math_fwd.hpp

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   template <class RT>
   RT double_factorial(unsigned i);
   template <class RT, class Policy>
   RT double_factorial(unsigned i, const Policy& pol);

   template <class RT>
   typename tools::promote_args<RT>::type falling_factorial(RT x, unsigned n);

   template <class RT, class Policy>
   typename tools::promote_args<RT>::type falling_factorial(RT x, unsigned n, const Policy& pol);

   template <class RT>
   typename tools::promote_args<RT>::type rising_factorial(RT x, int n);

   template <class RT, class Policy>
   typename tools::promote_args<RT>::type rising_factorial(RT x, int n, const Policy& pol);

   // Gamma functions.
   template <class RT>
   typename tools::promote_args<RT>::type tgamma(RT z);

   template <class RT>
   typename tools::promote_args<RT>::type tgamma1pm1(RT z);

   template <class RT, class Policy>
   typename tools::promote_args<RT>::type tgamma1pm1(RT z, const Policy& pol);

   template <class RT1, class RT2>
   typename tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z);

   template <class RT1, class RT2, class Policy>
   typename tools::promote_args<RT1, RT2>::type tgamma(RT1 a, RT2 z, const Policy& pol);

   template <class RT>
   typename tools::promote_args<RT>::type lgamma(RT z, int* sign);

   template <class RT, class Policy>
   typename tools::promote_args<RT>::type lgamma(RT z, int* sign, const Policy& pol);

   template <class RT>
   typename tools::promote_args<RT>::type lgamma(RT x);

   template <class RT, class Policy>
   typename tools::promote_args<RT>::type lgamma(RT x, const Policy& pol);

   template <class RT1, class RT2>
   typename tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z);

   template <class RT1, class RT2, class Policy>
   typename tools::promote_args<RT1, RT2>::type tgamma_lower(RT1 a, RT2 z, const Policy&);

   template <class RT1, class RT2>
   typename tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z);

   template <class RT1, class RT2, class Policy>
   typename tools::promote_args<RT1, RT2>::type gamma_q(RT1 a, RT2 z, const Policy&);

   template <class RT1, class RT2>
   typename tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z);

   template <class RT1, class RT2, class Policy>
   typename tools::promote_args<RT1, RT2>::type gamma_p(RT1 a, RT2 z, const Policy&);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type tgamma_delta_ratio(T1 z, T2 delta, const Policy&);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type tgamma_ratio(T1 a, T2 b, const Policy&);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type gamma_p_derivative(T1 a, T2 x, const Policy&);

   // gamma inverse.
   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p, const Policy&);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type gamma_p_inva(T1 a, T2 p);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type gamma_p_inv(T1 a, T2 p, const Policy&);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type gamma_q_inv(T1 a, T2 q, const Policy&);

   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type gamma_q_inva(T1 a, T2 q, const Policy&);

   // digamma:
   template <class T>
   typename tools::promote_args<T>::type digamma(T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type digamma(T x, const Policy&);

   // Hypotenuse function sqrt(x ^ 2 + y ^ 2).
   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type 
         hypot(T1 x, T2 y);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type 
         hypot(T1 x, T2 y, const Policy&);

   // cbrt - cube root.
   template <class RT>
   typename tools::promote_args<RT>::type cbrt(RT z);

   template <class RT, class Policy>
   typename tools::promote_args<RT>::type cbrt(RT z, const Policy&);

   // log1p is log(x + 1)
   template <class T>
   typename tools::promote_args<T>::type log1p(T);

   template <class T, class Policy>
   typename tools::promote_args<T>::type log1p(T, const Policy&);

   // log1pmx is log(x + 1) - x
   template <class T>
   typename tools::promote_args<T>::type log1pmx(T);

   template <class T, class Policy>
   typename tools::promote_args<T>::type log1pmx(T, const Policy&);

   // Exp (x) minus 1 functions.
   template <class T>
   typename tools::promote_args<T>::type expm1(T);

   template <class T, class Policy>
   typename tools::promote_args<T>::type expm1(T, const Policy&);

   // Power - 1
   template <class T1, class T2>
   typename tools::promote_args<T1, T2>::type 
         powm1(const T1 a, const T2 z);

   template <class T1, class T2, class Policy>
   typename tools::promote_args<T1, T2>::type 
         powm1(const T1 a, const T2 z, const Policy&);

   // sqrt(1+x) - 1
   template <class T>
   typename tools::promote_args<T>::type sqrt1pm1(const T& val);

   template <class T, class Policy>
   typename tools::promote_args<T>::type sqrt1pm1(const T& val, const Policy&);

   // sinus cardinals:
   template <class T>
   typename tools::promote_args<T>::type sinc_pi(T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type sinc_pi(T x, const Policy&);

   template <class T>
   typename tools::promote_args<T>::type sinhc_pi(T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type sinhc_pi(T x, const Policy&);

   // inverse hyperbolics:
   template<typename T>
   typename tools::promote_args<T>::type asinh(T x);

   template<typename T, class Policy>
   typename tools::promote_args<T>::type asinh(T x, const Policy&);

   template<typename T>
   typename tools::promote_args<T>::type acosh(T x);

   template<typename T, class Policy>
   typename tools::promote_args<T>::type acosh(T x, const Policy&);

   template<typename T>
   typename tools::promote_args<T>::type atanh(T x);

   template<typename T, class Policy>
   typename tools::promote_args<T>::type atanh(T x, const Policy&);

   namespace detail{

      typedef mpl::int_<0> bessel_no_int_tag;      // No integer optimisation possible.
      typedef mpl::int_<1> bessel_maybe_int_tag;   // Maybe integer optimisation.
      typedef mpl::int_<2> bessel_int_tag;         // Definite integer optimistaion.

      template <class T1, class T2, class Policy>
      struct bessel_traits
      {
         typedef typename tools::promote_args<
            T1, T2
         >::type result_type;

         typedef typename policies::precision<result_type, Policy>::type precision_type;

         typedef typename mpl::if_<
            mpl::or_<
               mpl::less_equal<precision_type, mpl::int_<0> >,
               mpl::greater<precision_type, mpl::int_<64> > >,
            bessel_no_int_tag,
            typename mpl::if_<
               is_integral<T1>,
               bessel_int_tag,
               bessel_maybe_int_tag
            >::type
         >::type optimisation_tag;
      };
   } // detail

   // Bessel functions:
   template <class T1, class T2, class Policy>
   typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_j(T1 v, T2 x, const Policy& pol);

   template <class T1, class T2>
   typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_j(T1 v, T2 x);

   template <class T, class Policy>
   typename detail::bessel_traits<T, T, Policy>::result_type sph_bessel(unsigned v, T x, const Policy& pol);

   template <class T>
   typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_bessel(unsigned v, T x);

   template <class T1, class T2, class Policy>
   typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_i(T1 v, T2 x, const Policy& pol);

   template <class T1, class T2>
   typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_i(T1 v, T2 x);

   template <class T1, class T2, class Policy>
   typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_bessel_k(T1 v, T2 x, const Policy& pol);

   template <class T1, class T2>
   typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_bessel_k(T1 v, T2 x);

   template <class T1, class T2, class Policy>
   typename detail::bessel_traits<T1, T2, Policy>::result_type cyl_neumann(T1 v, T2 x, const Policy& pol);

   template <class T1, class T2>
   typename detail::bessel_traits<T1, T2, policies::policy<> >::result_type cyl_neumann(T1 v, T2 x);

   template <class T, class Policy>
   typename detail::bessel_traits<T, T, Policy>::result_type sph_neumann(unsigned v, T x, const Policy& pol);

   template <class T>
   typename detail::bessel_traits<T, T, policies::policy<> >::result_type sph_neumann(unsigned v, T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type sin_pi(T x, const Policy&);

   template <class T>
   typename tools::promote_args<T>::type sin_pi(T x);

   template <class T, class Policy>
   typename tools::promote_args<T>::type cos_pi(T x, const Policy&);

   template <class T>
   typename tools::promote_args<T>::type cos_pi(T x);

   template <class T>
   int fpclassify BOOST_NO_MACRO_EXPAND(T t);

   template <class T>
   bool isfinite BOOST_NO_MACRO_EXPAND(T z);

   template <class T>
   bool isinf BOOST_NO_MACRO_EXPAND(T t);

   template <class T>
   bool isnan BOOST_NO_MACRO_EXPAND(T t);

   template <class T>
   bool isnormal BOOST_NO_MACRO_EXPAND(T t);

   // Exponential integrals:
   namespace detail{

   template <class T, class U>
   struct expint_result
   {
      typedef typename mpl::if_<
         policies::is_policy<U>,
         typename tools::promote_args<T>::type,
         typename tools::promote_args<U>::type
      >::type type;
   };

   } // namespace detail

   template <class T, class Policy>
   typename tools::promote_args<T>::type expint(unsigned n, T z, const Policy&);

   template <class T, class U>
   typename detail::expint_result<T, U>::type expint(T const z, U const u);

   template <class T>
   typename tools::promote_args<T>::type expint(T z);

   // Zeta:
   template <class T, class Policy>
   typename tools::promote_args<T>::type zeta(T s, const Policy&);

   template <class T>
   typename tools::promote_args<T>::type zeta(T s);

   // pow:
   template <int N, typename T, class Policy>
   typename tools::promote_args<T>::type pow(T base, const Policy& policy);

   template <int N, typename T>
   typename tools::promote_args<T>::type pow(T base);

   // next:
   template <class T, class Policy>
   T nextafter(const T&, const T&, const Policy&);
   template <class T>
   T nextafter(const T&, const T&);
   template <class T, class Policy>
   T float_next(const T&, const Policy&);
   template <class T>
   T float_next(const T&);
   template <class T, class Policy>
   T float_prior(const T&, const Policy&);
   template <class T>
   T float_prior(const T&);
   template <class T, class Policy>
   T float_distance(const T&, const T&, const Policy&);
   template <class T>
   T float_distance(const T&, const T&);

    } // namespace math
} // namespace boost

#ifdef BOOST_HAS_LONG_LONG
#define BOOST_MATH_DETAIL_LL_FUNC(Policy)\