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Diffstat (limited to 'boost/math/special_functions/detail/bessel_j0.hpp')
| -rw-r--r-- | boost/math/special_functions/detail/bessel_j0.hpp | 153 |
1 files changed, 153 insertions, 0 deletions
diff --git a/boost/math/special_functions/detail/bessel_j0.hpp b/boost/math/special_functions/detail/bessel_j0.hpp new file mode 100644 index 0000000000..ee25d46f61 --- /dev/null +++ b/boost/math/special_functions/detail/bessel_j0.hpp @@ -0,0 +1,153 @@ +// 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_J0_HPP +#define BOOST_MATH_BESSEL_J0_HPP + +#ifdef _MSC_VER +#pragma once +#endif + +#include <boost/math/constants/constants.hpp> +#include <boost/math/tools/rational.hpp> +#include <boost/math/tools/big_constant.hpp> +#include <boost/assert.hpp> + +// Bessel function of the first kind of order zero +// x <= 8, minimax rational approximations on root-bracketing intervals +// x > 8, Hankel asymptotic expansion in Hart, Computer Approximations, 1968 + +namespace boost { namespace math { namespace detail{ + +template <typename T> +T bessel_j0(T x) +{ + static const T P1[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.1298668500990866786e+11)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.7282507878605942706e+10)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.2140700423540120665e+08)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.6302997904833794242e+06)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.6629814655107086448e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0344222815443188943e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.2117036164593528341e-01)) + }; + static const T Q1[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3883787996332290397e+12)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.6328198300859648632e+10)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3985097372263433271e+08)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.5612696224219938200e+05)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.3614022392337710626e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0)) + }; + static const T P2[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8319397969392084011e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.2254078161378989535e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -7.2879702464464618998e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0341910641583726701e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1725046279757103576e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4176707025325087628e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.4321196680624245801e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.8591703355916499363e+01)) + }; + static const T Q2[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.5783478026152301072e+05)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.4599102262586308984e+05)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.4055062591169562211e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8680990008359188352e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9458766545509337327e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3307310774649071172e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.5258076240801555057e+01)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) + }; + static const T PC[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2779090197304684302e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.1345386639580765797e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1170523380864944322e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4806486443249270347e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5376201909008354296e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.8961548424210455236e-01)) + }; + static const T QC[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2779090197304684318e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.1370412495510416640e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1215350561880115730e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.5028735138235608207e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5711159858080893649e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) + }; + static const T PS[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.9226600200800094098e+01)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8591953644342993800e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1183429920482737611e+02)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2300261666214198472e+01)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.2441026745835638459e+00)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.8033303048680751817e-03)) + }; + static const T QS[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.7105024128512061905e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1951131543434613647e+04)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.2642780169211018836e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4887231232283756582e+03)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.0593769594993125859e+01)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) + }; + static const T x1 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.4048255576957727686e+00)), + x2 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.5200781102863106496e+00)), + x11 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.160e+02)), + x12 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.42444230422723137837e-03)), + x21 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4130e+03)), + x22 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.46860286310649596604e-04)); + + T value, factor, r, rc, rs; + + BOOST_MATH_STD_USING + using namespace boost::math::tools; + using namespace boost::math::constants; + + if (x < 0) + { + x = -x; // even function + } + if (x == 0) + { + return static_cast<T>(1); + } + if (x <= 4) // x in (0, 4] + { + T y = x * x; + BOOST_ASSERT(sizeof(P1) == sizeof(Q1)); + r = evaluate_rational(P1, Q1, y); + factor = (x + x1) * ((x - x11/256) - x12); + value = factor * r; + } + else if (x <= 8.0) // x in (4, 8] + { + T y = 1 - (x * x)/64; + BOOST_ASSERT(sizeof(P2) == sizeof(Q2)); + r = evaluate_rational(P2, Q2, y); + factor = (x + x2) * ((x - x21/256) - x22); + value = factor * r; + } + else // x in (8, \infty) + { + T y = 8 / x; + T y2 = y * y; + T z = x - 0.25f * pi<T>(); + BOOST_ASSERT(sizeof(PC) == sizeof(QC)); + BOOST_ASSERT(sizeof(PS) == sizeof(QS)); + rc = evaluate_rational(PC, QC, y2); + rs = evaluate_rational(PS, QS, y2); + factor = sqrt(2 / (x * pi<T>())); + value = factor * (rc * cos(z) - y * rs * sin(z)); + } + + return value; +} + +}}} // namespaces + +#endif // BOOST_MATH_BESSEL_J0_HPP + |