134 lines
5.1 KiB
Plaintext
134 lines
5.1 KiB
Plaintext
// Copyright (c) 2006 Xiaogang Zhang
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_BESSEL_I1_HPP
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#define BOOST_MATH_BESSEL_I1_HPP
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#ifdef _MSC_VER
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#pragma once
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#endif
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#include <boost/math/tools/rational.hpp>
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#include <boost/math/tools/big_constant.hpp>
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#include <boost/assert.hpp>
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// Modified Bessel function of the first kind of order one
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// minimax rational approximations on intervals, see
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// Blair and Edwards, Chalk River Report AECL-4928, 1974
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namespace boost { namespace math { namespace detail{
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template <typename T>
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T bessel_i1(T x);
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template <class T>
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struct bessel_i1_initializer
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{
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struct init
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{
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init()
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{
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do_init();
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}
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static void do_init()
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{
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bessel_i1(T(1));
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}
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void force_instantiate()const{}
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};
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static const init initializer;
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static void force_instantiate()
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{
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initializer.force_instantiate();
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}
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};
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template <class T>
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const typename bessel_i1_initializer<T>::init bessel_i1_initializer<T>::initializer;
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template <typename T>
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T bessel_i1(T x)
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{
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bessel_i1_initializer<T>::force_instantiate();
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static const T P1[] = {
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4577180278143463643e+15)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7732037840791591320e+14)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.9876779648010090070e+12)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3357437682275493024e+11)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4828267606612366099e+09)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0588550724769347106e+07)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.1894091982308017540e+04)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8225946631657315931e+02)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.7207090827310162436e-01)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.1746443287817501309e-04)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3466829827635152875e-06)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4831904935994647675e-09)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1928788903603238754e-12)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.5245515583151902910e-16)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.9705291802535139930e-19)),
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};
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static const T Q1[] = {
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9154360556286927285e+15)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.7887501377547640438e+12)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4386907088588283434e+10)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1594225856856884006e+07)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.1326864679904189920e+03)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
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};
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static const T P2[] = {
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4582087408985668208e-05)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.9359825138577646443e-04)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.9204895411257790122e-02)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.4198728018058047439e-01)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3960118277609544334e+00)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.9746376087200685843e+00)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.5591872901933459000e-01)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.0437159056137599999e-02)),
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};
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static const T Q2[] = {
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7510433111922824643e-05)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2835624489492512649e-03)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.4212010813186530069e-02)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.5017476463217924408e-01)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.2593714889036996297e+00)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.8806586721556593450e+00)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
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};
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T value, factor, r, w;
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BOOST_MATH_STD_USING
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using namespace boost::math::tools;
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BOOST_ASSERT(x >= 0); // negative x is handled before we get here
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w = abs(x);
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if (x == 0)
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{
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return static_cast<T>(0);
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}
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if (w <= 15) // w in (0, 15]
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{
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T y = x * x;
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r = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
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factor = w;
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value = factor * r;
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}
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else // w in (15, \infty)
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{
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T y = 1 / w - T(1) / 15;
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r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
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factor = exp(w) / sqrt(w);
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value = factor * r;
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}
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return value;
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}
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}}} // namespaces
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#endif // BOOST_MATH_BESSEL_I1_HPP
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