boost/math/special_functions/detail/bessel_k0.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_K0_HPP
   7 #define BOOST_MATH_BESSEL_K0_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 zero
  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_k0(T x, const Policy&);
  26
  27 template <class T, class Policy>
  28 struct bessel_k0_initializer
  29 {
  30    struct init
  31    {
  32       init()
  33       {
  34          do_init();
  35       }
  36       static void do_init()
  37       {
  38          bessel_k0(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_k0_initializer<T, Policy>::init bessel_k0_initializer<T, Policy>::initializer;
  51
  52 template <typename T, typename Policy>
  53 T bessel_k0(T x, const Policy& pol)
  54 {
  55     BOOST_MATH_INSTRUMENT_CODE(x);
  56
  57     bessel_k0_initializer<T, Policy>::force_instantiate();
  58
  59     static const T P1[] = {
  60          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.4708152720399552679e+03)),
  61          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.9169059852270512312e+03)),
  62          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.6850901201934832188e+02)),
  63          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1999463724910714109e+01)),
  64          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3166052564989571850e-01)),
  65          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8599221412826100000e-04))
  66     };
  67     static const T Q1[] = {
  68          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1312714303849120380e+04)),
  69         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.4994418972832303646e+02)),
  70          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
  71     };
  72     static const T P2[] = {
  73         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6128136304458193998e+06)),
  74         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.7333769444840079748e+05)),
  75         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7984434409411765813e+04)),
  76         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9501657892958843865e+02)),
  77         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6414452837299064100e+00))
  78     };
  79     static const T Q2[] = {
  80         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6128136304458193998e+06)),
  81         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.9865713163054025489e+04)),
  82         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.5064972445877992730e+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, 1.1600249425076035558e+02)),
  87          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3444738764199315021e+03)),
  88          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8321525870183537725e+04)),
  89          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1557062783764037541e+04)),
  90          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5097646353289914539e+05)),
  91          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7398867902565686251e+05)),
  92          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0577068948034021957e+05)),
  93          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1075408980684392399e+04)),
  94          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6832589957340267940e+03)),
  95          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1394980557384778174e+02))
  96     };
  97     static const T Q3[] = {
  98          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.2556599177304839811e+01)),
  99          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8821890840982713696e+03)),
 100          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4847228371802360957e+04)),
 101          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.8824616785857027752e+04)),
 102          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2689839587977598727e+05)),
 103          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5144644673520157801e+05)),
 104          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.7418829762268075784e+04)),
 105          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1474655750295278825e+04)),
 106          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4329628889746408858e+03)),
 107          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.0013443064949242491e+02)),
 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_k0<%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;
 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         BOOST_MATH_INSTRUMENT_CODE("y = " << y);
 141         BOOST_MATH_INSTRUMENT_CODE("r = " << r);
 142         BOOST_MATH_INSTRUMENT_CODE("factor = " << factor);
 143         BOOST_MATH_INSTRUMENT_CODE("value = " << value);
 144     }
 145
 146     return value;
 147 }
 148
 149 }}} // namespaces
 150
 151 #endif // BOOST_MATH_BESSEL_K0_HPP
 152