libstdc++-v3/testsuite/tr1/5_numerical_facilities/special_functions/03_beta/check_value.cc

   1 // { dg-do run { target c++11 } }
   2 // { dg-options "-D__STDCPP_WANT_MATH_SPEC_FUNCS__" }
   3 //
   4 // Copyright (C) 2016-2019 Free Software Foundation, Inc.
   5 //
   6 // This file is part of the GNU ISO C++ Library.  This library is free
   7 // software; you can redistribute it and/or modify it under the
   8 // terms of the GNU General Public License as published by the
   9 // Free Software Foundation; either version 3, or (at your option)
  10 // any later version.
  11 //
  12 // This library is distributed in the hope that it will be useful,
  13 // but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 // GNU General Public License for more details.
  16 //
  17 // You should have received a copy of the GNU General Public License along
  18 // with this library; see the file COPYING3.  If not see
  19 // <http://www.gnu.org/licenses/>.
  20
  21 //  beta
  22 //  Compare against values generated by the GNU Scientific Library.
  23 //  The GSL can be found on the web: http://www.gnu.org/software/gsl/
  24 #include <limits>
  25 #include <tr1/cmath>
  26 #if defined(__TEST_DEBUG)
  27 #  include <iostream>
  28 #  define VERIFY(A) \
  29   if (!(A)) \
  30     { \
  31       std::cout << "line " << __LINE__ \
  32         << "  max_abs_frac = " << max_abs_frac \
  33         << std::endl; \
  34     }
  35 #else
  36 #  include <testsuite_hooks.h>
  37 #endif
  38 #include <specfun_testcase.h>
  39
  40 // Test data for x=10.000000000000000.
  41 // max(|f - f_GSL|): 3.5542916945637908e-26 at index 4
  42 // max(|f - f_GSL| / |f_GSL|): 2.2331030499795109e-14
  43 // mean(f - f_GSL): -1.0876419730734700e-27
  44 // variance(f - f_GSL): 1.4090082527689930e-55
  45 // stddev(f - f_GSL): 3.7536758687571747e-28
  46 const testcase_beta<double>
  47 data001[10] =
  48 {
  49   { 1.0825088224469029e-06, 10.000000000000000, 10.000000000000000, 0.0 },
  50   { 4.9925087406346778e-09, 10.000000000000000, 20.000000000000000, 0.0 },
  51   { 1.5729567312509485e-10, 10.000000000000000, 30.000000000000000, 0.0 },
  52   { 1.2168673582561288e-11, 10.000000000000000, 40.000000000000000, 0.0 },
  53   { 1.5916380099863291e-12, 10.000000000000000, 50.000000000000000, 0.0 },
  54   { 2.9408957938463963e-13, 10.000000000000000, 60.000000000000000, 0.0 },
  55   { 6.9411637980691676e-14, 10.000000000000000, 70.000000000000000, 0.0 },
  56   { 1.9665612972502651e-14, 10.000000000000000, 80.000000000000000, 0.0 },
  57   { 6.4187824828154399e-15, 10.000000000000000, 90.000000000000000, 0.0 },
  58   { 2.3455339739604842e-15, 10.000000000000000, 100.00000000000000, 0.0 },
  59 };
  60 const double toler001 = 2.5000000000000015e-12;
  61
  62 // Test data for x=20.000000000000000.
  63 // max(|f - f_GSL|): 1.9721522630525295e-31 at index 2
  64 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
  65 // mean(f - f_GSL): 1.9831607786682398e-32
  66 // variance(f - f_GSL): 4.8554947092912269e-65
  67 // stddev(f - f_GSL): 6.9681379932455613e-33
  68 const testcase_beta<double>
  69 data002[10] =
  70 {
  71   { 4.9925087406346778e-09, 20.000000000000000, 10.000000000000000, 0.0 },
  72   { 7.2544445519248436e-13, 20.000000000000000, 20.000000000000000, 0.0 },
  73   { 1.7681885473062028e-15, 20.000000000000000, 30.000000000000000, 0.0 },
  74   { 1.7891885039182335e-17, 20.000000000000000, 40.000000000000000, 0.0 },
  75   { 4.3240677875623635e-19, 20.000000000000000, 50.000000000000000, 0.0 },
  76   { 1.8857342309689053e-20, 20.000000000000000, 60.000000000000000, 0.0 },
  77   { 1.2609804003539998e-21, 20.000000000000000, 70.000000000000000, 0.0 },
  78   { 1.1660809542079041e-22, 20.000000000000000, 80.000000000000000, 0.0 },
  79   { 1.3907944279729071e-23, 20.000000000000000, 90.000000000000000, 0.0 },
  80   { 2.0365059099917614e-24, 20.000000000000000, 100.00000000000000, 0.0 },
  81 };
  82 const double toler002 = 2.5000000000000020e-13;
  83
  84 // Test data for x=30.000000000000000.
  85 // max(|f - f_GSL|): 2.5849394142282115e-26 at index 0
  86 // max(|f - f_GSL| / |f_GSL|): 1.6433633315345226e-16
  87 // mean(f - f_GSL): 2.5849591357601703e-27
  88 // variance(f - f_GSL): 8.2493996710493413e-55
  89 // stddev(f - f_GSL): 9.0826205860694966e-28
  90 const testcase_beta<double>
  91 data003[10] =
  92 {
  93   { 1.5729567312509485e-10, 30.000000000000000, 10.000000000000000, 0.0 },
  94   { 1.7681885473062028e-15, 30.000000000000000, 20.000000000000000, 0.0 },
  95   { 5.6370779640482451e-19, 30.000000000000000, 30.000000000000000, 0.0 },
  96   { 1.0539424603796547e-21, 30.000000000000000, 40.000000000000000, 0.0 },
  97   { 6.0118197777273843e-24, 30.000000000000000, 50.000000000000000, 0.0 },
  98   { 7.4279528553260153e-26, 30.000000000000000, 60.000000000000000, 0.0 },
  99   { 1.6212207780604767e-27, 30.000000000000000, 70.000000000000000, 0.0 },
 100   { 5.4783729715317616e-29, 30.000000000000000, 80.000000000000000, 0.0 },
 101   { 2.6183005659681346e-30, 30.000000000000000, 90.000000000000000, 0.0 },
 102   { 1.6587948222122229e-31, 30.000000000000000, 100.00000000000000, 0.0 },
 103 };
 104 const double toler003 = 2.5000000000000020e-13;
 105
 106 // Test data for x=40.000000000000000.
 107 // max(|f - f_GSL|): 3.9012149246802907e-41 at index 4
 108 // max(|f - f_GSL| / |f_GSL|): 0.0000000000000000
 109 // mean(f - f_GSL): -3.9072897597887440e-42
 110 // variance(f - f_GSL): 1.8848041017931125e-84
 111 // stddev(f - f_GSL): 1.3728816780018271e-42
 112 const testcase_beta<double>
 113 data004[10] =
 114 {
 115   { 1.2168673582561288e-11, 40.000000000000000, 10.000000000000000, 0.0 },
 116   { 1.7891885039182335e-17, 40.000000000000000, 20.000000000000000, 0.0 },
 117   { 1.0539424603796547e-21, 40.000000000000000, 30.000000000000000, 0.0 },
 118   { 4.6508509140090659e-25, 40.000000000000000, 40.000000000000000, 0.0 },
 119   { 7.5161712118557728e-28, 40.000000000000000, 50.000000000000000, 0.0 },
 120   { 3.0311331979886071e-30, 40.000000000000000, 60.000000000000000, 0.0 },
 121   { 2.4175035070466313e-32, 40.000000000000000, 70.000000000000000, 0.0 },
 122   { 3.2734839142758369e-34, 40.000000000000000, 80.000000000000000, 0.0 },
 123   { 6.7690629601315579e-36, 40.000000000000000, 90.000000000000000, 0.0 },
 124   { 1.9797337118810115e-37, 40.000000000000000, 100.00000000000000, 0.0 },
 125 };
 126 const double toler004 = 2.5000000000000020e-13;
 127
 128 // Test data for x=50.000000000000000.
 129 // max(|f - f_GSL|): 3.5542916945637908e-26 at index 0
 130 // max(|f - f_GSL| / |f_GSL|): 2.2331030499795109e-14
 131 // mean(f - f_GSL): -3.5542916415910235e-27
 132 // variance(f - f_GSL): 1.5596282806770138e-54
 133 // stddev(f - f_GSL): 1.2488507839918322e-27
 134 const testcase_beta<double>
 135 data005[10] =
 136 {
 137   { 1.5916380099863291e-12, 50.000000000000000, 10.000000000000000, 0.0 },
 138   { 4.3240677875623635e-19, 50.000000000000000, 20.000000000000000, 0.0 },
 139   { 6.0118197777273843e-24, 50.000000000000000, 30.000000000000000, 0.0 },
 140   { 7.5161712118557728e-28, 50.000000000000000, 40.000000000000000, 0.0 },
 141   { 3.9646612085674138e-31, 50.000000000000000, 50.000000000000000, 0.0 },
 142   { 5.8425643906418403e-34, 50.000000000000000, 60.000000000000000, 0.0 },
 143   { 1.8672362180783552e-36, 50.000000000000000, 70.000000000000000, 0.0 },
 144   { 1.0939382296458963e-38, 50.000000000000000, 80.000000000000000, 0.0 },
 145   { 1.0442781609879874e-40, 50.000000000000000, 90.000000000000000, 0.0 },
 146   { 1.4904121110954370e-42, 50.000000000000000, 100.00000000000000, 0.0 },
 147 };
 148 const double toler005 = 2.5000000000000015e-12;
 149
 150 // Test data for x=60.000000000000000.
 151 // max(|f - f_GSL|): 9.0876776281460560e-28 at index 0
 152 // max(|f - f_GSL| / |f_GSL|): 3.0901052826017635e-15
 153 // mean(f - f_GSL): -9.0876709777057221e-29
 154 // variance(f - f_GSL): 1.0195773308522824e-57
 155 // stddev(f - f_GSL): 3.1930821017510377e-29
 156 const testcase_beta<double>
 157 data006[10] =
 158 {
 159   { 2.9408957938463963e-13, 60.000000000000000, 10.000000000000000, 0.0 },
 160   { 1.8857342309689053e-20, 60.000000000000000, 20.000000000000000, 0.0 },
 161   { 7.4279528553260153e-26, 60.000000000000000, 30.000000000000000, 0.0 },
 162   { 3.0311331979886071e-30, 60.000000000000000, 40.000000000000000, 0.0 },
 163   { 5.8425643906418403e-34, 60.000000000000000, 50.000000000000000, 0.0 },
 164   { 3.4501231469782229e-37, 60.000000000000000, 60.000000000000000, 0.0 },
 165   { 4.7706855386086599e-40, 60.000000000000000, 70.000000000000000, 0.0 },
 166   { 1.2902663809721126e-42, 60.000000000000000, 80.000000000000000, 0.0 },
 167   { 6.0105571058570508e-45, 60.000000000000000, 90.000000000000000, 0.0 },
 168   { 4.3922898898347209e-47, 60.000000000000000, 100.00000000000000, 0.0 },
 169 };
 170 const double toler006 = 2.5000000000000020e-13;
 171
 172 // Test data for x=70.000000000000000.
 173 // max(|f - f_GSL|): 1.7670484276950664e-28 at index 0
 174 // max(|f - f_GSL| / |f_GSL|): 2.5457523825998871e-15
 175 // mean(f - f_GSL): -1.7670492778129898e-29
 176 // variance(f - f_GSL): 3.8548927780486536e-59
 177 // stddev(f - f_GSL): 6.2087782840496516e-30
 178 const testcase_beta<double>
 179 data007[10] =
 180 {
 181   { 6.9411637980691676e-14, 70.000000000000000, 10.000000000000000, 0.0 },
 182   { 1.2609804003539998e-21, 70.000000000000000, 20.000000000000000, 0.0 },
 183   { 1.6212207780604767e-27, 70.000000000000000, 30.000000000000000, 0.0 },
 184   { 2.4175035070466313e-32, 70.000000000000000, 40.000000000000000, 0.0 },
 185   { 1.8672362180783552e-36, 70.000000000000000, 50.000000000000000, 0.0 },
 186   { 4.7706855386086599e-40, 70.000000000000000, 60.000000000000000, 0.0 },
 187   { 3.0453137143482908e-43, 70.000000000000000, 70.000000000000000, 0.0 },
 188   { 4.0192274082013779e-46, 70.000000000000000, 80.000000000000000, 0.0 },
 189   { 9.5865870063501807e-49, 70.000000000000000, 90.000000000000000, 0.0 },
 190   { 3.7409127305819802e-51, 70.000000000000000, 100.00000000000000, 0.0 },
 191 };
 192 const double toler007 = 2.5000000000000020e-13;
 193
 194 // Test data for x=80.000000000000000.
 195 // max(|f - f_GSL|): 5.3642541555028803e-29 at index 0
 196 // max(|f - f_GSL| / |f_GSL|): 2.7277330043072765e-15
 197 // mean(f - f_GSL): -5.3642549571904701e-30
 198 // variance(f - f_GSL): 3.5524976846595722e-60
 199 // stddev(f - f_GSL): 1.8848070682856566e-30
 200 const testcase_beta<double>
 201 data008[10] =
 202 {
 203   { 1.9665612972502651e-14, 80.000000000000000, 10.000000000000000, 0.0 },
 204   { 1.1660809542079041e-22, 80.000000000000000, 20.000000000000000, 0.0 },
 205   { 5.4783729715317616e-29, 80.000000000000000, 30.000000000000000, 0.0 },
 206   { 3.2734839142758369e-34, 80.000000000000000, 40.000000000000000, 0.0 },
 207   { 1.0939382296458963e-38, 80.000000000000000, 50.000000000000000, 0.0 },
 208   { 1.2902663809721126e-42, 80.000000000000000, 60.000000000000000, 0.0 },
 209   { 4.0192274082013779e-46, 80.000000000000000, 70.000000000000000, 0.0 },
 210   { 2.7160590828669411e-49, 80.000000000000000, 80.000000000000000, 0.0 },
 211   { 3.4593773902125368e-52, 80.000000000000000, 90.000000000000000, 0.0 },
 212   { 7.4807039968503468e-55, 80.000000000000000, 100.00000000000000, 0.0 },
 213 };
 214 const double toler008 = 2.5000000000000020e-13;
 215
 216 // Test data for x=90.000000000000000.
 217 // max(|f - f_GSL|): 2.4454688061851366e-29 at index 0
 218 // max(|f - f_GSL| / |f_GSL|): 3.8098639621021905e-15
 219 // mean(f - f_GSL): -2.4454688799474037e-30
 220 // variance(f - f_GSL): 7.3831086948039631e-61
 221 // stddev(f - f_GSL): 8.5925017863274033e-31
 222 const testcase_beta<double>
 223 data009[10] =
 224 {
 225   { 6.4187824828154399e-15, 90.000000000000000, 10.000000000000000, 0.0 },
 226   { 1.3907944279729071e-23, 90.000000000000000, 20.000000000000000, 0.0 },
 227   { 2.6183005659681346e-30, 90.000000000000000, 30.000000000000000, 0.0 },
 228   { 6.7690629601315579e-36, 90.000000000000000, 40.000000000000000, 0.0 },
 229   { 1.0442781609879874e-40, 90.000000000000000, 50.000000000000000, 0.0 },
 230   { 6.0105571058570508e-45, 90.000000000000000, 60.000000000000000, 0.0 },
 231   { 9.5865870063501807e-49, 90.000000000000000, 70.000000000000000, 0.0 },
 232   { 3.4593773902125368e-52, 90.000000000000000, 80.000000000000000, 0.0 },
 233   { 2.4416737907558036e-55, 90.000000000000000, 90.000000000000000, 0.0 },
 234   { 3.0238531916564250e-58, 90.000000000000000, 100.00000000000000, 0.0 },
 235 };
 236 const double toler009 = 2.5000000000000020e-13;
 237
 238 // Test data for x=100.00000000000000.
 239 // max(|f - f_GSL|): 1.9327092177914789e-29 at index 0
 240 // max(|f - f_GSL| / |f_GSL|): 8.2399540541638715e-15
 241 // mean(f - f_GSL): -1.9327092238526215e-30
 242 // variance(f - f_GSL): 4.6115616592160521e-61
 243 // stddev(f - f_GSL): 6.7908480024339023e-31
 244 const testcase_beta<double>
 245 data010[10] =
 246 {
 247   { 2.3455339739604842e-15, 100.00000000000000, 10.000000000000000, 0.0 },
 248   { 2.0365059099917614e-24, 100.00000000000000, 20.000000000000000, 0.0 },
 249   { 1.6587948222122229e-31, 100.00000000000000, 30.000000000000000, 0.0 },
 250   { 1.9797337118810115e-37, 100.00000000000000, 40.000000000000000, 0.0 },
 251   { 1.4904121110954370e-42, 100.00000000000000, 50.000000000000000, 0.0 },
 252   { 4.3922898898347209e-47, 100.00000000000000, 60.000000000000000, 0.0 },
 253   { 3.7409127305819802e-51, 100.00000000000000, 70.000000000000000, 0.0 },
 254   { 7.4807039968503468e-55, 100.00000000000000, 80.000000000000000, 0.0 },
 255   { 3.0238531916564250e-58, 100.00000000000000, 90.000000000000000, 0.0 },
 256   { 2.2087606931991849e-61, 100.00000000000000, 100.00000000000000, 0.0 },
 257 };
 258 const double toler010 = 5.0000000000000039e-13;
 259
 260 template<typename Ret, unsigned int Num>
 261   void
 262   test(const testcase_beta<Ret> (&data)[Num], Ret toler)
 263   {
 264     bool test __attribute__((unused)) = true;
 265     const Ret eps = std::numeric_limits<Ret>::epsilon();
 266     Ret max_abs_diff = -Ret(1);
 267     Ret max_abs_frac = -Ret(1);
 268     unsigned int num_datum = Num;
 269     for (unsigned int i = 0; i < num_datum; ++i)
 270       {
 271         const Ret f = std::tr1::beta(data[i].x, data[i].y);
 272         const Ret f0 = data[i].f0;
 273         const Ret diff = f - f0;
 274         if (std::abs(diff) > max_abs_diff)
 275           max_abs_diff = std::abs(diff);
 276         if (std::abs(f0) > Ret(10) * eps
 277          && std::abs(f) > Ret(10) * eps)
 278           {
 279             const Ret frac = diff / f0;
 280             if (std::abs(frac) > max_abs_frac)
 281               max_abs_frac = std::abs(frac);
 282           }
 283       }
 284     VERIFY(max_abs_frac < toler);
 285   }
 286
 287 int
 288 main()
 289 {
 290   test(data001, toler001);
 291   test(data002, toler002);
 292   test(data003, toler003);
 293   test(data004, toler004);
 294   test(data005, toler005);
 295   test(data006, toler006);
 296   test(data007, toler007);
 297   test(data008, toler008);
 298   test(data009, toler009);
 299   test(data010, toler010);
 300   return 0;
 301 }