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Diffstat (limited to 'src/third_party/boost-1.60.0/boost/math/special_functions/detail/bessel_i1.hpp')
-rw-r--r-- | src/third_party/boost-1.60.0/boost/math/special_functions/detail/bessel_i1.hpp | 133 |
1 files changed, 133 insertions, 0 deletions
diff --git a/src/third_party/boost-1.60.0/boost/math/special_functions/detail/bessel_i1.hpp b/src/third_party/boost-1.60.0/boost/math/special_functions/detail/bessel_i1.hpp new file mode 100644 index 00000000000..b85bc675463 --- /dev/null +++ b/src/third_party/boost-1.60.0/boost/math/special_functions/detail/bessel_i1.hpp @@ -0,0 +1,133 @@ +// 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); + +template <class T> +struct bessel_i1_initializer +{ + struct init + { + init() + { + do_init(); + } + static void do_init() + { + bessel_i1(T(1)); + } + void force_instantiate()const{} + }; + static const init initializer; + static void force_instantiate() + { + initializer.force_instantiate(); + } +}; + +template <class T> +const typename bessel_i1_initializer<T>::init bessel_i1_initializer<T>::initializer; + +template <typename T> +T bessel_i1(T x) +{ + + bessel_i1_initializer<T>::force_instantiate(); + + 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; + + BOOST_ASSERT(x >= 0); // negative x is handled before we get here + 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; + } + + return value; +} + +}}} // namespaces + +#endif // BOOST_MATH_BESSEL_I1_HPP + |