// 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_K0_HPP | |
#define BOOST_MATH_BESSEL_K0_HPP | |
#ifdef _MSC_VER | |
#pragma once | |
#endif | |
#include <boost/math/tools/rational.hpp> | |
#include <boost/math/policies/error_handling.hpp> | |
#include <boost/assert.hpp> | |
// Modified Bessel function of the second kind of order zero | |
// 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_k0(T x, const Policy& pol) | |
{ | |
BOOST_MATH_INSTRUMENT_CODE(x); | |
static const T P1[] = { | |
static_cast<T>(2.4708152720399552679e+03L), | |
static_cast<T>(5.9169059852270512312e+03L), | |
static_cast<T>(4.6850901201934832188e+02L), | |
static_cast<T>(1.1999463724910714109e+01L), | |
static_cast<T>(1.3166052564989571850e-01L), | |
static_cast<T>(5.8599221412826100000e-04L) | |
}; | |
static const T Q1[] = { | |
static_cast<T>(2.1312714303849120380e+04L), | |
static_cast<T>(-2.4994418972832303646e+02L), | |
static_cast<T>(1.0L) | |
}; | |
static const T P2[] = { | |
static_cast<T>(-1.6128136304458193998e+06L), | |
static_cast<T>(-3.7333769444840079748e+05L), | |
static_cast<T>(-1.7984434409411765813e+04L), | |
static_cast<T>(-2.9501657892958843865e+02L), | |
static_cast<T>(-1.6414452837299064100e+00L) | |
}; | |
static const T Q2[] = { | |
static_cast<T>(-1.6128136304458193998e+06L), | |
static_cast<T>(2.9865713163054025489e+04L), | |
static_cast<T>(-2.5064972445877992730e+02L), | |
static_cast<T>(1.0L) | |
}; | |
static const T P3[] = { | |
static_cast<T>(1.1600249425076035558e+02L), | |
static_cast<T>(2.3444738764199315021e+03L), | |
static_cast<T>(1.8321525870183537725e+04L), | |
static_cast<T>(7.1557062783764037541e+04L), | |
static_cast<T>(1.5097646353289914539e+05L), | |
static_cast<T>(1.7398867902565686251e+05L), | |
static_cast<T>(1.0577068948034021957e+05L), | |
static_cast<T>(3.1075408980684392399e+04L), | |
static_cast<T>(3.6832589957340267940e+03L), | |
static_cast<T>(1.1394980557384778174e+02L) | |
}; | |
static const T Q3[] = { | |
static_cast<T>(9.2556599177304839811e+01L), | |
static_cast<T>(1.8821890840982713696e+03L), | |
static_cast<T>(1.4847228371802360957e+04L), | |
static_cast<T>(5.8824616785857027752e+04L), | |
static_cast<T>(1.2689839587977598727e+05L), | |
static_cast<T>(1.5144644673520157801e+05L), | |
static_cast<T>(9.7418829762268075784e+04L), | |
static_cast<T>(3.1474655750295278825e+04L), | |
static_cast<T>(4.4329628889746408858e+03L), | |
static_cast<T>(2.0013443064949242491e+02L), | |
static_cast<T>(1.0L) | |
}; | |
T value, factor, r, r1, r2; | |
BOOST_MATH_STD_USING | |
using namespace boost::math::tools; | |
static const char* function = "boost::math::bessel_k0<%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; | |
} | |
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; | |
BOOST_MATH_INSTRUMENT_CODE("y = " << y); | |
BOOST_MATH_INSTRUMENT_CODE("r = " << r); | |
BOOST_MATH_INSTRUMENT_CODE("factor = " << factor); | |
BOOST_MATH_INSTRUMENT_CODE("value = " << value); | |
} | |
return value; | |
} | |
}}} // namespaces | |
#endif // BOOST_MATH_BESSEL_K0_HPP | |