ceph/src/boost/libs/random/test/sobol_validate.cpp

   1 // Copyright Justinas Vygintas Daugmaudis, 2010-2018.
   2 // Use, modification and distribution is subject to the
   3 // Boost Software License, Version 1.0. (See accompanying
   4 // file LICENSE-1.0 or http://www.boost.org/LICENSE-1.0)
   5
   6 #include <boost/random/sobol.hpp>
   7
   8 #include <boost/utility.hpp>
   9
  10 #define BOOST_TEST_MAIN
  11 #include <boost/test/unit_test.hpp>
  12
  13 #include "test_qrng_functions.hpp"
  14
  15
  16 //
  17 // DESCRIPTION:
  18 // ~~~~~~~~~~~~
  19 //
  20 // This file tests the sobol quasi-random number generator.
  21 // These tests compare our results with values produced by the
  22 // original sobol.cc program http://web.maths.unsw.edu.au/~fkuo/sobol/,
  23 // using the new-joe-kuo-6.21201 direction polynomials and direction vectors.
  24 //
  25 // Generally, the command line used to generate the datasets was
  26 // sobol SKIP+N+1 DIMENSION new-joe-kuo-6.21201 | tail -n N
  27 // Note that we asked to show +1 sample from sobol.cc program, because
  28 // it outputs trivial zeros as the first sample.
  29
  30 // Spatial dimension: 2
  31 // N: 99
  32 // Vectors skipped: 0
  33 static const double sobol_02_99[99][2] =
  34 {
  35   { 0.5000000002, 0.5000000002 },
  36   { 0.7500000003, 0.2500000001 },
  37   { 0.2500000001, 0.7500000003 },
  38   { 0.3750000002, 0.3750000002 },
  39   { 0.8750000004, 0.8750000004 },
  40   { 0.6250000003, 0.1250000001 },
  41   { 0.1250000001, 0.6250000003 },
  42   { 0.1875000001, 0.3125000001 },
  43   { 0.6875000003, 0.8125000004 },
  44   { 0.9375000004, 0.0625000000 },
  45   { 0.4375000002, 0.5625000003 },
  46   { 0.3125000001, 0.1875000001 },
  47   { 0.8125000004, 0.6875000003 },
  48   { 0.5625000003, 0.4375000002 },
  49   { 0.0625000000, 0.9375000004 },
  50   { 0.0937500000, 0.4687500002 },
  51   { 0.5937500003, 0.9687500005 },
  52   { 0.8437500004, 0.2187500001 },
  53   { 0.3437500002, 0.7187500003 },
  54   { 0.4687500002, 0.0937500000 },
  55   { 0.9687500005, 0.5937500003 },
  56   { 0.7187500003, 0.3437500002 },
  57   { 0.2187500001, 0.8437500004 },
  58   { 0.1562500001, 0.1562500001 },
  59   { 0.6562500003, 0.6562500003 },
  60   { 0.9062500004, 0.4062500002 },
  61   { 0.4062500002, 0.9062500004 },
  62   { 0.2812500001, 0.2812500001 },
  63   { 0.7812500004, 0.7812500004 },
  64   { 0.5312500002, 0.0312500000 },
  65   { 0.0312500000, 0.5312500002 },
  66   { 0.0468750000, 0.2656250001 },
  67   { 0.5468750003, 0.7656250004 },
  68   { 0.7968750004, 0.0156250000 },
  69   { 0.2968750001, 0.5156250002 },
  70   { 0.4218750002, 0.1406250001 },
  71   { 0.9218750004, 0.6406250003 },
  72   { 0.6718750003, 0.3906250002 },
  73   { 0.1718750001, 0.8906250004 },
  74   { 0.2343750001, 0.0781250000 },
  75   { 0.7343750003, 0.5781250003 },
  76   { 0.9843750005, 0.3281250002 },
  77   { 0.4843750002, 0.8281250004 },
  78   { 0.3593750002, 0.4531250002 },
  79   { 0.8593750004, 0.9531250004 },
  80   { 0.6093750003, 0.2031250001 },
  81   { 0.1093750001, 0.7031250003 },
  82   { 0.0781250000, 0.2343750001 },
  83   { 0.5781250003, 0.7343750003 },
  84   { 0.8281250004, 0.4843750002 },
  85   { 0.3281250002, 0.9843750005 },
  86   { 0.4531250002, 0.3593750002 },
  87   { 0.9531250004, 0.8593750004 },
  88   { 0.7031250003, 0.1093750001 },
  89   { 0.2031250001, 0.6093750003 },
  90   { 0.1406250001, 0.4218750002 },
  91   { 0.6406250003, 0.9218750004 },
  92   { 0.8906250004, 0.1718750001 },
  93   { 0.3906250002, 0.6718750003 },
  94   { 0.2656250001, 0.0468750000 },
  95   { 0.7656250004, 0.5468750003 },
  96   { 0.5156250002, 0.2968750001 },
  97   { 0.0156250000, 0.7968750004 },
  98   { 0.0234375000, 0.3984375002 },
  99   { 0.5234375002, 0.8984375004 },
 100   { 0.7734375004, 0.1484375001 },
 101   { 0.2734375001, 0.6484375003 },
 102   { 0.3984375002, 0.0234375000 },
 103   { 0.8984375004, 0.5234375002 },
 104   { 0.6484375003, 0.2734375001 },
 105   { 0.1484375001, 0.7734375004 },
 106   { 0.2109375001, 0.2109375001 },
 107   { 0.7109375003, 0.7109375003 },
 108   { 0.9609375004, 0.4609375002 },
 109   { 0.4609375002, 0.9609375004 },
 110   { 0.3359375002, 0.3359375002 },
 111   { 0.8359375004, 0.8359375004 },
 112   { 0.5859375003, 0.0859375000 },
 113   { 0.0859375000, 0.5859375003 },
 114   { 0.1171875001, 0.1171875001 },
 115   { 0.6171875003, 0.6171875003 },
 116   { 0.8671875004, 0.3671875002 },
 117   { 0.3671875002, 0.8671875004 },
 118   { 0.4921875002, 0.4921875002 },
 119   { 0.9921875005, 0.9921875005 },
 120   { 0.7421875003, 0.2421875001 },
 121   { 0.2421875001, 0.7421875003 },
 122   { 0.1796875001, 0.3046875001 },
 123   { 0.6796875003, 0.8046875004 },
 124   { 0.9296875004, 0.0546875000 },
 125   { 0.4296875002, 0.5546875003 },
 126   { 0.3046875001, 0.1796875001 },
 127   { 0.8046875004, 0.6796875003 },
 128   { 0.5546875003, 0.4296875002 },
 129   { 0.0546875000, 0.9296875004 },
 130   { 0.0390625000, 0.1328125001 },
 131   { 0.5390625003, 0.6328125003 },
 132   { 0.7890625004, 0.3828125002 },
 133   { 0.2890625001, 0.8828125004 }
 134 };
 135
 136 // Spatial dimension: 7
 137 // N: 100
 138 // Vectors skipped: 127
 139 static const double sobol_07_100[100][7] =
 140 {
 141   { 0.0117187500, 0.3320312500, 0.2929687500, 0.1914062500, 0.9023437500, 0.6757812500, 0.8632812500 },
 142   { 0.5117187500, 0.8320312500, 0.7929687500, 0.6914062500, 0.4023437500, 0.1757812500, 0.3632812500 },
 143   { 0.7617187500, 0.0820312500, 0.0429687500, 0.4414062500, 0.1523437500, 0.4257812500, 0.6132812500 },
 144   { 0.2617187500, 0.5820312500, 0.5429687500, 0.9414062500, 0.6523437500, 0.9257812500, 0.1132812500 },
 145   { 0.3867187500, 0.2070312500, 0.9179687500, 0.8164062500, 0.5273437500, 0.5507812500, 0.7382812500 },
 146   { 0.8867187500, 0.7070312500, 0.4179687500, 0.3164062500, 0.0273437500, 0.0507812500, 0.2382812500 },
 147   { 0.6367187500, 0.4570312500, 0.6679687500, 0.5664062500, 0.2773437500, 0.3007812500, 0.9882812500 },
 148   { 0.1367187500, 0.9570312500, 0.1679687500, 0.0664062500, 0.7773437500, 0.8007812500, 0.4882812500 },
 149   { 0.1992187500, 0.0195312500, 0.7304687500, 0.2539062500, 0.4648437500, 0.9882812500, 0.6757812500 },
 150   { 0.6992187500, 0.5195312500, 0.2304687500, 0.7539062500, 0.9648437500, 0.4882812500, 0.1757812500 },
 151   { 0.9492187500, 0.2695312500, 0.9804687500, 0.0039062500, 0.7148437500, 0.2382812500, 0.9257812500 },
 152   { 0.4492187500, 0.7695312500, 0.4804687500, 0.5039062500, 0.2148437500, 0.7382812500, 0.4257812500 },
 153   { 0.3242187500, 0.3945312500, 0.1054687500, 0.6289062500, 0.0898437500, 0.8632812500, 0.8007812500 },
 154   { 0.8242187500, 0.8945312500, 0.6054687500, 0.1289062500, 0.5898437500, 0.3632812500, 0.3007812500 },
 155   { 0.5742187500, 0.1445312500, 0.3554687500, 0.8789062500, 0.8398437500, 0.1132812500, 0.5507812500 },
 156   { 0.0742187500, 0.6445312500, 0.8554687500, 0.3789062500, 0.3398437500, 0.6132812500, 0.0507812500 },
 157   { 0.1054687500, 0.1757812500, 0.1992187500, 0.5976562500, 0.6835937500, 0.3320312500, 0.3320312500 },
 158   { 0.6054687500, 0.6757812500, 0.6992187500, 0.0976562500, 0.1835937500, 0.8320312500, 0.8320312500 },
 159   { 0.8554687500, 0.4257812500, 0.4492187500, 0.8476562500, 0.4335937500, 0.5820312500, 0.0820312500 },
 160   { 0.3554687500, 0.9257812500, 0.9492187500, 0.3476562500, 0.9335937500, 0.0820312500, 0.5820312500 },
 161   { 0.4804687500, 0.3007812500, 0.5742187500, 0.4726562500, 0.8085937500, 0.4570312500, 0.2070312500 },
 162   { 0.9804687500, 0.8007812500, 0.0742187500, 0.9726562500, 0.3085937500, 0.9570312500, 0.7070312500 },
 163   { 0.7304687500, 0.0507812500, 0.8242187500, 0.2226562500, 0.0585937500, 0.7070312500, 0.4570312500 },
 164   { 0.2304687500, 0.5507812500, 0.3242187500, 0.7226562500, 0.5585937500, 0.2070312500, 0.9570312500 },
 165   { 0.1679687500, 0.4882812500, 0.7617187500, 0.9101562500, 0.2460937500, 0.0195312500, 0.1445312500 },
 166   { 0.6679687500, 0.9882812500, 0.2617187500, 0.4101562500, 0.7460937500, 0.5195312500, 0.6445312500 },
 167   { 0.9179687500, 0.2382812500, 0.5117187500, 0.6601562500, 0.9960937500, 0.7695312500, 0.3945312500 },
 168   { 0.4179687500, 0.7382812500, 0.0117187500, 0.1601562500, 0.4960937500, 0.2695312500, 0.8945312500 },
 169   { 0.2929687500, 0.1132812500, 0.3867187500, 0.0351562500, 0.3710937500, 0.1445312500, 0.2695312500 },
 170   { 0.7929687500, 0.6132812500, 0.8867187500, 0.5351562500, 0.8710937500, 0.6445312500, 0.7695312500 },
 171   { 0.5429687500, 0.3632812500, 0.1367187500, 0.2851562500, 0.6210937500, 0.8945312500, 0.0195312500 },
 172   { 0.0429687500, 0.8632812500, 0.6367187500, 0.7851562500, 0.1210937500, 0.3945312500, 0.5195312500 },
 173   { 0.0585937500, 0.0664062500, 0.9960937500, 0.7382812500, 0.7617187500, 0.2539062500, 0.0664062500 },
 174   { 0.5585937500, 0.5664062500, 0.4960937500, 0.2382812500, 0.2617187500, 0.7539062500, 0.5664062500 },
 175   { 0.8085937500, 0.3164062500, 0.7460937500, 0.9882812500, 0.0117187500, 0.5039062500, 0.3164062500 },
 176   { 0.3085937500, 0.8164062500, 0.2460937500, 0.4882812500, 0.5117187500, 0.0039062500, 0.8164062500 },
 177   { 0.4335937500, 0.4414062500, 0.3710937500, 0.3632812500, 0.6367187500, 0.3789062500, 0.4414062500 },
 178   { 0.9335937500, 0.9414062500, 0.8710937500, 0.8632812500, 0.1367187500, 0.8789062500, 0.9414062500 },
 179   { 0.6835937500, 0.1914062500, 0.1210937500, 0.1132812500, 0.3867187500, 0.6289062500, 0.1914062500 },
 180   { 0.1835937500, 0.6914062500, 0.6210937500, 0.6132812500, 0.8867187500, 0.1289062500, 0.6914062500 },
 181   { 0.2460937500, 0.2539062500, 0.0585937500, 0.8007812500, 0.3242187500, 0.0664062500, 0.3789062500 },
 182   { 0.7460937500, 0.7539062500, 0.5585937500, 0.3007812500, 0.8242187500, 0.5664062500, 0.8789062500 },
 183   { 0.9960937500, 0.0039062500, 0.3085937500, 0.5507812500, 0.5742187500, 0.8164062500, 0.1289062500 },
 184   { 0.4960937500, 0.5039062500, 0.8085937500, 0.0507812500, 0.0742187500, 0.3164062500, 0.6289062500 },
 185   { 0.3710937500, 0.1289062500, 0.6835937500, 0.1757812500, 0.1992187500, 0.1914062500, 0.0039062500 },
 186   { 0.8710937500, 0.6289062500, 0.1835937500, 0.6757812500, 0.6992187500, 0.6914062500, 0.5039062500 },
 187   { 0.6210937500, 0.3789062500, 0.9335937500, 0.4257812500, 0.9492187500, 0.9414062500, 0.2539062500 },
 188   { 0.1210937500, 0.8789062500, 0.4335937500, 0.9257812500, 0.4492187500, 0.4414062500, 0.7539062500 },
 189   { 0.0898437500, 0.4101562500, 0.5273437500, 0.0820312500, 0.5429687500, 0.7226562500, 0.5976562500 },
 190   { 0.5898437500, 0.9101562500, 0.0273437500, 0.5820312500, 0.0429687500, 0.2226562500, 0.0976562500 },
 191   { 0.8398437500, 0.1601562500, 0.7773437500, 0.3320312500, 0.2929687500, 0.4726562500, 0.8476562500 },
 192   { 0.3398437500, 0.6601562500, 0.2773437500, 0.8320312500, 0.7929687500, 0.9726562500, 0.3476562500 },
 193   { 0.4648437500, 0.0351562500, 0.1523437500, 0.9570312500, 0.9179687500, 0.5976562500, 0.9726562500 },
 194   { 0.9648437500, 0.5351562500, 0.6523437500, 0.4570312500, 0.4179687500, 0.0976562500, 0.4726562500 },
 195   { 0.7148437500, 0.2851562500, 0.4023437500, 0.7070312500, 0.1679687500, 0.3476562500, 0.7226562500 },
 196   { 0.2148437500, 0.7851562500, 0.9023437500, 0.2070312500, 0.6679687500, 0.8476562500, 0.2226562500 },
 197   { 0.1523437500, 0.2226562500, 0.4648437500, 0.3945312500, 0.1054687500, 0.9101562500, 0.9101562500 },
 198   { 0.6523437500, 0.7226562500, 0.9648437500, 0.8945312500, 0.6054687500, 0.4101562500, 0.4101562500 },
 199   { 0.9023437500, 0.4726562500, 0.2148437500, 0.1445312500, 0.8554687500, 0.1601562500, 0.6601562500 },
 200   { 0.4023437500, 0.9726562500, 0.7148437500, 0.6445312500, 0.3554687500, 0.6601562500, 0.1601562500 },
 201   { 0.2773437500, 0.3476562500, 0.8398437500, 0.5195312500, 0.4804687500, 0.7851562500, 0.5351562500 },
 202   { 0.7773437500, 0.8476562500, 0.3398437500, 0.0195312500, 0.9804687500, 0.2851562500, 0.0351562500 },
 203   { 0.5273437500, 0.0976562500, 0.5898437500, 0.7695312500, 0.7304687500, 0.0351562500, 0.7851562500 },
 204   { 0.0273437500, 0.5976562500, 0.0898437500, 0.2695312500, 0.2304687500, 0.5351562500, 0.2851562500 },
 205   { 0.0195312500, 0.1992187500, 0.5976562500, 0.9023437500, 0.2539062500, 0.8710937500, 0.4648437500 },
 206   { 0.5195312500, 0.6992187500, 0.0976562500, 0.4023437500, 0.7539062500, 0.3710937500, 0.9648437500 },
 207   { 0.7695312500, 0.4492187500, 0.8476562500, 0.6523437500, 0.5039062500, 0.1210937500, 0.2148437500 },
 208   { 0.2695312500, 0.9492187500, 0.3476562500, 0.1523437500, 0.0039062500, 0.6210937500, 0.7148437500 },
 209   { 0.3945312500, 0.3242187500, 0.2226562500, 0.0273437500, 0.1289062500, 0.9960937500, 0.0898437500 },
 210   { 0.8945312500, 0.8242187500, 0.7226562500, 0.5273437500, 0.6289062500, 0.4960937500, 0.5898437500 },
 211   { 0.6445312500, 0.0742187500, 0.4726562500, 0.2773437500, 0.8789062500, 0.2460937500, 0.3398437500 },
 212   { 0.1445312500, 0.5742187500, 0.9726562500, 0.7773437500, 0.3789062500, 0.7460937500, 0.8398437500 },
 213   { 0.2070312500, 0.3867187500, 0.4101562500, 0.5898437500, 0.8164062500, 0.5585937500, 0.0273437500 },
 214   { 0.7070312500, 0.8867187500, 0.9101562500, 0.0898437500, 0.3164062500, 0.0585937500, 0.5273437500 },
 215   { 0.9570312500, 0.1367187500, 0.1601562500, 0.8398437500, 0.0664062500, 0.3085937500, 0.2773437500 },
 216   { 0.4570312500, 0.6367187500, 0.6601562500, 0.3398437500, 0.5664062500, 0.8085937500, 0.7773437500 },
 217   { 0.3320312500, 0.0117187500, 0.7851562500, 0.4648437500, 0.6914062500, 0.6835937500, 0.4023437500 },
 218   { 0.8320312500, 0.5117187500, 0.2851562500, 0.9648437500, 0.1914062500, 0.1835937500, 0.9023437500 },
 219   { 0.5820312500, 0.2617187500, 0.5351562500, 0.2148437500, 0.4414062500, 0.4335937500, 0.1523437500 },
 220   { 0.0820312500, 0.7617187500, 0.0351562500, 0.7148437500, 0.9414062500, 0.9335937500, 0.6523437500 },
 221   { 0.1132812500, 0.2929687500, 0.8789062500, 0.3085937500, 0.0351562500, 0.1523437500, 0.9960937500 },
 222   { 0.6132812500, 0.7929687500, 0.3789062500, 0.8085937500, 0.5351562500, 0.6523437500, 0.4960937500 },
 223   { 0.8632812500, 0.0429687500, 0.6289062500, 0.0585937500, 0.7851562500, 0.9023437500, 0.7460937500 },
 224   { 0.3632812500, 0.5429687500, 0.1289062500, 0.5585937500, 0.2851562500, 0.4023437500, 0.2460937500 },
 225   { 0.4882812500, 0.1679687500, 0.2539062500, 0.6835937500, 0.4101562500, 0.0273437500, 0.6210937500 },
 226   { 0.9882812500, 0.6679687500, 0.7539062500, 0.1835937500, 0.9101562500, 0.5273437500, 0.1210937500 },
 227   { 0.7382812500, 0.4179687500, 0.0039062500, 0.9335937500, 0.6601562500, 0.7773437500, 0.8710937500 },
 228   { 0.2382812500, 0.9179687500, 0.5039062500, 0.4335937500, 0.1601562500, 0.2773437500, 0.3710937500 },
 229   { 0.1757812500, 0.1054687500, 0.0664062500, 0.2460937500, 0.5976562500, 0.4648437500, 0.5585937500 },
 230   { 0.6757812500, 0.6054687500, 0.5664062500, 0.7460937500, 0.0976562500, 0.9648437500, 0.0585937500 },
 231   { 0.9257812500, 0.3554687500, 0.3164062500, 0.4960937500, 0.3476562500, 0.7148437500, 0.8085937500 },
 232   { 0.4257812500, 0.8554687500, 0.8164062500, 0.9960937500, 0.8476562500, 0.2148437500, 0.3085937500 },
 233   { 0.3007812500, 0.4804687500, 0.6914062500, 0.8710937500, 0.9726562500, 0.3398437500, 0.9335937500 },
 234   { 0.8007812500, 0.9804687500, 0.1914062500, 0.3710937500, 0.4726562500, 0.8398437500, 0.4335937500 },
 235   { 0.5507812500, 0.2304687500, 0.9414062500, 0.6210937500, 0.2226562500, 0.5898437500, 0.6835937500 },
 236   { 0.0507812500, 0.7304687500, 0.4414062500, 0.1210937500, 0.7226562500, 0.0898437500, 0.1835937500 },
 237   { 0.0351562500, 0.4648437500, 0.1757812500, 0.4179687500, 0.3945312500, 0.1992187500, 0.7304687500 },
 238   { 0.5351562500, 0.9648437500, 0.6757812500, 0.9179687500, 0.8945312500, 0.6992187500, 0.2304687500 },
 239   { 0.7851562500, 0.2148437500, 0.4257812500, 0.1679687500, 0.6445312500, 0.9492187500, 0.9804687500 },
 240   { 0.2851562500, 0.7148437500, 0.9257812500, 0.6679687500, 0.1445312500, 0.4492187500, 0.4804687500 }
 241 };
 242
 243 // Spatial dimension: 16
 244 // N: 100
 245 // Vectors skipped: 127
 246 static const double sobol_16_100[100][16] =
 247 {
 248   { 0.0117187500, 0.3320312500, 0.2929687500, 0.1914062500, 0.9023437500, 0.6757812500, 0.8632812500, 0.2460937500, 0.1054687500, 0.8164062500, 0.7382812500, 0.7382812500, 0.8164062500, 0.8789062500, 0.0273437500, 0.7617187500 },
 249   { 0.5117187500, 0.8320312500, 0.7929687500, 0.6914062500, 0.4023437500, 0.1757812500, 0.3632812500, 0.7460937500, 0.6054687500, 0.3164062500, 0.2382812500, 0.2382812500, 0.3164062500, 0.3789062500, 0.5273437500, 0.2617187500 },
 250   { 0.7617187500, 0.0820312500, 0.0429687500, 0.4414062500, 0.1523437500, 0.4257812500, 0.6132812500, 0.9960937500, 0.8554687500, 0.0664062500, 0.4882812500, 0.4882812500, 0.5664062500, 0.6289062500, 0.7773437500, 0.5117187500 },
 251   { 0.2617187500, 0.5820312500, 0.5429687500, 0.9414062500, 0.6523437500, 0.9257812500, 0.1132812500, 0.4960937500, 0.3554687500, 0.5664062500, 0.9882812500, 0.9882812500, 0.0664062500, 0.1289062500, 0.2773437500, 0.0117187500 },
 252   { 0.3867187500, 0.2070312500, 0.9179687500, 0.8164062500, 0.5273437500, 0.5507812500, 0.7382812500, 0.8710937500, 0.9804687500, 0.4414062500, 0.3632812500, 0.8632812500, 0.6914062500, 0.2539062500, 0.4023437500, 0.1367187500 },
 253   { 0.8867187500, 0.7070312500, 0.4179687500, 0.3164062500, 0.0273437500, 0.0507812500, 0.2382812500, 0.3710937500, 0.4804687500, 0.9414062500, 0.8632812500, 0.3632812500, 0.1914062500, 0.7539062500, 0.9023437500, 0.6367187500 },
 254   { 0.6367187500, 0.4570312500, 0.6679687500, 0.5664062500, 0.2773437500, 0.3007812500, 0.9882812500, 0.1210937500, 0.2304687500, 0.6914062500, 0.6132812500, 0.1132812500, 0.9414062500, 0.0039062500, 0.6523437500, 0.3867187500 },
 255   { 0.1367187500, 0.9570312500, 0.1679687500, 0.0664062500, 0.7773437500, 0.8007812500, 0.4882812500, 0.6210937500, 0.7304687500, 0.1914062500, 0.1132812500, 0.6132812500, 0.4414062500, 0.5039062500, 0.1523437500, 0.8867187500 },
 256   { 0.1992187500, 0.0195312500, 0.7304687500, 0.2539062500, 0.4648437500, 0.9882812500, 0.6757812500, 0.8085937500, 0.9179687500, 0.5039062500, 0.0507812500, 0.6757812500, 0.1289062500, 0.0664062500, 0.8398437500, 0.1992187500 },
 257   { 0.6992187500, 0.5195312500, 0.2304687500, 0.7539062500, 0.9648437500, 0.4882812500, 0.1757812500, 0.3085937500, 0.4179687500, 0.0039062500, 0.5507812500, 0.1757812500, 0.6289062500, 0.5664062500, 0.3398437500, 0.6992187500 },
 258   { 0.9492187500, 0.2695312500, 0.9804687500, 0.0039062500, 0.7148437500, 0.2382812500, 0.9257812500, 0.0585937500, 0.1679687500, 0.2539062500, 0.8007812500, 0.4257812500, 0.3789062500, 0.3164062500, 0.0898437500, 0.4492187500 },
 259   { 0.4492187500, 0.7695312500, 0.4804687500, 0.5039062500, 0.2148437500, 0.7382812500, 0.4257812500, 0.5585937500, 0.6679687500, 0.7539062500, 0.3007812500, 0.9257812500, 0.8789062500, 0.8164062500, 0.5898437500, 0.9492187500 },
 260   { 0.3242187500, 0.3945312500, 0.1054687500, 0.6289062500, 0.0898437500, 0.8632812500, 0.8007812500, 0.1835937500, 0.0429687500, 0.1289062500, 0.9257812500, 0.8007812500, 0.2539062500, 0.6914062500, 0.7148437500, 0.8242187500 },
 261   { 0.8242187500, 0.8945312500, 0.6054687500, 0.1289062500, 0.5898437500, 0.3632812500, 0.3007812500, 0.6835937500, 0.5429687500, 0.6289062500, 0.4257812500, 0.3007812500, 0.7539062500, 0.1914062500, 0.2148437500, 0.3242187500 },
 262   { 0.5742187500, 0.1445312500, 0.3554687500, 0.8789062500, 0.8398437500, 0.1132812500, 0.5507812500, 0.9335937500, 0.7929687500, 0.8789062500, 0.1757812500, 0.0507812500, 0.0039062500, 0.9414062500, 0.4648437500, 0.5742187500 },
 263   { 0.0742187500, 0.6445312500, 0.8554687500, 0.3789062500, 0.3398437500, 0.6132812500, 0.0507812500, 0.4335937500, 0.2929687500, 0.3789062500, 0.6757812500, 0.5507812500, 0.5039062500, 0.4414062500, 0.9648437500, 0.0742187500 },
 264   { 0.1054687500, 0.1757812500, 0.1992187500, 0.5976562500, 0.6835937500, 0.3320312500, 0.3320312500, 0.9023437500, 0.3867187500, 0.9726562500, 0.6445312500, 0.8320312500, 0.4726562500, 0.2851562500, 0.3710937500, 0.7929687500 },
 265   { 0.6054687500, 0.6757812500, 0.6992187500, 0.0976562500, 0.1835937500, 0.8320312500, 0.8320312500, 0.4023437500, 0.8867187500, 0.4726562500, 0.1445312500, 0.3320312500, 0.9726562500, 0.7851562500, 0.8710937500, 0.2929687500 },
 266   { 0.8554687500, 0.4257812500, 0.4492187500, 0.8476562500, 0.4335937500, 0.5820312500, 0.0820312500, 0.1523437500, 0.6367187500, 0.2226562500, 0.3945312500, 0.0820312500, 0.2226562500, 0.0351562500, 0.6210937500, 0.5429687500 },
 267   { 0.3554687500, 0.9257812500, 0.9492187500, 0.3476562500, 0.9335937500, 0.0820312500, 0.5820312500, 0.6523437500, 0.1367187500, 0.7226562500, 0.8945312500, 0.5820312500, 0.7226562500, 0.5351562500, 0.1210937500, 0.0429687500 },
 268   { 0.4804687500, 0.3007812500, 0.5742187500, 0.4726562500, 0.8085937500, 0.4570312500, 0.2070312500, 0.0273437500, 0.5117187500, 0.3476562500, 0.2695312500, 0.7070312500, 0.0976562500, 0.9101562500, 0.2460937500, 0.1679687500 },
 269   { 0.9804687500, 0.8007812500, 0.0742187500, 0.9726562500, 0.3085937500, 0.9570312500, 0.7070312500, 0.5273437500, 0.0117187500, 0.8476562500, 0.7695312500, 0.2070312500, 0.5976562500, 0.4101562500, 0.7460937500, 0.6679687500 },
 270   { 0.7304687500, 0.0507812500, 0.8242187500, 0.2226562500, 0.0585937500, 0.7070312500, 0.4570312500, 0.7773437500, 0.2617187500, 0.5976562500, 0.5195312500, 0.4570312500, 0.3476562500, 0.6601562500, 0.9960937500, 0.4179687500 },
 271   { 0.2304687500, 0.5507812500, 0.3242187500, 0.7226562500, 0.5585937500, 0.2070312500, 0.9570312500, 0.2773437500, 0.7617187500, 0.0976562500, 0.0195312500, 0.9570312500, 0.8476562500, 0.1601562500, 0.4960937500, 0.9179687500 },
 272   { 0.1679687500, 0.4882812500, 0.7617187500, 0.9101562500, 0.2460937500, 0.0195312500, 0.1445312500, 0.0898437500, 0.5742187500, 0.6601562500, 0.0820312500, 0.7695312500, 0.5351562500, 0.7226562500, 0.5585937500, 0.2304687500 },
 273   { 0.6679687500, 0.9882812500, 0.2617187500, 0.4101562500, 0.7460937500, 0.5195312500, 0.6445312500, 0.5898437500, 0.0742187500, 0.1601562500, 0.5820312500, 0.2695312500, 0.0351562500, 0.2226562500, 0.0585937500, 0.7304687500 },
 274   { 0.9179687500, 0.2382812500, 0.5117187500, 0.6601562500, 0.9960937500, 0.7695312500, 0.3945312500, 0.8398437500, 0.3242187500, 0.4101562500, 0.8320312500, 0.0195312500, 0.7851562500, 0.9726562500, 0.3085937500, 0.4804687500 },
 275   { 0.4179687500, 0.7382812500, 0.0117187500, 0.1601562500, 0.4960937500, 0.2695312500, 0.8945312500, 0.3398437500, 0.8242187500, 0.9101562500, 0.3320312500, 0.5195312500, 0.2851562500, 0.4726562500, 0.8085937500, 0.9804687500 },
 276   { 0.2929687500, 0.1132812500, 0.3867187500, 0.0351562500, 0.3710937500, 0.1445312500, 0.2695312500, 0.9648437500, 0.4492187500, 0.0351562500, 0.9570312500, 0.6445312500, 0.9101562500, 0.0976562500, 0.9335937500, 0.8554687500 },
 277   { 0.7929687500, 0.6132812500, 0.8867187500, 0.5351562500, 0.8710937500, 0.6445312500, 0.7695312500, 0.4648437500, 0.9492187500, 0.5351562500, 0.4570312500, 0.1445312500, 0.4101562500, 0.5976562500, 0.4335937500, 0.3554687500 },
 278   { 0.5429687500, 0.3632812500, 0.1367187500, 0.2851562500, 0.6210937500, 0.8945312500, 0.0195312500, 0.2148437500, 0.6992187500, 0.7851562500, 0.2070312500, 0.3945312500, 0.6601562500, 0.3476562500, 0.1835937500, 0.6054687500 },
 279   { 0.0429687500, 0.8632812500, 0.6367187500, 0.7851562500, 0.1210937500, 0.3945312500, 0.5195312500, 0.7148437500, 0.1992187500, 0.2851562500, 0.7070312500, 0.8945312500, 0.1601562500, 0.8476562500, 0.6835937500, 0.1054687500 },
 280   { 0.0585937500, 0.0664062500, 0.9960937500, 0.7382812500, 0.7617187500, 0.2539062500, 0.0664062500, 0.5742187500, 0.9023437500, 0.8632812500, 0.8476562500, 0.2851562500, 0.6445312500, 0.1132812500, 0.9804687500, 0.8710937500 },
 281   { 0.5585937500, 0.5664062500, 0.4960937500, 0.2382812500, 0.2617187500, 0.7539062500, 0.5664062500, 0.0742187500, 0.4023437500, 0.3632812500, 0.3476562500, 0.7851562500, 0.1445312500, 0.6132812500, 0.4804687500, 0.3710937500 },
 282   { 0.8085937500, 0.3164062500, 0.7460937500, 0.9882812500, 0.0117187500, 0.5039062500, 0.3164062500, 0.3242187500, 0.1523437500, 0.1132812500, 0.0976562500, 0.5351562500, 0.8945312500, 0.3632812500, 0.2304687500, 0.6210937500 },
 283   { 0.3085937500, 0.8164062500, 0.2460937500, 0.4882812500, 0.5117187500, 0.0039062500, 0.8164062500, 0.8242187500, 0.6523437500, 0.6132812500, 0.5976562500, 0.0351562500, 0.3945312500, 0.8632812500, 0.7304687500, 0.1210937500 },
 284   { 0.4335937500, 0.4414062500, 0.3710937500, 0.3632812500, 0.6367187500, 0.3789062500, 0.4414062500, 0.4492187500, 0.0273437500, 0.4882812500, 0.2226562500, 0.1601562500, 0.7695312500, 0.7382812500, 0.6054687500, 0.2460937500 },
 285   { 0.9335937500, 0.9414062500, 0.8710937500, 0.8632812500, 0.1367187500, 0.8789062500, 0.9414062500, 0.9492187500, 0.5273437500, 0.9882812500, 0.7226562500, 0.6601562500, 0.2695312500, 0.2382812500, 0.1054687500, 0.7460937500 },
 286   { 0.6835937500, 0.1914062500, 0.1210937500, 0.1132812500, 0.3867187500, 0.6289062500, 0.1914062500, 0.6992187500, 0.7773437500, 0.7382812500, 0.9726562500, 0.9101562500, 0.5195312500, 0.9882812500, 0.3554687500, 0.4960937500 },
 287   { 0.1835937500, 0.6914062500, 0.6210937500, 0.6132812500, 0.8867187500, 0.1289062500, 0.6914062500, 0.1992187500, 0.2773437500, 0.2382812500, 0.4726562500, 0.4101562500, 0.0195312500, 0.4882812500, 0.8554687500, 0.9960937500 },
 288   { 0.2460937500, 0.2539062500, 0.0585937500, 0.8007812500, 0.3242187500, 0.0664062500, 0.3789062500, 0.3867187500, 0.0898437500, 0.5507812500, 0.4101562500, 0.3476562500, 0.3320312500, 0.9257812500, 0.1679687500, 0.1835937500 },
 289   { 0.7460937500, 0.7539062500, 0.5585937500, 0.3007812500, 0.8242187500, 0.5664062500, 0.8789062500, 0.8867187500, 0.5898437500, 0.0507812500, 0.9101562500, 0.8476562500, 0.8320312500, 0.4257812500, 0.6679687500, 0.6835937500 },
 290   { 0.9960937500, 0.0039062500, 0.3085937500, 0.5507812500, 0.5742187500, 0.8164062500, 0.1289062500, 0.6367187500, 0.8398437500, 0.3007812500, 0.6601562500, 0.5976562500, 0.0820312500, 0.6757812500, 0.9179687500, 0.4335937500 },
 291   { 0.4960937500, 0.5039062500, 0.8085937500, 0.0507812500, 0.0742187500, 0.3164062500, 0.6289062500, 0.1367187500, 0.3398437500, 0.8007812500, 0.1601562500, 0.0976562500, 0.5820312500, 0.1757812500, 0.4179687500, 0.9335937500 },
 292   { 0.3710937500, 0.1289062500, 0.6835937500, 0.1757812500, 0.1992187500, 0.1914062500, 0.0039062500, 0.5117187500, 0.9648437500, 0.1757812500, 0.5351562500, 0.2226562500, 0.2070312500, 0.3007812500, 0.2929687500, 0.8085937500 },
 293   { 0.8710937500, 0.6289062500, 0.1835937500, 0.6757812500, 0.6992187500, 0.6914062500, 0.5039062500, 0.0117187500, 0.4648437500, 0.6757812500, 0.0351562500, 0.7226562500, 0.7070312500, 0.8007812500, 0.7929687500, 0.3085937500 },
 294   { 0.6210937500, 0.3789062500, 0.9335937500, 0.4257812500, 0.9492187500, 0.9414062500, 0.2539062500, 0.2617187500, 0.2148437500, 0.9257812500, 0.2851562500, 0.9726562500, 0.4570312500, 0.0507812500, 0.5429687500, 0.5585937500 },
 295   { 0.1210937500, 0.8789062500, 0.4335937500, 0.9257812500, 0.4492187500, 0.4414062500, 0.7539062500, 0.7617187500, 0.7148437500, 0.4257812500, 0.7851562500, 0.4726562500, 0.9570312500, 0.5507812500, 0.0429687500, 0.0585937500 },
 296   { 0.0898437500, 0.4101562500, 0.5273437500, 0.0820312500, 0.5429687500, 0.7226562500, 0.5976562500, 0.2929687500, 0.6210937500, 0.9570312500, 0.7539062500, 0.1289062500, 0.0507812500, 0.7070312500, 0.6367187500, 0.8398437500 },
 297   { 0.5898437500, 0.9101562500, 0.0273437500, 0.5820312500, 0.0429687500, 0.2226562500, 0.0976562500, 0.7929687500, 0.1210937500, 0.4570312500, 0.2539062500, 0.6289062500, 0.5507812500, 0.2070312500, 0.1367187500, 0.3398437500 },
 298   { 0.8398437500, 0.1601562500, 0.7773437500, 0.3320312500, 0.2929687500, 0.4726562500, 0.8476562500, 0.5429687500, 0.3710937500, 0.2070312500, 0.0039062500, 0.8789062500, 0.3007812500, 0.9570312500, 0.3867187500, 0.5898437500 },
 299   { 0.3398437500, 0.6601562500, 0.2773437500, 0.8320312500, 0.7929687500, 0.9726562500, 0.3476562500, 0.0429687500, 0.8710937500, 0.7070312500, 0.5039062500, 0.3789062500, 0.8007812500, 0.4570312500, 0.8867187500, 0.0898437500 },
 300   { 0.4648437500, 0.0351562500, 0.1523437500, 0.9570312500, 0.9179687500, 0.5976562500, 0.9726562500, 0.6679687500, 0.4960937500, 0.3320312500, 0.1289062500, 0.2539062500, 0.4257812500, 0.0820312500, 0.7617187500, 0.2148437500 },
 301   { 0.9648437500, 0.5351562500, 0.6523437500, 0.4570312500, 0.4179687500, 0.0976562500, 0.4726562500, 0.1679687500, 0.9960937500, 0.8320312500, 0.6289062500, 0.7539062500, 0.9257812500, 0.5820312500, 0.2617187500, 0.7148437500 },
 302   { 0.7148437500, 0.2851562500, 0.4023437500, 0.7070312500, 0.1679687500, 0.3476562500, 0.7226562500, 0.4179687500, 0.7460937500, 0.5820312500, 0.8789062500, 0.5039062500, 0.1757812500, 0.3320312500, 0.0117187500, 0.4648437500 },
 303   { 0.2148437500, 0.7851562500, 0.9023437500, 0.2070312500, 0.6679687500, 0.8476562500, 0.2226562500, 0.9179687500, 0.2460937500, 0.0820312500, 0.3789062500, 0.0039062500, 0.6757812500, 0.8320312500, 0.5117187500, 0.9648437500 },
 304   { 0.1523437500, 0.2226562500, 0.4648437500, 0.3945312500, 0.1054687500, 0.9101562500, 0.9101562500, 0.7304687500, 0.4335937500, 0.6445312500, 0.4414062500, 0.1914062500, 0.9882812500, 0.2695312500, 0.4492187500, 0.1523437500 },
 305   { 0.6523437500, 0.7226562500, 0.9648437500, 0.8945312500, 0.6054687500, 0.4101562500, 0.4101562500, 0.2304687500, 0.9335937500, 0.1445312500, 0.9414062500, 0.6914062500, 0.4882812500, 0.7695312500, 0.9492187500, 0.6523437500 },
 306   { 0.9023437500, 0.4726562500, 0.2148437500, 0.1445312500, 0.8554687500, 0.1601562500, 0.6601562500, 0.4804687500, 0.6835937500, 0.3945312500, 0.6914062500, 0.9414062500, 0.7382812500, 0.0195312500, 0.6992187500, 0.4023437500 },
 307   { 0.4023437500, 0.9726562500, 0.7148437500, 0.6445312500, 0.3554687500, 0.6601562500, 0.1601562500, 0.9804687500, 0.1835937500, 0.8945312500, 0.1914062500, 0.4414062500, 0.2382812500, 0.5195312500, 0.1992187500, 0.9023437500 },
 308   { 0.2773437500, 0.3476562500, 0.8398437500, 0.5195312500, 0.4804687500, 0.7851562500, 0.5351562500, 0.3554687500, 0.5585937500, 0.0195312500, 0.5664062500, 0.3164062500, 0.6132812500, 0.8945312500, 0.0742187500, 0.7773437500 },
 309   { 0.7773437500, 0.8476562500, 0.3398437500, 0.0195312500, 0.9804687500, 0.2851562500, 0.0351562500, 0.8554687500, 0.0585937500, 0.5195312500, 0.0664062500, 0.8164062500, 0.1132812500, 0.3945312500, 0.5742187500, 0.2773437500 },
 310   { 0.5273437500, 0.0976562500, 0.5898437500, 0.7695312500, 0.7304687500, 0.0351562500, 0.7851562500, 0.6054687500, 0.3085937500, 0.7695312500, 0.3164062500, 0.5664062500, 0.8632812500, 0.6445312500, 0.8242187500, 0.5273437500 },
 311   { 0.0273437500, 0.5976562500, 0.0898437500, 0.2695312500, 0.2304687500, 0.5351562500, 0.2851562500, 0.1054687500, 0.8085937500, 0.2695312500, 0.8164062500, 0.0664062500, 0.3632812500, 0.1445312500, 0.3242187500, 0.0273437500 },
 312   { 0.0195312500, 0.1992187500, 0.5976562500, 0.9023437500, 0.2539062500, 0.8710937500, 0.4648437500, 0.0351562500, 0.6445312500, 0.8085937500, 0.3085937500, 0.5273437500, 0.7460937500, 0.4023437500, 0.7851562500, 0.2539062500 },
 313   { 0.5195312500, 0.6992187500, 0.0976562500, 0.4023437500, 0.7539062500, 0.3710937500, 0.9648437500, 0.5351562500, 0.1445312500, 0.3085937500, 0.8085937500, 0.0273437500, 0.2460937500, 0.9023437500, 0.2851562500, 0.7539062500 },
 314   { 0.7695312500, 0.4492187500, 0.8476562500, 0.6523437500, 0.5039062500, 0.1210937500, 0.2148437500, 0.7851562500, 0.3945312500, 0.0585937500, 0.5585937500, 0.2773437500, 0.9960937500, 0.1523437500, 0.0351562500, 0.0039062500 },
 315   { 0.2695312500, 0.9492187500, 0.3476562500, 0.1523437500, 0.0039062500, 0.6210937500, 0.7148437500, 0.2851562500, 0.8945312500, 0.5585937500, 0.0585937500, 0.7773437500, 0.4960937500, 0.6523437500, 0.5351562500, 0.5039062500 },
 316   { 0.3945312500, 0.3242187500, 0.2226562500, 0.0273437500, 0.1289062500, 0.9960937500, 0.0898437500, 0.9101562500, 0.2695312500, 0.4335937500, 0.6835937500, 0.9023437500, 0.8710937500, 0.7773437500, 0.6601562500, 0.6289062500 },
 317   { 0.8945312500, 0.8242187500, 0.7226562500, 0.5273437500, 0.6289062500, 0.4960937500, 0.5898437500, 0.4101562500, 0.7695312500, 0.9335937500, 0.1835937500, 0.4023437500, 0.3710937500, 0.2773437500, 0.1601562500, 0.1289062500 },
 318   { 0.6445312500, 0.0742187500, 0.4726562500, 0.2773437500, 0.8789062500, 0.2460937500, 0.3398437500, 0.1601562500, 0.5195312500, 0.6835937500, 0.4335937500, 0.1523437500, 0.6210937500, 0.5273437500, 0.4101562500, 0.8789062500 },
 319   { 0.1445312500, 0.5742187500, 0.9726562500, 0.7773437500, 0.3789062500, 0.7460937500, 0.8398437500, 0.6601562500, 0.0195312500, 0.1835937500, 0.9335937500, 0.6523437500, 0.1210937500, 0.0273437500, 0.9101562500, 0.3789062500 },
 320   { 0.2070312500, 0.3867187500, 0.4101562500, 0.5898437500, 0.8164062500, 0.5585937500, 0.0273437500, 0.9726562500, 0.3320312500, 0.6210937500, 0.9960937500, 0.5898437500, 0.3085937500, 0.5898437500, 0.0976562500, 0.6914062500 },
 321   { 0.7070312500, 0.8867187500, 0.9101562500, 0.0898437500, 0.3164062500, 0.0585937500, 0.5273437500, 0.4726562500, 0.8320312500, 0.1210937500, 0.4960937500, 0.0898437500, 0.8085937500, 0.0898437500, 0.5976562500, 0.1914062500 },
 322   { 0.9570312500, 0.1367187500, 0.1601562500, 0.8398437500, 0.0664062500, 0.3085937500, 0.2773437500, 0.2226562500, 0.5820312500, 0.3710937500, 0.2460937500, 0.3398437500, 0.0585937500, 0.8398437500, 0.8476562500, 0.9414062500 },
 323   { 0.4570312500, 0.6367187500, 0.6601562500, 0.3398437500, 0.5664062500, 0.8085937500, 0.7773437500, 0.7226562500, 0.0820312500, 0.8710937500, 0.7460937500, 0.8398437500, 0.5585937500, 0.3398437500, 0.3476562500, 0.4414062500 },
 324   { 0.3320312500, 0.0117187500, 0.7851562500, 0.4648437500, 0.6914062500, 0.6835937500, 0.4023437500, 0.0976562500, 0.7070312500, 0.2460937500, 0.1210937500, 0.9648437500, 0.1835937500, 0.2148437500, 0.4726562500, 0.3164062500 },
 325   { 0.8320312500, 0.5117187500, 0.2851562500, 0.9648437500, 0.1914062500, 0.1835937500, 0.9023437500, 0.5976562500, 0.2070312500, 0.7460937500, 0.6210937500, 0.4648437500, 0.6835937500, 0.7148437500, 0.9726562500, 0.8164062500 },
 326   { 0.5820312500, 0.2617187500, 0.5351562500, 0.2148437500, 0.4414062500, 0.4335937500, 0.1523437500, 0.8476562500, 0.4570312500, 0.9960937500, 0.8710937500, 0.2148437500, 0.4335937500, 0.4648437500, 0.7226562500, 0.0664062500 },
 327   { 0.0820312500, 0.7617187500, 0.0351562500, 0.7148437500, 0.9414062500, 0.9335937500, 0.6523437500, 0.3476562500, 0.9570312500, 0.4960937500, 0.3710937500, 0.7148437500, 0.9335937500, 0.9648437500, 0.2226562500, 0.5664062500 },
 328   { 0.1132812500, 0.2929687500, 0.8789062500, 0.3085937500, 0.0351562500, 0.1523437500, 0.9960937500, 0.8164062500, 0.8632812500, 0.9023437500, 0.3398437500, 0.9335937500, 0.0898437500, 0.8085937500, 0.5664062500, 0.2851562500 },
 329   { 0.6132812500, 0.7929687500, 0.3789062500, 0.8085937500, 0.5351562500, 0.6523437500, 0.4960937500, 0.3164062500, 0.3632812500, 0.4023437500, 0.8398437500, 0.4335937500, 0.5898437500, 0.3085937500, 0.0664062500, 0.7851562500 },
 330   { 0.8632812500, 0.0429687500, 0.6289062500, 0.0585937500, 0.7851562500, 0.9023437500, 0.7460937500, 0.0664062500, 0.1132812500, 0.1523437500, 0.5898437500, 0.1835937500, 0.3398437500, 0.5585937500, 0.3164062500, 0.0351562500 },
 331   { 0.3632812500, 0.5429687500, 0.1289062500, 0.5585937500, 0.2851562500, 0.4023437500, 0.2460937500, 0.5664062500, 0.6132812500, 0.6523437500, 0.0898437500, 0.6835937500, 0.8398437500, 0.0585937500, 0.8164062500, 0.5351562500 },
 332   { 0.4882812500, 0.1679687500, 0.2539062500, 0.6835937500, 0.4101562500, 0.0273437500, 0.6210937500, 0.1914062500, 0.2382812500, 0.2773437500, 0.7148437500, 0.5585937500, 0.4648437500, 0.4335937500, 0.9414062500, 0.6601562500 },
 333   { 0.9882812500, 0.6679687500, 0.7539062500, 0.1835937500, 0.9101562500, 0.5273437500, 0.1210937500, 0.6914062500, 0.7382812500, 0.7773437500, 0.2148437500, 0.0585937500, 0.9648437500, 0.9335937500, 0.4414062500, 0.1601562500 },
 334   { 0.7382812500, 0.4179687500, 0.0039062500, 0.9335937500, 0.6601562500, 0.7773437500, 0.8710937500, 0.9414062500, 0.9882812500, 0.5273437500, 0.4648437500, 0.3085937500, 0.2148437500, 0.1835937500, 0.1914062500, 0.9101562500 },
 335   { 0.2382812500, 0.9179687500, 0.5039062500, 0.4335937500, 0.1601562500, 0.2773437500, 0.3710937500, 0.4414062500, 0.4882812500, 0.0273437500, 0.9648437500, 0.8085937500, 0.7148437500, 0.6835937500, 0.6914062500, 0.4101562500 },
 336   { 0.1757812500, 0.1054687500, 0.0664062500, 0.2460937500, 0.5976562500, 0.4648437500, 0.5585937500, 0.1289062500, 0.1757812500, 0.7148437500, 0.9023437500, 0.9960937500, 0.9023437500, 0.2460937500, 0.2539062500, 0.7226562500 },
 337   { 0.6757812500, 0.6054687500, 0.5664062500, 0.7460937500, 0.0976562500, 0.9648437500, 0.0585937500, 0.6289062500, 0.6757812500, 0.2148437500, 0.4023437500, 0.4960937500, 0.4023437500, 0.7460937500, 0.7539062500, 0.2226562500 },
 338   { 0.9257812500, 0.3554687500, 0.3164062500, 0.4960937500, 0.3476562500, 0.7148437500, 0.8085937500, 0.8789062500, 0.9257812500, 0.4648437500, 0.1523437500, 0.2460937500, 0.6523437500, 0.4960937500, 0.5039062500, 0.9726562500 },
 339   { 0.4257812500, 0.8554687500, 0.8164062500, 0.9960937500, 0.8476562500, 0.2148437500, 0.3085937500, 0.3789062500, 0.4257812500, 0.9648437500, 0.6523437500, 0.7460937500, 0.1523437500, 0.9960937500, 0.0039062500, 0.4726562500 },
 340   { 0.3007812500, 0.4804687500, 0.6914062500, 0.8710937500, 0.9726562500, 0.3398437500, 0.9335937500, 0.7539062500, 0.8007812500, 0.0898437500, 0.0273437500, 0.6210937500, 0.5273437500, 0.6210937500, 0.1289062500, 0.3476562500 },
 341   { 0.8007812500, 0.9804687500, 0.1914062500, 0.3710937500, 0.4726562500, 0.8398437500, 0.4335937500, 0.2539062500, 0.3007812500, 0.5898437500, 0.5273437500, 0.1210937500, 0.0273437500, 0.1210937500, 0.6289062500, 0.8476562500 },
 342   { 0.5507812500, 0.2304687500, 0.9414062500, 0.6210937500, 0.2226562500, 0.5898437500, 0.6835937500, 0.0039062500, 0.0507812500, 0.8398437500, 0.7773437500, 0.3710937500, 0.7773437500, 0.8710937500, 0.8789062500, 0.0976562500 },
 343   { 0.0507812500, 0.7304687500, 0.4414062500, 0.1210937500, 0.7226562500, 0.0898437500, 0.1835937500, 0.5039062500, 0.5507812500, 0.3398437500, 0.2773437500, 0.8710937500, 0.2773437500, 0.3710937500, 0.3789062500, 0.5976562500 },
 344   { 0.0351562500, 0.4648437500, 0.1757812500, 0.4179687500, 0.3945312500, 0.1992187500, 0.7304687500, 0.6445312500, 0.3476562500, 0.7617187500, 0.1679687500, 0.4492187500, 0.7929687500, 0.6054687500, 0.2070312500, 0.3632812500 },
 345   { 0.5351562500, 0.9648437500, 0.6757812500, 0.9179687500, 0.8945312500, 0.6992187500, 0.2304687500, 0.1445312500, 0.8476562500, 0.2617187500, 0.6679687500, 0.9492187500, 0.2929687500, 0.1054687500, 0.7070312500, 0.8632812500 },
 346   { 0.7851562500, 0.2148437500, 0.4257812500, 0.1679687500, 0.6445312500, 0.9492187500, 0.9804687500, 0.3945312500, 0.5976562500, 0.0117187500, 0.9179687500, 0.6992187500, 0.5429687500, 0.8554687500, 0.9570312500, 0.1132812500 },
 347   { 0.2851562500, 0.7148437500, 0.9257812500, 0.6679687500, 0.1445312500, 0.4492187500, 0.4804687500, 0.8945312500, 0.0976562500, 0.5117187500, 0.4179687500, 0.1992187500, 0.0429687500, 0.3554687500, 0.4570312500, 0.6132812500 }
 348 };
 349
 350
 351 QRNG_VALIDATION_TEST_FUNCTIONS(sobol)
 352 QRNG_VALIDATION_TEST_DISCARD(sobol)
 353
 354 BOOST_AUTO_TEST_CASE( check_generator_limits )
 355 {
 356   test_sobol_max_seed();
 357   test_sobol_max_discard();
 358   test_sobol_max_dimension(BOOST_RANDOM_SOBOL_MAX_DIMENSION);
 359 }
 360
 361 BOOST_AUTO_TEST_CASE( validate_sobol )
 362 {
 363   test_sobol_values(sobol_02_99, 0);
 364   test_sobol_values(sobol_07_100, 127);
 365   test_sobol_values(sobol_16_100, 127);
 366 }
 367
 368 BOOST_AUTO_TEST_CASE( validate_sobol_seed )
 369 {
 370   test_sobol_seed(sobol_02_99, 0);
 371   test_sobol_seed(sobol_07_100, 127);
 372   test_sobol_seed(sobol_16_100, 127);
 373 }
 374
 375 BOOST_AUTO_TEST_CASE( validate_sobol_discard )
 376 {
 377   test_sobol_discard(sobol_02_99, 0);
 378   test_sobol_discard(sobol_07_100, 127);
 379   test_sobol_discard(sobol_16_100, 127);
 380 }