47 lines
2.0 KiB
C++
47 lines
2.0 KiB
C++
// (C) Copyright Nick Thompson 2020.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#include <iostream>
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#include <boost/math/constants/constants.hpp>
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#include <boost/math/tools/centered_continued_fraction.hpp>
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#include <boost/multiprecision/mpfr.hpp>
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using boost::math::constants::root_two;
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using boost::math::constants::phi;
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using boost::math::constants::pi;
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using boost::math::constants::e;
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using boost::math::constants::zeta_three;
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using boost::math::tools::centered_continued_fraction;
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using boost::multiprecision::mpfr_float;
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int main()
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{
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using Real = mpfr_float;
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int p = 10000;
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mpfr_float::default_precision(p);
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auto phi_cfrac = centered_continued_fraction(phi<Real>());
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std::cout << "φ ≈ " << phi_cfrac << "\n";
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std::cout << "Khinchin mean: " << std::setprecision(10) << phi_cfrac.khinchin_geometric_mean() << "\n\n\n";
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auto pi_cfrac = centered_continued_fraction(pi<Real>());
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std::cout << "π ≈ " << pi_cfrac << "\n";
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std::cout << "Khinchin mean: " << std::setprecision(10) << pi_cfrac.khinchin_geometric_mean() << "\n\n\n";
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auto rt_cfrac = centered_continued_fraction(root_two<Real>());
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std::cout << "√2 ≈ " << rt_cfrac << "\n";
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std::cout << "Khinchin mean: " << std::setprecision(10) << rt_cfrac.khinchin_geometric_mean() << "\n\n\n";
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auto e_cfrac = centered_continued_fraction(e<Real>());
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std::cout << "e ≈ " << e_cfrac << "\n";
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std::cout << "Khinchin mean: " << std::setprecision(10) << e_cfrac.khinchin_geometric_mean() << "\n\n\n";
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auto z_cfrac = centered_continued_fraction(zeta_three<Real>());
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std::cout << "ζ(3) ≈ " << z_cfrac << "\n";
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std::cout << "Khinchin mean: " << std::setprecision(10) << z_cfrac.khinchin_geometric_mean() << "\n\n\n";
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// http://jeremiebourdon.free.fr/data/Khintchine.pdf
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std::cout << "The expected Khinchin mean for a random centered continued fraction is 5.45451724454\n";
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}
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