| // 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/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>(-4.1298668500990866786e+11L), |
| static_cast<T>(2.7282507878605942706e+10L), |
| static_cast<T>(-6.2140700423540120665e+08L), |
| static_cast<T>(6.6302997904833794242e+06L), |
| static_cast<T>(-3.6629814655107086448e+04L), |
| static_cast<T>(1.0344222815443188943e+02L), |
| static_cast<T>(-1.2117036164593528341e-01L) |
| }; |
| static const T Q1[] = { |
| static_cast<T>(2.3883787996332290397e+12L), |
| static_cast<T>(2.6328198300859648632e+10L), |
| static_cast<T>(1.3985097372263433271e+08L), |
| static_cast<T>(4.5612696224219938200e+05L), |
| static_cast<T>(9.3614022392337710626e+02L), |
| static_cast<T>(1.0L), |
| static_cast<T>(0.0L) |
| }; |
| static const T P2[] = { |
| static_cast<T>(-1.8319397969392084011e+03L), |
| static_cast<T>(-1.2254078161378989535e+04L), |
| static_cast<T>(-7.2879702464464618998e+03L), |
| static_cast<T>(1.0341910641583726701e+04L), |
| static_cast<T>(1.1725046279757103576e+04L), |
| static_cast<T>(4.4176707025325087628e+03L), |
| static_cast<T>(7.4321196680624245801e+02L), |
| static_cast<T>(4.8591703355916499363e+01L) |
| }; |
| static const T Q2[] = { |
| static_cast<T>(-3.5783478026152301072e+05L), |
| static_cast<T>(2.4599102262586308984e+05L), |
| static_cast<T>(-8.4055062591169562211e+04L), |
| static_cast<T>(1.8680990008359188352e+04L), |
| static_cast<T>(-2.9458766545509337327e+03L), |
| static_cast<T>(3.3307310774649071172e+02L), |
| static_cast<T>(-2.5258076240801555057e+01L), |
| static_cast<T>(1.0L) |
| }; |
| static const T PC[] = { |
| static_cast<T>(2.2779090197304684302e+04L), |
| static_cast<T>(4.1345386639580765797e+04L), |
| static_cast<T>(2.1170523380864944322e+04L), |
| static_cast<T>(3.4806486443249270347e+03L), |
| static_cast<T>(1.5376201909008354296e+02L), |
| static_cast<T>(8.8961548424210455236e-01L) |
| }; |
| static const T QC[] = { |
| static_cast<T>(2.2779090197304684318e+04L), |
| static_cast<T>(4.1370412495510416640e+04L), |
| static_cast<T>(2.1215350561880115730e+04L), |
| static_cast<T>(3.5028735138235608207e+03L), |
| static_cast<T>(1.5711159858080893649e+02L), |
| static_cast<T>(1.0L) |
| }; |
| static const T PS[] = { |
| static_cast<T>(-8.9226600200800094098e+01L), |
| static_cast<T>(-1.8591953644342993800e+02L), |
| static_cast<T>(-1.1183429920482737611e+02L), |
| static_cast<T>(-2.2300261666214198472e+01L), |
| static_cast<T>(-1.2441026745835638459e+00L), |
| static_cast<T>(-8.8033303048680751817e-03L) |
| }; |
| static const T QS[] = { |
| static_cast<T>(5.7105024128512061905e+03L), |
| static_cast<T>(1.1951131543434613647e+04L), |
| static_cast<T>(7.2642780169211018836e+03L), |
| static_cast<T>(1.4887231232283756582e+03L), |
| static_cast<T>(9.0593769594993125859e+01L), |
| static_cast<T>(1.0L) |
| }; |
| static const T x1 = static_cast<T>(2.4048255576957727686e+00L), |
| x2 = static_cast<T>(5.5200781102863106496e+00L), |
| x11 = static_cast<T>(6.160e+02L), |
| x12 = static_cast<T>(-1.42444230422723137837e-03L), |
| x21 = static_cast<T>(1.4130e+03L), |
| x22 = static_cast<T>(5.46860286310649596604e-04L); |
| |
| 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 |
| |