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)
6 #ifndef BOOST_MATH_BESSEL_I0_HPP
7 #define BOOST_MATH_BESSEL_I0_HPP
13 #include <boost/math/tools/rational.hpp>
14 #include <boost/math/tools/big_constant.hpp>
15 #include <boost/assert.hpp>
17 // Modified Bessel function of the first kind of order zero
18 // minimax rational approximations on intervals, see
19 // Blair and Edwards, Chalk River Report AECL-4928, 1974
21 namespace boost { namespace math { namespace detail{
27 struct bessel_i0_initializer
39 void force_instantiate()const{}
41 static const init initializer;
42 static void force_instantiate()
44 initializer.force_instantiate();
49 const typename bessel_i0_initializer<T>::init bessel_i0_initializer<T>::initializer;
54 bessel_i0_initializer<T>::force_instantiate();
56 static const T P1[] = {
57 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2335582639474375249e+15)),
58 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.5050369673018427753e+14)),
59 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.2940087627407749166e+13)),
60 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.4925101247114157499e+11)),
61 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1912746104985237192e+10)),
62 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0313066708737980747e+08)),
63 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.9545626019847898221e+05)),
64 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.4125195876041896775e+03)),
65 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -7.0935347449210549190e+00)),
66 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5453977791786851041e-02)),
67 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.5172644670688975051e-05)),
68 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.0517226450451067446e-08)),
69 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.6843448573468483278e-11)),
70 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5982226675653184646e-14)),
71 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.2487866627945699800e-18)),
73 static const T Q1[] = {
74 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2335582639474375245e+15)),
75 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.8858692566751002988e+12)),
76 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.2207067397808979846e+10)),
77 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0377081058062166144e+07)),
78 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.8527560179962773045e+03)),
79 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
81 static const T P2[] = {
82 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2210262233306573296e-04)),
83 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3067392038106924055e-02)),
84 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4700805721174453923e-01)),
85 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.5674518371240761397e+00)),
86 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.3517945679239481621e+01)),
87 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1611322818701131207e+01)),
88 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.6090021968656180000e+00)),
90 static const T Q2[] = {
91 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.5194330231005480228e-04)),
92 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.2547697594819615062e-02)),
93 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1151759188741312645e+00)),
94 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3982595353892851542e+01)),
95 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.0228002066743340583e+01)),
96 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.5539563258012929600e+01)),
97 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.1446690275135491500e+01)),
98 static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
103 using namespace boost::math::tools;
107 x = -x; // even function
111 return static_cast<T>(1);
113 if (x <= 15) // x in (0, 15]
116 value = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
118 else // x in (15, \infty)
120 T y = 1 / x - T(1) / 15;
121 r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
122 factor = exp(x) / sqrt(x);
131 #endif // BOOST_MATH_BESSEL_I0_HPP