ceph/src/boost/libs/math/include/boost/math/special_functions/jacobi_zeta.hpp

   1 //  Copyright (c) 2015 John Maddock
   2 //  Use, modification and distribution are subject to the
   3 //  Boost Software License, Version 1.0. (See accompanying file
   4 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   5 //
   6
   7 #ifndef BOOST_MATH_ELLINT_JZ_HPP
   8 #define BOOST_MATH_ELLINT_JZ_HPP
   9
  10 #ifdef _MSC_VER
  11 #pragma once
  12 #endif
  13
  14 #include <boost/math/special_functions/math_fwd.hpp>
  15 #include <boost/math/special_functions/ellint_1.hpp>
  16 #include <boost/math/special_functions/ellint_rj.hpp>
  17 #include <boost/math/constants/constants.hpp>
  18 #include <boost/math/policies/error_handling.hpp>
  19 #include <boost/math/tools/workaround.hpp>
  20
  21 // Elliptic integral the Jacobi Zeta function.
  22
  23 namespace boost { namespace math {
  24
  25 namespace detail{
  26
  27 // Elliptic integral - Jacobi Zeta
  28 template <typename T, typename Policy>
  29 T jacobi_zeta_imp(T phi, T k, const Policy& pol)
  30 {
  31     BOOST_MATH_STD_USING
  32     using namespace boost::math::tools;
  33     using namespace boost::math::constants;
  34
  35     bool invert = false;
  36     if(phi < 0)
  37     {
  38        phi = fabs(phi);
  39        invert = true;
  40     }
  41
  42     T result;
  43     T sinp = sin(phi);
  44     T cosp = cos(phi);
  45     T s2 = sinp * sinp;
  46     T k2 = k * k;
  47     T kp = 1 - k2;
  48     if(k == 1)
  49        result = sinp * (boost::math::sign)(cosp);  // We get here by simplifying JacobiZeta[w, 1] in Mathematica, and the fact that 0 <= phi.
  50     else
  51        result = k2 * sinp * cosp * sqrt(1 - k2 * s2) * ellint_rj_imp(T(0), kp, T(1), T(1 - k2 * s2), pol) / (3 * ellint_k_imp(k, pol));
  52     return invert ? T(-result) : result;
  53 }
  54
  55 } // detail
  56
  57 template <class T1, class T2, class Policy>
  58 inline typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi, const Policy& pol)
  59 {
  60    typedef typename tools::promote_args<T1, T2>::type result_type;
  61    typedef typename policies::evaluation<result_type, Policy>::type value_type;
  62    return policies::checked_narrowing_cast<result_type, Policy>(detail::jacobi_zeta_imp(static_cast<value_type>(phi), static_cast<value_type>(k), pol), "boost::math::jacobi_zeta<%1%>(%1%,%1%)");
  63 }
  64
  65 template <class T1, class T2>
  66 inline typename tools::promote_args<T1, T2>::type jacobi_zeta(T1 k, T2 phi)
  67 {
  68    return boost::math::jacobi_zeta(k, phi, policies::policy<>());
  69 }
  70
  71 }} // namespaces
  72
  73 #endif // BOOST_MATH_ELLINT_D_HPP
  74