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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_K1_HPP
#define BOOST_MATH_BESSEL_K1_HPP
#ifdef _MSC_VER
#pragma once
#pragma warning(push)
#pragma warning(disable:4702) // Unreachable code (release mode only warning)
#endif
#include <boost/math/tools/rational.hpp>
#include <boost/math/tools/big_constant.hpp>
#include <boost/math/policies/error_handling.hpp>
#include <boost/assert.hpp>
// Modified Bessel function of the second kind of order one
// minimax rational approximations on intervals, see
// Russon and Blair, Chalk River Report AECL-3461, 1969
namespace boost { namespace math { namespace detail{
template <typename T, typename Policy>
T bessel_k1(T x, const Policy&);
template <class T, class Policy>
struct bessel_k1_initializer
{
struct init
{
init()
{
do_init();
}
static void do_init()
{
bessel_k1(T(1), Policy());
}
void force_instantiate()const{}
};
static const init initializer;
static void force_instantiate()
{
initializer.force_instantiate();
}
};
template <class T, class Policy>
const typename bessel_k1_initializer<T, Policy>::init bessel_k1_initializer<T, Policy>::initializer;
template <typename T, typename Policy>
T bessel_k1(T x, const Policy& pol)
{
bessel_k1_initializer<T, Policy>::force_instantiate();
static const T P1[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1938920065420586101e+05)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7733324035147015630e+05)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1885382604084798576e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.9991373567429309922e+01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.8127070456878442310e-01))
};
static const T Q1[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7264298672067697862e+04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.8143915754538725829e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
};
static const T P2[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3531161492785421328e+06)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4758069205414222471e+05)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.5051623763436087023e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.3103913335180275253e+01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2795590826955002390e-01))
};
static const T Q2[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.7062322985570842656e+06)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.3117653211351080007e+04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.0507151578787595807e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
};
static const T P3[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2196792496874548962e+00)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4137176114230414036e+01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4122953486801312910e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3319486433183221990e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.8590657697910288226e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4540675585544584407e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3123742209168871550e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.1094256146537402173e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3182609918569941308e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.5584584631176030810e+00)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4257745859173138767e-02))
};
static const T Q3[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7710478032601086579e+00)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4552228452758912848e+01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.5951223655579051357e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.6929165726802648634e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.9448440788918006154e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1181000487171943810e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2082692316002348638e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3031020088765390854e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6001069306861518855e+01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
};
T value, factor, r, r1, r2;
BOOST_MATH_STD_USING
using namespace boost::math::tools;
static const char* function = "boost::math::bessel_k1<%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 (x <= 1) // x in (0, 1]
{
T y = x * x;
r1 = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
r2 = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
factor = log(x);
value = (r1 + factor * r2) / x;
}
else // x in (1, \infty)
{
T y = 1 / x;
r = evaluate_polynomial(P3, y) / evaluate_polynomial(Q3, y);
factor = exp(-x) / sqrt(x);
value = factor * r;
}
return value;
}
}}} // namespaces
#ifdef _MSC_VER
#pragma warning(pop)
#endif
#endif // BOOST_MATH_BESSEL_K1_HPP
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