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// 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/math/tools/big_constant.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);
template <class T>
struct bessel_i0_initializer
{
struct init
{
init()
{
do_init();
}
static void do_init()
{
bessel_i0(T(1));
}
void force_instantiate()const{}
};
static const init initializer;
static void force_instantiate()
{
initializer.force_instantiate();
}
};
template <class T>
const typename bessel_i0_initializer<T>::init bessel_i0_initializer<T>::initializer;
template <typename T>
T bessel_i0(T x)
{
bessel_i0_initializer<T>::force_instantiate();
static const T P1[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2335582639474375249e+15)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.5050369673018427753e+14)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.2940087627407749166e+13)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.4925101247114157499e+11)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1912746104985237192e+10)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0313066708737980747e+08)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.9545626019847898221e+05)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.4125195876041896775e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -7.0935347449210549190e+00)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5453977791786851041e-02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.5172644670688975051e-05)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.0517226450451067446e-08)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.6843448573468483278e-11)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5982226675653184646e-14)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.2487866627945699800e-18)),
};
static const T Q1[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2335582639474375245e+15)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.8858692566751002988e+12)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.2207067397808979846e+10)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0377081058062166144e+07)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.8527560179962773045e+03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
};
static const T P2[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2210262233306573296e-04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3067392038106924055e-02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4700805721174453923e-01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.5674518371240761397e+00)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.3517945679239481621e+01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1611322818701131207e+01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.6090021968656180000e+00)),
};
static const T Q2[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.5194330231005480228e-04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.2547697594819615062e-02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1151759188741312645e+00)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3982595353892851542e+01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.0228002066743340583e+01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.5539563258012929600e+01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.1446690275135491500e+01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
};
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
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