agm.hpp
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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)
#ifndef BOOST_MATH_TOOLS_AGM_HPP
#define BOOST_MATH_TOOLS_AGM_HPP
#include <limits>
#include <cmath>
namespace boost { namespace math { namespace tools {
template<typename Real>
Real agm(Real a, Real g)
{
using std::sqrt;
if (a < g)
{
// Mathematica, mpfr, and mpmath are all symmetric functions:
return agm(g, a);
}
// Use: M(rx, ry) = rM(x,y)
if (a <= 0 || g <= 0) {
if (a < 0 || g < 0) {
return std::numeric_limits<Real>::quiet_NaN();
}
return Real(0);
}
// The number of correct digits doubles on each iteration.
// Divide by 512 for some leeway:
const Real scale = sqrt(std::numeric_limits<Real>::epsilon())/512;
while (a-g > scale*g)
{
Real anp1 = (a + g)/2;
g = sqrt(a*g);
a = anp1;
}
// Final cleanup iteration recovers down to ~2ULPs:
return (a + g)/2;
}
}}}
#endif