ceph/src/boost/libs/math/example/centered_continued_fraction.cpp

   1 //  (C) Copyright Nick Thompson 2020.
   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 // Deliberately contains some unicode characters:
   7 //
   8 // boost-no-inspect
   9 //
  10 #include <iostream>
  11 #include <boost/math/constants/constants.hpp>
  12 #include <boost/math/tools/centered_continued_fraction.hpp>
  13 #include <boost/multiprecision/mpfr.hpp>
  14
  15 using boost::math::constants::root_two;
  16 using boost::math::constants::phi;
  17 using boost::math::constants::pi;
  18 using boost::math::constants::e;
  19 using boost::math::constants::zeta_three;
  20 using boost::math::tools::centered_continued_fraction;
  21 using boost::multiprecision::mpfr_float;
  22
  23 int main()
  24 {
  25     using Real = mpfr_float;
  26     int p = 10000;
  27     mpfr_float::default_precision(p);
  28     auto phi_cfrac = centered_continued_fraction(phi<Real>());
  29     std::cout << "φ ≈ " << phi_cfrac << "\n";
  30     std::cout << "Khinchin mean: " << std::setprecision(10) << phi_cfrac.khinchin_geometric_mean() << "\n\n\n";
  31
  32     auto pi_cfrac = centered_continued_fraction(pi<Real>());
  33     std::cout << "π ≈ " << pi_cfrac << "\n";
  34     std::cout << "Khinchin mean: " << std::setprecision(10) << pi_cfrac.khinchin_geometric_mean() << "\n\n\n";
  35
  36     auto rt_cfrac = centered_continued_fraction(root_two<Real>());
  37     std::cout << "√2 ≈ " << rt_cfrac << "\n";
  38     std::cout << "Khinchin mean: " << std::setprecision(10) <<  rt_cfrac.khinchin_geometric_mean() << "\n\n\n";
  39
  40     auto e_cfrac = centered_continued_fraction(e<Real>());
  41     std::cout << "e ≈ " << e_cfrac << "\n";
  42     std::cout << "Khinchin mean: " << std::setprecision(10) <<  e_cfrac.khinchin_geometric_mean() << "\n\n\n";
  43
  44     auto z_cfrac = centered_continued_fraction(zeta_three<Real>());
  45     std::cout << "ζ(3) ≈ " << z_cfrac << "\n";
  46     std::cout << "Khinchin mean: " << std::setprecision(10) <<  z_cfrac.khinchin_geometric_mean() << "\n\n\n";
  47
  48
  49     // http://jeremiebourdon.free.fr/data/Khintchine.pdf
  50     std::cout << "The expected Khinchin mean for a random centered continued fraction is 5.45451724454\n";
  51 }