boost/math/special_functions/detail/bessel_k1.hpp

   1 //  Copyright (c) 2006 Xiaogang Zhang
   2 //  Use, modification and distribution are subject to the
   3 //  Boost Software License, Version 1.0. (See accompanying file
   4 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   5
   6 #ifndef BOOST_MATH_BESSEL_K1_HPP
   7 #define BOOST_MATH_BESSEL_K1_HPP
   8
   9 #ifdef _MSC_VER
  10 #pragma once
  11 #endif
  12
  13 #include <boost/math/tools/rational.hpp>
  14 #include <boost/math/tools/big_constant.hpp>
  15 #include <boost/math/policies/error_handling.hpp>
  16 #include <boost/assert.hpp>
  17
  18 // Modified Bessel function of the second kind of order one
  19 // minimax rational approximations on intervals, see
  20 // Russon and Blair, Chalk River Report AECL-3461, 1969
  21
  22 namespace boost { namespace math { namespace detail{
  23
  24 template <typename T, typename Policy>
  25 T bessel_k1(T x, const Policy&);
  26
  27 template <class T, class Policy>
  28 struct bessel_k1_initializer
  29 {
  30    struct init
  31    {
  32       init()
  33       {
  34          do_init();
  35       }
  36       static void do_init()
  37       {
  38          bessel_k1(T(1), Policy());
  39       }
  40       void force_instantiate()const{}
  41    };
  42    static const init initializer;
  43    static void force_instantiate()
  44    {
  45       initializer.force_instantiate();
  46    }
  47 };
  48
  49 template <class T, class Policy>
  50 const typename bessel_k1_initializer<T, Policy>::init bessel_k1_initializer<T, Policy>::initializer;
  51
  52 template <typename T, typename Policy>
  53 T bessel_k1(T x, const Policy& pol)
  54 {
  55     bessel_k1_initializer<T, Policy>::force_instantiate();
  56
  57     static const T P1[] = {
  58         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
  59          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1938920065420586101e+05)),
  60          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7733324035147015630e+05)),
  61          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1885382604084798576e+03)),
  62          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.9991373567429309922e+01)),
  63          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.8127070456878442310e-01))
  64     };
  65     static const T Q1[] = {
  66         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
  67          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7264298672067697862e+04)),
  68         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.8143915754538725829e+02)),
  69          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
  70     };
  71     static const T P2[] = {
  72          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0)),
  73         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3531161492785421328e+06)),
  74         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4758069205414222471e+05)),
  75         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.5051623763436087023e+03)),
  76         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.3103913335180275253e+01)),
  77         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2795590826955002390e-01))
  78     };
  79     static const T Q2[] = {
  80         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.7062322985570842656e+06)),
  81         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.3117653211351080007e+04)),
  82         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.0507151578787595807e+02)),
  83         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
  84     };
  85     static const T P3[] = {
  86          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2196792496874548962e+00)),
  87          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4137176114230414036e+01)),
  88          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4122953486801312910e+02)),
  89          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3319486433183221990e+03)),
  90          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.8590657697910288226e+03)),
  91          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4540675585544584407e+03)),
  92          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3123742209168871550e+03)),
  93          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.1094256146537402173e+02)),
  94          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3182609918569941308e+02)),
  95          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.5584584631176030810e+00)),
  96          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4257745859173138767e-02))
  97     };
  98     static const T Q3[] = {
  99          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7710478032601086579e+00)),
 100          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4552228452758912848e+01)),
 101          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.5951223655579051357e+02)),
 102          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.6929165726802648634e+02)),
 103          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.9448440788918006154e+03)),
 104          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1181000487171943810e+03)),
 105          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2082692316002348638e+03)),
 106          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3031020088765390854e+02)),
 107          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6001069306861518855e+01)),
 108          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
 109     };
 110     T value, factor, r, r1, r2;
 111
 112     BOOST_MATH_STD_USING
 113     using namespace boost::math::tools;
 114
 115     static const char* function = "boost::math::bessel_k1<%1%>(%1%,%1%)";
 116
 117     if (x < 0)
 118     {
 119        return policies::raise_domain_error<T>(function,
 120             "Got x = %1%, but argument x must be non-negative, complex number result not supported.", x, pol);
 121     }
 122     if (x == 0)
 123     {
 124        return policies::raise_overflow_error<T>(function, 0, pol);
 125     }
 126     if (x <= 1)                         // x in (0, 1]
 127     {
 128         T y = x * x;
 129         r1 = evaluate_polynomial(P1, y) /  evaluate_polynomial(Q1, y);
 130         r2 = evaluate_polynomial(P2, y) /  evaluate_polynomial(Q2, y);
 131         factor = log(x);
 132         value = (r1 + factor * r2) / x;
 133     }
 134     else                                // x in (1, \infty)
 135     {
 136         T y = 1 / x;
 137         r = evaluate_polynomial(P3, y) /  evaluate_polynomial(Q3, y);
 138         factor = exp(-x) / sqrt(x);
 139         value = factor * r;
 140     }
 141
 142     return value;
 143 }
 144
 145 }}} // namespaces
 146
 147 #endif // BOOST_MATH_BESSEL_K1_HPP
 148