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// (C) Copyright Nick Thompson 2020.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#include <cmath>
#include <iostream>
#include <iomanip>
#include <boost/math/tools/agm.hpp>
#include <boost/math/constants/constants.hpp>
#ifndef BOOST_MATH_STANDALONE
#include <boost/multiprecision/cpp_bin_float.hpp>
#endif
// This example computes the lemniscate constant to high precision using the agm:
using boost::math::tools::agm;
using boost::math::constants::pi;
int main() {
using std::sqrt;
#ifndef BOOST_MATH_STANDALONE
using Real = boost::multiprecision::cpp_bin_float_100;
#else
using Real = long double;
#endif
Real G = agm(sqrt(Real(2)), Real(1));
std::cout << std::setprecision(std::numeric_limits<Real>::max_digits10);
std::cout << " Gauss's lemniscate constant = " << pi<Real>()/G << "\n";
std::cout << "Expected lemniscate constant = " << "2.62205755429211981046483958989111941368275495143162316281682170380079058707041425023029553296142909344613\n";
}
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