// 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 | |