ceph/src/boost/libs/math/tools/rational_tests.cpp

   1 //  (C) Copyright John Maddock 2007.
   2 //  Use, modification and distribution are subject to the
   3 //  Boost Software License, Version 1.0. (See accompanying file
   4 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   5
   6 #include "mp_t.hpp"
   7 #include <boost/random.hpp>
   8 #include <boost/math/tools/rational.hpp>
   9 #include <iostream>
  10 #include <fstream>
  11
  12 int main()
  13 {
  14    using namespace boost::math;
  15    using namespace boost::math::tools;
  16
  17    std::cout << std::scientific << std::setprecision(40);
  18
  19    boost::mt19937 rnd;
  20    boost::variate_generator<
  21       boost::mt19937,
  22       boost::uniform_int<> > gen(rnd, boost::uniform_int<>(1, 12));
  23
  24    for(unsigned i = 1; i < 12; ++i)
  25    {
  26       std::vector<int> coef;
  27       for(unsigned j = 0; j < i; ++j)
  28       {
  29          coef.push_back(gen());
  30       }
  31       std::cout <<
  32 "   //\n"
  33 "   // Polynomials of order " << i-1 << "\n"
  34 "   //\n"
  35 "   static const U n" << i << "c[" << i << "] = { ";
  36       for(unsigned j = 0; j < i; ++j)
  37       {
  38          if(j)
  39             std::cout  << ", ";
  40          std::cout << coef[j];
  41       }
  42       std::cout << " };\n";
  43       std::cout <<
  44          "   static const std::array<U, " << i << "> n" << i << "a = { ";
  45       for(unsigned j = 0; j < i; ++j)
  46       {
  47          if(j)
  48             std::cout  << ", ";
  49          std::cout << coef[j];
  50       }
  51       std::cout << " };\n";
  52
  53       mp_t r1 = boost::math::tools::evaluate_polynomial(&coef[0], mp_t(0.125), i);
  54       mp_t r2 = boost::math::tools::evaluate_polynomial(&coef[0], mp_t(0.25), i);
  55       mp_t r3 = boost::math::tools::evaluate_polynomial(&coef[0], mp_t(0.75), i);
  56       mp_t r4 = boost::math::tools::evaluate_polynomial(&coef[0], mp_t(1) - mp_t(1) / 64, i);
  57
  58       std::cout <<
  59          "   BOOST_CHECK_CLOSE(\n"
  60          "      boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast<T>(0.125), " << i << "),\n"
  61          "      static_cast<T>(" << r1 << "L),\n"
  62          "      tolerance);\n";
  63       std::cout <<
  64          "   BOOST_CHECK_CLOSE(\n"
  65          "      boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast<T>(0.25), " << i << "),\n"
  66          "      static_cast<T>(" << r2 << "L),\n"
  67          "      tolerance);\n";
  68       std::cout <<
  69          "   BOOST_CHECK_CLOSE(\n"
  70          "      boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast<T>(0.75), " << i << "),\n"
  71          "      static_cast<T>(" << r3 << "L),\n"
  72          "      tolerance);\n";
  73       std::cout <<
  74          "   BOOST_CHECK_CLOSE(\n"
  75          "      boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast<T>(1.0f - 1.0f/64.0f), " << i << "),\n"
  76          "      static_cast<T>(" << r4 << "L),\n"
  77          "      tolerance);\n\n";
  78
  79       std::cout <<
  80          "   BOOST_CHECK_CLOSE(\n"
  81          "      boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast<T>(0.125)),\n"
  82          "      static_cast<T>(" << r1 << "L),\n"
  83          "      tolerance);\n";
  84       std::cout <<
  85          "   BOOST_CHECK_CLOSE(\n"
  86          "      boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast<T>(0.25)),\n"
  87          "      static_cast<T>(" << r2 << "L),\n"
  88          "      tolerance);\n";
  89       std::cout <<
  90          "   BOOST_CHECK_CLOSE(\n"
  91          "      boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast<T>(0.75)),\n"
  92          "      static_cast<T>(" << r3 << "L),\n"
  93          "      tolerance);\n";
  94       std::cout <<
  95          "   BOOST_CHECK_CLOSE(\n"
  96          "      boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast<T>(1.0f - 1.0f/64.0f)),\n"
  97          "      static_cast<T>(" << r4 << "L),\n"
  98          "      tolerance);\n\n";
  99
 100       std::cout <<
 101          "   BOOST_CHECK_CLOSE(\n"
 102          "      boost::math::tools::evaluate_polynomial(n" << i << "a, static_cast<T>(0.125)),\n"
 103          "      static_cast<T>(" << r1 << "L),\n"
 104          "      tolerance);\n";
 105       std::cout <<
 106          "   BOOST_CHECK_CLOSE(\n"
 107          "      boost::math::tools::evaluate_polynomial(n" << i << "a, static_cast<T>(0.25)),\n"
 108          "      static_cast<T>(" << r2 << "L),\n"
 109          "      tolerance);\n";
 110       std::cout <<
 111          "   BOOST_CHECK_CLOSE(\n"
 112          "      boost::math::tools::evaluate_polynomial(n" << i << "a, static_cast<T>(0.75)),\n"
 113          "      static_cast<T>(" << r3 << "L),\n"
 114          "      tolerance);\n";
 115       std::cout <<
 116          "   BOOST_CHECK_CLOSE(\n"
 117          "      boost::math::tools::evaluate_polynomial(n" << i << "a, static_cast<T>(1.0f - 1.0f/64.0f)),\n"
 118          "      static_cast<T>(" << r4 << "L),\n"
 119          "      tolerance);\n\n";
 120
 121       r1 = boost::math::tools::evaluate_even_polynomial(&coef[0], mp_t(0.125), i);
 122       r2 = boost::math::tools::evaluate_even_polynomial(&coef[0], mp_t(0.25), i);
 123       r3 = boost::math::tools::evaluate_even_polynomial(&coef[0], mp_t(0.75), i);
 124       r4 = boost::math::tools::evaluate_even_polynomial(&coef[0], mp_t(1) - mp_t(1) / 64, i);
 125
 126       std::cout <<
 127          "   BOOST_CHECK_CLOSE(\n"
 128          "      boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast<T>(0.125), " << i << "),\n"
 129          "      static_cast<T>(" << r1 << "L),\n"
 130          "      tolerance);\n";
 131       std::cout <<
 132          "   BOOST_CHECK_CLOSE(\n"
 133          "      boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast<T>(0.25), " << i << "),\n"
 134          "      static_cast<T>(" << r2 << "L),\n"
 135          "      tolerance);\n";
 136       std::cout <<
 137          "   BOOST_CHECK_CLOSE(\n"
 138          "      boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast<T>(0.75), " << i << "),\n"
 139          "      static_cast<T>(" << r3 << "L),\n"
 140          "      tolerance);\n";
 141       std::cout <<
 142          "   BOOST_CHECK_CLOSE(\n"
 143          "      boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast<T>(1.0f - 1.0f/64.0f), " << i << "),\n"
 144          "      static_cast<T>(" << r4 << "L),\n"
 145          "      tolerance);\n\n";
 146
 147       std::cout <<
 148          "   BOOST_CHECK_CLOSE(\n"
 149          "      boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast<T>(0.125)),\n"
 150          "      static_cast<T>(" << r1 << "L),\n"
 151          "      tolerance);\n";
 152       std::cout <<
 153          "   BOOST_CHECK_CLOSE(\n"
 154          "      boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast<T>(0.25)),\n"
 155          "      static_cast<T>(" << r2 << "L),\n"
 156          "      tolerance);\n";
 157       std::cout <<
 158          "   BOOST_CHECK_CLOSE(\n"
 159          "      boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast<T>(0.75)),\n"
 160          "      static_cast<T>(" << r3 << "L),\n"
 161          "      tolerance);\n";
 162       std::cout <<
 163          "   BOOST_CHECK_CLOSE(\n"
 164          "      boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast<T>(1.0f - 1.0f/64.0f)),\n"
 165          "      static_cast<T>(" << r4 << "L),\n"
 166          "      tolerance);\n\n";
 167
 168       std::cout <<
 169          "   BOOST_CHECK_CLOSE(\n"
 170          "      boost::math::tools::evaluate_even_polynomial(n" << i << "a, static_cast<T>(0.125)),\n"
 171          "      static_cast<T>(" << r1 << "L),\n"
 172          "      tolerance);\n";
 173       std::cout <<
 174          "   BOOST_CHECK_CLOSE(\n"
 175          "      boost::math::tools::evaluate_even_polynomial(n" << i << "a, static_cast<T>(0.25)),\n"
 176          "      static_cast<T>(" << r2 << "L),\n"
 177          "      tolerance);\n";
 178       std::cout <<
 179          "   BOOST_CHECK_CLOSE(\n"
 180          "      boost::math::tools::evaluate_even_polynomial(n" << i << "a, static_cast<T>(0.75)),\n"
 181          "      static_cast<T>(" << r3 << "L),\n"
 182          "      tolerance);\n";
 183       std::cout <<
 184          "   BOOST_CHECK_CLOSE(\n"
 185          "      boost::math::tools::evaluate_even_polynomial(n" << i << "a, static_cast<T>(1.0f - 1.0f/64.0f)),\n"
 186          "      static_cast<T>(" << r4 << "L),\n"
 187          "      tolerance);\n\n";
 188
 189       if(i > 1)
 190       {
 191          r1 = boost::math::tools::evaluate_odd_polynomial(&coef[0], mp_t(0.125), i);
 192          r2 = boost::math::tools::evaluate_odd_polynomial(&coef[0], mp_t(0.25), i);
 193          r3 = boost::math::tools::evaluate_odd_polynomial(&coef[0], mp_t(0.75), i);
 194          r4 = boost::math::tools::evaluate_odd_polynomial(&coef[0], mp_t(1) - mp_t(1) / 64, i);
 195
 196          std::cout <<
 197             "   BOOST_CHECK_CLOSE(\n"
 198             "      boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast<T>(0.125), " << i << "),\n"
 199             "      static_cast<T>(" << r1 << "L),\n"
 200             "      tolerance);\n";
 201          std::cout <<
 202             "   BOOST_CHECK_CLOSE(\n"
 203             "      boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast<T>(0.25), " << i << "),\n"
 204             "      static_cast<T>(" << r2 << "L),\n"
 205             "      tolerance);\n";
 206          std::cout <<
 207             "   BOOST_CHECK_CLOSE(\n"
 208             "      boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast<T>(0.75), " << i << "),\n"
 209             "      static_cast<T>(" << r3 << "L),\n"
 210             "      tolerance);\n";
 211          std::cout <<
 212             "   BOOST_CHECK_CLOSE(\n"
 213             "      boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast<T>(1.0f - 1.0f/64.0f), " << i << "),\n"
 214             "      static_cast<T>(" << r4 << "L),\n"
 215             "      tolerance);\n\n";
 216
 217          std::cout <<
 218             "   BOOST_CHECK_CLOSE(\n"
 219             "      boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast<T>(0.125)),\n"
 220             "      static_cast<T>(" << r1 << "L),\n"
 221             "      tolerance);\n";
 222          std::cout <<
 223             "   BOOST_CHECK_CLOSE(\n"
 224             "      boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast<T>(0.25)),\n"
 225             "      static_cast<T>(" << r2 << "L),\n"
 226             "      tolerance);\n";
 227          std::cout <<
 228             "   BOOST_CHECK_CLOSE(\n"
 229             "      boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast<T>(0.75)),\n"
 230             "      static_cast<T>(" << r3 << "L),\n"
 231             "      tolerance);\n";
 232          std::cout <<
 233             "   BOOST_CHECK_CLOSE(\n"
 234             "      boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast<T>(1.0f - 1.0f/64.0f)),\n"
 235             "      static_cast<T>(" << r4 << "L),\n"
 236             "      tolerance);\n\n";
 237
 238          std::cout <<
 239             "   BOOST_CHECK_CLOSE(\n"
 240             "      boost::math::tools::evaluate_odd_polynomial(n" << i << "a, static_cast<T>(0.125)),\n"
 241             "      static_cast<T>(" << r1 << "L),\n"
 242             "      tolerance);\n";
 243          std::cout <<
 244             "   BOOST_CHECK_CLOSE(\n"
 245             "      boost::math::tools::evaluate_odd_polynomial(n" << i << "a, static_cast<T>(0.25)),\n"
 246             "      static_cast<T>(" << r2 << "L),\n"
 247             "      tolerance);\n";
 248          std::cout <<
 249             "   BOOST_CHECK_CLOSE(\n"
 250             "      boost::math::tools::evaluate_odd_polynomial(n" << i << "a, static_cast<T>(0.75)),\n"
 251             "      static_cast<T>(" << r3 << "L),\n"
 252             "      tolerance);\n";
 253          std::cout <<
 254             "   BOOST_CHECK_CLOSE(\n"
 255             "      boost::math::tools::evaluate_odd_polynomial(n" << i << "a, static_cast<T>(1.0f - 1.0f/64.0f)),\n"
 256             "      static_cast<T>(" << r4 << "L),\n"
 257             "      tolerance);\n\n";
 258       }
 259
 260       r1 = boost::math::tools::evaluate_polynomial(&coef[0], mp_t(0.125), i);
 261       r2 = boost::math::tools::evaluate_polynomial(&coef[0], mp_t(0.25), i);
 262       r3 = boost::math::tools::evaluate_polynomial(&coef[0], mp_t(0.75), i);
 263       r4 = boost::math::tools::evaluate_polynomial(&coef[0], mp_t(1) - mp_t(1) / 64, i);
 264
 265       coef.clear();
 266       for(unsigned j = 0; j < i; ++j)
 267       {
 268          coef.push_back(gen());
 269       }
 270       std::cout <<
 271 "   //\n"
 272 "   // Rational functions of order " << i-1 << "\n"
 273 "   //\n"
 274 "   static const U d" << i << "c[" << i << "] = { ";
 275       for(unsigned j = 0; j < i; ++j)
 276       {
 277          if(j)
 278             std::cout  << ", ";
 279          std::cout << coef[j];
 280       }
 281       std::cout << " };\n";
 282       std::cout <<
 283          "   static const std::array<U, " << i << "> d" << i << "a = { ";
 284       for(unsigned j = 0; j < i; ++j)
 285       {
 286          if(j)
 287             std::cout  << ", ";
 288          std::cout << coef[j];
 289       }
 290       std::cout << " };\n";
 291
 292       mp_t r1d = boost::math::tools::evaluate_polynomial(&coef[0], mp_t(0.125), i);
 293       mp_t r2d = boost::math::tools::evaluate_polynomial(&coef[0], mp_t(0.25), i);
 294       mp_t r3d = boost::math::tools::evaluate_polynomial(&coef[0], mp_t(0.75), i);
 295       mp_t r4d = boost::math::tools::evaluate_polynomial(&coef[0], mp_t(1) - mp_t(1) / 64, i);
 296
 297       std::cout <<
 298          "   BOOST_CHECK_CLOSE(\n"
 299          "      boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast<T>(0.125), " << i << "),\n"
 300          "      static_cast<T>(" << r1/r1d << "L),\n"
 301          "      tolerance);\n";
 302       std::cout <<
 303          "   BOOST_CHECK_CLOSE(\n"
 304          "      boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast<T>(0.25), " << i << "),\n"
 305          "      static_cast<T>(" << r2/r2d << "L),\n"
 306          "      tolerance);\n";
 307       std::cout <<
 308          "   BOOST_CHECK_CLOSE(\n"
 309          "      boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast<T>(0.75), " << i << "),\n"
 310          "      static_cast<T>(" << r3/r3d << "L),\n"
 311          "      tolerance);\n";
 312       std::cout <<
 313          "   BOOST_CHECK_CLOSE(\n"
 314          "      boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast<T>(1.0f - 1.0f/64.0f), " << i << "),\n"
 315          "      static_cast<T>(" << r4/r4d << "L),\n"
 316          "      tolerance);\n\n";
 317
 318       std::cout <<
 319          "   BOOST_CHECK_CLOSE(\n"
 320          "      boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast<T>(0.125)),\n"
 321          "      static_cast<T>(" << r1/r1d << "L),\n"
 322          "      tolerance);\n";
 323       std::cout <<
 324          "   BOOST_CHECK_CLOSE(\n"
 325          "      boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast<T>(0.25)),\n"
 326          "      static_cast<T>(" << r2/r2d << "L),\n"
 327          "      tolerance);\n";
 328       std::cout <<
 329          "   BOOST_CHECK_CLOSE(\n"
 330          "      boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast<T>(0.75)),\n"
 331          "      static_cast<T>(" << r3/r3d << "L),\n"
 332          "      tolerance);\n";
 333       std::cout <<
 334          "   BOOST_CHECK_CLOSE(\n"
 335          "      boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast<T>(1.0f - 1.0f/64.0f)),\n"
 336          "      static_cast<T>(" << r4/r4d << "L),\n"
 337          "      tolerance);\n\n";
 338
 339       std::cout <<
 340          "   BOOST_CHECK_CLOSE(\n"
 341          "      boost::math::tools::evaluate_rational(n" << i << "a, d" << i << "a, static_cast<T>(0.125)),\n"
 342          "      static_cast<T>(" << r1/r1d << "L),\n"
 343          "      tolerance);\n";
 344       std::cout <<
 345          "   BOOST_CHECK_CLOSE(\n"
 346          "      boost::math::tools::evaluate_rational(n" << i << "a, d" << i << "a, static_cast<T>(0.25)),\n"
 347          "      static_cast<T>(" << r2/r2d << "L),\n"
 348          "      tolerance);\n";
 349       std::cout <<
 350          "   BOOST_CHECK_CLOSE(\n"
 351          "      boost::math::tools::evaluate_rational(n" << i << "a, d" << i << "a, static_cast<T>(0.75)),\n"
 352          "      static_cast<T>(" << r3/r3d << "L),\n"
 353          "      tolerance);\n";
 354       std::cout <<
 355          "   BOOST_CHECK_CLOSE(\n"
 356          "      boost::math::tools::evaluate_rational(n" << i << "a, d" << i << "a, static_cast<T>(1.0f - 1.0f/64.0f)),\n"
 357          "      static_cast<T>(" << r4/r4d << "L),\n"
 358          "      tolerance);\n\n";
 359    }
 360
 361    return 0;
 362 }
 363
 364
 365