ceph/src/boost/libs/math/include/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 #pragma warning(push)
  12 #pragma warning(disable:4702) // Unreachable code (release mode only warning)
  13 #endif
  14
  15 #include <boost/math/tools/rational.hpp>
  16 #include <boost/math/tools/big_constant.hpp>
  17 #include <boost/math/policies/error_handling.hpp>
  18 #include <boost/assert.hpp>
  19
  20 // Modified Bessel function of the second kind of order one
  21 // minimax rational approximations on intervals, see
  22 // Russon and Blair, Chalk River Report AECL-3461, 1969
  23
  24 namespace boost { namespace math { namespace detail{
  25
  26 template <typename T, typename Policy>
  27 T bessel_k1(T x, const Policy&);
  28
  29 template <class T, class Policy>
  30 struct bessel_k1_initializer
  31 {
  32    struct init
  33    {
  34       init()
  35       {
  36          do_init();
  37       }
  38       static void do_init()
  39       {
  40          bessel_k1(T(1), Policy());
  41       }
  42       void force_instantiate()const{}
  43    };
  44    static const init initializer;
  45    static void force_instantiate()
  46    {
  47       initializer.force_instantiate();
  48    }
  49 };
  50
  51 template <class T, class Policy>
  52 const typename bessel_k1_initializer<T, Policy>::init bessel_k1_initializer<T, Policy>::initializer;
  53
  54 template <typename T, typename Policy>
  55 T bessel_k1(T x, const Policy& pol)
  56 {
  57     bessel_k1_initializer<T, Policy>::force_instantiate();
  58
  59     static const T P1[] = {
  60         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
  61          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1938920065420586101e+05)),
  62          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7733324035147015630e+05)),
  63          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.1885382604084798576e+03)),
  64          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.9991373567429309922e+01)),
  65          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.8127070456878442310e-01))
  66     };
  67     static const T Q1[] = {
  68         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2149374878243304548e+06)),
  69          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7264298672067697862e+04)),
  70         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.8143915754538725829e+02)),
  71          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
  72     };
  73     static const T P2[] = {
  74          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0)),
  75         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3531161492785421328e+06)),
  76         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4758069205414222471e+05)),
  77         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.5051623763436087023e+03)),
  78         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.3103913335180275253e+01)),
  79         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2795590826955002390e-01))
  80     };
  81     static const T Q2[] = {
  82         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.7062322985570842656e+06)),
  83         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.3117653211351080007e+04)),
  84         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.0507151578787595807e+02)),
  85         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
  86     };
  87     static const T P3[] = {
  88          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2196792496874548962e+00)),
  89          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4137176114230414036e+01)),
  90          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4122953486801312910e+02)),
  91          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3319486433183221990e+03)),
  92          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.8590657697910288226e+03)),
  93          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4540675585544584407e+03)),
  94          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3123742209168871550e+03)),
  95          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.1094256146537402173e+02)),
  96          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3182609918569941308e+02)),
  97          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.5584584631176030810e+00)),
  98          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4257745859173138767e-02))
  99     };
 100     static const T Q3[] = {
 101          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7710478032601086579e+00)),
 102          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4552228452758912848e+01)),
 103          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.5951223655579051357e+02)),
 104          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.6929165726802648634e+02)),
 105          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.9448440788918006154e+03)),
 106          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1181000487171943810e+03)),
 107          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.2082692316002348638e+03)),
 108          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3031020088765390854e+02)),
 109          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.6001069306861518855e+01)),
 110          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
 111     };
 112     T value, factor, r, r1, r2;
 113
 114     BOOST_MATH_STD_USING
 115     using namespace boost::math::tools;
 116
 117     static const char* function = "boost::math::bessel_k1<%1%>(%1%,%1%)";
 118
 119     if (x < 0)
 120     {
 121        return policies::raise_domain_error<T>(function,
 122             "Got x = %1%, but argument x must be non-negative, complex number result not supported.", x, pol);
 123     }
 124     if (x == 0)
 125     {
 126        return policies::raise_overflow_error<T>(function, 0, pol);
 127     }
 128     if (x <= 1)                         // x in (0, 1]
 129     {
 130         T y = x * x;
 131         r1 = evaluate_polynomial(P1, y) /  evaluate_polynomial(Q1, y);
 132         r2 = evaluate_polynomial(P2, y) /  evaluate_polynomial(Q2, y);
 133         factor = log(x);
 134         value = (r1 + factor * r2) / x;
 135     }
 136     else                                // x in (1, \infty)
 137     {
 138         T y = 1 / x;
 139         r = evaluate_polynomial(P3, y) /  evaluate_polynomial(Q3, y);
 140         factor = exp(-x) / sqrt(x);
 141         value = factor * r;
 142     }
 143
 144     return value;
 145 }
 146
 147 }}} // namespaces
 148
 149 #ifdef _MSC_VER
 150 #pragma warning(pop)
 151 #endif
 152
 153 #endif // BOOST_MATH_BESSEL_K1_HPP
 154