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