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// Copyright (c) 2006 Xiaogang Zhang
// 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_BESSEL_KN_HPP
#define BOOST_MATH_BESSEL_KN_HPP
#ifdef _MSC_VER
#pragma once
#endif
#include <boost/math/special_functions/detail/bessel_k0.hpp>
#include <boost/math/special_functions/detail/bessel_k1.hpp>
#include <boost/math/policies/error_handling.hpp>
// Modified Bessel function of the second kind of integer order
// K_n(z) is the dominant solution, forward recurrence always OK (though unstable)
namespace boost { namespace math { namespace detail{
template <typename T, typename Policy>
T bessel_kn(int n, T x, const Policy& pol)
{
BOOST_MATH_STD_USING
T value, current, prev;
using namespace boost::math::tools;
static const char* function = "boost::math::bessel_kn<%1%>(%1%,%1%)";
if (x < 0)
{
return policies::raise_domain_error<T>(function,
"Got x = %1%, but argument x must be non-negative, complex number result not supported.", x, pol);
}
if (x == 0)
{
return policies::raise_overflow_error<T>(function, 0, pol);
}
if (n < 0)
{
n = -n; // K_{-n}(z) = K_n(z)
}
if (n == 0)
{
value = bessel_k0(x, pol);
}
else if (n == 1)
{
value = bessel_k1(x, pol);
}
else
{
prev = bessel_k0(x, pol);
current = bessel_k1(x, pol);
int k = 1;
BOOST_ASSERT(k < n);
T scale = 1;
do
{
T fact = 2 * k / x;
if((tools::max_value<T>() - fabs(prev)) / fact < fabs(current))
{
scale /= current;
prev /= current;
current = 1;
}
value = fact * current + prev;
prev = current;
current = value;
++k;
}
while(k < n);
if(tools::max_value<T>() * scale < fabs(value))
return sign(scale) * sign(value) * policies::raise_overflow_error<T>(function, 0, pol);
value /= scale;
}
return value;
}
}}} // namespaces
#endif // BOOST_MATH_BESSEL_KN_HPP
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