boost/math/special_functions/detail/bessel_i1.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_I1_HPP
   7 #define BOOST_MATH_BESSEL_I1_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/assert.hpp>
  16
  17 // Modified Bessel function of the first kind of order one
  18 // minimax rational approximations on intervals, see
  19 // Blair and Edwards, Chalk River Report AECL-4928, 1974
  20
  21 namespace boost { namespace math { namespace detail{
  22
  23 template <typename T>
  24 T bessel_i1(T x);
  25
  26 template <class T>
  27 struct bessel_i1_initializer
  28 {
  29    struct init
  30    {
  31       init()
  32       {
  33          do_init();
  34       }
  35       static void do_init()
  36       {
  37          bessel_i1(T(1));
  38       }
  39       void force_instantiate()const{}
  40    };
  41    static const init initializer;
  42    static void force_instantiate()
  43    {
  44       initializer.force_instantiate();
  45    }
  46 };
  47
  48 template <class T>
  49 const typename bessel_i1_initializer<T>::init bessel_i1_initializer<T>::initializer;
  50
  51 template <typename T>
  52 T bessel_i1(T x)
  53 {
  54
  55     bessel_i1_initializer<T>::force_instantiate();
  56
  57     static const T P1[] = {
  58         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4577180278143463643e+15)),
  59         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7732037840791591320e+14)),
  60         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.9876779648010090070e+12)),
  61         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3357437682275493024e+11)),
  62         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4828267606612366099e+09)),
  63         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0588550724769347106e+07)),
  64         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.1894091982308017540e+04)),
  65         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8225946631657315931e+02)),
  66         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.7207090827310162436e-01)),
  67         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.1746443287817501309e-04)),
  68         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3466829827635152875e-06)),
  69         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4831904935994647675e-09)),
  70         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1928788903603238754e-12)),
  71         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.5245515583151902910e-16)),
  72         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.9705291802535139930e-19)),
  73     };
  74     static const T Q1[] = {
  75         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9154360556286927285e+15)),
  76         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.7887501377547640438e+12)),
  77         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4386907088588283434e+10)),
  78         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1594225856856884006e+07)),
  79         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.1326864679904189920e+03)),
  80         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
  81     };
  82     static const T P2[] = {
  83         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4582087408985668208e-05)),
  84         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.9359825138577646443e-04)),
  85         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.9204895411257790122e-02)),
  86         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.4198728018058047439e-01)),
  87         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3960118277609544334e+00)),
  88         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.9746376087200685843e+00)),
  89         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.5591872901933459000e-01)),
  90         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.0437159056137599999e-02)),
  91     };
  92     static const T Q2[] = {
  93         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7510433111922824643e-05)),
  94         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2835624489492512649e-03)),
  95         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.4212010813186530069e-02)),
  96         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.5017476463217924408e-01)),
  97         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.2593714889036996297e+00)),
  98         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.8806586721556593450e+00)),
  99         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
 100     };
 101     T value, factor, r, w;
 102
 103     BOOST_MATH_STD_USING
 104     using namespace boost::math::tools;
 105
 106     w = abs(x);
 107     if (x == 0)
 108     {
 109         return static_cast<T>(0);
 110     }
 111     if (w <= 15)                        // w in (0, 15]
 112     {
 113         T y = x * x;
 114         r = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
 115         factor = w;
 116         value = factor * r;
 117     }
 118     else                                // w in (15, \infty)
 119     {
 120         T y = 1 / w - T(1) / 15;
 121         r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
 122         factor = exp(w) / sqrt(w);
 123         value = factor * r;
 124     }
 125
 126     if (x < 0)
 127     {
 128         value *= -value;                 // odd function
 129     }
 130     return value;
 131 }
 132
 133 }}} // namespaces
 134
 135 #endif // BOOST_MATH_BESSEL_I1_HPP
 136