137 lines
4.2 KiB
Plaintext
137 lines
4.2 KiB
Plaintext
// Copyright (c) 2015 John Maddock
|
|
// 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_ELLINT_RG_HPP
|
|
#define BOOST_MATH_ELLINT_RG_HPP
|
|
|
|
#ifdef _MSC_VER
|
|
#pragma once
|
|
#endif
|
|
|
|
#include <boost/math/special_functions/math_fwd.hpp>
|
|
#include <boost/math/tools/config.hpp>
|
|
#include <boost/math/constants/constants.hpp>
|
|
#include <boost/math/policies/error_handling.hpp>
|
|
#include <boost/math/special_functions/ellint_rd.hpp>
|
|
#include <boost/math/special_functions/ellint_rf.hpp>
|
|
#include <boost/math/special_functions/pow.hpp>
|
|
|
|
namespace boost { namespace math { namespace detail{
|
|
|
|
template <typename T, typename Policy>
|
|
T ellint_rg_imp(T x, T y, T z, const Policy& pol)
|
|
{
|
|
BOOST_MATH_STD_USING
|
|
static const char* function = "boost::math::ellint_rf<%1%>(%1%,%1%,%1%)";
|
|
|
|
if(x < 0 || y < 0 || z < 0)
|
|
{
|
|
return policies::raise_domain_error<T>(function,
|
|
"domain error, all arguments must be non-negative, "
|
|
"only sensible result is %1%.",
|
|
std::numeric_limits<T>::quiet_NaN(), pol);
|
|
}
|
|
//
|
|
// Function is symmetric in x, y and z, but we require
|
|
// (x - z)(y - z) >= 0 to avoid cancellation error in the result
|
|
// which implies (for example) x >= z >= y
|
|
//
|
|
using std::swap;
|
|
if(x < y)
|
|
swap(x, y);
|
|
if(x < z)
|
|
swap(x, z);
|
|
if(y > z)
|
|
swap(y, z);
|
|
|
|
BOOST_ASSERT(x >= z);
|
|
BOOST_ASSERT(z >= y);
|
|
//
|
|
// Special cases from http://dlmf.nist.gov/19.20#ii
|
|
//
|
|
if(x == z)
|
|
{
|
|
if(y == z)
|
|
{
|
|
// x = y = z
|
|
// This also works for x = y = z = 0 presumably.
|
|
return sqrt(x);
|
|
}
|
|
else if(y == 0)
|
|
{
|
|
// x = y, z = 0
|
|
return constants::pi<T>() * sqrt(x) / 4;
|
|
}
|
|
else
|
|
{
|
|
// x = z, y != 0
|
|
swap(x, y);
|
|
return (x == 0) ? T(sqrt(z) / 2) : T((z * ellint_rc_imp(x, z, pol) + sqrt(x)) / 2);
|
|
}
|
|
}
|
|
else if(y == z)
|
|
{
|
|
if(x == 0)
|
|
return constants::pi<T>() * sqrt(y) / 4;
|
|
else
|
|
return (y == 0) ? T(sqrt(x) / 2) : T((y * ellint_rc_imp(x, y, pol) + sqrt(x)) / 2);
|
|
}
|
|
else if(y == 0)
|
|
{
|
|
swap(y, z);
|
|
//
|
|
// Special handling for common case, from
|
|
// Numerical Computation of Real or Complex Elliptic Integrals, eq.46
|
|
//
|
|
T xn = sqrt(x);
|
|
T yn = sqrt(y);
|
|
T x0 = xn;
|
|
T y0 = yn;
|
|
T sum = 0;
|
|
T sum_pow = 0.25f;
|
|
|
|
while(fabs(xn - yn) >= 2.7 * tools::root_epsilon<T>() * fabs(xn))
|
|
{
|
|
T t = sqrt(xn * yn);
|
|
xn = (xn + yn) / 2;
|
|
yn = t;
|
|
sum_pow *= 2;
|
|
sum += sum_pow * boost::math::pow<2>(xn - yn);
|
|
}
|
|
T RF = constants::pi<T>() / (xn + yn);
|
|
return ((boost::math::pow<2>((x0 + y0) / 2) - sum) * RF) / 2;
|
|
}
|
|
return (z * ellint_rf_imp(x, y, z, pol)
|
|
- (x - z) * (y - z) * ellint_rd_imp(x, y, z, pol) / 3
|
|
+ sqrt(x * y / z)) / 2;
|
|
}
|
|
|
|
} // namespace detail
|
|
|
|
template <class T1, class T2, class T3, class Policy>
|
|
inline typename tools::promote_args<T1, T2, T3>::type
|
|
ellint_rg(T1 x, T2 y, T3 z, const Policy& pol)
|
|
{
|
|
typedef typename tools::promote_args<T1, T2, T3>::type result_type;
|
|
typedef typename policies::evaluation<result_type, Policy>::type value_type;
|
|
return policies::checked_narrowing_cast<result_type, Policy>(
|
|
detail::ellint_rg_imp(
|
|
static_cast<value_type>(x),
|
|
static_cast<value_type>(y),
|
|
static_cast<value_type>(z), pol), "boost::math::ellint_rf<%1%>(%1%,%1%,%1%)");
|
|
}
|
|
|
|
template <class T1, class T2, class T3>
|
|
inline typename tools::promote_args<T1, T2, T3>::type
|
|
ellint_rg(T1 x, T2 y, T3 z)
|
|
{
|
|
return ellint_rg(x, y, z, policies::policy<>());
|
|
}
|
|
|
|
}} // namespaces
|
|
|
|
#endif // BOOST_MATH_ELLINT_RG_HPP
|
|
|