FM / detail

/usr/include/boost/math/special_functions/detail/

/usr/include/boost/math/special_functions/detail

Name	Size	Mode	Actions
airy_ai_bi_zero.hpp	6294	0644	edit dl rm
bernoulli_details.hpp	26513	0644	edit dl rm
bessel_derivatives_linear.hpp	3378	0644	edit dl rm
bessel_i0.hpp	28135	0644	edit dl rm
bessel_i1.hpp	29933	0644	edit dl rm
bessel_ik.hpp	13917	0644	edit dl rm
bessel_j0.hpp	8585	0644	edit dl rm
bessel_j1.hpp	8951	0644	edit dl rm
bessel_jn.hpp	3909	0644	edit dl rm
bessel_jy.hpp	21868	0644	edit dl rm
bessel_jy_asym.hpp	6488	0644	edit dl rm
bessel_jy_derivatives_asym.hpp	4649	0644	edit dl rm
bessel_jy_derivatives_series.hpp	6944	0644	edit dl rm
bessel_jy_series.hpp	7241	0644	edit dl rm
bessel_jy_zero.hpp	24967	0644	edit dl rm
bessel_k0.hpp	22178	0644	edit dl rm
bessel_k1.hpp	25465	0644	edit dl rm
bessel_kn.hpp	2249	0644	edit dl rm
bessel_y0.hpp	10805	0644	edit dl rm
bessel_y1.hpp	9458	0644	edit dl rm
bessel_yn.hpp	3118	0644	edit dl rm
daubechies_scaling_integer_grid.hpp	233788	0644	edit dl rm
erf_inv.hpp	22738	0644	edit dl rm
fp_traits.hpp	17193	0644	edit dl rm
gamma_inva.hpp	7066	0644	edit dl rm
hypergeometric_0F1_bessel.hpp	1543	0644	edit dl rm
hypergeometric_1F1_addition_theorems_on_z.hpp	12980	0644	edit dl rm
hypergeometric_1F1_bessel.hpp	32781	0644	edit dl rm
hypergeometric_1F1_by_ratios.hpp	33540	0644	edit dl rm
hypergeometric_1F1_cf.hpp	1830	0644	edit dl rm
hypergeometric_1F1_large_a.hpp	1159	0644	edit dl rm
hypergeometric_1F1_large_abz.hpp	22101	0644	edit dl rm
hypergeometric_1F1_negative_b_regions.hpp	33376	0644	edit dl rm
hypergeometric_1F1_recurrence.hpp	17295	0644	edit dl rm
hypergeometric_1F1_scaled_series.hpp	2183	0644	edit dl rm
hypergeometric_1F1_small_a_negative_b_by_ratio.hpp	3893	0644	edit dl rm
hypergeometric_asym.hpp	5902	0644	edit dl rm
hypergeometric_cf.hpp	5826	0644	edit dl rm
hypergeometric_pade.hpp	3837	0644	edit dl rm
hypergeometric_pFq_checked_series.hpp	27943	0644	edit dl rm
hypergeometric_rational.hpp	5068	0644	edit dl rm
hypergeometric_separated_series.hpp	1449	0644	edit dl rm
hypergeometric_series.hpp	14422	0644	edit dl rm
ibeta_inverse.hpp	34072	0644	edit dl rm
ibeta_inv_ab.hpp	10363	0644	edit dl rm
iconv.hpp	1009	0644	edit dl rm
igamma_inverse.hpp	17414	0644	edit dl rm
igamma_large.hpp	39534	0644	edit dl rm
lambert_w_lookup_table.ipp	15601	0644	edit dl rm
lanczos_sse2.hpp	8916	0644	edit dl rm
lgamma_small.hpp	23295	0644	edit dl rm
polygamma.hpp	22596	0644	edit dl rm
round_fwd.hpp	2794	0644	edit dl rm
t_distribution_inv.hpp	17735	0644	edit dl rm
unchecked_bernoulli.hpp	76437	0644	edit dl rm
unchecked_factorial.hpp	46290	0644	edit dl rm

Edit: /usr/include/boost/math/special_functions/detail/bessel_j1.hpp (8951B)

//  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>

#if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128)
//
// This is the only way we can avoid
// warning: non-standard suffix on floating constant [-Wpedantic]
// when building with -Wall -pedantic.  Neither __extension__
// nor #pragma diagnostic ignored work :(
//
#pragma GCC system_header
#endif

// 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

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