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Warning, file /include/boost/math/special_functions/detail/bessel_j0.hpp was not indexed or was modified since last indexation (in which case cross-reference links may be missing, inaccurate or erroneous).

0001 //  Copyright (c) 2006 Xiaogang Zhang
0002 //  Use, modification and distribution are subject to the
0003 //  Boost Software License, Version 1.0. (See accompanying file
0004 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
0005 
0006 #ifndef BOOST_MATH_BESSEL_J0_HPP
0007 #define BOOST_MATH_BESSEL_J0_HPP
0008 
0009 #ifdef _MSC_VER
0010 #pragma once
0011 #endif
0012 
0013 #include <boost/math/constants/constants.hpp>
0014 #include <boost/math/tools/rational.hpp>
0015 #include <boost/math/tools/big_constant.hpp>
0016 #include <boost/math/tools/assert.hpp>
0017 
0018 #if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128)
0019 //
0020 // This is the only way we can avoid
0021 // warning: non-standard suffix on floating constant [-Wpedantic]
0022 // when building with -Wall -pedantic.  Neither __extension__
0023 // nor #pragma diagnostic ignored work :(
0024 //
0025 #pragma GCC system_header
0026 #endif
0027 
0028 // Bessel function of the first kind of order zero
0029 // x <= 8, minimax rational approximations on root-bracketing intervals
0030 // x > 8, Hankel asymptotic expansion in Hart, Computer Approximations, 1968
0031 
0032 namespace boost { namespace math { namespace detail{
0033 
0034 template <typename T>
0035 T bessel_j0(T x);
0036 
0037 template <typename T>
0038 T bessel_j0(T x)
0039 {
0040 #ifdef BOOST_MATH_INSTRUMENT
0041     static bool b = false;
0042     if (!b)
0043     {
0044        std::cout << "bessel_j0 called with " << typeid(x).name() << std::endl;
0045        std::cout << "double      = " << typeid(double).name() << std::endl;
0046        std::cout << "long double = " << typeid(long double).name() << std::endl;
0047        b = true;
0048     }
0049 #endif
0050 
0051     static const T P1[] = {
0052          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.1298668500990866786e+11)),
0053          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.7282507878605942706e+10)),
0054          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.2140700423540120665e+08)),
0055          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.6302997904833794242e+06)),
0056          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.6629814655107086448e+04)),
0057          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0344222815443188943e+02)),
0058          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.2117036164593528341e-01))
0059     };
0060     static const T Q1[] = {
0061          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.3883787996332290397e+12)),
0062          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.6328198300859648632e+10)),
0063          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3985097372263433271e+08)),
0064          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.5612696224219938200e+05)),
0065          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.3614022392337710626e+02)),
0066          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
0067          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0))
0068     };
0069     static const T P2[] = {
0070          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8319397969392084011e+03)),
0071          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.2254078161378989535e+04)),
0072          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -7.2879702464464618998e+03)),
0073          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0341910641583726701e+04)),
0074          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1725046279757103576e+04)),
0075          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.4176707025325087628e+03)),
0076          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.4321196680624245801e+02)),
0077          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.8591703355916499363e+01))
0078     };
0079     static const T Q2[] = {
0080          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.5783478026152301072e+05)),
0081          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.4599102262586308984e+05)),
0082          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.4055062591169562211e+04)),
0083          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8680990008359188352e+04)),
0084          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9458766545509337327e+03)),
0085          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3307310774649071172e+02)),
0086          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.5258076240801555057e+01)),
0087          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
0088     };
0089     static const T PC[] = {
0090          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2779090197304684302e+04)),
0091          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.1345386639580765797e+04)),
0092          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1170523380864944322e+04)),
0093          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.4806486443249270347e+03)),
0094          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5376201909008354296e+02)),
0095          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.8961548424210455236e-01))
0096     };
0097     static const T QC[] = {
0098          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.2779090197304684318e+04)),
0099          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.1370412495510416640e+04)),
0100          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.1215350561880115730e+04)),
0101          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.5028735138235608207e+03)),
0102          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.5711159858080893649e+02)),
0103          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
0104     };
0105     static const T PS[] = {
0106         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.9226600200800094098e+01)),
0107         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8591953644342993800e+02)),
0108         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1183429920482737611e+02)),
0109         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2300261666214198472e+01)),
0110         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.2441026745835638459e+00)),
0111         static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.8033303048680751817e-03))
0112     };
0113     static const T QS[] = {
0114          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.7105024128512061905e+03)),
0115          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1951131543434613647e+04)),
0116          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.2642780169211018836e+03)),
0117          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4887231232283756582e+03)),
0118          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.0593769594993125859e+01)),
0119          static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
0120     };
0121     static const T x1  =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.4048255576957727686e+00)),
0122                    x2  =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.5200781102863106496e+00)),
0123                    x11 =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.160e+02)),
0124                    x12 =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.42444230422723137837e-03)),
0125                    x21 =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4130e+03)),
0126                    x22 =  static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.46860286310649596604e-04));
0127 
0128     T value, factor, r, rc, rs;
0129 
0130     BOOST_MATH_STD_USING
0131     using namespace boost::math::tools;
0132     using namespace boost::math::constants;
0133 
0134     BOOST_MATH_ASSERT(x >= 0); // reflection handled elsewhere.
0135 
0136     if (x == 0)
0137     {
0138         return static_cast<T>(1);
0139     }
0140     if (x <= 4)                       // x in (0, 4]
0141     {
0142         T y = x * x;
0143         BOOST_MATH_ASSERT(sizeof(P1) == sizeof(Q1));
0144         r = evaluate_rational(P1, Q1, y);
0145         factor = (x + x1) * ((x - x11/256) - x12);
0146         value = factor * r;
0147     }
0148     else if (x <= 8.0)                  // x in (4, 8]
0149     {
0150         T y = 1 - (x * x)/64;
0151         BOOST_MATH_ASSERT(sizeof(P2) == sizeof(Q2));
0152         r = evaluate_rational(P2, Q2, y);
0153         factor = (x + x2) * ((x - x21/256) - x22);
0154         value = factor * r;
0155     }
0156     else                                // x in (8, \infty)
0157     {
0158         T y = 8 / x;
0159         T y2 = y * y;
0160         BOOST_MATH_ASSERT(sizeof(PC) == sizeof(QC));
0161         BOOST_MATH_ASSERT(sizeof(PS) == sizeof(QS));
0162         rc = evaluate_rational(PC, QC, y2);
0163         rs = evaluate_rational(PS, QS, y2);
0164         factor = constants::one_div_root_pi<T>() / sqrt(x);
0165         //
0166         // What follows is really just:
0167         //
0168         // T z = x - pi/4;
0169         // value = factor * (rc * cos(z) - y * rs * sin(z));
0170         //
0171         // But using the addition formulae for sin and cos, plus
0172         // the special values for sin/cos of pi/4.
0173         //
0174         T sx = sin(x);
0175         T cx = cos(x);
0176         BOOST_MATH_INSTRUMENT_VARIABLE(rc);
0177         BOOST_MATH_INSTRUMENT_VARIABLE(rs);
0178         BOOST_MATH_INSTRUMENT_VARIABLE(factor);
0179         BOOST_MATH_INSTRUMENT_VARIABLE(sx);
0180         BOOST_MATH_INSTRUMENT_VARIABLE(cx);
0181         value = factor * (rc * (cx + sx) - y * rs * (sx - cx));
0182     }
0183 
0184     return value;
0185 }
0186 
0187 }}} // namespaces
0188 
0189 #endif // BOOST_MATH_BESSEL_J0_HPP
0190
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