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 2018.
  // Modifications copyright (c) 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.
  
  #ifndef BOOST_GEOMETRY_PROJECTIONS_PROJ_MDIST_HPP
  #define BOOST_GEOMETRY_PROJECTIONS_PROJ_MDIST_HPP
  
  
  #include <boost/geometry/util/math.hpp>
  
  
  namespace boost { namespace geometry { namespace projections
  {
  namespace detail
  {
      template <typename T>
      struct mdist
      {
          static const int static_size = 20;
  
          int nb;
          T es;
          T E;
          T b[static_size];
      };
  
      template <typename T>
      inline bool proj_mdist_ini(T const& es, mdist<T>& b)
      {
          T numf, numfi, twon1, denf, denfi, ens, t, twon;
          T den, El, Es;
          T E[mdist<T>::static_size];
          int i, j;
  
          /* generate E(e^2) and its terms E[] */
          ens = es;
          numf = twon1 = denfi = 1.;
          denf = 1.;
          twon = 4.;
          Es = El = E[0] = 1.;
          for (i = 1; i < mdist<T>::static_size ; ++i)
          {
              numf *= (twon1 * twon1);
              den = twon * denf * denf * twon1;
              t = numf/den;
              E[i] = t * ens;
              Es -= E[i];
              ens *= es;
              twon *= 4.;
              denf *= ++denfi;
              twon1 += 2.;
              if (Es == El) /* jump out if no change */
                  break;
              El = Es;
          }
          b.nb = i - 1;
          b.es = es;
          b.E = Es;
          /* generate b_n coefficients--note: collapse with prefix ratios */
          b.b[0] = Es = 1. - Es;
          numf = denf = 1.;
          numfi = 2.;
          denfi = 3.;
          for (j = 1; j < i; ++j)
          {
              Es -= E[j];
              numf *= numfi;
              denf *= denfi;
              b.b[j] = Es * numf / denf;
              numfi += 2.;
              denfi += 2.;
          }
          return true;
      }
  
      template <typename T>
      inline T proj_mdist(T const& phi, T const& sphi, T const& cphi, mdist<T> const& b)
      {
          T sc, sum, sphi2, D;
          int i;
  
          sc = sphi * cphi;
          sphi2 = sphi * sphi;
          D = phi * b.E - b.es * sc / sqrt(1. - b.es * sphi2);
          sum = b.b[i = b.nb];
          while (i) sum = b.b[--i] + sphi2 * sum;
          return(D + sc * sum);
      }
  
      template <typename T>
      inline T proj_inv_mdist(T const& dist, mdist<T> const& b)
      {
          static const T TOL = 1e-14;
          T s, t, phi, k;
          int i;
  
          k = 1./(1.- b.es);
          i = mdist<T>::static_size;
          phi = dist;
          while ( i-- ) {
              s = sin(phi);
              t = 1. - b.es * s * s;
              phi -= t = (proj_mdist(phi, s, cos(phi), b) - dist) *
                  (t * sqrt(t)) * k;
              if (geometry::math::abs(t) < TOL) /* that is no change */
                  return phi;
          }
              /* convergence failed */
          BOOST_THROW_EXCEPTION( projection_exception(error_non_conv_inv_meri_dist) );
      }
  } // namespace detail
  
  }}} // namespace boost::geometry::projections
  
  #endif
  