// 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_I1_HPP | |
#define BOOST_MATH_BESSEL_I1_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 one | |
// 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_i1(T x) | |
{ | |
static const T P1[] = { | |
static_cast<T>(-1.4577180278143463643e+15L), | |
static_cast<T>(-1.7732037840791591320e+14L), | |
static_cast<T>(-6.9876779648010090070e+12L), | |
static_cast<T>(-1.3357437682275493024e+11L), | |
static_cast<T>(-1.4828267606612366099e+09L), | |
static_cast<T>(-1.0588550724769347106e+07L), | |
static_cast<T>(-5.1894091982308017540e+04L), | |
static_cast<T>(-1.8225946631657315931e+02L), | |
static_cast<T>(-4.7207090827310162436e-01L), | |
static_cast<T>(-9.1746443287817501309e-04L), | |
static_cast<T>(-1.3466829827635152875e-06L), | |
static_cast<T>(-1.4831904935994647675e-09L), | |
static_cast<T>(-1.1928788903603238754e-12L), | |
static_cast<T>(-6.5245515583151902910e-16L), | |
static_cast<T>(-1.9705291802535139930e-19L), | |
}; | |
static const T Q1[] = { | |
static_cast<T>(-2.9154360556286927285e+15L), | |
static_cast<T>(9.7887501377547640438e+12L), | |
static_cast<T>(-1.4386907088588283434e+10L), | |
static_cast<T>(1.1594225856856884006e+07L), | |
static_cast<T>(-5.1326864679904189920e+03L), | |
static_cast<T>(1.0L), | |
}; | |
static const T P2[] = { | |
static_cast<T>(1.4582087408985668208e-05L), | |
static_cast<T>(-8.9359825138577646443e-04L), | |
static_cast<T>(2.9204895411257790122e-02L), | |
static_cast<T>(-3.4198728018058047439e-01L), | |
static_cast<T>(1.3960118277609544334e+00L), | |
static_cast<T>(-1.9746376087200685843e+00L), | |
static_cast<T>(8.5591872901933459000e-01L), | |
static_cast<T>(-6.0437159056137599999e-02L), | |
}; | |
static const T Q2[] = { | |
static_cast<T>(3.7510433111922824643e-05L), | |
static_cast<T>(-2.2835624489492512649e-03L), | |
static_cast<T>(7.4212010813186530069e-02L), | |
static_cast<T>(-8.5017476463217924408e-01L), | |
static_cast<T>(3.2593714889036996297e+00L), | |
static_cast<T>(-3.8806586721556593450e+00L), | |
static_cast<T>(1.0L), | |
}; | |
T value, factor, r, w; | |
BOOST_MATH_STD_USING | |
using namespace boost::math::tools; | |
w = abs(x); | |
if (x == 0) | |
{ | |
return static_cast<T>(0); | |
} | |
if (w <= 15) // w in (0, 15] | |
{ | |
T y = x * x; | |
r = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y); | |
factor = w; | |
value = factor * r; | |
} | |
else // w in (15, \infty) | |
{ | |
T y = 1 / w - T(1) / 15; | |
r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y); | |
factor = exp(w) / sqrt(w); | |
value = factor * r; | |
} | |
if (x < 0) | |
{ | |
value *= -value; // odd function | |
} | |
return value; | |
} | |
}}} // namespaces | |
#endif // BOOST_MATH_BESSEL_I1_HPP | |