text: // Boost.Geometry (aka GGL, Generic Geometry Library)
  // This file is manually converted from PROJ4
  
  // Copyright (c) 2008-2012 Barend Gehrels, Amsterdam, the Netherlands.
  
  // This file was modified by Oracle on 2017, 2018.
  // Modifications copyright (c) 2017-2018, Oracle and/or its affiliates.
  // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
  
  // Use, modification and distribution is 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 file is converted from PROJ4, http://trac.osgeo.org/proj
  // PROJ4 is originally written by Gerald Evenden (then of the USGS)
  // PROJ4 is maintained by Frank Warmerdam
  // PROJ4 is converted to Geometry Library by Barend Gehrels (Geodan, Amsterdam)
  
  // Original copyright notice:
  
  // Permission is hereby granted, free of charge, to any person obtaining a
  // copy of this software and associated documentation files (the "Software"),
  // to deal in the Software without restriction, including without limitation
  // the rights to use, copy, modify, merge, publish, distribute, sublicense,
  // and/or sell copies of the Software, and to permit persons to whom the
  // Software is furnished to do so, subject to the following conditions:
  
  // The above copyright notice and this permission notice shall be included
  // in all copies or substantial portions of the Software.
  
  // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  // OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
  // THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
  // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
  // DEALINGS IN THE SOFTWARE.
  
  /* meridional distance for ellipsoid and inverse
  **	8th degree - accurate to < 1e-5 meters when used in conjunction
  **		with typical major axis values.
  **	Inverse determines phi to EPS (1e-11) radians, about 1e-6 seconds.
  */
  
  #ifndef BOOST_GEOMETRY_PROJECTIONS_PJ_MLFN_HPP
  #define BOOST_GEOMETRY_PROJECTIONS_PJ_MLFN_HPP
  
  
  #include <cstdlib>
  
  #include <boost/geometry/srs/projections/exception.hpp>
  #include <boost/geometry/srs/projections/impl/pj_strerrno.hpp>
  #include <boost/geometry/util/math.hpp>
  
  
  namespace boost { namespace geometry { namespace projections {
  
  namespace detail {
  
  template <typename T>
  struct en
  {
      static const std::size_t size = 5;
  
      T const& operator[](size_t i) const { return data[i]; }
      T & operator[](size_t i) { return data[i]; }
  
  private:
      T data[5];
  };
  
  template <typename T>
  inline en<T> pj_enfn(T const& es)
  {
      static const T C00 = 1.;
      static const T C02 = .25;
      static const T C04 = .046875;
      static const T C06 = .01953125;
      static const T C08 = .01068115234375;
      static const T C22 = .75;
      static const T C44 = .46875;
      static const T C46 = .01302083333333333333;
      static const T C48 = .00712076822916666666;
      static const T C66 = .36458333333333333333;
      static const T C68 = .00569661458333333333;
      static const T C88 = .3076171875;
  
      T t;
      detail::en<T> en;
  
      {
          en[0] = C00 - es * (C02 + es * (C04 + es * (C06 + es * C08)));
          en[1] = es * (C22 - es * (C04 + es * (C06 + es * C08)));
          en[2] = (t = es * es) * (C44 - es * (C46 + es * C48));
          en[3] = (t *= es) * (C66 - es * C68);
          en[4] = t * es * C88;
      }
      
      return en;
  }
  
  template <typename T>
  inline T pj_mlfn(T const& phi, T sphi, T cphi, detail::en<T> const& en)
  {
      cphi *= sphi;
      sphi *= sphi;
      return(en[0] * phi - cphi * (en[1] + sphi*(en[2]
          + sphi*(en[3] + sphi*en[4]))));
  }
  
  template <typename T>
  inline T pj_inv_mlfn(T const& arg, T const& es, detail::en<T> const& en)
  {
      static const T EPS = 1e-11;
      static const int MAX_ITER = 10;
  
      T s, t, phi, k = 1./(1.-es);
      int i;
  
      phi = arg;
      for (i = MAX_ITER; i ; --i) { /* rarely goes over 2 iterations */
          s = sin(phi);
          t = 1. - es * s * s;
          phi -= t = (pj_mlfn(phi, s, cos(phi), en) - arg) * (t * sqrt(t)) * k;
          if (geometry::math::abs(t) < EPS)
              return phi;
      }
      BOOST_THROW_EXCEPTION( projection_exception(error_non_conv_inv_meri_dist) );
      return phi;
  }
  
  } // namespace detail
  }}} // namespace boost::geometry::projections
  
  #endif
  