| // 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_J1_HPP |
| #define BOOST_MATH_BESSEL_J1_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 one |
| // 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_j1(T x); |
| |
| template <class T> |
| struct bessel_j1_initializer |
| { |
| struct init |
| { |
| init() |
| { |
| do_init(); |
| } |
| static void do_init() |
| { |
| bessel_j1(T(1)); |
| } |
| void force_instantiate()const{} |
| }; |
| static const init initializer; |
| static void force_instantiate() |
| { |
| initializer.force_instantiate(); |
| } |
| }; |
| |
| template <class T> |
| const typename bessel_j1_initializer<T>::init bessel_j1_initializer<T>::initializer; |
| |
| template <typename T> |
| T bessel_j1(T x) |
| { |
| bessel_j1_initializer<T>::force_instantiate(); |
| |
| static const T P1[] = { |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4258509801366645672e+11)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.6781041261492395835e+09)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1548696764841276794e+08)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.8062904098958257677e+05)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4615792982775076130e+03)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0650724020080236441e+01)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0767857011487300348e-02)) |
| }; |
| static const T Q1[] = { |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.1868604460820175290e+12)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.2091902282580133541e+10)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.0228375140097033958e+08)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.9117614494174794095e+05)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0742272239517380498e+03)), |
| 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, -1.7527881995806511112e+16)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.6608531731299018674e+15)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.6658018905416665164e+13)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.5580665670910619166e+11)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8113931269860667829e+09)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.0793266148011179143e+06)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -7.5023342220781607561e+03)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.6179191852758252278e+00)) |
| }; |
| static const T Q2[] = { |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7253905888447681194e+18)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7128800897135812012e+16)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.4899346165481429307e+13)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.7622777286244082666e+11)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4872502899596389593e+08)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1267125065029138050e+06)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3886978985861357615e+03)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) |
| }; |
| static const T PC[] = { |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4357578167941278571e+06)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.9422465050776411957e+06)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.6033732483649391093e+06)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5235293511811373833e+06)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0982405543459346727e+05)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6116166443246101165e+03)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0)) |
| }; |
| static const T QC[] = { |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4357578167941278568e+06)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.9341243899345856590e+06)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.5853394797230870728e+06)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5118095066341608816e+06)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0726385991103820119e+05)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4550094401904961825e+03)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) |
| }; |
| static const T PS[] = { |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3220913409857223519e+04)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.5145160675335701966e+04)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.6178836581270835179e+04)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8494262873223866797e+04)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7063754290207680021e+03)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.5265133846636032186e+01)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0)) |
| }; |
| static const T QS[] = { |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.0871281941028743574e+05)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8194580422439972989e+06)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4194606696037208929e+06)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.0029443582266975117e+05)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7890229745772202641e+04)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.6383677696049909675e+02)), |
| static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)) |
| }; |
| static const T x1 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.8317059702075123156e+00)), |
| x2 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.0155866698156187535e+00)), |
| x11 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.810e+02)), |
| x12 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.2527979248768438556e-04)), |
| x21 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7960e+03)), |
| x22 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.8330184381246462950e-05)); |
| |
| T value, factor, r, rc, rs, w; |
| |
| BOOST_MATH_STD_USING |
| using namespace boost::math::tools; |
| using namespace boost::math::constants; |
| |
| w = abs(x); |
| if (x == 0) |
| { |
| return static_cast<T>(0); |
| } |
| if (w <= 4) // w in (0, 4] |
| { |
| T y = x * x; |
| BOOST_ASSERT(sizeof(P1) == sizeof(Q1)); |
| r = evaluate_rational(P1, Q1, y); |
| factor = w * (w + x1) * ((w - x11/256) - x12); |
| value = factor * r; |
| } |
| else if (w <= 8) // w in (4, 8] |
| { |
| T y = x * x; |
| BOOST_ASSERT(sizeof(P2) == sizeof(Q2)); |
| r = evaluate_rational(P2, Q2, y); |
| factor = w * (w + x2) * ((w - x21/256) - x22); |
| value = factor * r; |
| } |
| else // w in (8, \infty) |
| { |
| T y = 8 / w; |
| T y2 = y * y; |
| 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 = 1 / (sqrt(w) * constants::root_pi<T>()); |
| // |
| // What follows is really just: |
| // |
| // T z = w - 0.75f * pi<T>(); |
| // value = factor * (rc * cos(z) - y * rs * sin(z)); |
| // |
| // but using the sin/cos addition rules plus constants |
| // for the values of sin/cos of 3PI/4 which then cancel |
| // out with corresponding terms in "factor". |
| // |
| T sx = sin(x); |
| T cx = cos(x); |
| value = factor * (rc * (sx - cx) + y * rs * (sx + cx)); |
| } |
| |
| if (x < 0) |
| { |
| value *= -1; // odd function |
| } |
| return value; |
| } |
| |
| }}} // namespaces |
| |
| #endif // BOOST_MATH_BESSEL_J1_HPP |
| |
