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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_I1_HPP
#define BOOST_MATH_BESSEL_I1_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 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>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4577180278143463643e+15)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7732037840791591320e+14)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.9876779648010090070e+12)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3357437682275493024e+11)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4828267606612366099e+09)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0588550724769347106e+07)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.1894091982308017540e+04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8225946631657315931e+02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.7207090827310162436e-01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.1746443287817501309e-04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3466829827635152875e-06)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4831904935994647675e-09)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1928788903603238754e-12)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.5245515583151902910e-16)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.9705291802535139930e-19)),
};
static const T Q1[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9154360556286927285e+15)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.7887501377547640438e+12)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4386907088588283434e+10)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1594225856856884006e+07)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.1326864679904189920e+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, 1.4582087408985668208e-05)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.9359825138577646443e-04)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.9204895411257790122e-02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.4198728018058047439e-01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3960118277609544334e+00)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.9746376087200685843e+00)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.5591872901933459000e-01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.0437159056137599999e-02)),
};
static const T Q2[] = {
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7510433111922824643e-05)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2835624489492512649e-03)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.4212010813186530069e-02)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.5017476463217924408e-01)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.2593714889036996297e+00)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.8806586721556593450e+00)),
static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
};
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
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