libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/16_hermite/check_value.cc

   1 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
   2 //
   3 // Copyright (C) 2016 Free Software Foundation, Inc.
   4 //
   5 // This file is part of the GNU ISO C++ Library.  This library is free
   6 // software; you can redistribute it and/or modify it under the
   7 // terms of the GNU General Public License as published by the
   8 // Free Software Foundation; either version 3, or (at your option)
   9 // any later version.
  10 //
  11 // This library is distributed in the hope that it will be useful,
  12 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14 // GNU General Public License for more details.
  15 //
  16 // You should have received a copy of the GNU General Public License along
  17 // with this library; see the file COPYING3.  If not see
  18 // <http://www.gnu.org/licenses/>.
  19
  20 //  hermite
  21 //  Compare against values generated by the GNU Scientific Library.
  22 //  The GSL can be found on the web: http://www.gnu.org/software/gsl/
  23 #include <limits>
  24 #include <tr1/cmath>
  25 #if defined(__TEST_DEBUG)
  26 #  include <iostream>
  27 #  define VERIFY(A) \
  28   if (!(A)) \
  29     { \
  30       std::cout << "line " << __LINE__ \
  31         << "  max_abs_frac = " << max_abs_frac \
  32         << std::endl; \
  33     }
  34 #else
  35 #  include <testsuite_hooks.h>
  36 #endif
  37 #include <specfun_testcase.h>
  38
  39
  40 // Test data for n=0.
  41 // max(|f - f_GSL|): 0.0000000000000000
  42 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
  43 testcase_hermite<double>
  44 data001[] =
  45 {
  46   { 1.0000000000000000, 0, -10.000000000000000 },
  47   { 1.0000000000000000, 0, -9.9000000000000004 },
  48   { 1.0000000000000000, 0, -9.8000000000000007 },
  49   { 1.0000000000000000, 0, -9.6999999999999993 },
  50   { 1.0000000000000000, 0, -9.5999999999999996 },
  51   { 1.0000000000000000, 0, -9.5000000000000000 },
  52   { 1.0000000000000000, 0, -9.4000000000000004 },
  53   { 1.0000000000000000, 0, -9.3000000000000007 },
  54   { 1.0000000000000000, 0, -9.1999999999999993 },
  55   { 1.0000000000000000, 0, -9.0999999999999996 },
  56   { 1.0000000000000000, 0, -9.0000000000000000 },
  57   { 1.0000000000000000, 0, -8.9000000000000004 },
  58   { 1.0000000000000000, 0, -8.8000000000000007 },
  59   { 1.0000000000000000, 0, -8.6999999999999993 },
  60   { 1.0000000000000000, 0, -8.5999999999999996 },
  61   { 1.0000000000000000, 0, -8.5000000000000000 },
  62   { 1.0000000000000000, 0, -8.4000000000000004 },
  63   { 1.0000000000000000, 0, -8.3000000000000007 },
  64   { 1.0000000000000000, 0, -8.1999999999999993 },
  65   { 1.0000000000000000, 0, -8.0999999999999996 },
  66   { 1.0000000000000000, 0, -8.0000000000000000 },
  67   { 1.0000000000000000, 0, -7.9000000000000004 },
  68   { 1.0000000000000000, 0, -7.7999999999999998 },
  69   { 1.0000000000000000, 0, -7.7000000000000002 },
  70   { 1.0000000000000000, 0, -7.5999999999999996 },
  71   { 1.0000000000000000, 0, -7.5000000000000000 },
  72   { 1.0000000000000000, 0, -7.4000000000000004 },
  73   { 1.0000000000000000, 0, -7.2999999999999998 },
  74   { 1.0000000000000000, 0, -7.2000000000000002 },
  75   { 1.0000000000000000, 0, -7.0999999999999996 },
  76   { 1.0000000000000000, 0, -7.0000000000000000 },
  77   { 1.0000000000000000, 0, -6.9000000000000004 },
  78   { 1.0000000000000000, 0, -6.7999999999999998 },
  79   { 1.0000000000000000, 0, -6.7000000000000002 },
  80   { 1.0000000000000000, 0, -6.5999999999999996 },
  81   { 1.0000000000000000, 0, -6.5000000000000000 },
  82   { 1.0000000000000000, 0, -6.4000000000000004 },
  83   { 1.0000000000000000, 0, -6.2999999999999998 },
  84   { 1.0000000000000000, 0, -6.2000000000000002 },
  85   { 1.0000000000000000, 0, -6.0999999999999996 },
  86   { 1.0000000000000000, 0, -6.0000000000000000 },
  87   { 1.0000000000000000, 0, -5.9000000000000004 },
  88   { 1.0000000000000000, 0, -5.7999999999999998 },
  89   { 1.0000000000000000, 0, -5.7000000000000002 },
  90   { 1.0000000000000000, 0, -5.5999999999999996 },
  91   { 1.0000000000000000, 0, -5.5000000000000000 },
  92   { 1.0000000000000000, 0, -5.4000000000000004 },
  93   { 1.0000000000000000, 0, -5.2999999999999998 },
  94   { 1.0000000000000000, 0, -5.2000000000000002 },
  95   { 1.0000000000000000, 0, -5.0999999999999996 },
  96   { 1.0000000000000000, 0, -5.0000000000000000 },
  97   { 1.0000000000000000, 0, -4.9000000000000004 },
  98   { 1.0000000000000000, 0, -4.7999999999999998 },
  99   { 1.0000000000000000, 0, -4.7000000000000002 },
 100   { 1.0000000000000000, 0, -4.5999999999999996 },
 101   { 1.0000000000000000, 0, -4.5000000000000000 },
 102   { 1.0000000000000000, 0, -4.4000000000000004 },
 103   { 1.0000000000000000, 0, -4.2999999999999998 },
 104   { 1.0000000000000000, 0, -4.2000000000000002 },
 105   { 1.0000000000000000, 0, -4.0999999999999996 },
 106   { 1.0000000000000000, 0, -4.0000000000000000 },
 107   { 1.0000000000000000, 0, -3.9000000000000004 },
 108   { 1.0000000000000000, 0, -3.7999999999999998 },
 109   { 1.0000000000000000, 0, -3.7000000000000002 },
 110   { 1.0000000000000000, 0, -3.5999999999999996 },
 111   { 1.0000000000000000, 0, -3.5000000000000000 },
 112   { 1.0000000000000000, 0, -3.4000000000000004 },
 113   { 1.0000000000000000, 0, -3.2999999999999998 },
 114   { 1.0000000000000000, 0, -3.2000000000000002 },
 115   { 1.0000000000000000, 0, -3.0999999999999996 },
 116   { 1.0000000000000000, 0, -3.0000000000000000 },
 117   { 1.0000000000000000, 0, -2.9000000000000004 },
 118   { 1.0000000000000000, 0, -2.7999999999999998 },
 119   { 1.0000000000000000, 0, -2.7000000000000002 },
 120   { 1.0000000000000000, 0, -2.5999999999999996 },
 121   { 1.0000000000000000, 0, -2.5000000000000000 },
 122   { 1.0000000000000000, 0, -2.4000000000000004 },
 123   { 1.0000000000000000, 0, -2.2999999999999998 },
 124   { 1.0000000000000000, 0, -2.2000000000000002 },
 125   { 1.0000000000000000, 0, -2.0999999999999996 },
 126   { 1.0000000000000000, 0, -2.0000000000000000 },
 127   { 1.0000000000000000, 0, -1.9000000000000004 },
 128   { 1.0000000000000000, 0, -1.8000000000000007 },
 129   { 1.0000000000000000, 0, -1.6999999999999993 },
 130   { 1.0000000000000000, 0, -1.5999999999999996 },
 131   { 1.0000000000000000, 0, -1.5000000000000000 },
 132   { 1.0000000000000000, 0, -1.4000000000000004 },
 133   { 1.0000000000000000, 0, -1.3000000000000007 },
 134   { 1.0000000000000000, 0, -1.1999999999999993 },
 135   { 1.0000000000000000, 0, -1.0999999999999996 },
 136   { 1.0000000000000000, 0, -1.0000000000000000 },
 137   { 1.0000000000000000, 0, -0.90000000000000036 },
 138   { 1.0000000000000000, 0, -0.80000000000000071 },
 139   { 1.0000000000000000, 0, -0.69999999999999929 },
 140   { 1.0000000000000000, 0, -0.59999999999999964 },
 141   { 1.0000000000000000, 0, -0.50000000000000000 },
 142   { 1.0000000000000000, 0, -0.40000000000000036 },
 143   { 1.0000000000000000, 0, -0.30000000000000071 },
 144   { 1.0000000000000000, 0, -0.19999999999999929 },
 145   { 1.0000000000000000, 0, -0.099999999999999645 },
 146   { 1.0000000000000000, 0, 0.0000000000000000 },
 147   { 1.0000000000000000, 0, 0.099999999999999645 },
 148   { 1.0000000000000000, 0, 0.19999999999999929 },
 149   { 1.0000000000000000, 0, 0.30000000000000071 },
 150   { 1.0000000000000000, 0, 0.40000000000000036 },
 151   { 1.0000000000000000, 0, 0.50000000000000000 },
 152   { 1.0000000000000000, 0, 0.59999999999999964 },
 153   { 1.0000000000000000, 0, 0.69999999999999929 },
 154   { 1.0000000000000000, 0, 0.80000000000000071 },
 155   { 1.0000000000000000, 0, 0.90000000000000036 },
 156   { 1.0000000000000000, 0, 1.0000000000000000 },
 157   { 1.0000000000000000, 0, 1.0999999999999996 },
 158   { 1.0000000000000000, 0, 1.1999999999999993 },
 159   { 1.0000000000000000, 0, 1.3000000000000007 },
 160   { 1.0000000000000000, 0, 1.4000000000000004 },
 161   { 1.0000000000000000, 0, 1.5000000000000000 },
 162   { 1.0000000000000000, 0, 1.5999999999999996 },
 163   { 1.0000000000000000, 0, 1.6999999999999993 },
 164   { 1.0000000000000000, 0, 1.8000000000000007 },
 165   { 1.0000000000000000, 0, 1.9000000000000004 },
 166   { 1.0000000000000000, 0, 2.0000000000000000 },
 167   { 1.0000000000000000, 0, 2.0999999999999996 },
 168   { 1.0000000000000000, 0, 2.1999999999999993 },
 169   { 1.0000000000000000, 0, 2.3000000000000007 },
 170   { 1.0000000000000000, 0, 2.4000000000000004 },
 171   { 1.0000000000000000, 0, 2.5000000000000000 },
 172   { 1.0000000000000000, 0, 2.5999999999999996 },
 173   { 1.0000000000000000, 0, 2.6999999999999993 },
 174   { 1.0000000000000000, 0, 2.8000000000000007 },
 175   { 1.0000000000000000, 0, 2.9000000000000004 },
 176   { 1.0000000000000000, 0, 3.0000000000000000 },
 177   { 1.0000000000000000, 0, 3.0999999999999996 },
 178   { 1.0000000000000000, 0, 3.1999999999999993 },
 179   { 1.0000000000000000, 0, 3.3000000000000007 },
 180   { 1.0000000000000000, 0, 3.4000000000000004 },
 181   { 1.0000000000000000, 0, 3.5000000000000000 },
 182   { 1.0000000000000000, 0, 3.5999999999999996 },
 183   { 1.0000000000000000, 0, 3.6999999999999993 },
 184   { 1.0000000000000000, 0, 3.8000000000000007 },
 185   { 1.0000000000000000, 0, 3.9000000000000004 },
 186   { 1.0000000000000000, 0, 4.0000000000000000 },
 187   { 1.0000000000000000, 0, 4.0999999999999996 },
 188   { 1.0000000000000000, 0, 4.1999999999999993 },
 189   { 1.0000000000000000, 0, 4.3000000000000007 },
 190   { 1.0000000000000000, 0, 4.4000000000000004 },
 191   { 1.0000000000000000, 0, 4.5000000000000000 },
 192   { 1.0000000000000000, 0, 4.5999999999999996 },
 193   { 1.0000000000000000, 0, 4.6999999999999993 },
 194   { 1.0000000000000000, 0, 4.8000000000000007 },
 195   { 1.0000000000000000, 0, 4.9000000000000004 },
 196   { 1.0000000000000000, 0, 5.0000000000000000 },
 197   { 1.0000000000000000, 0, 5.0999999999999996 },
 198   { 1.0000000000000000, 0, 5.1999999999999993 },
 199   { 1.0000000000000000, 0, 5.3000000000000007 },
 200   { 1.0000000000000000, 0, 5.4000000000000004 },
 201   { 1.0000000000000000, 0, 5.5000000000000000 },
 202   { 1.0000000000000000, 0, 5.5999999999999996 },
 203   { 1.0000000000000000, 0, 5.6999999999999993 },
 204   { 1.0000000000000000, 0, 5.8000000000000007 },
 205   { 1.0000000000000000, 0, 5.9000000000000004 },
 206   { 1.0000000000000000, 0, 6.0000000000000000 },
 207   { 1.0000000000000000, 0, 6.1000000000000014 },
 208   { 1.0000000000000000, 0, 6.1999999999999993 },
 209   { 1.0000000000000000, 0, 6.3000000000000007 },
 210   { 1.0000000000000000, 0, 6.3999999999999986 },
 211   { 1.0000000000000000, 0, 6.5000000000000000 },
 212   { 1.0000000000000000, 0, 6.6000000000000014 },
 213   { 1.0000000000000000, 0, 6.6999999999999993 },
 214   { 1.0000000000000000, 0, 6.8000000000000007 },
 215   { 1.0000000000000000, 0, 6.8999999999999986 },
 216   { 1.0000000000000000, 0, 7.0000000000000000 },
 217   { 1.0000000000000000, 0, 7.1000000000000014 },
 218   { 1.0000000000000000, 0, 7.1999999999999993 },
 219   { 1.0000000000000000, 0, 7.3000000000000007 },
 220   { 1.0000000000000000, 0, 7.3999999999999986 },
 221   { 1.0000000000000000, 0, 7.5000000000000000 },
 222   { 1.0000000000000000, 0, 7.6000000000000014 },
 223   { 1.0000000000000000, 0, 7.6999999999999993 },
 224   { 1.0000000000000000, 0, 7.8000000000000007 },
 225   { 1.0000000000000000, 0, 7.8999999999999986 },
 226   { 1.0000000000000000, 0, 8.0000000000000000 },
 227   { 1.0000000000000000, 0, 8.1000000000000014 },
 228   { 1.0000000000000000, 0, 8.1999999999999993 },
 229   { 1.0000000000000000, 0, 8.3000000000000007 },
 230   { 1.0000000000000000, 0, 8.3999999999999986 },
 231   { 1.0000000000000000, 0, 8.5000000000000000 },
 232   { 1.0000000000000000, 0, 8.6000000000000014 },
 233   { 1.0000000000000000, 0, 8.6999999999999993 },
 234   { 1.0000000000000000, 0, 8.8000000000000007 },
 235   { 1.0000000000000000, 0, 8.8999999999999986 },
 236   { 1.0000000000000000, 0, 9.0000000000000000 },
 237   { 1.0000000000000000, 0, 9.1000000000000014 },
 238   { 1.0000000000000000, 0, 9.1999999999999993 },
 239   { 1.0000000000000000, 0, 9.3000000000000007 },
 240   { 1.0000000000000000, 0, 9.3999999999999986 },
 241   { 1.0000000000000000, 0, 9.5000000000000000 },
 242   { 1.0000000000000000, 0, 9.6000000000000014 },
 243   { 1.0000000000000000, 0, 9.6999999999999993 },
 244   { 1.0000000000000000, 0, 9.8000000000000007 },
 245   { 1.0000000000000000, 0, 9.8999999999999986 },
 246   { 1.0000000000000000, 0, 10.000000000000000 },
 247 };
 248
 249 // Test function for n=0.
 250 template<typename Tp>
 251   void
 252   test001()
 253   {
 254     bool test __attribute__((unused)) = true;
 255     const Tp eps = std::numeric_limits<Tp>::epsilon();
 256     Tp max_abs_diff = -Tp(1);
 257     Tp max_abs_frac = -Tp(1);
 258     unsigned int num_datum = sizeof(data001)
 259                            / sizeof(testcase_hermite<double>);
 260     for (unsigned int i = 0; i < num_datum; ++i)
 261       {
 262         const Tp f = std::tr1::hermite(Tp(data001[i].n), Tp(data001[i].x));
 263         const Tp f0 = data001[i].f0;
 264         const Tp diff = f - f0;
 265         if (std::abs(diff) > max_abs_diff)
 266           max_abs_diff = std::abs(diff);
 267         if (std::abs(f0) > Tp(10) * eps
 268          && std::abs(f) > Tp(10) * eps)
 269           {
 270             const Tp frac = diff / f0;
 271             if (std::abs(frac) > max_abs_frac)
 272               max_abs_frac = std::abs(frac);
 273           }
 274       }
 275     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 276   }
 277
 278 // Test data for n=1.
 279 // max(|f - f_GSL|): 0.0000000000000000
 280 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 281 testcase_hermite<double>
 282 data002[] =
 283 {
 284   { -20.000000000000000, 1, -10.000000000000000 },
 285   { -19.800000000000001, 1, -9.9000000000000004 },
 286   { -19.600000000000001, 1, -9.8000000000000007 },
 287   { -19.399999999999999, 1, -9.6999999999999993 },
 288   { -19.199999999999999, 1, -9.5999999999999996 },
 289   { -19.000000000000000, 1, -9.5000000000000000 },
 290   { -18.800000000000001, 1, -9.4000000000000004 },
 291   { -18.600000000000001, 1, -9.3000000000000007 },
 292   { -18.399999999999999, 1, -9.1999999999999993 },
 293   { -18.199999999999999, 1, -9.0999999999999996 },
 294   { -18.000000000000000, 1, -9.0000000000000000 },
 295   { -17.800000000000001, 1, -8.9000000000000004 },
 296   { -17.600000000000001, 1, -8.8000000000000007 },
 297   { -17.399999999999999, 1, -8.6999999999999993 },
 298   { -17.199999999999999, 1, -8.5999999999999996 },
 299   { -17.000000000000000, 1, -8.5000000000000000 },
 300   { -16.800000000000001, 1, -8.4000000000000004 },
 301   { -16.600000000000001, 1, -8.3000000000000007 },
 302   { -16.399999999999999, 1, -8.1999999999999993 },
 303   { -16.199999999999999, 1, -8.0999999999999996 },
 304   { -16.000000000000000, 1, -8.0000000000000000 },
 305   { -15.800000000000001, 1, -7.9000000000000004 },
 306   { -15.600000000000000, 1, -7.7999999999999998 },
 307   { -15.400000000000000, 1, -7.7000000000000002 },
 308   { -15.199999999999999, 1, -7.5999999999999996 },
 309   { -15.000000000000000, 1, -7.5000000000000000 },
 310   { -14.800000000000001, 1, -7.4000000000000004 },
 311   { -14.600000000000000, 1, -7.2999999999999998 },
 312   { -14.400000000000000, 1, -7.2000000000000002 },
 313   { -14.199999999999999, 1, -7.0999999999999996 },
 314   { -14.000000000000000, 1, -7.0000000000000000 },
 315   { -13.800000000000001, 1, -6.9000000000000004 },
 316   { -13.600000000000000, 1, -6.7999999999999998 },
 317   { -13.400000000000000, 1, -6.7000000000000002 },
 318   { -13.199999999999999, 1, -6.5999999999999996 },
 319   { -13.000000000000000, 1, -6.5000000000000000 },
 320   { -12.800000000000001, 1, -6.4000000000000004 },
 321   { -12.600000000000000, 1, -6.2999999999999998 },
 322   { -12.400000000000000, 1, -6.2000000000000002 },
 323   { -12.199999999999999, 1, -6.0999999999999996 },
 324   { -12.000000000000000, 1, -6.0000000000000000 },
 325   { -11.800000000000001, 1, -5.9000000000000004 },
 326   { -11.600000000000000, 1, -5.7999999999999998 },
 327   { -11.400000000000000, 1, -5.7000000000000002 },
 328   { -11.199999999999999, 1, -5.5999999999999996 },
 329   { -11.000000000000000, 1, -5.5000000000000000 },
 330   { -10.800000000000001, 1, -5.4000000000000004 },
 331   { -10.600000000000000, 1, -5.2999999999999998 },
 332   { -10.400000000000000, 1, -5.2000000000000002 },
 333   { -10.199999999999999, 1, -5.0999999999999996 },
 334   { -10.000000000000000, 1, -5.0000000000000000 },
 335   { -9.8000000000000007, 1, -4.9000000000000004 },
 336   { -9.5999999999999996, 1, -4.7999999999999998 },
 337   { -9.4000000000000004, 1, -4.7000000000000002 },
 338   { -9.1999999999999993, 1, -4.5999999999999996 },
 339   { -9.0000000000000000, 1, -4.5000000000000000 },
 340   { -8.8000000000000007, 1, -4.4000000000000004 },
 341   { -8.5999999999999996, 1, -4.2999999999999998 },
 342   { -8.4000000000000004, 1, -4.2000000000000002 },
 343   { -8.1999999999999993, 1, -4.0999999999999996 },
 344   { -8.0000000000000000, 1, -4.0000000000000000 },
 345   { -7.8000000000000007, 1, -3.9000000000000004 },
 346   { -7.5999999999999996, 1, -3.7999999999999998 },
 347   { -7.4000000000000004, 1, -3.7000000000000002 },
 348   { -7.1999999999999993, 1, -3.5999999999999996 },
 349   { -7.0000000000000000, 1, -3.5000000000000000 },
 350   { -6.8000000000000007, 1, -3.4000000000000004 },
 351   { -6.5999999999999996, 1, -3.2999999999999998 },
 352   { -6.4000000000000004, 1, -3.2000000000000002 },
 353   { -6.1999999999999993, 1, -3.0999999999999996 },
 354   { -6.0000000000000000, 1, -3.0000000000000000 },
 355   { -5.8000000000000007, 1, -2.9000000000000004 },
 356   { -5.5999999999999996, 1, -2.7999999999999998 },
 357   { -5.4000000000000004, 1, -2.7000000000000002 },
 358   { -5.1999999999999993, 1, -2.5999999999999996 },
 359   { -5.0000000000000000, 1, -2.5000000000000000 },
 360   { -4.8000000000000007, 1, -2.4000000000000004 },
 361   { -4.5999999999999996, 1, -2.2999999999999998 },
 362   { -4.4000000000000004, 1, -2.2000000000000002 },
 363   { -4.1999999999999993, 1, -2.0999999999999996 },
 364   { -4.0000000000000000, 1, -2.0000000000000000 },
 365   { -3.8000000000000007, 1, -1.9000000000000004 },
 366   { -3.6000000000000014, 1, -1.8000000000000007 },
 367   { -3.3999999999999986, 1, -1.6999999999999993 },
 368   { -3.1999999999999993, 1, -1.5999999999999996 },
 369   { -3.0000000000000000, 1, -1.5000000000000000 },
 370   { -2.8000000000000007, 1, -1.4000000000000004 },
 371   { -2.6000000000000014, 1, -1.3000000000000007 },
 372   { -2.3999999999999986, 1, -1.1999999999999993 },
 373   { -2.1999999999999993, 1, -1.0999999999999996 },
 374   { -2.0000000000000000, 1, -1.0000000000000000 },
 375   { -1.8000000000000007, 1, -0.90000000000000036 },
 376   { -1.6000000000000014, 1, -0.80000000000000071 },
 377   { -1.3999999999999986, 1, -0.69999999999999929 },
 378   { -1.1999999999999993, 1, -0.59999999999999964 },
 379   { -1.0000000000000000, 1, -0.50000000000000000 },
 380   { -0.80000000000000071, 1, -0.40000000000000036 },
 381   { -0.60000000000000142, 1, -0.30000000000000071 },
 382   { -0.39999999999999858, 1, -0.19999999999999929 },
 383   { -0.19999999999999929, 1, -0.099999999999999645 },
 384   { 0.0000000000000000, 1, 0.0000000000000000 },
 385   { 0.19999999999999929, 1, 0.099999999999999645 },
 386   { 0.39999999999999858, 1, 0.19999999999999929 },
 387   { 0.60000000000000142, 1, 0.30000000000000071 },
 388   { 0.80000000000000071, 1, 0.40000000000000036 },
 389   { 1.0000000000000000, 1, 0.50000000000000000 },
 390   { 1.1999999999999993, 1, 0.59999999999999964 },
 391   { 1.3999999999999986, 1, 0.69999999999999929 },
 392   { 1.6000000000000014, 1, 0.80000000000000071 },
 393   { 1.8000000000000007, 1, 0.90000000000000036 },
 394   { 2.0000000000000000, 1, 1.0000000000000000 },
 395   { 2.1999999999999993, 1, 1.0999999999999996 },
 396   { 2.3999999999999986, 1, 1.1999999999999993 },
 397   { 2.6000000000000014, 1, 1.3000000000000007 },
 398   { 2.8000000000000007, 1, 1.4000000000000004 },
 399   { 3.0000000000000000, 1, 1.5000000000000000 },
 400   { 3.1999999999999993, 1, 1.5999999999999996 },
 401   { 3.3999999999999986, 1, 1.6999999999999993 },
 402   { 3.6000000000000014, 1, 1.8000000000000007 },
 403   { 3.8000000000000007, 1, 1.9000000000000004 },
 404   { 4.0000000000000000, 1, 2.0000000000000000 },
 405   { 4.1999999999999993, 1, 2.0999999999999996 },
 406   { 4.3999999999999986, 1, 2.1999999999999993 },
 407   { 4.6000000000000014, 1, 2.3000000000000007 },
 408   { 4.8000000000000007, 1, 2.4000000000000004 },
 409   { 5.0000000000000000, 1, 2.5000000000000000 },
 410   { 5.1999999999999993, 1, 2.5999999999999996 },
 411   { 5.3999999999999986, 1, 2.6999999999999993 },
 412   { 5.6000000000000014, 1, 2.8000000000000007 },
 413   { 5.8000000000000007, 1, 2.9000000000000004 },
 414   { 6.0000000000000000, 1, 3.0000000000000000 },
 415   { 6.1999999999999993, 1, 3.0999999999999996 },
 416   { 6.3999999999999986, 1, 3.1999999999999993 },
 417   { 6.6000000000000014, 1, 3.3000000000000007 },
 418   { 6.8000000000000007, 1, 3.4000000000000004 },
 419   { 7.0000000000000000, 1, 3.5000000000000000 },
 420   { 7.1999999999999993, 1, 3.5999999999999996 },
 421   { 7.3999999999999986, 1, 3.6999999999999993 },
 422   { 7.6000000000000014, 1, 3.8000000000000007 },
 423   { 7.8000000000000007, 1, 3.9000000000000004 },
 424   { 8.0000000000000000, 1, 4.0000000000000000 },
 425   { 8.1999999999999993, 1, 4.0999999999999996 },
 426   { 8.3999999999999986, 1, 4.1999999999999993 },
 427   { 8.6000000000000014, 1, 4.3000000000000007 },
 428   { 8.8000000000000007, 1, 4.4000000000000004 },
 429   { 9.0000000000000000, 1, 4.5000000000000000 },
 430   { 9.1999999999999993, 1, 4.5999999999999996 },
 431   { 9.3999999999999986, 1, 4.6999999999999993 },
 432   { 9.6000000000000014, 1, 4.8000000000000007 },
 433   { 9.8000000000000007, 1, 4.9000000000000004 },
 434   { 10.000000000000000, 1, 5.0000000000000000 },
 435   { 10.199999999999999, 1, 5.0999999999999996 },
 436   { 10.399999999999999, 1, 5.1999999999999993 },
 437   { 10.600000000000001, 1, 5.3000000000000007 },
 438   { 10.800000000000001, 1, 5.4000000000000004 },
 439   { 11.000000000000000, 1, 5.5000000000000000 },
 440   { 11.199999999999999, 1, 5.5999999999999996 },
 441   { 11.399999999999999, 1, 5.6999999999999993 },
 442   { 11.600000000000001, 1, 5.8000000000000007 },
 443   { 11.800000000000001, 1, 5.9000000000000004 },
 444   { 12.000000000000000, 1, 6.0000000000000000 },
 445   { 12.200000000000003, 1, 6.1000000000000014 },
 446   { 12.399999999999999, 1, 6.1999999999999993 },
 447   { 12.600000000000001, 1, 6.3000000000000007 },
 448   { 12.799999999999997, 1, 6.3999999999999986 },
 449   { 13.000000000000000, 1, 6.5000000000000000 },
 450   { 13.200000000000003, 1, 6.6000000000000014 },
 451   { 13.399999999999999, 1, 6.6999999999999993 },
 452   { 13.600000000000001, 1, 6.8000000000000007 },
 453   { 13.799999999999997, 1, 6.8999999999999986 },
 454   { 14.000000000000000, 1, 7.0000000000000000 },
 455   { 14.200000000000003, 1, 7.1000000000000014 },
 456   { 14.399999999999999, 1, 7.1999999999999993 },
 457   { 14.600000000000001, 1, 7.3000000000000007 },
 458   { 14.799999999999997, 1, 7.3999999999999986 },
 459   { 15.000000000000000, 1, 7.5000000000000000 },
 460   { 15.200000000000003, 1, 7.6000000000000014 },
 461   { 15.399999999999999, 1, 7.6999999999999993 },
 462   { 15.600000000000001, 1, 7.8000000000000007 },
 463   { 15.799999999999997, 1, 7.8999999999999986 },
 464   { 16.000000000000000, 1, 8.0000000000000000 },
 465   { 16.200000000000003, 1, 8.1000000000000014 },
 466   { 16.399999999999999, 1, 8.1999999999999993 },
 467   { 16.600000000000001, 1, 8.3000000000000007 },
 468   { 16.799999999999997, 1, 8.3999999999999986 },
 469   { 17.000000000000000, 1, 8.5000000000000000 },
 470   { 17.200000000000003, 1, 8.6000000000000014 },
 471   { 17.399999999999999, 1, 8.6999999999999993 },
 472   { 17.600000000000001, 1, 8.8000000000000007 },
 473   { 17.799999999999997, 1, 8.8999999999999986 },
 474   { 18.000000000000000, 1, 9.0000000000000000 },
 475   { 18.200000000000003, 1, 9.1000000000000014 },
 476   { 18.399999999999999, 1, 9.1999999999999993 },
 477   { 18.600000000000001, 1, 9.3000000000000007 },
 478   { 18.799999999999997, 1, 9.3999999999999986 },
 479   { 19.000000000000000, 1, 9.5000000000000000 },
 480   { 19.200000000000003, 1, 9.6000000000000014 },
 481   { 19.399999999999999, 1, 9.6999999999999993 },
 482   { 19.600000000000001, 1, 9.8000000000000007 },
 483   { 19.799999999999997, 1, 9.8999999999999986 },
 484   { 20.000000000000000, 1, 10.000000000000000 },
 485 };
 486
 487 // Test function for n=1.
 488 template<typename Tp>
 489   void
 490   test002()
 491   {
 492     bool test __attribute__((unused)) = true;
 493     const Tp eps = std::numeric_limits<Tp>::epsilon();
 494     Tp max_abs_diff = -Tp(1);
 495     Tp max_abs_frac = -Tp(1);
 496     unsigned int num_datum = sizeof(data002)
 497                            / sizeof(testcase_hermite<double>);
 498     for (unsigned int i = 0; i < num_datum; ++i)
 499       {
 500         const Tp f = std::tr1::hermite(Tp(data002[i].n), Tp(data002[i].x));
 501         const Tp f0 = data002[i].f0;
 502         const Tp diff = f - f0;
 503         if (std::abs(diff) > max_abs_diff)
 504           max_abs_diff = std::abs(diff);
 505         if (std::abs(f0) > Tp(10) * eps
 506          && std::abs(f) > Tp(10) * eps)
 507           {
 508             const Tp frac = diff / f0;
 509             if (std::abs(frac) > max_abs_frac)
 510               max_abs_frac = std::abs(frac);
 511           }
 512       }
 513     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 514   }
 515
 516 // Test data for n=2.
 517 // max(|f - f_GSL|): 0.0000000000000000
 518 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 519 testcase_hermite<double>
 520 data003[] =
 521 {
 522   { 398.00000000000000, 2, -10.000000000000000 },
 523   { 390.04000000000002, 2, -9.9000000000000004 },
 524   { 382.16000000000008, 2, -9.8000000000000007 },
 525   { 374.35999999999996, 2, -9.6999999999999993 },
 526   { 366.63999999999999, 2, -9.5999999999999996 },
 527   { 359.00000000000000, 2, -9.5000000000000000 },
 528   { 351.44000000000005, 2, -9.4000000000000004 },
 529   { 343.96000000000004, 2, -9.3000000000000007 },
 530   { 336.55999999999995, 2, -9.1999999999999993 },
 531   { 329.23999999999995, 2, -9.0999999999999996 },
 532   { 322.00000000000000, 2, -9.0000000000000000 },
 533   { 314.84000000000003, 2, -8.9000000000000004 },
 534   { 307.76000000000005, 2, -8.8000000000000007 },
 535   { 300.75999999999993, 2, -8.6999999999999993 },
 536   { 293.83999999999997, 2, -8.5999999999999996 },
 537   { 287.00000000000000, 2, -8.5000000000000000 },
 538   { 280.24000000000001, 2, -8.4000000000000004 },
 539   { 273.56000000000006, 2, -8.3000000000000007 },
 540   { 266.95999999999998, 2, -8.1999999999999993 },
 541   { 260.44000000000000, 2, -8.0999999999999996 },
 542   { 254.00000000000000, 2, -8.0000000000000000 },
 543   { 247.64000000000001, 2, -7.9000000000000004 },
 544   { 241.35999999999999, 2, -7.7999999999999998 },
 545   { 235.16000000000003, 2, -7.7000000000000002 },
 546   { 229.03999999999999, 2, -7.5999999999999996 },
 547   { 223.00000000000000, 2, -7.5000000000000000 },
 548   { 217.04000000000002, 2, -7.4000000000000004 },
 549   { 211.16000000000000, 2, -7.2999999999999998 },
 550   { 205.36000000000001, 2, -7.2000000000000002 },
 551   { 199.63999999999999, 2, -7.0999999999999996 },
 552   { 194.00000000000000, 2, -7.0000000000000000 },
 553   { 188.44000000000003, 2, -6.9000000000000004 },
 554   { 182.95999999999998, 2, -6.7999999999999998 },
 555   { 177.56000000000000, 2, -6.7000000000000002 },
 556   { 172.23999999999998, 2, -6.5999999999999996 },
 557   { 167.00000000000000, 2, -6.5000000000000000 },
 558   { 161.84000000000003, 2, -6.4000000000000004 },
 559   { 156.75999999999999, 2, -6.2999999999999998 },
 560   { 151.76000000000002, 2, -6.2000000000000002 },
 561   { 146.83999999999997, 2, -6.0999999999999996 },
 562   { 142.00000000000000, 2, -6.0000000000000000 },
 563   { 137.24000000000001, 2, -5.9000000000000004 },
 564   { 132.56000000000000, 2, -5.7999999999999998 },
 565   { 127.96000000000001, 2, -5.7000000000000002 },
 566   { 123.43999999999998, 2, -5.5999999999999996 },
 567   { 119.00000000000000, 2, -5.5000000000000000 },
 568   { 114.64000000000001, 2, -5.4000000000000004 },
 569   { 110.36000000000000, 2, -5.2999999999999998 },
 570   { 106.16000000000001, 2, -5.2000000000000002 },
 571   { 102.03999999999999, 2, -5.0999999999999996 },
 572   { 98.000000000000000, 2, -5.0000000000000000 },
 573   { 94.040000000000020, 2, -4.9000000000000004 },
 574   { 90.159999999999997, 2, -4.7999999999999998 },
 575   { 86.360000000000014, 2, -4.7000000000000002 },
 576   { 82.639999999999986, 2, -4.5999999999999996 },
 577   { 79.000000000000000, 2, -4.5000000000000000 },
 578   { 75.440000000000012, 2, -4.4000000000000004 },
 579   { 71.959999999999994, 2, -4.2999999999999998 },
 580   { 68.560000000000002, 2, -4.2000000000000002 },
 581   { 65.239999999999995, 2, -4.0999999999999996 },
 582   { 62.000000000000000, 2, -4.0000000000000000 },
 583   { 58.840000000000011, 2, -3.9000000000000004 },
 584   { 55.759999999999998, 2, -3.7999999999999998 },
 585   { 52.760000000000005, 2, -3.7000000000000002 },
 586   { 49.839999999999989, 2, -3.5999999999999996 },
 587   { 47.000000000000000, 2, -3.5000000000000000 },
 588   { 44.240000000000009, 2, -3.4000000000000004 },
 589   { 41.559999999999995, 2, -3.2999999999999998 },
 590   { 38.960000000000008, 2, -3.2000000000000002 },
 591   { 36.439999999999991, 2, -3.0999999999999996 },
 592   { 34.000000000000000, 2, -3.0000000000000000 },
 593   { 31.640000000000008, 2, -2.9000000000000004 },
 594   { 29.359999999999996, 2, -2.7999999999999998 },
 595   { 27.160000000000004, 2, -2.7000000000000002 },
 596   { 25.039999999999992, 2, -2.5999999999999996 },
 597   { 23.000000000000000, 2, -2.5000000000000000 },
 598   { 21.040000000000006, 2, -2.4000000000000004 },
 599   { 19.159999999999997, 2, -2.2999999999999998 },
 600   { 17.360000000000003, 2, -2.2000000000000002 },
 601   { 15.639999999999993, 2, -2.0999999999999996 },
 602   { 14.000000000000000, 2, -2.0000000000000000 },
 603   { 12.440000000000005, 2, -1.9000000000000004 },
 604   { 10.960000000000010, 2, -1.8000000000000007 },
 605   { 9.5599999999999898, 2, -1.6999999999999993 },
 606   { 8.2399999999999949, 2, -1.5999999999999996 },
 607   { 7.0000000000000000, 2, -1.5000000000000000 },
 608   { 5.8400000000000043, 2, -1.4000000000000004 },
 609   { 4.7600000000000078, 2, -1.3000000000000007 },
 610   { 3.7599999999999936, 2, -1.1999999999999993 },
 611   { 2.8399999999999972, 2, -1.0999999999999996 },
 612   { 2.0000000000000000, 2, -1.0000000000000000 },
 613   { 1.2400000000000024, 2, -0.90000000000000036 },
 614   { 0.56000000000000449, 2, -0.80000000000000071 },
 615   { -0.040000000000004032, 2, -0.69999999999999929 },
 616   { -0.56000000000000161, 2, -0.59999999999999964 },
 617   { -1.0000000000000000, 2, -0.50000000000000000 },
 618   { -1.3599999999999990, 2, -0.40000000000000036 },
 619   { -1.6399999999999983, 2, -0.30000000000000071 },
 620   { -1.8400000000000012, 2, -0.19999999999999929 },
 621   { -1.9600000000000002, 2, -0.099999999999999645 },
 622   { -2.0000000000000000, 2, 0.0000000000000000 },
 623   { -1.9600000000000002, 2, 0.099999999999999645 },
 624   { -1.8400000000000012, 2, 0.19999999999999929 },
 625   { -1.6399999999999983, 2, 0.30000000000000071 },
 626   { -1.3599999999999990, 2, 0.40000000000000036 },
 627   { -1.0000000000000000, 2, 0.50000000000000000 },
 628   { -0.56000000000000161, 2, 0.59999999999999964 },
 629   { -0.040000000000004032, 2, 0.69999999999999929 },
 630   { 0.56000000000000449, 2, 0.80000000000000071 },
 631   { 1.2400000000000024, 2, 0.90000000000000036 },
 632   { 2.0000000000000000, 2, 1.0000000000000000 },
 633   { 2.8399999999999972, 2, 1.0999999999999996 },
 634   { 3.7599999999999936, 2, 1.1999999999999993 },
 635   { 4.7600000000000078, 2, 1.3000000000000007 },
 636   { 5.8400000000000043, 2, 1.4000000000000004 },
 637   { 7.0000000000000000, 2, 1.5000000000000000 },
 638   { 8.2399999999999949, 2, 1.5999999999999996 },
 639   { 9.5599999999999898, 2, 1.6999999999999993 },
 640   { 10.960000000000010, 2, 1.8000000000000007 },
 641   { 12.440000000000005, 2, 1.9000000000000004 },
 642   { 14.000000000000000, 2, 2.0000000000000000 },
 643   { 15.639999999999993, 2, 2.0999999999999996 },
 644   { 17.359999999999989, 2, 2.1999999999999993 },
 645   { 19.160000000000014, 2, 2.3000000000000007 },
 646   { 21.040000000000006, 2, 2.4000000000000004 },
 647   { 23.000000000000000, 2, 2.5000000000000000 },
 648   { 25.039999999999992, 2, 2.5999999999999996 },
 649   { 27.159999999999986, 2, 2.6999999999999993 },
 650   { 29.360000000000017, 2, 2.8000000000000007 },
 651   { 31.640000000000008, 2, 2.9000000000000004 },
 652   { 34.000000000000000, 2, 3.0000000000000000 },
 653   { 36.439999999999991, 2, 3.0999999999999996 },
 654   { 38.959999999999980, 2, 3.1999999999999993 },
 655   { 41.560000000000016, 2, 3.3000000000000007 },
 656   { 44.240000000000009, 2, 3.4000000000000004 },
 657   { 47.000000000000000, 2, 3.5000000000000000 },
 658   { 49.839999999999989, 2, 3.5999999999999996 },
 659   { 52.759999999999977, 2, 3.6999999999999993 },
 660   { 55.760000000000019, 2, 3.8000000000000007 },
 661   { 58.840000000000011, 2, 3.9000000000000004 },
 662   { 62.000000000000000, 2, 4.0000000000000000 },
 663   { 65.239999999999995, 2, 4.0999999999999996 },
 664   { 68.559999999999974, 2, 4.1999999999999993 },
 665   { 71.960000000000022, 2, 4.3000000000000007 },
 666   { 75.440000000000012, 2, 4.4000000000000004 },
 667   { 79.000000000000000, 2, 4.5000000000000000 },
 668   { 82.639999999999986, 2, 4.5999999999999996 },
 669   { 86.359999999999971, 2, 4.6999999999999993 },
 670   { 90.160000000000025, 2, 4.8000000000000007 },
 671   { 94.040000000000020, 2, 4.9000000000000004 },
 672   { 98.000000000000000, 2, 5.0000000000000000 },
 673   { 102.03999999999999, 2, 5.0999999999999996 },
 674   { 106.15999999999997, 2, 5.1999999999999993 },
 675   { 110.36000000000003, 2, 5.3000000000000007 },
 676   { 114.64000000000001, 2, 5.4000000000000004 },
 677   { 119.00000000000000, 2, 5.5000000000000000 },
 678   { 123.43999999999998, 2, 5.5999999999999996 },
 679   { 127.95999999999998, 2, 5.6999999999999993 },
 680   { 132.56000000000003, 2, 5.8000000000000007 },
 681   { 137.24000000000001, 2, 5.9000000000000004 },
 682   { 142.00000000000000, 2, 6.0000000000000000 },
 683   { 146.84000000000006, 2, 6.1000000000000014 },
 684   { 151.75999999999996, 2, 6.1999999999999993 },
 685   { 156.76000000000005, 2, 6.3000000000000007 },
 686   { 161.83999999999992, 2, 6.3999999999999986 },
 687   { 167.00000000000000, 2, 6.5000000000000000 },
 688   { 172.24000000000007, 2, 6.6000000000000014 },
 689   { 177.55999999999997, 2, 6.6999999999999993 },
 690   { 182.96000000000004, 2, 6.8000000000000007 },
 691   { 188.43999999999991, 2, 6.8999999999999986 },
 692   { 194.00000000000000, 2, 7.0000000000000000 },
 693   { 199.64000000000007, 2, 7.1000000000000014 },
 694   { 205.35999999999996, 2, 7.1999999999999993 },
 695   { 211.16000000000005, 2, 7.3000000000000007 },
 696   { 217.03999999999991, 2, 7.3999999999999986 },
 697   { 223.00000000000000, 2, 7.5000000000000000 },
 698   { 229.04000000000008, 2, 7.6000000000000014 },
 699   { 235.15999999999997, 2, 7.6999999999999993 },
 700   { 241.36000000000004, 2, 7.8000000000000007 },
 701   { 247.63999999999990, 2, 7.8999999999999986 },
 702   { 254.00000000000000, 2, 8.0000000000000000 },
 703   { 260.44000000000011, 2, 8.1000000000000014 },
 704   { 266.95999999999998, 2, 8.1999999999999993 },
 705   { 273.56000000000006, 2, 8.3000000000000007 },
 706   { 280.23999999999990, 2, 8.3999999999999986 },
 707   { 287.00000000000000, 2, 8.5000000000000000 },
 708   { 293.84000000000009, 2, 8.6000000000000014 },
 709   { 300.75999999999993, 2, 8.6999999999999993 },
 710   { 307.76000000000005, 2, 8.8000000000000007 },
 711   { 314.83999999999992, 2, 8.8999999999999986 },
 712   { 322.00000000000000, 2, 9.0000000000000000 },
 713   { 329.24000000000012, 2, 9.1000000000000014 },
 714   { 336.55999999999995, 2, 9.1999999999999993 },
 715   { 343.96000000000004, 2, 9.3000000000000007 },
 716   { 351.43999999999988, 2, 9.3999999999999986 },
 717   { 359.00000000000000, 2, 9.5000000000000000 },
 718   { 366.64000000000010, 2, 9.6000000000000014 },
 719   { 374.35999999999996, 2, 9.6999999999999993 },
 720   { 382.16000000000008, 2, 9.8000000000000007 },
 721   { 390.03999999999991, 2, 9.8999999999999986 },
 722   { 398.00000000000000, 2, 10.000000000000000 },
 723 };
 724
 725 // Test function for n=2.
 726 template<typename Tp>
 727   void
 728   test003()
 729   {
 730     bool test __attribute__((unused)) = true;
 731     const Tp eps = std::numeric_limits<Tp>::epsilon();
 732     Tp max_abs_diff = -Tp(1);
 733     Tp max_abs_frac = -Tp(1);
 734     unsigned int num_datum = sizeof(data003)
 735                            / sizeof(testcase_hermite<double>);
 736     for (unsigned int i = 0; i < num_datum; ++i)
 737       {
 738         const Tp f = std::tr1::hermite(Tp(data003[i].n), Tp(data003[i].x));
 739         const Tp f0 = data003[i].f0;
 740         const Tp diff = f - f0;
 741         if (std::abs(diff) > max_abs_diff)
 742           max_abs_diff = std::abs(diff);
 743         if (std::abs(f0) > Tp(10) * eps
 744          && std::abs(f) > Tp(10) * eps)
 745           {
 746             const Tp frac = diff / f0;
 747             if (std::abs(frac) > max_abs_frac)
 748               max_abs_frac = std::abs(frac);
 749           }
 750       }
 751     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 752   }
 753
 754 // Test data for n=5.
 755 // max(|f - f_GSL|): 0.0000000000000000
 756 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 757 testcase_hermite<double>
 758 data004[] =
 759 {
 760   { -3041200.0000000000, 5, -10.000000000000000 },
 761   { -2889108.3196800007, 5, -9.9000000000000004 },
 762   { -2743131.8297600015, 5, -9.8000000000000007 },
 763   { -2603085.2022399991, 5, -9.6999999999999993 },
 764   { -2468786.8723199992, 5, -9.5999999999999996 },
 765   { -2340059.0000000000, 5, -9.5000000000000000 },
 766   { -2216727.4316800009, 5, -9.4000000000000004 },
 767   { -2098621.6617600010, 5, -9.3000000000000007 },
 768   { -1985574.7942399993, 5, -9.1999999999999993 },
 769   { -1877423.5043199996, 5, -9.0999999999999996 },
 770   { -1774008.0000000000, 5, -9.0000000000000000 },
 771   { -1675171.9836800008, 5, -8.9000000000000004 },
 772   { -1580762.6137600006, 5, -8.8000000000000007 },
 773   { -1490630.4662399990, 5, -8.6999999999999993 },
 774   { -1404629.4963199999, 5, -8.5999999999999996 },
 775   { -1322617.0000000000, 5, -8.5000000000000000 },
 776   { -1244453.5756800002, 5, -8.4000000000000004 },
 777   { -1170003.0857600006, 5, -8.3000000000000007 },
 778   { -1099132.6182399995, 5, -8.1999999999999993 },
 779   { -1031712.4483199996, 5, -8.0999999999999996 },
 780   { -967616.00000000000, 5, -8.0000000000000000 },
 781   { -906719.80768000009, 5, -7.9000000000000004 },
 782   { -848903.47775999992, 5, -7.7999999999999998 },
 783   { -794049.65024000010, 5, -7.7000000000000002 },
 784   { -742043.96031999995, 5, -7.5999999999999996 },
 785   { -692775.00000000000, 5, -7.5000000000000000 },
 786   { -646134.27968000027, 5, -7.4000000000000004 },
 787   { -602016.18975999986, 5, -7.2999999999999998 },
 788   { -560317.96224000002, 5, -7.2000000000000002 },
 789   { -520939.63231999992, 5, -7.0999999999999996 },
 790   { -483784.00000000000, 5, -7.0000000000000000 },
 791   { -448756.59168000019, 5, -6.9000000000000004 },
 792   { -415765.62176000001, 5, -6.7999999999999998 },
 793   { -384721.95424000005, 5, -6.7000000000000002 },
 794   { -355539.06431999995, 5, -6.5999999999999996 },
 795   { -328133.00000000000, 5, -6.5000000000000000 },
 796   { -302422.34368000011, 5, -6.4000000000000004 },
 797   { -278328.17375999998, 5, -6.2999999999999998 },
 798   { -255774.02624000004, 5, -6.2000000000000002 },
 799   { -234685.85631999990, 5, -6.0999999999999996 },
 800   { -214992.00000000000, 5, -6.0000000000000000 },
 801   { -196623.13568000006, 5, -5.9000000000000004 },
 802   { -179512.24575999999, 5, -5.7999999999999998 },
 803   { -163594.57824000003, 5, -5.7000000000000002 },
 804   { -148807.60831999997, 5, -5.5999999999999996 },
 805   { -135091.00000000000, 5, -5.5000000000000000 },
 806   { -122386.56768000004, 5, -5.4000000000000004 },
 807   { -110638.23776000000, 5, -5.2999999999999998 },
 808   { -99792.010240000047, 5, -5.2000000000000002 },
 809   { -89795.920319999976, 5, -5.0999999999999996 },
 810   { -80600.000000000000, 5, -5.0000000000000000 },
 811   { -72156.239680000028, 5, -4.9000000000000004 },
 812   { -64418.549759999994, 5, -4.7999999999999998 },
 813   { -57342.722240000010, 5, -4.7000000000000002 },
 814   { -50886.392319999970, 5, -4.5999999999999996 },
 815   { -45009.000000000000, 5, -4.5000000000000000 },
 816   { -39671.751680000008, 5, -4.4000000000000004 },
 817   { -34837.581759999986, 5, -4.2999999999999998 },
 818   { -30471.114240000010, 5, -4.2000000000000002 },
 819   { -26538.624319999992, 5, -4.0999999999999996 },
 820   { -23008.000000000000, 5, -4.0000000000000000 },
 821   { -19848.703680000013, 5, -3.9000000000000004 },
 822   { -17031.733759999996, 5, -3.7999999999999998 },
 823   { -14529.586240000001, 5, -3.7000000000000002 },
 824   { -12316.216319999992, 5, -3.5999999999999996 },
 825   { -10367.000000000000, 5, -3.5000000000000000 },
 826   { -8658.6956800000080, 5, -3.4000000000000004 },
 827   { -7169.4057599999960, 5, -3.2999999999999998 },
 828   { -5878.5382400000035, 5, -3.2000000000000002 },
 829   { -4766.7683199999965, 5, -3.0999999999999996 },
 830   { -3816.0000000000000, 5, -3.0000000000000000 },
 831   { -3009.3276800000026, 5, -2.9000000000000004 },
 832   { -2330.9977599999988, 5, -2.7999999999999998 },
 833   { -1766.3702400000002, 5, -2.7000000000000002 },
 834   { -1301.8803199999984, 5, -2.5999999999999996 },
 835   { -925.00000000000000, 5, -2.5000000000000000 },
 836   { -624.19968000000074, 5, -2.4000000000000004 },
 837   { -388.90975999999978, 5, -2.2999999999999998 },
 838   { -209.48224000000022, 5, -2.2000000000000002 },
 839   { -77.152319999999520, 5, -2.0999999999999996 },
 840   { 16.000000000000000, 5, -2.0000000000000000 },
 841   { 77.088319999999840, 5, -1.9000000000000004 },
 842   { 112.45823999999980, 5, -1.8000000000000007 },
 843   { 127.72576000000002, 5, -1.6999999999999993 },
 844   { 127.81567999999996, 5, -1.5999999999999996 },
 845   { 117.00000000000000, 5, -1.5000000000000000 },
 846   { 98.936320000000080, 5, -1.4000000000000004 },
 847   { 76.706240000000179, 5, -1.3000000000000007 },
 848   { 52.853759999999838, 5, -1.1999999999999993 },
 849   { 29.423679999999933, 5, -1.0999999999999996 },
 850   { 8.0000000000000000, 5, -1.0000000000000000 },
 851   { -10.255679999999948, 5, -0.90000000000000036 },
 852   { -24.565759999999916, 5, -0.80000000000000071 },
 853   { -34.498240000000052, 5, -0.69999999999999929 },
 854   { -39.928320000000006, 5, -0.59999999999999964 },
 855   { -41.000000000000000, 5, -0.50000000000000000 },
 856   { -38.087680000000020, 5, -0.40000000000000036 },
 857   { -31.757760000000054, 5, -0.30000000000000071 },
 858   { -22.730239999999931, 5, -0.19999999999999929 },
 859   { -11.840319999999959, 5, -0.099999999999999645 },
 860   { 0.0000000000000000, 5, 0.0000000000000000 },
 861   { 11.840319999999959, 5, 0.099999999999999645 },
 862   { 22.730239999999931, 5, 0.19999999999999929 },
 863   { 31.757760000000054, 5, 0.30000000000000071 },
 864   { 38.087680000000020, 5, 0.40000000000000036 },
 865   { 41.000000000000000, 5, 0.50000000000000000 },
 866   { 39.928320000000006, 5, 0.59999999999999964 },
 867   { 34.498240000000052, 5, 0.69999999999999929 },
 868   { 24.565759999999916, 5, 0.80000000000000071 },
 869   { 10.255679999999948, 5, 0.90000000000000036 },
 870   { -8.0000000000000000, 5, 1.0000000000000000 },
 871   { -29.423679999999933, 5, 1.0999999999999996 },
 872   { -52.853759999999838, 5, 1.1999999999999993 },
 873   { -76.706240000000179, 5, 1.3000000000000007 },
 874   { -98.936320000000080, 5, 1.4000000000000004 },
 875   { -117.00000000000000, 5, 1.5000000000000000 },
 876   { -127.81567999999996, 5, 1.5999999999999996 },
 877   { -127.72576000000002, 5, 1.6999999999999993 },
 878   { -112.45823999999980, 5, 1.8000000000000007 },
 879   { -77.088319999999840, 5, 1.9000000000000004 },
 880   { -16.000000000000000, 5, 2.0000000000000000 },
 881   { 77.152319999999520, 5, 2.0999999999999996 },
 882   { 209.48223999999891, 5, 2.1999999999999993 },
 883   { 388.90976000000148, 5, 2.3000000000000007 },
 884   { 624.19968000000074, 5, 2.4000000000000004 },
 885   { 925.00000000000000, 5, 2.5000000000000000 },
 886   { 1301.8803199999984, 5, 2.5999999999999996 },
 887   { 1766.3702399999963, 5, 2.6999999999999993 },
 888   { 2330.9977600000047, 5, 2.8000000000000007 },
 889   { 3009.3276800000026, 5, 2.9000000000000004 },
 890   { 3816.0000000000000, 5, 3.0000000000000000 },
 891   { 4766.7683199999965, 5, 3.0999999999999996 },
 892   { 5878.5382399999908, 5, 3.1999999999999993 },
 893   { 7169.4057600000087, 5, 3.3000000000000007 },
 894   { 8658.6956800000080, 5, 3.4000000000000004 },
 895   { 10367.000000000000, 5, 3.5000000000000000 },
 896   { 12316.216319999992, 5, 3.5999999999999996 },
 897   { 14529.586239999979, 5, 3.6999999999999993 },
 898   { 17031.733760000021, 5, 3.8000000000000007 },
 899   { 19848.703680000013, 5, 3.9000000000000004 },
 900   { 23008.000000000000, 5, 4.0000000000000000 },
 901   { 26538.624319999992, 5, 4.0999999999999996 },
 902   { 30471.114239999963, 5, 4.1999999999999993 },
 903   { 34837.581760000037, 5, 4.3000000000000007 },
 904   { 39671.751680000008, 5, 4.4000000000000004 },
 905   { 45009.000000000000, 5, 4.5000000000000000 },
 906   { 50886.392319999970, 5, 4.5999999999999996 },
 907   { 57342.722239999952, 5, 4.6999999999999993 },
 908   { 64418.549760000053, 5, 4.8000000000000007 },
 909   { 72156.239680000028, 5, 4.9000000000000004 },
 910   { 80600.000000000000, 5, 5.0000000000000000 },
 911   { 89795.920319999976, 5, 5.0999999999999996 },
 912   { 99792.010239999945, 5, 5.1999999999999993 },
 913   { 110638.23776000006, 5, 5.3000000000000007 },
 914   { 122386.56768000004, 5, 5.4000000000000004 },
 915   { 135091.00000000000, 5, 5.5000000000000000 },
 916   { 148807.60831999997, 5, 5.5999999999999996 },
 917   { 163594.57823999992, 5, 5.6999999999999993 },
 918   { 179512.24576000011, 5, 5.8000000000000007 },
 919   { 196623.13568000006, 5, 5.9000000000000004 },
 920   { 214992.00000000000, 5, 6.0000000000000000 },
 921   { 234685.85632000031, 5, 6.1000000000000014 },
 922   { 255774.02623999983, 5, 6.1999999999999993 },
 923   { 278328.17376000021, 5, 6.3000000000000007 },
 924   { 302422.34367999958, 5, 6.3999999999999986 },
 925   { 328133.00000000000, 5, 6.5000000000000000 },
 926   { 355539.06432000035, 5, 6.6000000000000014 },
 927   { 384721.95423999976, 5, 6.6999999999999993 },
 928   { 415765.62176000018, 5, 6.8000000000000007 },
 929   { 448756.59167999960, 5, 6.8999999999999986 },
 930   { 483784.00000000000, 5, 7.0000000000000000 },
 931   { 520939.63232000044, 5, 7.1000000000000014 },
 932   { 560317.96223999979, 5, 7.1999999999999993 },
 933   { 602016.18976000033, 5, 7.3000000000000007 },
 934   { 646134.27967999945, 5, 7.3999999999999986 },
 935   { 692775.00000000000, 5, 7.5000000000000000 },
 936   { 742043.96032000054, 5, 7.6000000000000014 },
 937   { 794049.65023999964, 5, 7.6999999999999993 },
 938   { 848903.47776000027, 5, 7.8000000000000007 },
 939   { 906719.80767999915, 5, 7.8999999999999986 },
 940   { 967616.00000000000, 5, 8.0000000000000000 },
 941   { 1031712.4483200011, 5, 8.1000000000000014 },
 942   { 1099132.6182399995, 5, 8.1999999999999993 },
 943   { 1170003.0857600006, 5, 8.3000000000000007 },
 944   { 1244453.5756799988, 5, 8.3999999999999986 },
 945   { 1322617.0000000000, 5, 8.5000000000000000 },
 946   { 1404629.4963200013, 5, 8.6000000000000014 },
 947   { 1490630.4662399990, 5, 8.6999999999999993 },
 948   { 1580762.6137600006, 5, 8.8000000000000007 },
 949   { 1675171.9836799989, 5, 8.8999999999999986 },
 950   { 1774008.0000000000, 5, 9.0000000000000000 },
 951   { 1877423.5043200015, 5, 9.1000000000000014 },
 952   { 1985574.7942399993, 5, 9.1999999999999993 },
 953   { 2098621.6617600010, 5, 9.3000000000000007 },
 954   { 2216727.4316799981, 5, 9.3999999999999986 },
 955   { 2340059.0000000000, 5, 9.5000000000000000 },
 956   { 2468786.8723200019, 5, 9.6000000000000014 },
 957   { 2603085.2022399991, 5, 9.6999999999999993 },
 958   { 2743131.8297600015, 5, 9.8000000000000007 },
 959   { 2889108.3196799983, 5, 9.8999999999999986 },
 960   { 3041200.0000000000, 5, 10.000000000000000 },
 961 };
 962
 963 // Test function for n=5.
 964 template<typename Tp>
 965   void
 966   test004()
 967   {
 968     bool test __attribute__((unused)) = true;
 969     const Tp eps = std::numeric_limits<Tp>::epsilon();
 970     Tp max_abs_diff = -Tp(1);
 971     Tp max_abs_frac = -Tp(1);
 972     unsigned int num_datum = sizeof(data004)
 973                            / sizeof(testcase_hermite<double>);
 974     for (unsigned int i = 0; i < num_datum; ++i)
 975       {
 976         const Tp f = std::tr1::hermite(Tp(data004[i].n), Tp(data004[i].x));
 977         const Tp f0 = data004[i].f0;
 978         const Tp diff = f - f0;
 979         if (std::abs(diff) > max_abs_diff)
 980           max_abs_diff = std::abs(diff);
 981         if (std::abs(f0) > Tp(10) * eps
 982          && std::abs(f) > Tp(10) * eps)
 983           {
 984             const Tp frac = diff / f0;
 985             if (std::abs(frac) > max_abs_frac)
 986               max_abs_frac = std::abs(frac);
 987           }
 988       }
 989     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
 990   }
 991
 992 // Test data for n=10.
 993 // max(|f - f_GSL|): 0.0000000000000000
 994 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 995 testcase_hermite<double>
 996 data005[] =
 997 {
 998   { 8093278209760.0000, 10, -10.000000000000000 },
 999   { 7282867075495.3066, 10, -9.9000000000000004 },
1000   { 6545846221520.6768, 10, -9.8000000000000007 },
1001   { 5876279006180.6377, 10, -9.6999999999999993 },
1002   { 5268651052510.4668, 10, -9.5999999999999996 },
1003   { 4717844376391.0000, 10, -9.5000000000000000 },
1004   { 4219112842239.1147, 10, -9.4000000000000004 },
1005   { 3768058891466.0469, 10, -9.3000000000000007 },
1006   { 3360611490639.0889, 10, -9.1999999999999993 },
1007   { 2993005247949.7607, 10, -9.0999999999999996 },
1008   { 2661760648224.0000, 10, -9.0000000000000000 },
1009   { 2363665358307.8496, 10, -8.9000000000000004 },
1010   { 2095756556225.3428, 10, -8.8000000000000007 },
1011   { 1855304239034.7983, 10, -8.6999999999999993 },
1012   { 1639795465805.4746, 10, -8.5999999999999996 },
1013   { 1446919493599.0000, 10, -8.5000000000000000 },
1014   { 1274553765769.7463, 10, -8.4000000000000004 },
1015   { 1120750713295.2778, 10, -8.3000000000000007 },
1016   { 983725331213.07190, 10, -8.1999999999999993 },
1017   { 861843493572.90051, 10, -8.0999999999999996 },
1018   { 753610971616.00000, 10, -8.0000000000000000 },
1019   { 657663121163.02454, 10, -7.9000000000000004 },
1020   { 572755206432.81335, 10, -7.7999999999999998 },
1021   { 497753328723.87518, 10, -7.7000000000000002 },
1022   { 431625929570.40063, 10, -7.5999999999999996 },
1023   { 373435839135.00000, 10, -7.5000000000000000 },
1024   { 322332841721.55731, 10, -7.4000000000000004 },
1025   { 277546731384.01782, 10, -7.2999999999999998 },
1026   { 238380831670.89990, 10, -7.2000000000000002 },
1027   { 204205954581.24731, 10, -7.0999999999999996 },
1028   { 174454774816.00000, 10, -7.0000000000000000 },
1029   { 148616596389.67230, 10, -6.9000000000000004 },
1030   { 126232489621.23923, 10, -6.7999999999999998 },
1031   { 106890777450.54663, 10, -6.7000000000000002 },
1032   { 90222850927.787979, 10, -6.5999999999999996 },
1033   { 75899294599.000000, 10, -6.5000000000000000 },
1034   { 63626303360.468109, 10, -6.4000000000000004 },
1035   { 53142373179.806053, 10, -6.2999999999999998 },
1036   { 44215248881.625534, 10, -6.2000000000000002 },
1037   { 36639112971.527679, 10, -6.0999999999999996 },
1038   { 30232000224.000000, 10, -6.0000000000000000 },
1039   { 24833423488.050617, 10, -5.9000000000000004 },
1040   { 20302196869.444584, 10, -5.7999999999999998 },
1041   { 16514443130.579359, 10, -5.7000000000000002 },
1042   { 13361772808.732477, 10, -5.5999999999999996 },
1043   { 10749623191.000000, 10, -5.5000000000000000 },
1044   { 8595745900.0898170, 10, -5.4000000000000004 },
1045   { 6828832439.6160822, 10, -5.2999999999999998 },
1046   { 5387267621.0259018, 10, -5.2000000000000002 },
1047   { 4218001347.1524582, 10, -5.0999999999999996 },
1048   { 3275529760.0000000, 10, -5.0000000000000000 },
1049   { 2520977273.0966806, 10, -4.9000000000000004 },
1050   { 1921271501.9744270, 10, -4.7999999999999998 },
1051   { 1448403580.4203825, 10, -4.7000000000000002 },
1052   { 1078766805.4651456, 10, -4.5999999999999996 },
1053   { 792566991.00000000, 10, -4.5000000000000000 },
1054   { 573298328.81993556, 10, -4.4000000000000004 },
1055   { 407278957.14375639, 10, -4.2999999999999998 },
1056   { 283240820.63788313, 10, -4.2000000000000002 },
1057   { 191968773.03860721, 10, -4.0999999999999996 },
1058   { 125984224.00000000, 10, -4.0000000000000000 },
1059   { 79268966.162877649, 10, -3.9000000000000004 },
1060   { 47025137.016035721, 10, -3.7999999999999998 },
1061   { 25467573.275709353, 10, -3.7000000000000002 },
1062   { 11645103.614666298, 10, -3.5999999999999996 },
1063   { 3287599.0000000000, 10, -3.5000000000000000 },
1064   { -1324140.9798373245, 10, -3.4000000000000004 },
1065   { -3468342.2313268245, 10, -3.2999999999999998 },
1066   { -4074495.5241857050, 10, -3.2000000000000002 },
1067   { -3800107.4878923763, 10, -3.0999999999999996 },
1068   { -3093984.0000000000, 10, -3.0000000000000000 },
1069   { -2247873.5653938209, 10, -2.9000000000000004 },
1070   { -1438117.1978829810, 10, -2.7999999999999998 },
1071   { -758781.93281034287, 10, -2.7000000000000002 },
1072   { -247597.05012469599, 10, -2.5999999999999996 },
1073   { 94135.000000000000, 10, -2.5000000000000000 },
1074   { 286617.47398410190, 10, -2.4000000000000004 },
1075   { 360718.79745525768, 10, -2.2999999999999998 },
1076   { 350419.82826741762, 10, -2.2000000000000002 },
1077   { 287863.09027338214, 10, -2.0999999999999996 },
1078   { 200416.00000000000, 10, -2.0000000000000000 },
1079   { 109249.22783242268, 10, -1.9000000000000004 },
1080   { 29012.094015898125, 10, -1.8000000000000007 },
1081   { -31740.330680422732, 10, -1.6999999999999993 },
1082   { -69648.597834137676, 10, -1.5999999999999996 },
1083   { -85401.000000000000, 10, -1.5000000000000000 },
1084   { -82507.675752857642, 10, -1.4000000000000004 },
1085   { -66123.413033062563, 10, -1.3000000000000007 },
1086   { -42007.465141862223, 10, -1.1999999999999993 },
1087   { -15676.055823257526, 10, -1.0999999999999996 },
1088   { 8224.0000000000000, 10, -1.0000000000000000 },
1089   { 26314.366684262357, 10, -0.90000000000000036 },
1090   { 36668.344916377559, 10, -0.80000000000000071 },
1091   { 38802.826035097583, 10, -0.69999999999999929 },
1092   { 33513.167890022363, 10, -0.59999999999999964 },
1093   { 22591.000000000000, 10, -0.50000000000000000 },
1094   { 8467.6907597824556, 10, -0.40000000000000036 },
1095   { -6173.8524877822965, 10, -0.30000000000000071 },
1096   { -18778.856957542470, 10, -0.19999999999999929 },
1097   { -27256.158950297624, 10, -0.099999999999999645 },
1098   { -30240.000000000000, 10, 0.0000000000000000 },
1099   { -27256.158950297624, 10, 0.099999999999999645 },
1100   { -18778.856957542470, 10, 0.19999999999999929 },
1101   { -6173.8524877822965, 10, 0.30000000000000071 },
1102   { 8467.6907597824556, 10, 0.40000000000000036 },
1103   { 22591.000000000000, 10, 0.50000000000000000 },
1104   { 33513.167890022363, 10, 0.59999999999999964 },
1105   { 38802.826035097583, 10, 0.69999999999999929 },
1106   { 36668.344916377559, 10, 0.80000000000000071 },
1107   { 26314.366684262357, 10, 0.90000000000000036 },
1108   { 8224.0000000000000, 10, 1.0000000000000000 },
1109   { -15676.055823257526, 10, 1.0999999999999996 },
1110   { -42007.465141862223, 10, 1.1999999999999993 },
1111   { -66123.413033062563, 10, 1.3000000000000007 },
1112   { -82507.675752857642, 10, 1.4000000000000004 },
1113   { -85401.000000000000, 10, 1.5000000000000000 },
1114   { -69648.597834137676, 10, 1.5999999999999996 },
1115   { -31740.330680422732, 10, 1.6999999999999993 },
1116   { 29012.094015898125, 10, 1.8000000000000007 },
1117   { 109249.22783242268, 10, 1.9000000000000004 },
1118   { 200416.00000000000, 10, 2.0000000000000000 },
1119   { 287863.09027338214, 10, 2.0999999999999996 },
1120   { 350419.82826741732, 10, 2.1999999999999993 },
1121   { 360718.79745525745, 10, 2.3000000000000007 },
1122   { 286617.47398410190, 10, 2.4000000000000004 },
1123   { 94135.000000000000, 10, 2.5000000000000000 },
1124   { -247597.05012469599, 10, 2.5999999999999996 },
1125   { -758781.93281033845, 10, 2.6999999999999993 },
1126   { -1438117.1978829878, 10, 2.8000000000000007 },
1127   { -2247873.5653938209, 10, 2.9000000000000004 },
1128   { -3093984.0000000000, 10, 3.0000000000000000 },
1129   { -3800107.4878923763, 10, 3.0999999999999996 },
1130   { -4074495.5241857003, 10, 3.1999999999999993 },
1131   { -3468342.2313268133, 10, 3.3000000000000007 },
1132   { -1324140.9798373245, 10, 3.4000000000000004 },
1133   { 3287599.0000000000, 10, 3.5000000000000000 },
1134   { 11645103.614666298, 10, 3.5999999999999996 },
1135   { 25467573.275709212, 10, 3.6999999999999993 },
1136   { 47025137.016035900, 10, 3.8000000000000007 },
1137   { 79268966.162877649, 10, 3.9000000000000004 },
1138   { 125984224.00000000, 10, 4.0000000000000000 },
1139   { 191968773.03860721, 10, 4.0999999999999996 },
1140   { 283240820.63788199, 10, 4.1999999999999993 },
1141   { 407278957.14375770, 10, 4.3000000000000007 },
1142   { 573298328.81993556, 10, 4.4000000000000004 },
1143   { 792566991.00000000, 10, 4.5000000000000000 },
1144   { 1078766805.4651456, 10, 4.5999999999999996 },
1145   { 1448403580.4203794, 10, 4.6999999999999993 },
1146   { 1921271501.9744320, 10, 4.8000000000000007 },
1147   { 2520977273.0966806, 10, 4.9000000000000004 },
1148   { 3275529760.0000000, 10, 5.0000000000000000 },
1149   { 4218001347.1524582, 10, 5.0999999999999996 },
1150   { 5387267621.0258913, 10, 5.1999999999999993 },
1151   { 6828832439.6160927, 10, 5.3000000000000007 },
1152   { 8595745900.0898170, 10, 5.4000000000000004 },
1153   { 10749623191.000000, 10, 5.5000000000000000 },
1154   { 13361772808.732477, 10, 5.5999999999999996 },
1155   { 16514443130.579332, 10, 5.6999999999999993 },
1156   { 20302196869.444618, 10, 5.8000000000000007 },
1157   { 24833423488.050617, 10, 5.9000000000000004 },
1158   { 30232000224.000000, 10, 6.0000000000000000 },
1159   { 36639112971.527824, 10, 6.1000000000000014 },
1160   { 44215248881.625443, 10, 6.1999999999999993 },
1161   { 53142373179.806152, 10, 6.3000000000000007 },
1162   { 63626303360.467911, 10, 6.3999999999999986 },
1163   { 75899294599.000000, 10, 6.5000000000000000 },
1164   { 90222850927.788208, 10, 6.6000000000000014 },
1165   { 106890777450.54652, 10, 6.6999999999999993 },
1166   { 126232489621.23946, 10, 6.8000000000000007 },
1167   { 148616596389.67184, 10, 6.8999999999999986 },
1168   { 174454774816.00000, 10, 7.0000000000000000 },
1169   { 204205954581.24780, 10, 7.1000000000000014 },
1170   { 238380831670.89960, 10, 7.1999999999999993 },
1171   { 277546731384.01831, 10, 7.3000000000000007 },
1172   { 322332841721.55646, 10, 7.3999999999999986 },
1173   { 373435839135.00000, 10, 7.5000000000000000 },
1174   { 431625929570.40161, 10, 7.6000000000000014 },
1175   { 497753328723.87476, 10, 7.6999999999999993 },
1176   { 572755206432.81396, 10, 7.8000000000000007 },
1177   { 657663121163.02307, 10, 7.8999999999999986 },
1178   { 753610971616.00000, 10, 8.0000000000000000 },
1179   { 861843493572.90283, 10, 8.1000000000000014 },
1180   { 983725331213.07190, 10, 8.1999999999999993 },
1181   { 1120750713295.2778, 10, 8.3000000000000007 },
1182   { 1274553765769.7439, 10, 8.3999999999999986 },
1183   { 1446919493599.0000, 10, 8.5000000000000000 },
1184   { 1639795465805.4785, 10, 8.6000000000000014 },
1185   { 1855304239034.7983, 10, 8.6999999999999993 },
1186   { 2095756556225.3428, 10, 8.8000000000000007 },
1187   { 2363665358307.8442, 10, 8.8999999999999986 },
1188   { 2661760648224.0000, 10, 9.0000000000000000 },
1189   { 2993005247949.7671, 10, 9.1000000000000014 },
1190   { 3360611490639.0889, 10, 9.1999999999999993 },
1191   { 3768058891466.0469, 10, 9.3000000000000007 },
1192   { 4219112842239.1055, 10, 9.3999999999999986 },
1193   { 4717844376391.0000, 10, 9.5000000000000000 },
1194   { 5268651052510.4785, 10, 9.6000000000000014 },
1195   { 5876279006180.6377, 10, 9.6999999999999993 },
1196   { 6545846221520.6768, 10, 9.8000000000000007 },
1197   { 7282867075495.2949, 10, 9.8999999999999986 },
1198   { 8093278209760.0000, 10, 10.000000000000000 },
1199 };
1200
1201 // Test function for n=10.
1202 template<typename Tp>
1203   void
1204   test005()
1205   {
1206     bool test __attribute__((unused)) = true;
1207     const Tp eps = std::numeric_limits<Tp>::epsilon();
1208     Tp max_abs_diff = -Tp(1);
1209     Tp max_abs_frac = -Tp(1);
1210     unsigned int num_datum = sizeof(data005)
1211                            / sizeof(testcase_hermite<double>);
1212     for (unsigned int i = 0; i < num_datum; ++i)
1213       {
1214         const Tp f = std::tr1::hermite(Tp(data005[i].n), Tp(data005[i].x));
1215         const Tp f0 = data005[i].f0;
1216         const Tp diff = f - f0;
1217         if (std::abs(diff) > max_abs_diff)
1218           max_abs_diff = std::abs(diff);
1219         if (std::abs(f0) > Tp(10) * eps
1220          && std::abs(f) > Tp(10) * eps)
1221           {
1222             const Tp frac = diff / f0;
1223             if (std::abs(frac) > max_abs_frac)
1224               max_abs_frac = std::abs(frac);
1225           }
1226       }
1227     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
1228   }
1229
1230 // Test data for n=20.
1231 // max(|f - f_GSL|): 0.0000000000000000
1232 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1233 testcase_hermite<double>
1234 data006[] =
1235 {
1236   { 3.6536710970888030e+25, 20, -10.000000000000000 },
1237   { 2.9174932703098834e+25, 20, -9.9000000000000004 },
1238   { 2.3228769039548404e+25, 20, -9.8000000000000007 },
1239   { 1.8439144509496016e+25, 20, -9.6999999999999993 },
1240   { 1.4591971834545420e+25, 20, -9.5999999999999996 },
1241   { 1.1510764882450827e+25, 20, -9.5000000000000000 },
1242   { 9.0503941245991605e+24, 20, -9.4000000000000004 },
1243   { 7.0918188910312152e+24, 20, -9.3000000000000007 },
1244   { 5.5376531405202033e+24, 20, -9.1999999999999993 },
1245   { 4.3084410724035914e+24, 20, -9.0999999999999996 },
1246   { 3.3395360269524137e+24, 20, -9.0000000000000000 },
1247   { 2.5784910430831484e+24, 20, -8.9000000000000004 },
1248   { 1.9828824261062853e+24, 20, -8.8000000000000007 },
1249   { 1.5184989558235974e+24, 20, -8.6999999999999993 },
1250   { 1.1578391431515818e+24, 20, -8.5999999999999996 },
1251   { 8.7886740525023878e+23, 20, -8.5000000000000000 },
1252   { 6.6398733801206072e+23, 20, -8.4000000000000004 },
1253   { 4.9919656538201190e+23, 20, -8.3000000000000007 },
1254   { 3.7339306542317994e+23, 20, -8.1999999999999993 },
1255   { 2.7780752653950559e+23, 20, -8.0999999999999996 },
1256   { 2.0554027373991249e+23, 20, -8.0000000000000000 },
1257   { 1.5118471231121695e+23, 20, -7.9000000000000004 },
1258   { 1.1052214218386250e+23, 20, -7.7999999999999998 },
1259   { 8.0275268594719504e+22, 20, -7.7000000000000002 },
1260   { 5.7909832934009042e+22, 20, -7.5999999999999996 },
1261   { 4.1475563998692745e+22, 20, -7.5000000000000000 },
1262   { 2.9479149729249250e+22, 20, -7.4000000000000004 },
1263   { 2.0783192485964573e+22, 20, -7.2999999999999998 },
1264   { 1.4526171451238503e+22, 20, -7.2000000000000002 },
1265   { 1.0059323685871305e+22, 20, -7.0999999999999996 },
1266   { 6.8970965604502329e+21, 20, -7.0000000000000000 },
1267   { 4.6784410379528280e+21, 20, -6.9000000000000004 },
1268   { 3.1367268160419670e+21, 20, -6.7999999999999998 },
1269   { 2.0764831558419748e+21, 20, -6.7000000000000002 },
1270   { 1.3555174744148132e+21, 20, -6.5999999999999996 },
1271   { 8.7124954970091579e+20, 20, -6.5000000000000000 },
1272   { 5.5033278133788108e+20, 20, -6.4000000000000004 },
1273   { 3.4082412197533739e+20, 20, -6.2999999999999998 },
1274   { 2.0631845648712185e+20, 20, -6.2000000000000002 },
1275   { 1.2158762212269028e+20, 20, -6.0999999999999996 },
1276   { 6.9364200641629315e+19, 20, -6.0000000000000000 },
1277   { 3.7990093270095905e+19, 20, -5.9000000000000004 },
1278   { 1.9713403927925858e+19, 20, -5.7999999999999998 },
1279   { 9.4673798488533340e+18, 20, -5.7000000000000002 },
1280   { 4.0046403628787825e+18, 20, -5.5999999999999996 },
1281   { 1.2907686705724293e+18, 20, -5.5000000000000000 },
1282   { 85277679782823936., 20, -5.4000000000000004 },
1283   { -3.4359547179069376e+17, 20, -5.2999999999999998 },
1284   { -4.0970873501577555e+17, 20, -5.2000000000000002 },
1285   { -3.3419585613348250e+17, 20, -5.0999999999999996 },
1286   { -2.2571776716382720e+17, 20, -5.0000000000000000 },
1287   { -1.3051120203565566e+17, 20, -4.9000000000000004 },
1288   { -62555669197021992., 20, -4.7999999999999998 },
1289   { -20974173561010048., 20, -4.7000000000000002 },
1290   { 519073301695656.00, 20, -4.5999999999999996 },
1291   { 8939556693761121.0, 20, -4.5000000000000000 },
1292   { 10070625675125180., 20, -4.4000000000000004 },
1293   { 7940371996960715.0, 20, -4.2999999999999998 },
1294   { 4973623686173568.0, 20, -4.2000000000000002 },
1295   { 2389023282480410.0, 20, -4.0999999999999996 },
1296   { 619678016654336.00, 20, -4.0000000000000000 },
1297   { -339773491011946.00, 20, -3.9000000000000004 },
1298   { -687467334428204.38, 20, -3.7999999999999998 },
1299   { -663019129550482.75, 20, -3.7000000000000002 },
1300   { -469585152350670.25, 20, -3.5999999999999996 },
1301   { -245659781875039.00, 20, -3.5000000000000000 },
1302   { -66042773886778.938, 20, -3.4000000000000004 },
1303   { 43442261337436.312, 20, -3.2999999999999998 },
1304   { 87626632986465.375, 20, -3.2000000000000002 },
1305   { 85786202388511.375, 20, -3.0999999999999996 },
1306   { 59990281399296.000, 20, -3.0000000000000000 },
1307   { 28343496696718.070, 20, -2.9000000000000004 },
1308   { 2296898915036.0859, 20, -2.7999999999999998 },
1309   { -13249381789941.502, 20, -2.7000000000000002 },
1310   { -18328180426561.059, 20, -2.5999999999999996 },
1311   { -15799429886575.000, 20, -2.5000000000000000 },
1312   { -9442592050214.3027, 20, -2.4000000000000004 },
1313   { -2602375356373.2393, 20, -2.2999999999999998 },
1314   { 2521759315047.8428, 20, -2.2000000000000002 },
1315   { 5027779307352.6660, 20, -2.0999999999999996 },
1316   { 5080118660096.0000, 20, -2.0000000000000000 },
1317   { 3490463276000.5425, 20, -1.9000000000000004 },
1318   { 1277254793997.1128, 20, -1.8000000000000007 },
1319   { -682119355279.28784, 20, -1.6999999999999993 },
1320   { -1851544254412.3203, 20, -1.5999999999999996 },
1321   { -2085387081039.0000, 20, -1.5000000000000000 },
1322   { -1559402933581.5054, 20, -1.4000000000000004 },
1323   { -634265763221.87231, 20, -1.3000000000000007 },
1324   { 295481874887.33429, 20, -1.1999999999999993 },
1325   { 924603483429.34241, 20, -1.0999999999999996 },
1326   { 1107214478336.0000, 20, -1.0000000000000000 },
1327   { 867235623835.12463, 20, -0.90000000000000036 },
1328   { 358848462745.15466, 20, -0.80000000000000071 },
1329   { -202944086511.71936, 20, -0.69999999999999929 },
1330   { -617730863561.32617, 20, -0.59999999999999964 },
1331   { -759627879679.00000, 20, -0.50000000000000000 },
1332   { -607451728035.03271, 20, -0.40000000000000036 },
1333   { -240424854484.42111, 20, -0.30000000000000071 },
1334   { 195759209122.61337, 20, -0.19999999999999929 },
1335   { 540334019322.52014, 20, -0.099999999999999645 },
1336   { 670442572800.00000, 20, 0.0000000000000000 },
1337   { 540334019322.52014, 20, 0.099999999999999645 },
1338   { 195759209122.61337, 20, 0.19999999999999929 },
1339   { -240424854484.42111, 20, 0.30000000000000071 },
1340   { -607451728035.03271, 20, 0.40000000000000036 },
1341   { -759627879679.00000, 20, 0.50000000000000000 },
1342   { -617730863561.32617, 20, 0.59999999999999964 },
1343   { -202944086511.71936, 20, 0.69999999999999929 },
1344   { 358848462745.15466, 20, 0.80000000000000071 },
1345   { 867235623835.12463, 20, 0.90000000000000036 },
1346   { 1107214478336.0000, 20, 1.0000000000000000 },
1347   { 924603483429.34241, 20, 1.0999999999999996 },
1348   { 295481874887.33429, 20, 1.1999999999999993 },
1349   { -634265763221.87231, 20, 1.3000000000000007 },
1350   { -1559402933581.5054, 20, 1.4000000000000004 },
1351   { -2085387081039.0000, 20, 1.5000000000000000 },
1352   { -1851544254412.3203, 20, 1.5999999999999996 },
1353   { -682119355279.28784, 20, 1.6999999999999993 },
1354   { 1277254793997.1128, 20, 1.8000000000000007 },
1355   { 3490463276000.5425, 20, 1.9000000000000004 },
1356   { 5080118660096.0000, 20, 2.0000000000000000 },
1357   { 5027779307352.6660, 20, 2.0999999999999996 },
1358   { 2521759315047.8770, 20, 2.1999999999999993 },
1359   { -2602375356373.2969, 20, 2.3000000000000007 },
1360   { -9442592050214.3027, 20, 2.4000000000000004 },
1361   { -15799429886575.000, 20, 2.5000000000000000 },
1362   { -18328180426561.059, 20, 2.5999999999999996 },
1363   { -13249381789941.586, 20, 2.6999999999999993 },
1364   { 2296898915036.2812, 20, 2.8000000000000007 },
1365   { 28343496696718.070, 20, 2.9000000000000004 },
1366   { 59990281399296.000, 20, 3.0000000000000000 },
1367   { 85786202388511.375, 20, 3.0999999999999996 },
1368   { 87626632986465.438, 20, 3.1999999999999993 },
1369   { 43442261337435.672, 20, 3.3000000000000007 },
1370   { -66042773886778.938, 20, 3.4000000000000004 },
1371   { -245659781875039.00, 20, 3.5000000000000000 },
1372   { -469585152350670.25, 20, 3.5999999999999996 },
1373   { -663019129550482.25, 20, 3.6999999999999993 },
1374   { -687467334428203.38, 20, 3.8000000000000007 },
1375   { -339773491011946.00, 20, 3.9000000000000004 },
1376   { 619678016654336.00, 20, 4.0000000000000000 },
1377   { 2389023282480410.0, 20, 4.0999999999999996 },
1378   { 4973623686173539.0, 20, 4.1999999999999993 },
1379   { 7940371996960741.0, 20, 4.3000000000000007 },
1380   { 10070625675125180., 20, 4.4000000000000004 },
1381   { 8939556693761121.0, 20, 4.5000000000000000 },
1382   { 519073301695656.00, 20, 4.5999999999999996 },
1383   { -20974173561009776., 20, 4.6999999999999993 },
1384   { -62555669197022528., 20, 4.8000000000000007 },
1385   { -1.3051120203565566e+17, 20, 4.9000000000000004 },
1386   { -2.2571776716382720e+17, 20, 5.0000000000000000 },
1387   { -3.3419585613348250e+17, 20, 5.0999999999999996 },
1388   { -4.0970873501577562e+17, 20, 5.1999999999999993 },
1389   { -3.4359547179069216e+17, 20, 5.3000000000000007 },
1390   { 85277679782823936., 20, 5.4000000000000004 },
1391   { 1.2907686705724293e+18, 20, 5.5000000000000000 },
1392   { 4.0046403628787825e+18, 20, 5.5999999999999996 },
1393   { 9.4673798488532767e+18, 20, 5.6999999999999993 },
1394   { 1.9713403927925973e+19, 20, 5.8000000000000007 },
1395   { 3.7990093270095905e+19, 20, 5.9000000000000004 },
1396   { 6.9364200641629315e+19, 20, 6.0000000000000000 },
1397   { 1.2158762212269156e+20, 20, 6.1000000000000014 },
1398   { 2.0631845648712086e+20, 20, 6.1999999999999993 },
1399   { 3.4082412197533902e+20, 20, 6.3000000000000007 },
1400   { 5.5033278133787696e+20, 20, 6.3999999999999986 },
1401   { 8.7124954970091579e+20, 20, 6.5000000000000000 },
1402   { 1.3555174744148243e+21, 20, 6.6000000000000014 },
1403   { 2.0764831558419680e+21, 20, 6.6999999999999993 },
1404   { 3.1367268160419775e+21, 20, 6.8000000000000007 },
1405   { 4.6784410379527966e+21, 20, 6.8999999999999986 },
1406   { 6.8970965604502329e+21, 20, 7.0000000000000000 },
1407   { 1.0059323685871368e+22, 20, 7.1000000000000014 },
1408   { 1.4526171451238465e+22, 20, 7.1999999999999993 },
1409   { 2.0783192485964666e+22, 20, 7.3000000000000007 },
1410   { 2.9479149729249048e+22, 20, 7.3999999999999986 },
1411   { 4.1475563998692745e+22, 20, 7.5000000000000000 },
1412   { 5.7909832934009378e+22, 20, 7.6000000000000014 },
1413   { 8.0275268594719286e+22, 20, 7.6999999999999993 },
1414   { 1.1052214218386286e+23, 20, 7.8000000000000007 },
1415   { 1.5118471231121604e+23, 20, 7.8999999999999986 },
1416   { 2.0554027373991249e+23, 20, 8.0000000000000000 },
1417   { 2.7780752653950703e+23, 20, 8.1000000000000014 },
1418   { 3.7339306542317994e+23, 20, 8.1999999999999993 },
1419   { 4.9919656538201190e+23, 20, 8.3000000000000007 },
1420   { 6.6398733801205790e+23, 20, 8.3999999999999986 },
1421   { 8.7886740525023878e+23, 20, 8.5000000000000000 },
1422   { 1.1578391431515869e+24, 20, 8.6000000000000014 },
1423   { 1.5184989558235974e+24, 20, 8.6999999999999993 },
1424   { 1.9828824261062853e+24, 20, 8.8000000000000007 },
1425   { 2.5784910430831355e+24, 20, 8.8999999999999986 },
1426   { 3.3395360269524137e+24, 20, 9.0000000000000000 },
1427   { 4.3084410724036123e+24, 20, 9.1000000000000014 },
1428   { 5.5376531405202033e+24, 20, 9.1999999999999993 },
1429   { 7.0918188910312152e+24, 20, 9.3000000000000007 },
1430   { 9.0503941245991197e+24, 20, 9.3999999999999986 },
1431   { 1.1510764882450827e+25, 20, 9.5000000000000000 },
1432   { 1.4591971834545491e+25, 20, 9.6000000000000014 },
1433   { 1.8439144509496016e+25, 20, 9.6999999999999993 },
1434   { 2.3228769039548404e+25, 20, 9.8000000000000007 },
1435   { 2.9174932703098731e+25, 20, 9.8999999999999986 },
1436   { 3.6536710970888030e+25, 20, 10.000000000000000 },
1437 };
1438
1439 // Test function for n=20.
1440 template<typename Tp>
1441   void
1442   test006()
1443   {
1444     bool test __attribute__((unused)) = true;
1445     const Tp eps = std::numeric_limits<Tp>::epsilon();
1446     Tp max_abs_diff = -Tp(1);
1447     Tp max_abs_frac = -Tp(1);
1448     unsigned int num_datum = sizeof(data006)
1449                            / sizeof(testcase_hermite<double>);
1450     for (unsigned int i = 0; i < num_datum; ++i)
1451       {
1452         const Tp f = std::tr1::hermite(Tp(data006[i].n), Tp(data006[i].x));
1453         const Tp f0 = data006[i].f0;
1454         const Tp diff = f - f0;
1455         if (std::abs(diff) > max_abs_diff)
1456           max_abs_diff = std::abs(diff);
1457         if (std::abs(f0) > Tp(10) * eps
1458          && std::abs(f) > Tp(10) * eps)
1459           {
1460             const Tp frac = diff / f0;
1461             if (std::abs(frac) > max_abs_frac)
1462               max_abs_frac = std::abs(frac);
1463           }
1464       }
1465     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
1466   }
1467
1468 // Test data for n=50.
1469 // max(|f - f_GSL|): 0.0000000000000000
1470 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1471 testcase_hermite<double>
1472 data007[] =
1473 {
1474   { 1.3516643049819314e+61, 50, -10.000000000000000 },
1475   { 5.8466703062266110e+60, 50, -9.9000000000000004 },
1476   { 2.4344814863741168e+60, 50, -9.8000000000000007 },
1477   { 9.6739828066585787e+59, 50, -9.6999999999999993 },
1478   { 3.6194312967780128e+59, 50, -9.5999999999999996 },
1479   { 1.2454022521696361e+59, 50, -9.5000000000000000 },
1480   { 3.7546881918013145e+58, 50, -9.4000000000000004 },
1481   { 8.6500158470917270e+57, 50, -9.3000000000000007 },
1482   { 5.3163209769527426e+56, 50, -9.1999999999999993 },
1483   { -9.7863165370930473e+56, 50, -9.0999999999999996 },
1484   { -8.0563930902368911e+56, 50, -9.0000000000000000 },
1485   { -4.3145937406321933e+56, 50, -8.9000000000000004 },
1486   { -1.8210771577645630e+56, 50, -8.8000000000000007 },
1487   { -6.0082225302289557e+55, 50, -8.6999999999999993 },
1488   { -1.2392013720948442e+55, 50, -8.5999999999999996 },
1489   { 1.5935887905806307e+54, 50, -8.5000000000000000 },
1490   { 3.4325365049909381e+54, 50, -8.4000000000000004 },
1491   { 2.2368641272300899e+54, 50, -8.3000000000000007 },
1492   { 1.0009712198862341e+54, 50, -8.1999999999999993 },
1493   { 3.0699480272357337e+53, 50, -8.0999999999999996 },
1494   { 2.9492797132685063e+52, 50, -8.0000000000000000 },
1495   { -3.9982544106300062e+52, 50, -7.9000000000000004 },
1496   { -3.5678031330023779e+52, 50, -7.7999999999999998 },
1497   { -1.8076371748762468e+52, 50, -7.7000000000000002 },
1498   { -5.7887622198708925e+51, 50, -7.5999999999999996 },
1499   { -3.5808467693113330e+50, 50, -7.5000000000000000 },
1500   { 1.0219511166806405e+51, 50, -7.4000000000000004 },
1501   { 8.4241263694549560e+50, 50, -7.2999999999999998 },
1502   { 3.9143899315095369e+50, 50, -7.2000000000000002 },
1503   { 9.3178966245756654e+49, 50, -7.0999999999999996 },
1504   { -2.4714855983436561e+49, 50, -7.0000000000000000 },
1505   { -4.1428217272044600e+49, 50, -6.9000000000000004 },
1506   { -2.4864980414057334e+49, 50, -6.7999999999999998 },
1507   { -8.0684355476447979e+48, 50, -6.7000000000000002 },
1508   { 4.2529238530179841e+47, 50, -6.5999999999999996 },
1509   { 2.4709663739849681e+48, 50, -6.5000000000000000 },
1510   { 1.7500305481204125e+48, 50, -6.4000000000000004 },
1511   { 6.3834558285146007e+47, 50, -6.2999999999999998 },
1512   { -1.1477672402381055e+46, 50, -6.2000000000000002 },
1513   { -1.9304630401841983e+47, 50, -6.0999999999999996 },
1514   { -1.4355266959903589e+47, 50, -6.0000000000000000 },
1515   { -5.1482200905566146e+46, 50, -5.9000000000000004 },
1516   { 4.6577356827463283e+45, 50, -5.7999999999999998 },
1517   { 1.9676012349652066e+46, 50, -5.7000000000000002 },
1518   { 1.3630554018675846e+46, 50, -5.5999999999999996 },
1519   { 4.0920495328093750e+45, 50, -5.5000000000000000 },
1520   { -1.3680638882145392e+45, 50, -5.4000000000000004 },
1521   { -2.4465265559935436e+45, 50, -5.2999999999999998 },
1522   { -1.4270495629649456e+45, 50, -5.2000000000000002 },
1523   { -2.4845518743338381e+44, 50, -5.0999999999999996 },
1524   { 3.1953926721271990e+44, 50, -5.0000000000000000 },
1525   { 3.4169399444879600e+44, 50, -4.9000000000000004 },
1526   { 1.4896819114978755e+44, 50, -4.7999999999999998 },
1527   { -1.3078430866968493e+43, 50, -4.7000000000000002 },
1528   { -6.8449168639700716e+43, 50, -4.5999999999999996 },
1529   { -4.9181639709997461e+43, 50, -4.5000000000000000 },
1530   { -1.1434943490345182e+43, 50, -4.4000000000000004 },
1531   { 1.1214652543461432e+43, 50, -4.2999999999999998 },
1532   { 1.3843548994480608e+43, 50, -4.2000000000000002 },
1533   { 6.3349790205303262e+42, 50, -4.0999999999999996 },
1534   { -9.5599640670553907e+41, 50, -4.0000000000000000 },
1535   { -3.6202558158287927e+42, 50, -3.9000000000000004 },
1536   { -2.5206461734624493e+42, 50, -3.7999999999999998 },
1537   { -3.7818051510732439e+41, 50, -3.7000000000000002 },
1538   { 8.8921371165335050e+41, 50, -3.5999999999999996 },
1539   { 9.2055485763852770e+41, 50, -3.5000000000000000 },
1540   { 3.2535765707283020e+41, 50, -3.4000000000000004 },
1541   { -1.9358941418244578e+41, 50, -3.2999999999999998 },
1542   { -3.3076282847915670e+41, 50, -3.2000000000000002 },
1543   { -1.7764977066639160e+41, 50, -3.0999999999999996 },
1544   { 2.6751882008697154e+40, 50, -3.0000000000000000 },
1545   { 1.2025382369996052e+41, 50, -2.9000000000000004 },
1546   { 8.8383035103557973e+40, 50, -2.7999999999999998 },
1547   { 7.7733606479641769e+39, 50, -2.7000000000000002 },
1548   { -4.4696811758713757e+40, 50, -2.5999999999999996 },
1549   { -4.3715062488963453e+40, 50, -2.5000000000000000 },
1550   { -1.1390080390575289e+40, 50, -2.4000000000000004 },
1551   { 1.6938519751181342e+40, 50, -2.2999999999999998 },
1552   { 2.2284509952956210e+40, 50, -2.2000000000000002 },
1553   { 9.0967994280570531e+39, 50, -2.0999999999999996 },
1554   { -6.4126677997472978e+39, 50, -2.0000000000000000 },
1555   { -1.1926839454034341e+40, 50, -1.9000000000000004 },
1556   { -6.5436654274699114e+39, 50, -1.8000000000000007 },
1557   { 2.2779499542550411e+39, 50, -1.6999999999999993 },
1558   { 6.7720530889699639e+39, 50, -1.5999999999999996 },
1559   { 4.6884851188034300e+39, 50, -1.5000000000000000 },
1560   { -5.9005001052557463e+38, 50, -1.4000000000000004 },
1561   { -4.1028320210430589e+39, 50, -1.3000000000000007 },
1562   { -3.4780049977083965e+39, 50, -1.1999999999999993 },
1563   { -1.3484918476373692e+38, 50, -1.0999999999999996 },
1564   { 2.6586815431645456e+39, 50, -1.0000000000000000 },
1565   { 2.7225429473661429e+39, 50, -0.90000000000000036 },
1566   { 4.7785441024951729e+38, 50, -0.80000000000000071 },
1567   { -1.8416784378790159e+39, 50, -0.69999999999999929 },
1568   { -2.2725918816693132e+39, 50, -0.59999999999999964 },
1569   { -6.7948375014926916e+38, 50, -0.50000000000000000 },
1570   { 1.3581645858905750e+39, 50, -0.40000000000000036 },
1571   { 2.0349661043040497e+39, 50, -0.30000000000000071 },
1572   { 8.5049248815817037e+38, 50, -0.19999999999999929 },
1573   { -1.0564542132990048e+39, 50, -0.099999999999999645 },
1574   { -1.9607814681608194e+39, 50, 0.0000000000000000 },
1575   { -1.0564542132990048e+39, 50, 0.099999999999999645 },
1576   { 8.5049248815817037e+38, 50, 0.19999999999999929 },
1577   { 2.0349661043040497e+39, 50, 0.30000000000000071 },
1578   { 1.3581645858905750e+39, 50, 0.40000000000000036 },
1579   { -6.7948375014926916e+38, 50, 0.50000000000000000 },
1580   { -2.2725918816693132e+39, 50, 0.59999999999999964 },
1581   { -1.8416784378790159e+39, 50, 0.69999999999999929 },
1582   { 4.7785441024951729e+38, 50, 0.80000000000000071 },
1583   { 2.7225429473661429e+39, 50, 0.90000000000000036 },
1584   { 2.6586815431645456e+39, 50, 1.0000000000000000 },
1585   { -1.3484918476373692e+38, 50, 1.0999999999999996 },
1586   { -3.4780049977083965e+39, 50, 1.1999999999999993 },
1587   { -4.1028320210430589e+39, 50, 1.3000000000000007 },
1588   { -5.9005001052557463e+38, 50, 1.4000000000000004 },
1589   { 4.6884851188034300e+39, 50, 1.5000000000000000 },
1590   { 6.7720530889699639e+39, 50, 1.5999999999999996 },
1591   { 2.2779499542550411e+39, 50, 1.6999999999999993 },
1592   { -6.5436654274699114e+39, 50, 1.8000000000000007 },
1593   { -1.1926839454034341e+40, 50, 1.9000000000000004 },
1594   { -6.4126677997472978e+39, 50, 2.0000000000000000 },
1595   { 9.0967994280570531e+39, 50, 2.0999999999999996 },
1596   { 2.2284509952956162e+40, 50, 2.1999999999999993 },
1597   { 1.6938519751181172e+40, 50, 2.3000000000000007 },
1598   { -1.1390080390575289e+40, 50, 2.4000000000000004 },
1599   { -4.3715062488963453e+40, 50, 2.5000000000000000 },
1600   { -4.4696811758713757e+40, 50, 2.5999999999999996 },
1601   { 7.7733606479635628e+39, 50, 2.6999999999999993 },
1602   { 8.8383035103558611e+40, 50, 2.8000000000000007 },
1603   { 1.2025382369996052e+41, 50, 2.9000000000000004 },
1604   { 2.6751882008697154e+40, 50, 3.0000000000000000 },
1605   { -1.7764977066639160e+41, 50, 3.0999999999999996 },
1606   { -3.3076282847915616e+41, 50, 3.1999999999999993 },
1607   { -1.9358941418244260e+41, 50, 3.3000000000000007 },
1608   { 3.2535765707283020e+41, 50, 3.4000000000000004 },
1609   { 9.2055485763852770e+41, 50, 3.5000000000000000 },
1610   { 8.8921371165335050e+41, 50, 3.5999999999999996 },
1611   { -3.7818051510730675e+41, 50, 3.6999999999999993 },
1612   { -2.5206461734624660e+42, 50, 3.8000000000000007 },
1613   { -3.6202558158287927e+42, 50, 3.9000000000000004 },
1614   { -9.5599640670553907e+41, 50, 4.0000000000000000 },
1615   { 6.3349790205303262e+42, 50, 4.0999999999999996 },
1616   { 1.3843548994480566e+43, 50, 4.1999999999999993 },
1617   { 1.1214652543461340e+43, 50, 4.3000000000000007 },
1618   { -1.1434943490345182e+43, 50, 4.4000000000000004 },
1619   { -4.9181639709997461e+43, 50, 4.5000000000000000 },
1620   { -6.8449168639700716e+43, 50, 4.5999999999999996 },
1621   { -1.3078430866969463e+43, 50, 4.6999999999999993 },
1622   { 1.4896819114978953e+44, 50, 4.8000000000000007 },
1623   { 3.4169399444879600e+44, 50, 4.9000000000000004 },
1624   { 3.1953926721271990e+44, 50, 5.0000000000000000 },
1625   { -2.4845518743338381e+44, 50, 5.0999999999999996 },
1626   { -1.4270495629649337e+45, 50, 5.1999999999999993 },
1627   { -2.4465265559935458e+45, 50, 5.3000000000000007 },
1628   { -1.3680638882145392e+45, 50, 5.4000000000000004 },
1629   { 4.0920495328093750e+45, 50, 5.5000000000000000 },
1630   { 1.3630554018675846e+46, 50, 5.5999999999999996 },
1631   { 1.9676012349652081e+46, 50, 5.6999999999999993 },
1632   { 4.6577356827460393e+45, 50, 5.8000000000000007 },
1633   { -5.1482200905566146e+46, 50, 5.9000000000000004 },
1634   { -1.4355266959903589e+47, 50, 6.0000000000000000 },
1635   { -1.9304630401841966e+47, 50, 6.1000000000000014 },
1636   { -1.1477672402384868e+46, 50, 6.1999999999999993 },
1637   { 6.3834558285146981e+47, 50, 6.3000000000000007 },
1638   { 1.7500305481203924e+48, 50, 6.3999999999999986 },
1639   { 2.4709663739849681e+48, 50, 6.5000000000000000 },
1640   { 4.2529238530171793e+47, 50, 6.6000000000000014 },
1641   { -8.0684355476446876e+48, 50, 6.6999999999999993 },
1642   { -2.4864980414057495e+49, 50, 6.8000000000000007 },
1643   { -4.1428217272044496e+49, 50, 6.8999999999999986 },
1644   { -2.4714855983436561e+49, 50, 7.0000000000000000 },
1645   { 9.3178966245760310e+49, 50, 7.1000000000000014 },
1646   { 3.9143899315095070e+50, 50, 7.1999999999999993 },
1647   { 8.4241263694549925e+50, 50, 7.3000000000000007 },
1648   { 1.0219511166806458e+51, 50, 7.3999999999999986 },
1649   { -3.5808467693113330e+50, 50, 7.5000000000000000 },
1650   { -5.7887622198710268e+51, 50, 7.6000000000000014 },
1651   { -1.8076371748762319e+52, 50, 7.6999999999999993 },
1652   { -3.5678031330023971e+52, 50, 7.8000000000000007 },
1653   { -3.9982544106300530e+52, 50, 7.8999999999999986 },
1654   { 2.9492797132685063e+52, 50, 8.0000000000000000 },
1655   { 3.0699480272358086e+53, 50, 8.1000000000000014 },
1656   { 1.0009712198862341e+54, 50, 8.1999999999999993 },
1657   { 2.2368641272300899e+54, 50, 8.3000000000000007 },
1658   { 3.4325365049909340e+54, 50, 8.3999999999999986 },
1659   { 1.5935887905806307e+54, 50, 8.5000000000000000 },
1660   { -1.2392013720948937e+55, 50, 8.6000000000000014 },
1661   { -6.0082225302289557e+55, 50, 8.6999999999999993 },
1662   { -1.8210771577645630e+56, 50, 8.8000000000000007 },
1663   { -4.3145937406321376e+56, 50, 8.8999999999999986 },
1664   { -8.0563930902368911e+56, 50, 9.0000000000000000 },
1665   { -9.7863165370930194e+56, 50, 9.1000000000000014 },
1666   { 5.3163209769527426e+56, 50, 9.1999999999999993 },
1667   { 8.6500158470917270e+57, 50, 9.3000000000000007 },
1668   { 3.7546881918012164e+58, 50, 9.3999999999999986 },
1669   { 1.2454022521696361e+59, 50, 9.5000000000000000 },
1670   { 3.6194312967780793e+59, 50, 9.6000000000000014 },
1671   { 9.6739828066585787e+59, 50, 9.6999999999999993 },
1672   { 2.4344814863741168e+60, 50, 9.8000000000000007 },
1673   { 5.8466703062265247e+60, 50, 9.8999999999999986 },
1674   { 1.3516643049819314e+61, 50, 10.000000000000000 },
1675 };
1676
1677 // Test function for n=50.
1678 template<typename Tp>
1679   void
1680   test007()
1681   {
1682     bool test __attribute__((unused)) = true;
1683     const Tp eps = std::numeric_limits<Tp>::epsilon();
1684     Tp max_abs_diff = -Tp(1);
1685     Tp max_abs_frac = -Tp(1);
1686     unsigned int num_datum = sizeof(data007)
1687                            / sizeof(testcase_hermite<double>);
1688     for (unsigned int i = 0; i < num_datum; ++i)
1689       {
1690         const Tp f = std::tr1::hermite(Tp(data007[i].n), Tp(data007[i].x));
1691         const Tp f0 = data007[i].f0;
1692         const Tp diff = f - f0;
1693         if (std::abs(diff) > max_abs_diff)
1694           max_abs_diff = std::abs(diff);
1695         if (std::abs(f0) > Tp(10) * eps
1696          && std::abs(f) > Tp(10) * eps)
1697           {
1698             const Tp frac = diff / f0;
1699             if (std::abs(frac) > max_abs_frac)
1700               max_abs_frac = std::abs(frac);
1701           }
1702       }
1703     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
1704   }
1705
1706 // Test data for n=100.
1707 // max(|f - f_GSL|): 0.0000000000000000
1708 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
1709 testcase_hermite<double>
1710 data008[] =
1711 {
1712   { -1.8738689223256612e+115, 100, -10.000000000000000 },
1713   { -4.4232904120311186e+114, 100, -9.9000000000000004 },
1714   { 8.3761676654305186e+113, 100, -9.8000000000000007 },
1715   { 9.4857435427570856e+113, 100, -9.6999999999999993 },
1716   { 2.4904626130429828e+113, 100, -9.5999999999999996 },
1717   { -4.2265051766934789e+112, 100, -9.5000000000000000 },
1718   { -5.3374224541142079e+112, 100, -9.4000000000000004 },
1719   { -1.3977488190034162e+112, 100, -9.3000000000000007 },
1720   { 2.9686037583393142e+111, 100, -9.1999999999999993 },
1721   { 3.3341330166544008e+111, 100, -9.0999999999999996 },
1722   { 7.7294136683043515e+110, 100, -9.0000000000000000 },
1723   { -2.6071876743328352e+110, 100, -8.9000000000000004 },
1724   { -2.2669773300293168e+110, 100, -8.8000000000000007 },
1725   { -3.8930624477368766e+109, 100, -8.6999999999999993 },
1726   { 2.5386102824684956e+109, 100, -8.5999999999999996 },
1727   { 1.6203702280499544e+109, 100, -8.5000000000000000 },
1728   { 1.2481735250539652e+108, 100, -8.4000000000000004 },
1729   { -2.5611278359589723e+108, 100, -8.3000000000000007 },
1730   { -1.1534178973583771e+108, 100, -8.1999999999999993 },
1731   { 8.4932594446954126e+106, 100, -8.0999999999999996 },
1732   { 2.5761505535443451e+107, 100, -8.0000000000000000 },
1733   { 7.3445622927437730e+106, 100, -7.9000000000000004 },
1734   { -2.7252309851017323e+106, 100, -7.7999999999999998 },
1735   { -2.4850432648124068e+106, 100, -7.7000000000000002 },
1736   { -2.7486638813238851e+105, 100, -7.5999999999999996 },
1737   { 4.4772364475394960e+105, 100, -7.5000000000000000 },
1738   { 2.1375121759800508e+105, 100, -7.4000000000000004 },
1739   { -2.9237691057265876e+104, 100, -7.2999999999999998 },
1740   { -5.9348804074874781e+104, 100, -7.2000000000000002 },
1741   { -1.2947583568692734e+104, 100, -7.0999999999999996 },
1742   { 1.0002273523275075e+104, 100, -7.0000000000000000 },
1743   { 6.4900499886057735e+103, 100, -6.9000000000000004 },
1744   { -3.7817730019124298e+102, 100, -6.7999999999999998 },
1745   { -1.7849709684883137e+103, 100, -6.7000000000000002 },
1746   { -4.8039047085580619e+102, 100, -6.5999999999999996 },
1747   { 3.2072472002047670e+102, 100, -6.5000000000000000 },
1748   { 2.3341289432999226e+102, 100, -6.4000000000000004 },
1749   { -1.4587350659146165e+101, 100, -6.2999999999999998 },
1750   { -7.0672139150705532e+101, 100, -6.2000000000000002 },
1751   { -1.8039133351601998e+101, 100, -6.0999999999999996 },
1752   { 1.5170693933260738e+101, 100, -6.0000000000000000 },
1753   { 1.0141407690966954e+101, 100, -5.9000000000000004 },
1754   { -1.5140717605507886e+100, 100, -5.7999999999999998 },
1755   { -3.6379102593330533e+100, 100, -5.7000000000000002 },
1756   { -6.2933057672779134e+99, 100, -5.5999999999999996 },
1757   { 9.9309186425970402e+99, 100, -5.5000000000000000 },
1758   { 5.0935670879056567e+99, 100, -5.4000000000000004 },
1759   { -1.8337906983006129e+99, 100, -5.2999999999999998 },
1760   { -2.3096466887887402e+99, 100, -5.2000000000000002 },
1761   { -4.0259235416602546e+97, 100, -5.0999999999999996 },
1762   { 8.1931937130591466e+98, 100, -5.0000000000000000 },
1763   { 2.5601172475776894e+98, 100, -4.9000000000000004 },
1764   { -2.3193021196802698e+98, 100, -4.7999999999999998 },
1765   { -1.6545238014142802e+98, 100, -4.7000000000000002 },
1766   { 4.2440218943299170e+97, 100, -4.5999999999999996 },
1767   { 7.8073853756187101e+97, 100, -4.5000000000000000 },
1768   { 5.2136163919277588e+96, 100, -4.4000000000000004 },
1769   { -3.0837503404959950e+97, 100, -4.2999999999999998 },
1770   { -1.0988290456447777e+97, 100, -4.2000000000000002 },
1771   { 1.0173847230741884e+97, 100, -4.0999999999999996 },
1772   { 7.7070682747643550e+96, 100, -4.0000000000000000 },
1773   { -2.3947326745293331e+96, 100, -3.9000000000000004 },
1774   { -4.1993887070961596e+96, 100, -3.7999999999999998 },
1775   { -5.5521768050542138e+94, 100, -3.7000000000000002 },
1776   { 1.9852724296241180e+96, 100, -3.5999999999999996 },
1777   { 5.7841213444838915e+95, 100, -3.5000000000000000 },
1778   { -8.2433116644948570e+95, 100, -3.4000000000000004 },
1779   { -5.2035951331058195e+95, 100, -3.2999999999999998 },
1780   { 2.8212012454566057e+95, 100, -3.2000000000000002 },
1781   { 3.5161870090563867e+95, 100, -3.0999999999999996 },
1782   { -5.5084542871196523e+94, 100, -3.0000000000000000 },
1783   { -2.0784160746797610e+95, 100, -2.9000000000000004 },
1784   { -2.6058116248679496e+94, 100, -2.7999999999999998 },
1785   { 1.1147132226581844e+95, 100, -2.7000000000000002 },
1786   { 4.5607706742532875e+94, 100, -2.5999999999999996 },
1787   { -5.3758761713337664e+94, 100, -2.5000000000000000 },
1788   { -4.2303228932575769e+94, 100, -2.4000000000000004 },
1789   { 2.1691501564685499e+94, 100, -2.2999999999999998 },
1790   { 3.2602488340116974e+94, 100, -2.2000000000000002 },
1791   { -5.0527155039787607e+93, 100, -2.0999999999999996 },
1792   { -2.2785574311661325e+94, 100, -2.0000000000000000 },
1793   { -2.8549527653152903e+93, 100, -1.9000000000000004 },
1794   { 1.4787573463714363e+94, 100, -1.8000000000000007 },
1795   { 6.0554070654771248e+93, 100, -1.6999999999999993 },
1796   { -8.8496828346970978e+93, 100, -1.5999999999999996 },
1797   { -6.8402151897169509e+93, 100, -1.5000000000000000 },
1798   { 4.6555468819923166e+93, 100, -1.4000000000000004 },
1799   { 6.4625437128323579e+93, 100, -1.3000000000000007 },
1800   { -1.7820042440391653e+93, 100, -1.1999999999999993 },
1801   { -5.5814393347235886e+93, 100, -1.0999999999999996 },
1802   { -1.4487067293379347e+92, 100, -1.0000000000000000 },
1803   { 4.5268398678911204e+93, 100, -0.90000000000000036 },
1804   { 1.4120762149478435e+93, 100, -0.80000000000000071 },
1805   { -3.4510765981144258e+93, 100, -0.69999999999999929 },
1806   { -2.2242581581553176e+93, 100, -0.59999999999999964 },
1807   { 2.4129827902061037e+93, 100, -0.50000000000000000 },
1808   { 2.7195429139752497e+93, 100, -0.40000000000000036 },
1809   { -1.4235309630836904e+93, 100, -0.30000000000000071 },
1810   { -2.9850618739468043e+93, 100, -0.19999999999999929 },
1811   { 4.7017027479251074e+92, 100, -0.099999999999999645 },
1812   { 3.0685187562549660e+93, 100, 0.0000000000000000 },
1813   { 4.7017027479251074e+92, 100, 0.099999999999999645 },
1814   { -2.9850618739468043e+93, 100, 0.19999999999999929 },
1815   { -1.4235309630836904e+93, 100, 0.30000000000000071 },
1816   { 2.7195429139752497e+93, 100, 0.40000000000000036 },
1817   { 2.4129827902061037e+93, 100, 0.50000000000000000 },
1818   { -2.2242581581553176e+93, 100, 0.59999999999999964 },
1819   { -3.4510765981144258e+93, 100, 0.69999999999999929 },
1820   { 1.4120762149478435e+93, 100, 0.80000000000000071 },
1821   { 4.5268398678911204e+93, 100, 0.90000000000000036 },
1822   { -1.4487067293379347e+92, 100, 1.0000000000000000 },
1823   { -5.5814393347235886e+93, 100, 1.0999999999999996 },
1824   { -1.7820042440391653e+93, 100, 1.1999999999999993 },
1825   { 6.4625437128323579e+93, 100, 1.3000000000000007 },
1826   { 4.6555468819923166e+93, 100, 1.4000000000000004 },
1827   { -6.8402151897169509e+93, 100, 1.5000000000000000 },
1828   { -8.8496828346970978e+93, 100, 1.5999999999999996 },
1829   { 6.0554070654771248e+93, 100, 1.6999999999999993 },
1830   { 1.4787573463714363e+94, 100, 1.8000000000000007 },
1831   { -2.8549527653152903e+93, 100, 1.9000000000000004 },
1832   { -2.2785574311661325e+94, 100, 2.0000000000000000 },
1833   { -5.0527155039787607e+93, 100, 2.0999999999999996 },
1834   { 3.2602488340116774e+94, 100, 2.1999999999999993 },
1835   { 2.1691501564685076e+94, 100, 2.3000000000000007 },
1836   { -4.2303228932575769e+94, 100, 2.4000000000000004 },
1837   { -5.3758761713337664e+94, 100, 2.5000000000000000 },
1838   { 4.5607706742532875e+94, 100, 2.5999999999999996 },
1839   { 1.1147132226581881e+95, 100, 2.6999999999999993 },
1840   { -2.6058116248681564e+94, 100, 2.8000000000000007 },
1841   { -2.0784160746797610e+95, 100, 2.9000000000000004 },
1842   { -5.5084542871196523e+94, 100, 3.0000000000000000 },
1843   { 3.5161870090563867e+95, 100, 3.0999999999999996 },
1844   { 2.8212012454566478e+95, 100, 3.1999999999999993 },
1845   { -5.2035951331058918e+95, 100, 3.3000000000000007 },
1846   { -8.2433116644948570e+95, 100, 3.4000000000000004 },
1847   { 5.7841213444838915e+95, 100, 3.5000000000000000 },
1848   { 1.9852724296241180e+96, 100, 3.5999999999999996 },
1849   { -5.5521768050503009e+94, 100, 3.6999999999999993 },
1850   { -4.1993887070961795e+96, 100, 3.8000000000000007 },
1851   { -2.3947326745293331e+96, 100, 3.9000000000000004 },
1852   { 7.7070682747643550e+96, 100, 4.0000000000000000 },
1853   { 1.0173847230741884e+97, 100, 4.0999999999999996 },
1854   { -1.0988290456447506e+97, 100, 4.1999999999999993 },
1855   { -3.0837503404959957e+97, 100, 4.3000000000000007 },
1856   { 5.2136163919277588e+96, 100, 4.4000000000000004 },
1857   { 7.8073853756187101e+97, 100, 4.5000000000000000 },
1858   { 4.2440218943299170e+97, 100, 4.5999999999999996 },
1859   { -1.6545238014142650e+98, 100, 4.6999999999999993 },
1860   { -2.3193021196802549e+98, 100, 4.8000000000000007 },
1861   { 2.5601172475776894e+98, 100, 4.9000000000000004 },
1862   { 8.1931937130591466e+98, 100, 5.0000000000000000 },
1863   { -4.0259235416602546e+97, 100, 5.0999999999999996 },
1864   { -2.3096466887887237e+99, 100, 5.1999999999999993 },
1865   { -1.8337906983005823e+99, 100, 5.3000000000000007 },
1866   { 5.0935670879056567e+99, 100, 5.4000000000000004 },
1867   { 9.9309186425970402e+99, 100, 5.5000000000000000 },
1868   { -6.2933057672779134e+99, 100, 5.5999999999999996 },
1869   { -3.6379102593330386e+100, 100, 5.6999999999999993 },
1870   { -1.5140717605507249e+100, 100, 5.8000000000000007 },
1871   { 1.0141407690966954e+101, 100, 5.9000000000000004 },
1872   { 1.5170693933260738e+101, 100, 6.0000000000000000 },
1873   { -1.8039133351602961e+101, 100, 6.1000000000000014 },
1874   { -7.0672139150705246e+101, 100, 6.1999999999999993 },
1875   { -1.4587350659144549e+101, 100, 6.3000000000000007 },
1876   { 2.3341289432998748e+102, 100, 6.3999999999999986 },
1877   { 3.2072472002047670e+102, 100, 6.5000000000000000 },
1878   { -4.8039047085582927e+102, 100, 6.6000000000000014 },
1879   { -1.7849709684883083e+103, 100, 6.6999999999999993 },
1880   { -3.7817730019120996e+102, 100, 6.8000000000000007 },
1881   { 6.4900499886056430e+103, 100, 6.8999999999999986 },
1882   { 1.0002273523275075e+104, 100, 7.0000000000000000 },
1883   { -1.2947583568693485e+104, 100, 7.1000000000000014 },
1884   { -5.9348804074874565e+104, 100, 7.1999999999999993 },
1885   { -2.9237691057264679e+104, 100, 7.3000000000000007 },
1886   { 2.1375121759799924e+105, 100, 7.3999999999999986 },
1887   { 4.4772364475394960e+105, 100, 7.5000000000000000 },
1888   { -2.7486638813241244e+105, 100, 7.6000000000000014 },
1889   { -2.4850432648123868e+106, 100, 7.6999999999999993 },
1890   { -2.7252309851017070e+106, 100, 7.8000000000000007 },
1891   { 7.3445622927434568e+106, 100, 7.8999999999999986 },
1892   { 2.5761505535443451e+107, 100, 8.0000000000000000 },
1893   { 8.4932594446944218e+106, 100, 8.1000000000000014 },
1894   { -1.1534178973583771e+108, 100, 8.1999999999999993 },
1895   { -2.5611278359589723e+108, 100, 8.3000000000000007 },
1896   { 1.2481735250538004e+108, 100, 8.3999999999999986 },
1897   { 1.6203702280499544e+109, 100, 8.5000000000000000 },
1898   { 2.5386102824684747e+109, 100, 8.6000000000000014 },
1899   { -3.8930624477368766e+109, 100, 8.6999999999999993 },
1900   { -2.2669773300293168e+110, 100, 8.8000000000000007 },
1901   { -2.6071876743328939e+110, 100, 8.8999999999999986 },
1902   { 7.7294136683043515e+110, 100, 9.0000000000000000 },
1903   { 3.3341330166544429e+111, 100, 9.1000000000000014 },
1904   { 2.9686037583393142e+111, 100, 9.1999999999999993 },
1905   { -1.3977488190034162e+112, 100, 9.3000000000000007 },
1906   { -5.3374224541141370e+112, 100, 9.3999999999999986 },
1907   { -4.2265051766934789e+112, 100, 9.5000000000000000 },
1908   { 2.4904626130430740e+113, 100, 9.6000000000000014 },
1909   { 9.4857435427570856e+113, 100, 9.6999999999999993 },
1910   { 8.3761676654305186e+113, 100, 9.8000000000000007 },
1911   { -4.4232904120309469e+114, 100, 9.8999999999999986 },
1912   { -1.8738689223256612e+115, 100, 10.000000000000000 },
1913 };
1914
1915 // Test function for n=100.
1916 template<typename Tp>
1917   void
1918   test008()
1919   {
1920     bool test __attribute__((unused)) = true;
1921     const Tp eps = std::numeric_limits<Tp>::epsilon();
1922     Tp max_abs_diff = -Tp(1);
1923     Tp max_abs_frac = -Tp(1);
1924     unsigned int num_datum = sizeof(data008)
1925                            / sizeof(testcase_hermite<double>);
1926     for (unsigned int i = 0; i < num_datum; ++i)
1927       {
1928         const Tp f = std::tr1::hermite(Tp(data008[i].n), Tp(data008[i].x));
1929         const Tp f0 = data008[i].f0;
1930         const Tp diff = f - f0;
1931         if (std::abs(diff) > max_abs_diff)
1932           max_abs_diff = std::abs(diff);
1933         if (std::abs(f0) > Tp(10) * eps
1934          && std::abs(f) > Tp(10) * eps)
1935           {
1936             const Tp frac = diff / f0;
1937             if (std::abs(frac) > max_abs_frac)
1938               max_abs_frac = std::abs(frac);
1939           }
1940       }
1941     VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
1942   }
1943
1944 int
1945 main()
1946 {
1947   test001<double>();
1948   test002<double>();
1949   test003<double>();
1950   test004<double>();
1951   test005<double>();
1952   test006<double>();
1953   test007<double>();
1954   test008<double>();
1955   return 0;
1956 }