Chris@16: //  Copyright (c) 2006 Xiaogang Zhang
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_MATH_BESSEL_K1_HPP
Chris@16: #define BOOST_MATH_BESSEL_K1_HPP
Chris@16: 
Chris@16: #ifdef _MSC_VER
Chris@16: #pragma once
Chris@16: #endif
Chris@16: 
Chris@16: #include <boost/math/tools/rational.hpp>
Chris@16: #include <boost/math/tools/big_constant.hpp>
Chris@16: #include <boost/math/policies/error_handling.hpp>
Chris@16: #include <boost/assert.hpp>
Chris@16: 
Chris@16: // Modified Bessel function of the second kind of order one
Chris@16: // minimax rational approximations on intervals, see
Chris@16: // Russon and Blair, Chalk River Report AECL-3461, 1969
Chris@16: 
Chris@16: namespace boost { namespace math { namespace detail{
Chris@16: 
Chris@16: template <typename T, typename Policy>
Chris@16: T bessel_k1(T x, const Policy&);
Chris@16: 
Chris@16: template <class T, class Policy>
Chris@16: struct bessel_k1_initializer
Chris@16: {
Chris@16:    struct init
Chris@16:    {
Chris@16:       init()
Chris@16:       {
Chris@16:          do_init();
Chris@16:       }
Chris@16:       static void do_init()
Chris@16:       {
Chris@16:          bessel_k1(T(1), Policy());
Chris@16:       }
Chris@16:       void force_instantiate()const{}
Chris@16:    };
Chris@16:    static const init initializer;
Chris@16:    static void force_instantiate()
Chris@16:    {
Chris@16:       initializer.force_instantiate();
Chris@16:    }
Chris@16: };
Chris@16: 
Chris@16: template <class T, class Policy>
Chris@16: const typename bessel_k1_initializer<T, Policy>::init bessel_k1_initializer<T, Policy>::initializer;
Chris@16: 
Chris@16: template <typename T, typename Policy>
Chris@16: T bessel_k1(T x, const Policy& pol)
Chris@16: {
Chris@16:     bessel_k1_initializer<T, Policy>::force_instantiate();
Chris@16: 
Chris@16:     static const T P1[] = {
Chris@16:         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1938920065420586101e+05)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7733324035147015630e+05)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1885382604084798576e+03)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.9991373567429309922e+01)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.8127070456878442310e-01))
Chris@16:     };
Chris@16:     static const T Q1[] = {
Chris@16:         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7264298672067697862e+04)),
Chris@16:         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.8143915754538725829e+02)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
Chris@16:     };
Chris@16:     static const T P2[] = {
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0)),
Chris@16:         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3531161492785421328e+06)),
Chris@16:         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4758069205414222471e+05)),
Chris@16:         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.5051623763436087023e+03)),
Chris@16:         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.3103913335180275253e+01)),
Chris@16:         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2795590826955002390e-01))
Chris@16:     };
Chris@16:     static const T Q2[] = {
Chris@16:         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.7062322985570842656e+06)),
Chris@16:         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.3117653211351080007e+04)),
Chris@16:         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.0507151578787595807e+02)),
Chris@16:         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
Chris@16:     };
Chris@16:     static const T P3[] = {
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2196792496874548962e+00)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4137176114230414036e+01)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4122953486801312910e+02)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3319486433183221990e+03)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.8590657697910288226e+03)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4540675585544584407e+03)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3123742209168871550e+03)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.1094256146537402173e+02)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3182609918569941308e+02)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.5584584631176030810e+00)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4257745859173138767e-02))
Chris@16:     };
Chris@16:     static const T Q3[] = {
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7710478032601086579e+00)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4552228452758912848e+01)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.5951223655579051357e+02)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.6929165726802648634e+02)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.9448440788918006154e+03)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1181000487171943810e+03)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2082692316002348638e+03)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3031020088765390854e+02)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6001069306861518855e+01)),
Chris@16:          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
Chris@16:     };
Chris@16:     T value, factor, r, r1, r2;
Chris@16: 
Chris@16:     BOOST_MATH_STD_USING
Chris@16:     using namespace boost::math::tools;
Chris@16: 
Chris@16:     static const char* function = "boost::math::bessel_k1<%1%>(%1%,%1%)";
Chris@16: 
Chris@16:     if (x < 0)
Chris@16:     {
Chris@16:        return policies::raise_domain_error<T>(function,
Chris@16:             "Got x = %1%, but argument x must be non-negative, complex number result not supported.", x, pol);
Chris@16:     }
Chris@16:     if (x == 0)
Chris@16:     {
Chris@16:        return policies::raise_overflow_error<T>(function, 0, pol);
Chris@16:     }
Chris@16:     if (x <= 1)                         // x in (0, 1]
Chris@16:     {
Chris@16:         T y = x * x;
Chris@16:         r1 = evaluate_polynomial(P1, y) /  evaluate_polynomial(Q1, y);
Chris@16:         r2 = evaluate_polynomial(P2, y) /  evaluate_polynomial(Q2, y);
Chris@16:         factor = log(x);
Chris@16:         value = (r1 + factor * r2) / x;
Chris@16:     }
Chris@16:     else                                // x in (1, \infty)
Chris@16:     {
Chris@16:         T y = 1 / x;
Chris@16:         r = evaluate_polynomial(P3, y) /  evaluate_polynomial(Q3, y);
Chris@16:         factor = exp(-x) / sqrt(x);
Chris@16:         value = factor * r;
Chris@16:     }
Chris@16: 
Chris@16:     return value;
Chris@16: }
Chris@16: 
Chris@16: }}} // namespaces
Chris@16: 
Chris@16: #endif // BOOST_MATH_BESSEL_K1_HPP
Chris@16: