libstdc++-v3/testsuite/special_functions/18_riemann_zeta/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 //  riemann_zeta
  21
  22 // This can take long on simulators, timing out the test.
  23 // { dg-additional-options "-DMAX_ITERATIONS=5" { target simulator } }
  24
  25 #ifndef MAX_ITERATIONS
  26 #define MAX_ITERATIONS (sizeof(data001) / sizeof(testcase_riemann_zeta<double>))
  27 #endif
  28
  29 //  Compare against values generated by the GNU Scientific Library.
  30 //  The GSL can be found on the web: http://www.gnu.org/software/gsl/
  31 #include <limits>
  32 #include <cmath>
  33 #if defined(__TEST_DEBUG)
  34 #  include <iostream>
  35 #  define VERIFY(A) \
  36   if (!(A)) \
  37     { \
  38       std::cout << "line " << __LINE__ \
  39         << "  max_abs_frac = " << max_abs_frac \
  40         << std::endl; \
  41     }
  42 #else
  43 #  include <testsuite_hooks.h>
  44 #endif
  45 #include <specfun_testcase.h>
  46
  47 // Test data.
  48 // max(|f - f_GSL|): 8.8817841970012523e-16
  49 // max(|f - f_GSL| / |f_GSL|): 3.7349082148991403e-15
  50 const testcase_riemann_zeta<double>
  51 data001[55] =
  52 {
  53   { 0.0000000000000000, -10.000000000000000 },
  54   { -0.0033669820451019579, -9.8000000000000007 },
  55   { -0.0058129517767319039, -9.5999999999999996 },
  56   { -0.0072908732290557004, -9.4000000000000004 },
  57   { -0.0078420910654484442, -9.1999999999999993 },
  58   { -0.0075757575757575803, -9.0000000000000000 },
  59   { -0.0066476555677551898, -8.8000000000000007 },
  60   { -0.0052400095350859429, -8.5999999999999996 },
  61   { -0.0035434308017674959, -8.4000000000000004 },
  62   { -0.0017417330388368585, -8.1999999999999993 },
  63   { 0.0000000000000000, -8.0000000000000000 },
  64   { 0.0015440036789213961, -7.7999999999999998 },
  65   { 0.0027852131086497423, -7.5999999999999996 },
  66   { 0.0036537321227995880, -7.4000000000000004 },
  67   { 0.0041147930817053468, -7.2000000000000002 },
  68   { 0.0041666666666666683, -7.0000000000000000 },
  69   { 0.0038369975032738366, -6.7999999999999998 },
  70   { 0.0031780270571782981, -6.5999999999999996 },
  71   { 0.0022611282027338573, -6.4000000000000004 },
  72   { 0.0011710237049390511, -6.2000000000000002 },
  73   { 0.0000000000000000, -6.0000000000000000 },
  74   { -0.0011576366649881879, -5.7999999999999998 },
  75   { -0.0022106784318564345, -5.5999999999999996 },
  76   { -0.0030755853460586891, -5.4000000000000004 },
  77   { -0.0036804380477934787, -5.2000000000000002 },
  78   { -0.0039682539682539698, -5.0000000000000000 },
  79   { -0.0038996891301999797, -4.7999999999999998 },
  80   { -0.0034551830834302711, -4.5999999999999996 },
  81   { -0.0026366345018725115, -4.4000000000000004 },
  82   { -0.0014687209305056974, -4.2000000000000002 },
  83   { 0.0000000000000000, -4.0000000000000000 },
  84   { 0.0016960463875825202, -3.7999999999999998 },
  85   { 0.0035198355903356747, -3.5999999999999996 },
  86   { 0.0053441503206513421, -3.4000000000000004 },
  87   { 0.0070119720770910540, -3.2000000000000002 },
  88   { 0.0083333333333333350, -3.0000000000000000 },
  89   { 0.0090807294856852811, -2.7999999999999998 },
  90   { 0.0089824623788396681, -2.5999999999999996 },
  91   { 0.0077130239874243630, -2.4000000000000004 },
  92   { 0.0048792123593036068, -2.2000000000000002 },
  93   { 0.0000000000000000, -2.0000000000000000 },
  94   { -0.0075229347765968010, -1.8000000000000007 },
  95   { -0.018448986678963775, -1.5999999999999996 },
  96   { -0.033764987694047593, -1.4000000000000004 },
  97   { -0.054788441243880631, -1.1999999999999993 },
  98   { -0.083333333333333398, -1.0000000000000000 },
  99   { -0.12198707766977103, -0.80000000000000071 },
 100   { -0.17459571193801401, -0.59999999999999964 },
 101   { -0.24716546083171492, -0.40000000000000036 },
 102   { -0.34966628059831484, -0.19999999999999929 },
 103   { -0.49999999999999994, 0.0000000000000000 },
 104   { -0.73392092489633953, 0.19999999999999929 },
 105   { -1.1347977838669825, 0.40000000000000036 },
 106   { -1.9526614482239983, 0.59999999999999964 },
 107   { -4.4375384158955677, 0.80000000000000071 },
 108 };
 109 const double toler001 = 2.5000000000000020e-13;
 110 //  riemann_zeta
 111
 112 #ifndef MAX_ITERATIONS
 113 #define MAX_ITERATIONS (sizeof(data001) / sizeof(testcase_riemann_zeta<double>))
 114 #endif
 115
 116
 117 // Test data.
 118 // max(|f - f_GSL|): 2.6645352591003757e-15
 119 // max(|f - f_GSL| / |f_GSL|): 1.1657079722157521e-15
 120 const testcase_riemann_zeta<double>
 121 data002[145] =
 122 {
 123   { 5.5915824411777502, 1.2000000000000000 },
 124   { 3.1055472779775792, 1.3999999999999999 },
 125   { 2.2857656656801324, 1.6000000000000001 },
 126   { 1.8822296181028220, 1.8000000000000000 },
 127   { 1.6449340668482275, 2.0000000000000000 },
 128   { 1.4905432565068937, 2.2000000000000002 },
 129   { 1.3833428588407359, 2.3999999999999999 },
 130   { 1.3054778090727803, 2.6000000000000001 },
 131   { 1.2470314223172541, 2.7999999999999998 },
 132   { 1.2020569031595945, 3.0000000000000000 },
 133   { 1.1667733709844674, 3.2000000000000002 },
 134   { 1.1386637757280420, 3.3999999999999999 },
 135   { 1.1159890791233376, 3.6000000000000001 },
 136   { 1.0975105764590047, 3.7999999999999998 },
 137   { 1.0823232337111381, 4.0000000000000000 },
 138   { 1.0697514772338095, 4.2000000000000002 },
 139   { 1.0592817259798355, 4.4000000000000004 },
 140   { 1.0505173825665735, 4.5999999999999996 },
 141   { 1.0431480133351789, 4.7999999999999998 },
 142   { 1.0369277551433700, 5.0000000000000000 },
 143   { 1.0316598766779168, 5.2000000000000002 },
 144   { 1.0271855389203537, 5.4000000000000004 },
 145   { 1.0233754792270300, 5.5999999999999996 },
 146   { 1.0201237683883446, 5.7999999999999998 },
 147   { 1.0173430619844492, 6.0000000000000000 },
 148   { 1.0149609451852233, 6.2000000000000002 },
 149   { 1.0129170887121841, 6.4000000000000004 },
 150   { 1.0111610141542708, 6.5999999999999996 },
 151   { 1.0096503223447120, 6.7999999999999998 },
 152   { 1.0083492773819229, 7.0000000000000000 },
 153   { 1.0072276664807169, 7.2000000000000002 },
 154   { 1.0062598756930512, 7.4000000000000004 },
 155   { 1.0054241359879634, 7.5999999999999996 },
 156   { 1.0047019048164696, 7.7999999999999998 },
 157   { 1.0040773561979444, 8.0000000000000000 },
 158   { 1.0035369583062013, 8.1999999999999993 },
 159   { 1.0030691220374448, 8.4000000000000004 },
 160   { 1.0026639074861505, 8.5999999999999996 },
 161   { 1.0023127779098220, 8.8000000000000007 },
 162   { 1.0020083928260823, 9.0000000000000000 },
 163   { 1.0017444334995897, 9.1999999999999993 },
 164   { 1.0015154553480514, 9.4000000000000004 },
 165   { 1.0013167628052648, 9.5999999999999996 },
 166   { 1.0011443029840295, 9.8000000000000007 },
 167   { 1.0009945751278182, 10.000000000000000 },
 168   { 1.0008645533615086, 10.199999999999999 },
 169   { 1.0007516206744649, 10.400000000000000 },
 170   { 1.0006535124140847, 10.600000000000000 },
 171   { 1.0005682678503411, 10.800000000000001 },
 172   { 1.0004941886041194, 11.000000000000000 },
 173   { 1.0004298029239944, 11.199999999999999 },
 174   { 1.0003738349551168, 11.400000000000000 },
 175   { 1.0003251782761946, 11.600000000000000 },
 176   { 1.0002828730909989, 11.800000000000001 },
 177   { 1.0002460865533080, 12.000000000000000 },
 178   { 1.0002140957818750, 12.199999999999999 },
 179   { 1.0001862731874056, 12.400000000000000 },
 180   { 1.0001620737887460, 12.600000000000000 },
 181   { 1.0001410242422089, 12.800000000000001 },
 182   { 1.0001227133475783, 13.000000000000000 },
 183   { 1.0001067838280169, 13.199999999999999 },
 184   { 1.0000929252097515, 13.400000000000000 },
 185   { 1.0000808676518718, 13.600000000000000 },
 186   { 1.0000703765974504, 13.800000000000001 },
 187   { 1.0000612481350588, 14.000000000000000 },
 188   { 1.0000533049750668, 14.199999999999999 },
 189   { 1.0000463929582293, 14.400000000000000 },
 190   { 1.0000403780253397, 14.600000000000000 },
 191   { 1.0000351435864272, 14.800000000000001 },
 192   { 1.0000305882363070, 15.000000000000000 },
 193   { 1.0000266237704787, 15.199999999999999 },
 194   { 1.0000231734615617, 15.400000000000000 },
 195   { 1.0000201705617975, 15.600000000000000 },
 196   { 1.0000175570017611, 15.800000000000001 },
 197   { 1.0000152822594086, 16.000000000000000 },
 198   { 1.0000133023770337, 16.199999999999999 },
 199   { 1.0000115791066830, 16.399999999999999 },
 200   { 1.0000100791671644, 16.600000000000001 },
 201   { 1.0000087735980010, 16.800000000000001 },
 202   { 1.0000076371976379, 17.000000000000000 },
 203   { 1.0000066480348633, 17.199999999999999 },
 204   { 1.0000057870238734, 17.399999999999999 },
 205   { 1.0000050375546607, 17.600000000000001 },
 206   { 1.0000043851715013, 17.800000000000001 },
 207   { 1.0000038172932648, 18.000000000000000 },
 208   { 1.0000033229700953, 18.199999999999999 },
 209   { 1.0000028926717153, 18.399999999999999 },
 210   { 1.0000025181032419, 18.600000000000001 },
 211   { 1.0000021920449287, 18.800000000000001 },
 212   { 1.0000019082127167, 19.000000000000000 },
 213   { 1.0000016611368951, 19.199999999999999 },
 214   { 1.0000014460565094, 19.399999999999999 },
 215   { 1.0000012588274738, 19.600000000000001 },
 216   { 1.0000010958426055, 19.800000000000001 },
 217   { 1.0000009539620338, 20.000000000000000 },
 218   { 1.0000008304526344, 20.199999999999999 },
 219   { 1.0000007229353187, 20.399999999999999 },
 220   { 1.0000006293391575, 20.600000000000001 },
 221   { 1.0000005478614529, 20.800000000000001 },
 222   { 1.0000004769329869, 21.000000000000000 },
 223   { 1.0000004151877719, 21.199999999999999 },
 224   { 1.0000003614367254, 21.399999999999999 },
 225   { 1.0000003146447527, 21.600000000000001 },
 226   { 1.0000002739108020, 21.800000000000001 },
 227   { 1.0000002384505029, 22.000000000000000 },
 228   { 1.0000002075810521, 22.199999999999999 },
 229   { 1.0000001807080625, 22.399999999999999 },
 230   { 1.0000001573141093, 22.600000000000001 },
 231   { 1.0000001369487659, 22.800000000000001 },
 232   { 1.0000001192199262, 23.000000000000000 },
 233   { 1.0000001037862520, 23.199999999999999 },
 234   { 1.0000000903506006, 23.399999999999999 },
 235   { 1.0000000786543011, 23.600000000000001 },
 236   { 1.0000000684721728, 23.800000000000001 },
 237   { 1.0000000596081891, 24.000000000000000 },
 238   { 1.0000000518917020, 24.199999999999999 },
 239   { 1.0000000451741575, 24.399999999999999 },
 240   { 1.0000000393262332, 24.600000000000001 },
 241   { 1.0000000342353501, 24.800000000000001 },
 242   { 1.0000000298035037, 25.000000000000000 },
 243   { 1.0000000259453767, 25.199999999999999 },
 244   { 1.0000000225866978, 25.399999999999999 },
 245   { 1.0000000196628109, 25.600000000000001 },
 246   { 1.0000000171174297, 25.800000000000001 },
 247   { 1.0000000149015549, 26.000000000000000 },
 248   { 1.0000000129725304, 26.199999999999999 },
 249   { 1.0000000112932221, 26.399999999999999 },
 250   { 1.0000000098313035, 26.600000000000001 },
 251   { 1.0000000085586331, 26.800000000000001 },
 252   { 1.0000000074507118, 27.000000000000000 },
 253   { 1.0000000064862125, 27.199999999999999 },
 254   { 1.0000000056465688, 27.399999999999999 },
 255   { 1.0000000049156179, 27.600000000000001 },
 256   { 1.0000000042792894, 27.800000000000001 },
 257   { 1.0000000037253340, 28.000000000000000 },
 258   { 1.0000000032430887, 28.199999999999999 },
 259   { 1.0000000028232703, 28.399999999999999 },
 260   { 1.0000000024577977, 28.600000000000001 },
 261   { 1.0000000021396356, 28.800000000000001 },
 262   { 1.0000000018626598, 29.000000000000000 },
 263   { 1.0000000016215385, 29.199999999999999 },
 264   { 1.0000000014116306, 29.399999999999999 },
 265   { 1.0000000012288952, 29.600000000000001 },
 266   { 1.0000000010698147, 29.800000000000001 },
 267   { 1.0000000009313275, 30.000000000000000 },
 268 };
 269 const double toler002 = 2.5000000000000020e-13;
 270
 271 template<typename Tp, unsigned int Num>
 272   void
 273   test(const testcase_riemann_zeta<Tp> (&data)[Num], Tp toler)
 274   {
 275     bool test __attribute__((unused)) = true;
 276     const Tp eps = std::numeric_limits<Tp>::epsilon();
 277     Tp max_abs_diff = -Tp(1);
 278     Tp max_abs_frac = -Tp(1);
 279     unsigned int num_datum = MAX_ITERATIONS;
 280     for (unsigned int i = 0; i < num_datum; ++i)
 281       {
 282         const Tp f = std::riemann_zeta(data[i].s);
 283         const Tp f0 = data[i].f0;
 284         const Tp diff = f - f0;
 285         if (std::abs(diff) > max_abs_diff)
 286           max_abs_diff = std::abs(diff);
 287         if (std::abs(f0) > Tp(10) * eps
 288          && std::abs(f) > Tp(10) * eps)
 289           {
 290             const Tp frac = diff / f0;
 291             if (std::abs(frac) > max_abs_frac)
 292               max_abs_frac = std::abs(frac);
 293           }
 294       }
 295     VERIFY(max_abs_frac < toler);
 296   }
 297
 298 int
 299 main()
 300 {
 301   test(data001, toler001);
 302   test(data002, toler002);
 303   return 0;
 304 }