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_I1_HPP
7 #define BOOST_MATH_BESSEL_I1_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 one
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_i1_initializer
39 void force_instantiate()const{}
41 static const init initializer;
42 static void force_instantiate()
44 initializer.force_instantiate();
49 const typename bessel_i1_initializer<T>::init bessel_i1_initializer<T>::initializer;
55 bessel_i1_initializer<T>::force_instantiate();
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)),
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)),
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)),
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)),
101 T value, factor, r, w;
104 using namespace boost::math::tools;
109 return static_cast<T>(0);
111 if (w <= 15) // w in (0, 15]
114 r = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
118 else // w in (15, \infty)
120 T y = 1 / w - T(1) / 15;
121 r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
122 factor = exp(w) / sqrt(w);
128 value *= -value; // odd function
135 #endif // BOOST_MATH_BESSEL_I1_HPP