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/airy_ai_bi_zero.hpp (6294B)

//  Copyright (c) 2013 Christopher Kormanyos
//  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)
//
// This work is based on an earlier work:
// "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations",
// in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469
//
// This header contains implementation details for estimating the zeros
// of the Airy functions airy_ai and airy_bi on the negative real axis.
//
#ifndef BOOST_MATH_AIRY_AI_BI_ZERO_2013_01_20_HPP_
  #define BOOST_MATH_AIRY_AI_BI_ZERO_2013_01_20_HPP_

#include <boost/math/constants/constants.hpp>
  #include <boost/math/special_functions/cbrt.hpp>

namespace boost { namespace math {
  namespace detail
  {
    // Forward declarations of the needed Airy function implementations.
    template <class T, class Policy>
    T airy_ai_imp(T x, const Policy& pol);
    template <class T, class Policy>
    T airy_bi_imp(T x, const Policy& pol);
    template <class T, class Policy>
    T airy_ai_prime_imp(T x, const Policy& pol);
    template <class T, class Policy>
    T airy_bi_prime_imp(T x, const Policy& pol);

namespace airy_zero
    {
      template<class T>
      T equation_as_10_4_105(const T& z)
      {
        const T one_over_z        (T(1) / z);
        const T one_over_z_squared(one_over_z * one_over_z);

const T z_pow_third     (boost::math::cbrt(z));
        const T z_pow_two_thirds(z_pow_third * z_pow_third);

// Implement the top line of Eq. 10.4.105.
        const T fz(z_pow_two_thirds * (((((                     + (T(162375596875.0) / 334430208UL)
                                           * one_over_z_squared - (   T(108056875.0) /   6967296UL))
                                           * one_over_z_squared + (       T(77125UL) /     82944UL))
                                           * one_over_z_squared - (           T(5U)  /        36U))
                                           * one_over_z_squared + (           T(5U)  /        48U))
                                           * one_over_z_squared + (1)));

return fz;
      }

namespace airy_ai_zero_detail
      {
        template<class T>
        T initial_guess(const int m)
        {
          T guess;

switch(m)
          {
            case  0: { guess = T(0);                       break; }
            case  1: { guess = T(-2.33810741045976703849); break; }
            case  2: { guess = T(-4.08794944413097061664); break; }
            case  3: { guess = T(-5.52055982809555105913); break; }
            case  4: { guess = T(-6.78670809007175899878); break; }
            case  5: { guess = T(-7.94413358712085312314); break; }
            case  6: { guess = T(-9.02265085334098038016); break; }
            case  7: { guess = T(-10.0401743415580859306); break; }
            case  8: { guess = T(-11.0085243037332628932); break; }
            case  9: { guess = T(-11.9360155632362625170); break; }
            case 10:{ guess = T(-12.8287767528657572004); break; }
            default:
            {
              const T t(((boost::math::constants::pi<T>() * 3) * ((T(m) * 4) - 1)) / 8);
              guess = -boost::math::detail::airy_zero::equation_as_10_4_105(t);
              break;
            }
          }

return guess;
        }

template<class T, class Policy>
        class function_object_ai_and_ai_prime
        {
        public:
          function_object_ai_and_ai_prime(const Policy& pol) : my_pol(pol) { }

boost::math::tuple<T, T> operator()(const T& x) const
          {
            // Return a tuple containing both Ai(x) and Ai'(x).
            return boost::math::make_tuple(
              boost::math::detail::airy_ai_imp      (x, my_pol),
              boost::math::detail::airy_ai_prime_imp(x, my_pol));
          }

private:
          const Policy& my_pol;
          const function_object_ai_and_ai_prime& operator=(const function_object_ai_and_ai_prime&);
        };
      } // namespace airy_ai_zero_detail

namespace airy_bi_zero_detail
      {
        template<class T>
        T initial_guess(const int m)
        {
          T guess;

switch(m)
          {
            case  0: { guess = T(0);                       break; }
            case  1: { guess = T(-1.17371322270912792492); break; }
            case  2: { guess = T(-3.27109330283635271568); break; }
            case  3: { guess = T(-4.83073784166201593267); break; }
            case  4: { guess = T(-6.16985212831025125983); break; }
            case  5: { guess = T(-7.37676207936776371360); break; }
            case  6: { guess = T(-8.49194884650938801345); break; }
            case  7: { guess = T(-9.53819437934623888663); break; }
            case  8: { guess = T(-10.5299135067053579244); break; }
            case  9: { guess = T(-11.4769535512787794379); break; }
            case 10: { guess = T(-12.3864171385827387456); break; }
            default:
            {
              const T t(((boost::math::constants::pi<T>() * 3) * ((T(m) * 4) - 3)) / 8);
              guess = -boost::math::detail::airy_zero::equation_as_10_4_105(t);
              break;
            }
          }

return guess;
        }

template<class T, class Policy>
        class function_object_bi_and_bi_prime
        {
        public:
          function_object_bi_and_bi_prime(const Policy& pol) : my_pol(pol) { }

boost::math::tuple<T, T> operator()(const T& x) const
          {
            // Return a tuple containing both Bi(x) and Bi'(x).
            return boost::math::make_tuple(
              boost::math::detail::airy_bi_imp      (x, my_pol),
              boost::math::detail::airy_bi_prime_imp(x, my_pol));
          }

private:
          const Policy& my_pol;
          const function_object_bi_and_bi_prime& operator=(const function_object_bi_and_bi_prime&);
        };
      } // namespace airy_bi_zero_detail
    } // namespace airy_zero
  } // namespace detail
  } // namespace math
  } // namespaces boost

#endif // BOOST_MATH_AIRY_AI_BI_ZERO_2013_01_20_HPP_

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