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+// 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.
+// Modifications copyright (c) 2017, 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_IMPL_PJ_AUTH_HPP
+#define BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_AUTH_HPP
+
+#include <cassert>
+#include <cmath>
+
+#include <boost/geometry/core/assert.hpp>
+
+namespace boost { namespace geometry { namespace projections {
+
+namespace detail {
+
+static const int APA_SIZE = 3;
+
+/* determine latitude from authalic latitude */
+template <typename T>
+inline bool pj_authset(T const& es, T* APA)
+{
+ BOOST_GEOMETRY_ASSERT(0 != APA);
+
+ static const T P00 = .33333333333333333333;
+ static const T P01 = .17222222222222222222;
+ static const T P02 = .10257936507936507936;
+ static const T P10 = .06388888888888888888;
+ static const T P11 = .06640211640211640211;
+ static const T P20 = .01641501294219154443;
+
+ T t = 0;
+
+ // if (APA = (double *)pj_malloc(APA_SIZE * sizeof(double)))
+ {
+ APA[0] = es * P00;
+ t = es * es;
+ APA[0] += t * P01;
+ APA[1] = t * P10;
+ t *= es;
+ APA[0] += t * P02;
+ APA[1] += t * P11;
+ APA[2] = t * P20;
+ }
+ return true;
+}
+
+template <typename T>
+inline T pj_authlat(T const& beta, const T* APA)
+{
+ BOOST_GEOMETRY_ASSERT(0 != APA);
+
+ T const t = beta + beta;
+
+ return(beta + APA[0] * sin(t) + APA[1] * sin(t + t) + APA[2] * sin(t + t + t));
+}
+
+} // namespace detail
+}}} // namespace boost::geometry::projections
+
+#endif // BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_AUTH_HPP