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_jn.hpp (3909B)

//  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_JN_HPP
#define BOOST_MATH_BESSEL_JN_HPP

#ifdef _MSC_VER
#pragma once
#endif

#include <boost/math/special_functions/detail/bessel_j0.hpp>
#include <boost/math/special_functions/detail/bessel_j1.hpp>
#include <boost/math/special_functions/detail/bessel_jy.hpp>
#include <boost/math/special_functions/detail/bessel_jy_asym.hpp>
#include <boost/math/special_functions/detail/bessel_jy_series.hpp>

// Bessel function of the first kind of integer order
// J_n(z) is the minimal solution
// n < abs(z), forward recurrence stable and usable
// n >= abs(z), forward recurrence unstable, use Miller's algorithm

namespace boost { namespace math { namespace detail{

template <typename T, typename Policy>
T bessel_jn(int n, T x, const Policy& pol)
{
    T value(0), factor, current, prev, next;

BOOST_MATH_STD_USING

//
    // Reflection has to come first:
    //
    if (n < 0)
    {
        factor = static_cast<T>((n & 0x1) ? -1 : 1);  // J_{-n}(z) = (-1)^n J_n(z)
        n = -n;
    }
    else
    {
        factor = 1;
    }
    if(x < 0)
    {
        factor *= (n & 0x1) ? -1 : 1;  // J_{n}(-z) = (-1)^n J_n(z)
        x = -x;
    }
    //
    // Special cases:
    //
    if(asymptotic_bessel_large_x_limit(T(n), x))
       return factor * asymptotic_bessel_j_large_x_2<T>(T(n), x);
    if (n == 0)
    {
        return factor * bessel_j0(x);
    }
    if (n == 1)
    {
        return factor * bessel_j1(x);
    }

if (x == 0)                             // n >= 2
    {
        return static_cast<T>(0);
    }

BOOST_ASSERT(n > 1);
    T scale = 1;
    if (n < abs(x))                         // forward recurrence
    {
        prev = bessel_j0(x);
        current = bessel_j1(x);
        policies::check_series_iterations<T>("boost::math::bessel_j_n<%1%>(%1%,%1%)", n, pol);
        for (int k = 1; k < n; k++)
        {
            T fact = 2 * k / x;
            //
            // rescale if we would overflow or underflow:
            //
            if((fabs(fact) > 1) && ((tools::max_value<T>() - fabs(prev)) / fabs(fact) < fabs(current)))
            {
               scale /= current;
               prev /= current;
               current = 1;
            }
            value = fact * current - prev;
            prev = current;
            current = value;
        }
    }
    else if((x < 1) || (n > x * x / 4) || (x < 5))
    {
       return factor * bessel_j_small_z_series(T(n), x, pol);
    }
    else                                    // backward recurrence
    {
        T fn; int s;                        // fn = J_(n+1) / J_n
        // |x| <= n, fast convergence for continued fraction CF1
        boost::math::detail::CF1_jy(static_cast<T>(n), x, &fn, &s, pol);
        prev = fn;
        current = 1;
        // Check recursion won't go on too far:
        policies::check_series_iterations<T>("boost::math::bessel_j_n<%1%>(%1%,%1%)", n, pol);
        for (int k = n; k > 0; k--)
        {
            T fact = 2 * k / x;
            if((fabs(fact) > 1) && ((tools::max_value<T>() - fabs(prev)) / fabs(fact) < fabs(current)))
            {
               prev /= current;
               scale /= current;
               current = 1;
            }
            next = fact * current - prev;
            prev = current;
            current = next;
        }
        value = bessel_j0(x) / current;       // normalization
        scale = 1 / scale;
    }
    value *= factor;

if(tools::max_value<T>() * scale < fabs(value))
       return policies::raise_overflow_error<T>("boost::math::bessel_jn<%1%>(%1%,%1%)", 0, pol);

return value / scale;
}

}}} // namespaces

#endif // BOOST_MATH_BESSEL_JN_HPP

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