| // Copyright (c) 2006 Xiaogang Zhang |
| // Use, modification and distribution are subject to the |
| // Boost Software License, Version 1.0. (See accompanying file |
| // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) |
| |
| #ifndef BOOST_MATH_BESSEL_I0_HPP |
| #define BOOST_MATH_BESSEL_I0_HPP |
| |
| #ifdef _MSC_VER |
| #pragma once |
| #endif |
| |
| #include <boost/math/tools/rational.hpp> |
| #include <boost/assert.hpp> |
| |
| // Modified Bessel function of the first kind of order zero |
| // minimax rational approximations on intervals, see |
| // Blair and Edwards, Chalk River Report AECL-4928, 1974 |
| |
| namespace boost { namespace math { namespace detail{ |
| |
| template <typename T> |
| T bessel_i0(T x) |
| { |
| static const T P1[] = { |
| static_cast<T>(-2.2335582639474375249e+15L), |
| static_cast<T>(-5.5050369673018427753e+14L), |
| static_cast<T>(-3.2940087627407749166e+13L), |
| static_cast<T>(-8.4925101247114157499e+11L), |
| static_cast<T>(-1.1912746104985237192e+10L), |
| static_cast<T>(-1.0313066708737980747e+08L), |
| static_cast<T>(-5.9545626019847898221e+05L), |
| static_cast<T>(-2.4125195876041896775e+03L), |
| static_cast<T>(-7.0935347449210549190e+00L), |
| static_cast<T>(-1.5453977791786851041e-02L), |
| static_cast<T>(-2.5172644670688975051e-05L), |
| static_cast<T>(-3.0517226450451067446e-08L), |
| static_cast<T>(-2.6843448573468483278e-11L), |
| static_cast<T>(-1.5982226675653184646e-14L), |
| static_cast<T>(-5.2487866627945699800e-18L), |
| }; |
| static const T Q1[] = { |
| static_cast<T>(-2.2335582639474375245e+15L), |
| static_cast<T>(7.8858692566751002988e+12L), |
| static_cast<T>(-1.2207067397808979846e+10L), |
| static_cast<T>(1.0377081058062166144e+07L), |
| static_cast<T>(-4.8527560179962773045e+03L), |
| static_cast<T>(1.0L), |
| }; |
| static const T P2[] = { |
| static_cast<T>(-2.2210262233306573296e-04L), |
| static_cast<T>(1.3067392038106924055e-02L), |
| static_cast<T>(-4.4700805721174453923e-01L), |
| static_cast<T>(5.5674518371240761397e+00L), |
| static_cast<T>(-2.3517945679239481621e+01L), |
| static_cast<T>(3.1611322818701131207e+01L), |
| static_cast<T>(-9.6090021968656180000e+00L), |
| }; |
| static const T Q2[] = { |
| static_cast<T>(-5.5194330231005480228e-04L), |
| static_cast<T>(3.2547697594819615062e-02L), |
| static_cast<T>(-1.1151759188741312645e+00L), |
| static_cast<T>(1.3982595353892851542e+01L), |
| static_cast<T>(-6.0228002066743340583e+01L), |
| static_cast<T>(8.5539563258012929600e+01L), |
| static_cast<T>(-3.1446690275135491500e+01L), |
| static_cast<T>(1.0L), |
| }; |
| T value, factor, r; |
| |
| BOOST_MATH_STD_USING |
| using namespace boost::math::tools; |
| |
| if (x < 0) |
| { |
| x = -x; // even function |
| } |
| if (x == 0) |
| { |
| return static_cast<T>(1); |
| } |
| if (x <= 15) // x in (0, 15] |
| { |
| T y = x * x; |
| value = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y); |
| } |
| else // x in (15, \infty) |
| { |
| T y = 1 / x - T(1) / 15; |
| r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y); |
| factor = exp(x) / sqrt(x); |
| value = factor * r; |
| } |
| |
| return value; |
| } |
| |
| }}} // namespaces |
| |
| #endif // BOOST_MATH_BESSEL_I0_HPP |
| |