ceph/src/boost/libs/math/test/test_remez.cpp

   1 //  Copyright John Maddock 2006
   2 //  Copyright Paul A. Bristow 2007
   3 //  Use, modification and distribution are subject to the
   4 //  Boost Software License, Version 1.0. (See accompanying file
   5 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   6
   7 #include <pch.hpp>
   8
   9 #ifdef _MSC_VER
  10 #  pragma warning(disable : 4267) // conversion from 'size_t' to 'const unsigned int', possible loss of data
  11 #  pragma warning(disable : 4180) // qualifier applied to function type has no meaning; ignored
  12 #  pragma warning(disable : 4224) // nonstandard extension used : formal parameter 'function_ptr' was previously defined as a type
  13 #  pragma warning(disable : 4100) // unreferenced formal parameter (in ublas/functional)
  14 #endif
  15
  16 #include <boost/math/tools/remez.hpp>
  17 #define BOOST_TEST_MAIN
  18 #include <boost/test/unit_test.hpp>
  19 #include <boost/test/tools/floating_point_comparison.hpp>
  20 #include <boost/math/special_functions/expm1.hpp>
  21 #include <iostream>
  22 #include <iomanip>
  23
  24
  25 void test_polynomial()
  26 {
  27 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
  28    double (*f)(double) = boost::math::expm1<double>;
  29 #else
  30    double (*f)(double) = boost::math::expm1;
  31 #endif
  32    std::cout << "Testing expm1 approximation, pinned to origin, absolute error, 6 term polynomial\n";
  33    boost::math::tools::remez_minimax<double> approx1(f, 6, 0, -1, 1, true, false);
  34    std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
  35    for(unsigned i = 0; i < 7; ++i)
  36    {
  37       approx1.iterate();
  38       std::cout << approx1.error_term() << " " << approx1.max_error() << " " << approx1.max_change() << std::endl;
  39    }
  40    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
  41    std::cout << "Testing expm1 approximation, pinned to origin, relative error, 6 term polynomial\n";
  42    boost::math::tools::remez_minimax<double> approx2(f, 6, 0, -1, 1, true, true);
  43    std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
  44    for(unsigned i = 0; i < 7; ++i)
  45    {
  46       approx2.iterate();
  47       std::cout << approx2.error_term() << " " << approx2.max_error() << " " << approx2.max_change() << std::endl;
  48    }
  49    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
  50
  51    f = std::exp;
  52    std::cout << "Testing exp approximation, not pinned to origin, absolute error, 6 term polynomial\n";
  53    boost::math::tools::remez_minimax<double> approx3(f, 6, 0, -1, 1, false, false);
  54    std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
  55    for(unsigned i = 0; i < 7; ++i)
  56    {
  57       approx3.iterate();
  58       std::cout << approx3.error_term() << " " << approx3.max_error() << " " << approx3.max_change() << std::endl;
  59    }
  60    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
  61    std::cout << "Testing exp approximation, not pinned to origin, relative error, 6 term polynomial\n";
  62    boost::math::tools::remez_minimax<double> approx4(f, 6, 0, -1, 1, false, true);
  63    std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
  64    for(unsigned i = 0; i < 7; ++i)
  65    {
  66       approx4.iterate();
  67       std::cout << approx4.error_term() << " " << approx4.max_error() << " " << approx4.max_change() << std::endl;
  68    }
  69    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
  70
  71    f = std::cos;
  72    std::cout << "Testing cos approximation, not pinned to origin, absolute error, 5 term polynomial\n";
  73    boost::math::tools::remez_minimax<double> approx5(f, 5, 0, -1, 1, false, false);
  74    std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
  75    for(unsigned i = 0; i < 7; ++i)
  76    {
  77       approx5.iterate();
  78       std::cout << approx5.error_term() << " " << approx5.max_error() << " " << approx5.max_change() << std::endl;
  79    }
  80    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
  81    std::cout << "Testing cos approximation, not pinned to origin, relative error, 5 term polynomial\n";
  82    boost::math::tools::remez_minimax<double> approx6(f, 5, 0, -1, 1, false, true);
  83    for(unsigned i = 0; i < 7; ++i)
  84    {
  85       approx6.iterate();
  86       std::cout << approx6.error_term() << " " << approx6.max_error() << " " << approx6.max_change() << std::endl;
  87    }
  88    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
  89
  90    f = std::sin;
  91    std::cout << "Testing sin approximation, pinned to origin, absolute error, 4 term polynomial\n";
  92    boost::math::tools::remez_minimax<double> approx7(f, 4, 0, 0, 1, true, false);
  93    for(unsigned i = 0; i < 7; ++i)
  94    {
  95       approx7.iterate();
  96       std::cout << approx7.error_term() << " " << approx7.max_error() << " " << approx7.max_change() << std::endl;
  97    }
  98    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
  99    std::cout << "Testing sin approximation, pinned to origin, relative error, 4 term polynomial\n";
 100    boost::math::tools::remez_minimax<double> approx8(f, 4, 0, 0, 1, true, true);
 101    for(unsigned i = 0; i < 7; ++i)
 102    {
 103       approx8.iterate();
 104       std::cout << approx8.error_term() << " " << approx8.max_error() << " " << approx8.max_change() << std::endl;
 105    }
 106    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
 107 }
 108
 109 void test_rational()
 110 {
 111 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
 112    double (*f)(double) = boost::math::expm1<double>;
 113 #else
 114    double (*f)(double) = boost::math::expm1;
 115 #endif
 116    std::cout << "Testing expm1 approximation, pinned to origin, absolute error, 3+3 term rational\n";
 117    boost::math::tools::remez_minimax<double> approx1(f, 3, 3, -1, 1, true, false);
 118    std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
 119    for(unsigned i = 0; i < 7; ++i)
 120    {
 121       approx1.iterate();
 122       std::cout << approx1.error_term() << " " << approx1.max_error() << " " << approx1.max_change() << std::endl;
 123    }
 124    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
 125 #if 0
 126    //
 127    // This one causes UBLAS to fail on some systems, so disabled for now.
 128    //
 129    std::cout << "Testing expm1 approximation, pinned to origin, relative error, 3+3 term rational\n";
 130    boost::math::tools::remez_minimax<double> approx2(f, 3, 3, -1, 1, true, true);
 131    std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
 132    for(unsigned i = 0; i < 7; ++i)
 133    {
 134       approx2.iterate();
 135       std::cout << approx2.error_term() << " " << approx2.max_error() << " " << approx2.max_change() << std::endl;
 136    }
 137    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
 138 #endif
 139    f = std::exp;
 140    std::cout << "Testing exp approximation, not pinned to origin, absolute error, 3+3 term rational\n";
 141    boost::math::tools::remez_minimax<double> approx3(f, 3, 3, -1, 1, false, false);
 142    std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
 143    for(unsigned i = 0; i < 7; ++i)
 144    {
 145       approx3.iterate();
 146       std::cout << approx3.error_term() << " " << approx3.max_error() << " " << approx3.max_change() << std::endl;
 147    }
 148    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
 149    std::cout << "Testing exp approximation, not pinned to origin, relative error, 3+3 term rational\n";
 150    boost::math::tools::remez_minimax<double> approx4(f, 3, 3, -1, 1, false, true);
 151    std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
 152    for(unsigned i = 0; i < 7; ++i)
 153    {
 154       approx4.iterate();
 155       std::cout << approx4.error_term() << " " << approx4.max_error() << " " << approx4.max_change() << std::endl;
 156    }
 157    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
 158
 159    f = std::cos;
 160    std::cout << "Testing cos approximation, not pinned to origin, absolute error, 2+2 term rational\n";
 161    boost::math::tools::remez_minimax<double> approx5(f, 2, 2, 0, 1, false, false);
 162    std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
 163    for(unsigned i = 0; i < 7; ++i)
 164    {
 165       approx5.iterate();
 166       std::cout << approx5.error_term() << " " << approx5.max_error() << " " << approx5.max_change() << std::endl;
 167    }
 168    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
 169    std::cout << "Testing cos approximation, not pinned to origin, relative error, 2+2 term rational\n";
 170    boost::math::tools::remez_minimax<double> approx6(f, 2, 2, 0, 1, false, true);
 171    std::cout << "Interpolation Error: " << approx1.max_error() << std::endl;
 172    for(unsigned i = 0; i < 7; ++i)
 173    {
 174       approx6.iterate();
 175       std::cout << approx6.error_term() << " " << approx6.max_error() << " " << approx6.max_change() << std::endl;
 176    }
 177    std::cout << "~~~~~~~~~~~~~~~~~~~~~~~~~" << std::endl;
 178 }
 179
 180 BOOST_AUTO_TEST_CASE( test_main )
 181 {
 182    test_polynomial();
 183    test_rational();
 184 }
 185
 186