0 = data010[i].f0;
 438       const Tp diff = f - f0;
 439       if (std::abs(diff) > max_abs_diff)
 440         max_abs_diff = std::abs(diff);
 441       if (std::abs(f0) > Tp(10) * eps
 442        && std::abs(f) > Tp(10) * eps)
 443         {
 444           const Tp frac = diff / f0;
 445           if (std::abs(frac) > max_abs_frac)
 446             max_abs_frac = std::abs(frac);
 447         }
 448     }
 449   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 450 }
 451
 452 // Test data for k=0.10000000000000009.
 453 testcase_comp_ellint_3<double> data011[] = {
 454   { 1.5747455615173562, 0.10000000000000009, 0.0000000000000000 },
 455   { 1.5013711111199950, 0.10000000000000009, 0.10000000000000001 },
 456   { 1.4373749386463430, 0.10000000000000009, 0.20000000000000001 },
 457   { 1.3809159606704959, 0.10000000000000009, 0.29999999999999999 },
 458   { 1.3306223265207477, 0.10000000000000009, 0.40000000000000002 },
 459   { 1.2854480708580160, 0.10000000000000009, 0.50000000000000000 },
 460   { 1.2445798942989255, 0.10000000000000009, 0.59999999999999998 },
 461   { 1.2073745911083187, 0.10000000000000009, 0.69999999999999996 },
 462   { 1.1733158866987732, 0.10000000000000009, 0.80000000000000004 },
 463   { 1.1419839485283374, 0.10000000000000009, 0.90000000000000002 },
 464 };
 465
 466 // Test function for k=0.10000000000000009.
 467 template <typename Tp>
 468 void test011()
 469 {
 470   const Tp eps = std::numeric_limits<Tp>::epsilon();
 471   Tp max_abs_diff = -Tp(1);
 472   Tp max_abs_frac = -Tp(1);
 473   unsigned int num_datum = sizeof(data011)
 474                          / sizeof(testcase_comp_ellint_3<double>);
 475   for (unsigned int i = 0; i < num_datum; ++i)
 476     {
 477       const Tp f = std::tr1::comp_ellint_3(Tp(data011[i].k), Tp(data011[i].nu));
 478       const Tp f0 = data011[i].f0;
 479       const Tp diff = f - f0;
 480       if (std::abs(diff) > max_abs_diff)
 481         max_abs_diff = std::abs(diff);
 482       if (std::abs(f0) > Tp(10) * eps
 483        && std::abs(f) > Tp(10) * eps)
 484         {
 485           const Tp frac = diff / f0;
 486           if (std::abs(frac) > max_abs_frac)
 487             max_abs_frac = std::abs(frac);
 488         }
 489     }
 490   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 491 }
 492
 493 // Test data for k=0.19999999999999996.
 494 testcase_comp_ellint_3<double> data012[] = {
 495   { 1.5868678474541664, 0.19999999999999996, 0.0000000000000000 },
 496   { 1.5126513474261092, 0.19999999999999996, 0.10000000000000001 },
 497   { 1.4479323932249568, 0.19999999999999996, 0.20000000000000001 },
 498   { 1.3908453514752481, 0.19999999999999996, 0.29999999999999999 },
 499   { 1.3400002519661010, 0.19999999999999996, 0.40000000000000002 },
 500   { 1.2943374404397376, 0.19999999999999996, 0.50000000000000000 },
 501   { 1.2530330675914561, 0.19999999999999996, 0.59999999999999998 },
 502   { 1.2154356555075867, 0.19999999999999996, 0.69999999999999996 },
 503   { 1.1810223448909913, 0.19999999999999996, 0.80000000000000004 },
 504   { 1.1493679916141863, 0.19999999999999996, 0.90000000000000002 },
 505 };
 506
 507 // Test function for k=0.19999999999999996.
 508 template <typename Tp>
 509 void test012()
 510 {
 511   const Tp eps = std::numeric_limits<Tp>::epsilon();
 512   Tp max_abs_diff = -Tp(1);
 513   Tp max_abs_frac = -Tp(1);
 514   unsigned int num_datum = sizeof(data012)
 515                          / sizeof(testcase_comp_ellint_3<double>);
 516   for (unsigned int i = 0; i < num_datum; ++i)
 517     {
 518       const Tp f = std::tr1::comp_ellint_3(Tp(data012[i].k), Tp(data012[i].nu));
 519       const Tp f0 = data012[i].f0;
 520       const Tp diff = f - f0;
 521       if (std::abs(diff) > max_abs_diff)
 522         max_abs_diff = std::abs(diff);
 523       if (std::abs(f0) > Tp(10) * eps
 524        && std::abs(f) > Tp(10) * eps)
 525         {
 526           const Tp frac = diff / f0;
 527           if (std::abs(frac) > max_abs_frac)
 528             max_abs_frac = std::abs(frac);
 529         }
 530     }
 531   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 532 }
 533
 534 // Test data for k=0.30000000000000004.
 535 testcase_comp_ellint_3<double> data013[] = {
 536   { 1.6080486199305126, 0.30000000000000004, 0.0000000000000000 },
 537   { 1.5323534693557526, 0.30000000000000004, 0.10000000000000001 },
 538   { 1.4663658145259875, 0.30000000000000004, 0.20000000000000001 },
 539   { 1.4081767433479089, 0.30000000000000004, 0.29999999999999999 },
 540   { 1.3563643538969761, 0.30000000000000004, 0.40000000000000002 },
 541   { 1.3098448759814960, 0.30000000000000004, 0.50000000000000000 },
 542   { 1.2677758800420666, 0.30000000000000004, 0.59999999999999998 },
 543   { 1.2294913236274980, 0.30000000000000004, 0.69999999999999996 },
 544   { 1.1944567571590046, 0.30000000000000004, 0.80000000000000004 },
 545   { 1.1622376896064912, 0.30000000000000004, 0.90000000000000002 },
 546 };
 547
 548 // Test function for k=0.30000000000000004.
 549 template <typename Tp>
 550 void test013()
 551 {
 552   const Tp eps = std::numeric_limits<Tp>::epsilon();
 553   Tp max_abs_diff = -Tp(1);
 554   Tp max_abs_frac = -Tp(1);
 555   unsigned int num_datum = sizeof(data013)
 556                          / sizeof(testcase_comp_ellint_3<double>);
 557   for (unsigned int i = 0; i < num_datum; ++i)
 558     {
 559       const Tp f = std::tr1::comp_ellint_3(Tp(data013[i].k), Tp(data013[i].nu));
 560       const Tp f0 = data013[i].f0;
 561       const Tp diff = f - f0;
 562       if (std::abs(diff) > max_abs_diff)
 563         max_abs_diff = std::abs(diff);
 564       if (std::abs(f0) > Tp(10) * eps
 565        && std::abs(f) > Tp(10) * eps)
 566         {
 567           const Tp frac = diff / f0;
 568           if (std::abs(frac) > max_abs_frac)
 569             max_abs_frac = std::abs(frac);
 570         }
 571     }
 572   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 573 }
 574
 575 // Test data for k=0.39999999999999991.
 576 testcase_comp_ellint_3<double> data014[] = {
 577   { 1.6399998658645112, 0.39999999999999991, 0.0000000000000000 },
 578   { 1.5620566886683604, 0.39999999999999991, 0.10000000000000001 },
 579   { 1.4941414344266770, 0.39999999999999991, 0.20000000000000001 },
 580   { 1.4342789859950078, 0.39999999999999991, 0.29999999999999999 },
 581   { 1.3809986210732901, 0.39999999999999991, 0.40000000000000002 },
 582   { 1.3331797176377398, 0.39999999999999991, 0.50000000000000000 },
 583   { 1.2899514672527024, 0.39999999999999991, 0.59999999999999998 },
 584   { 1.2506255923253344, 0.39999999999999991, 0.69999999999999996 },
 585   { 1.2146499565727209, 0.39999999999999991, 0.80000000000000004 },
 586   { 1.1815758115929846, 0.39999999999999991, 0.90000000000000002 },
 587 };
 588
 589 // Test function for k=0.39999999999999991.
 590 template <typename Tp>
 591 void test014()
 592 {
 593   const Tp eps = std::numeric_limits<Tp>::epsilon();
 594   Tp max_abs_diff = -Tp(1);
 595   Tp max_abs_frac = -Tp(1);
 596   unsigned int num_datum = sizeof(data014)
 597                          / sizeof(testcase_comp_ellint_3<double>);
 598   for (unsigned int i = 0; i < num_datum; ++i)
 599     {
 600       const Tp f = std::tr1::comp_ellint_3(Tp(data014[i].k), Tp(data014[i].nu));
 601       const Tp f0 = data014[i].f0;
 602       const Tp diff = f - f0;
 603       if (std::abs(diff) > max_abs_diff)
 604         max_abs_diff = std::abs(diff);
 605       if (std::abs(f0) > Tp(10) * eps
 606        && std::abs(f) > Tp(10) * eps)
 607         {
 608           const Tp frac = diff / f0;
 609           if (std::abs(frac) > max_abs_frac)
 610             max_abs_frac = std::abs(frac);
 611         }
 612     }
 613   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 614 }
 615
 616 // Test data for k=0.50000000000000000.
 617 testcase_comp_ellint_3<double> data015[] = {
 618   { 1.6857503548125963, 0.50000000000000000, 0.0000000000000000 },
 619   { 1.6045524936084892, 0.50000000000000000, 0.10000000000000001 },
 620   { 1.5338490483665983, 0.50000000000000000, 0.20000000000000001 },
 621   { 1.4715681939859637, 0.50000000000000000, 0.29999999999999999 },
 622   { 1.4161679518465340, 0.50000000000000000, 0.40000000000000002 },
 623   { 1.3664739530045971, 0.50000000000000000, 0.50000000000000000 },
 624   { 1.3215740290190876, 0.50000000000000000, 0.59999999999999998 },
 625   { 1.2807475181182502, 0.50000000000000000, 0.69999999999999996 },
 626   { 1.2434165408189539, 0.50000000000000000, 0.80000000000000004 },
 627   { 1.2091116095504744, 0.50000000000000000, 0.90000000000000002 },
 628 };
 629
 630 // Test function for k=0.50000000000000000.
 631 template <typename Tp>
 632 void test015()
 633 {
 634   const Tp eps = std::numeric_limits<Tp>::epsilon();
 635   Tp max_abs_diff = -Tp(1);
 636   Tp max_abs_frac = -Tp(1);
 637   unsigned int num_datum = sizeof(data015)
 638                          / sizeof(testcase_comp_ellint_3<double>);
 639   for (unsigned int i = 0; i < num_datum; ++i)
 640     {
 641       const Tp f = std::tr1::comp_ellint_3(Tp(data015[i].k), Tp(data015[i].nu));
 642       const Tp f0 = data015[i].f0;
 643       const Tp diff = f - f0;
 644       if (std::abs(diff) > max_abs_diff)
 645         max_abs_diff = std::abs(diff);
 646       if (std::abs(f0) > Tp(10) * eps
 647        && std::abs(f) > Tp(10) * eps)
 648         {
 649           const Tp frac = diff / f0;
 650           if (std::abs(frac) > max_abs_frac)
 651             max_abs_frac = std::abs(frac);
 652         }
 653     }
 654   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 655 }
 656
 657 // Test data for k=0.60000000000000009.
 658 testcase_comp_ellint_3<double> data016[] = {
 659   { 1.7507538029157526, 0.60000000000000009, 0.0000000000000000 },
 660   { 1.6648615773343014, 0.60000000000000009, 0.10000000000000001 },
 661   { 1.5901418016279374, 0.60000000000000009, 0.20000000000000001 },
 662   { 1.5243814243493585, 0.60000000000000009, 0.29999999999999999 },
 663   { 1.4659345278069984, 0.60000000000000009, 0.40000000000000002 },
 664   { 1.4135484285693078, 0.60000000000000009, 0.50000000000000000 },
 665   { 1.3662507535812816, 0.60000000000000009, 0.59999999999999998 },
 666   { 1.3232737468822811, 0.60000000000000009, 0.69999999999999996 },
 667   { 1.2840021261752192, 0.60000000000000009, 0.80000000000000004 },
 668   { 1.2479362973851875, 0.60000000000000009, 0.90000000000000002 },
 669 };
 670
 671 // Test function for k=0.60000000000000009.
 672 template <typename Tp>
 673 void test016()
 674 {
 675   const Tp eps = std::numeric_limits<Tp>::epsilon();
 676   Tp max_abs_diff = -Tp(1);
 677   Tp max_abs_frac = -Tp(1);
 678   unsigned int num_datum = sizeof(data016)
 679                          / sizeof(testcase_comp_ellint_3<double>);
 680   for (unsigned int i = 0; i < num_datum; ++i)
 681     {
 682       const Tp f = std::tr1::comp_ellint_3(Tp(data016[i].k), Tp(data016[i].nu));
 683       const Tp f0 = data016[i].f0;
 684       const Tp diff = f - f0;
 685       if (std::abs(diff) > max_abs_diff)
 686         max_abs_diff = std::abs(diff);
 687       if (std::abs(f0) > Tp(10) * eps
 688        && std::abs(f) > Tp(10) * eps)
 689         {
 690           const Tp frac = diff / f0;
 691           if (std::abs(frac) > max_abs_frac)
 692             max_abs_frac = std::abs(frac);
 693         }
 694     }
 695   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 696 }
 697
 698 // Test data for k=0.69999999999999996.
 699 testcase_comp_ellint_3<double> data017[] = {
 700   { 1.8456939983747236, 0.69999999999999996, 0.0000000000000000 },
 701   { 1.7528050171757608, 0.69999999999999996, 0.10000000000000001 },
 702   { 1.6721098780092147, 0.69999999999999996, 0.20000000000000001 },
 703   { 1.6011813647733213, 0.69999999999999996, 0.29999999999999999 },
 704   { 1.5382162002954762, 0.69999999999999996, 0.40000000000000002 },
 705   { 1.4818433192178544, 0.69999999999999996, 0.50000000000000000 },
 706   { 1.4309994736080540, 0.69999999999999996, 0.59999999999999998 },
 707   { 1.3848459188329196, 0.69999999999999996, 0.69999999999999996 },
 708   { 1.3427110650397533, 0.69999999999999996, 0.80000000000000004 },
 709   { 1.3040500499695911, 0.69999999999999996, 0.90000000000000002 },
 710 };
 711
 712 // Test function for k=0.69999999999999996.
 713 template <typename Tp>
 714 void test017()
 715 {
 716   const Tp eps = std::numeric_limits<Tp>::epsilon();
 717   Tp max_abs_diff = -Tp(1);
 718   Tp max_abs_frac = -Tp(1);
 719   unsigned int num_datum = sizeof(data017)
 720                          / sizeof(testcase_comp_ellint_3<double>);
 721   for (unsigned int i = 0; i < num_datum; ++i)
 722     {
 723       const Tp f = std::tr1::comp_ellint_3(Tp(data017[i].k), Tp(data017[i].nu));
 724       const Tp f0 = data017[i].f0;
 725       const Tp diff = f - f0;
 726       if (std::abs(diff) > max_abs_diff)
 727         max_abs_diff = std::abs(diff);
 728       if (std::abs(f0) > Tp(10) * eps
 729        && std::abs(f) > Tp(10) * eps)
 730         {
 731           const Tp frac = diff / f0;
 732           if (std::abs(frac) > max_abs_frac)
 733             max_abs_frac = std::abs(frac);
 734         }
 735     }
 736   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 737 }
 738
 739 // Test data for k=0.80000000000000004.
 740 testcase_comp_ellint_3<double> data018[] = {
 741   { 1.9953027776647296, 0.80000000000000004, 0.0000000000000000 },
 742   { 1.8910755418379521, 0.80000000000000004, 0.10000000000000001 },
 743   { 1.8007226661734588, 0.80000000000000004, 0.20000000000000001 },
 744   { 1.7214611048717301, 0.80000000000000004, 0.29999999999999999 },
 745   { 1.6512267838651289, 0.80000000000000004, 0.40000000000000002 },
 746   { 1.5884528947755532, 0.80000000000000004, 0.50000000000000000 },
 747   { 1.5319262547427865, 0.80000000000000004, 0.59999999999999998 },
 748   { 1.4806912324625332, 0.80000000000000004, 0.69999999999999996 },
 749   { 1.4339837018309474, 0.80000000000000004, 0.80000000000000004 },
 750   { 1.3911845406776222, 0.80000000000000004, 0.90000000000000002 },
 751 };
 752
 753 // Test function for k=0.80000000000000004.
 754 template <typename Tp>
 755 void test018()
 756 {
 757   const Tp eps = std::numeric_limits<Tp>::epsilon();
 758   Tp max_abs_diff = -Tp(1);
 759   Tp max_abs_frac = -Tp(1);
 760   unsigned int num_datum = sizeof(data018)
 761                          / sizeof(testcase_comp_ellint_3<double>);
 762   for (unsigned int i = 0; i < num_datum; ++i)
 763     {
 764       const Tp f = std::tr1::comp_ellint_3(Tp(data018[i].k), Tp(data018[i].nu));
 765       const Tp f0 = data018[i].f0;
 766       const Tp diff = f - f0;
 767       if (std::abs(diff) > max_abs_diff)
 768         max_abs_diff = std::abs(diff);
 769       if (std::abs(f0) > Tp(10) * eps
 770        && std::abs(f) > Tp(10) * eps)
 771         {
 772           const Tp frac = diff / f0;
 773           if (std::abs(frac) > max_abs_frac)
 774             max_abs_frac = std::abs(frac);
 775         }
 776     }
 777   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 778 }
 779
 780 // Test data for k=0.89999999999999991.
 781 testcase_comp_ellint_3<double> data019[] = {
 782   { 2.2805491384227699, 0.89999999999999991, 0.0000000000000000 },
 783   { 2.1537868513875282, 0.89999999999999991, 0.10000000000000001 },
 784   { 2.0443194576468890, 0.89999999999999991, 0.20000000000000001 },
 785   { 1.9486280260314424, 0.89999999999999991, 0.29999999999999999 },
 786   { 1.8641114227238347, 0.89999999999999991, 0.40000000000000002 },
 787   { 1.7888013241937859, 0.89999999999999991, 0.50000000000000000 },
 788   { 1.7211781128919521, 0.89999999999999991, 0.59999999999999998 },
 789   { 1.6600480747670936, 0.89999999999999991, 0.69999999999999996 },
 790   { 1.6044591960982200, 0.89999999999999991, 0.80000000000000004 },
 791   { 1.5536420236310944, 0.89999999999999991, 0.90000000000000002 },
 792 };
 793
 794 // Test function for k=0.89999999999999991.
 795 template <typename Tp>
 796 void test019()
 797 {
 798   const Tp eps = std::numeric_limits<Tp>::epsilon();
 799   Tp max_abs_diff = -Tp(1);
 800   Tp max_abs_frac = -Tp(1);
 801   unsigned int num_datum = sizeof(data019)
 802                          / sizeof(testcase_comp_ellint_3<double>);
 803   for (unsigned int i = 0; i < num_datum; ++i)
 804     {
 805       const Tp f = std::tr1::comp_ellint_3(Tp(data019[i].k), Tp(data019[i].nu));
 806       const Tp f0 = data019[i].f0;
 807       const Tp diff = f - f0;
 808       if (std::abs(diff) > max_abs_diff)
 809         max_abs_diff = std::abs(diff);
 810       if (std::abs(f0) > Tp(10) * eps
 811        && std::abs(f) > Tp(10) * eps)
 812         {
 813           const Tp frac = diff / f0;
 814           if (std::abs(frac) > max_abs_frac)
 815             max_abs_frac = std::abs(frac);
 816         }
 817     }
 818   VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 819 }
 820
 821 int main(int, char**)
 822 {
 823   test001<double>();
 824   test002<double>();
 825   test003<double>();
 826   test004<double>();
 827   test005<double>();
 828   test006<double>();
 829   test007<double>();
 830   test008<double>();
 831   test009<double>();
 832   test010<double>();
 833   test011<double>();
 834   test012<double>();
 835   test013<double>();
 836   test014<double>();
 837   test015<double>();
 838   test016<double>();
 839   test017<double>();
 840   test018<double>();
 841   test019<double>();
 842   return 0;
 843 }