// Copyright (c) 2001,2004  INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v5.5.2/Filtered_kernel/include/CGAL/Filtered_kernel/internal/Static_filters/Side_of_oriented_circle_2.h $
// $Id: Side_of_oriented_circle_2.h 5945e48 2021-09-17T08:14:06+02:00 Sébastien Loriot
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Sylvain Pion

#ifndef CGAL_INTERNAL_STATIC_FILTERS_SIDE_OF_ORIENTED_CIRCLE_2_H
#define CGAL_INTERNAL_STATIC_FILTERS_SIDE_OF_ORIENTED_CIRCLE_2_H

#include <CGAL/Profile_counter.h>
#include <CGAL/Filtered_kernel/internal/Static_filters/Static_filter_error.h>
#include <cmath>

namespace CGAL { namespace internal { namespace Static_filters_predicates {

template < typename K_base >
class Side_of_oriented_circle_2
  : public K_base::Side_of_oriented_circle_2
{
  typedef typename K_base::Point_2                      Point_2;
  typedef typename K_base::Side_of_oriented_circle_2    Base;

public:

  Oriented_side operator()(const Point_2 &p, const Point_2 &q,
                           const Point_2 &r, const Point_2 &t) const
  {
      CGAL_BRANCH_PROFILER_3("semi-static failures/attempts/calls to   : Side_of_oriented_circle_2", tmp);

      double px, py, qx, qy, rx, ry, tx, ty;

      if (fit_in_double(p.x(), px) && fit_in_double(p.y(), py) &&
          fit_in_double(q.x(), qx) && fit_in_double(q.y(), qy) &&
          fit_in_double(r.x(), rx) && fit_in_double(r.y(), ry) &&
          fit_in_double(t.x(), tx) && fit_in_double(t.y(), ty))
      {
          CGAL_BRANCH_PROFILER_BRANCH_1(tmp);

          double qpx = qx-px;
          double qpy = qy-py;
          double rpx = rx-px;
          double rpy = ry-py;
          double tpx = tx-px;
          double tpy = ty-py;

          double tqx = tx-qx;
          double tqy = ty-qy;
          double rqx = rx-qx;
          double rqy = ry-qy;

          double det = CGAL::determinant(qpx*tpy - qpy*tpx, tpx*tqx + tpy*tqy,
                                         qpx*rpy - qpy*rpx, rpx*rqx + rpy*rqy);

          // We compute the semi-static bound.
          double maxx = CGAL::abs(qpx);
          double maxy = CGAL::abs(qpy);

          double arpx = CGAL::abs(rpx);
          double arpy = CGAL::abs(rpy);

          double atqx = CGAL::abs(tqx);
          double atqy = CGAL::abs(tqy);

          double atpx = CGAL::abs(tpx);
          double atpy = CGAL::abs(tpy);

          double arqx = CGAL::abs(rqx);
          double arqy = CGAL::abs(rqy);

          if (maxx < arpx) maxx = arpx;
          if (maxx < atpx) maxx = atpx;
          if (maxx < atqx) maxx = atqx;
          if (maxx < arqx) maxx = arqx;

          if (maxy < arpy) maxy = arpy;
          if (maxy < atpy) maxy = atpy;
          if (maxy < atqy) maxy = atqy;
          if (maxy < arqy) maxy = arqy;

          if (maxx > maxy)  std::swap(maxx, maxy);

          // Protect against underflow in the computation of eps.
          if (maxx < 1e-73) {
            if (maxx == 0)
              return ON_ORIENTED_BOUNDARY;
          }
          else if (maxy < 1e76) /* sqrt(sqrt(max_double/16 [hadamard])) */ {
            double eps = 8.8878565762001373e-15 * maxx * maxy * (maxy*maxy);
            if (det > eps)  return ON_POSITIVE_SIDE;
            if (det < -eps) return ON_NEGATIVE_SIDE;
          }

          CGAL_BRANCH_PROFILER_BRANCH_2(tmp);
      }

      return Base::operator()(p, q, r, t);
  }

  // Computes the epsilon for Side_of_oriented_circle_2.
  static double compute_epsilon()
  {
    typedef internal::Static_filter_error F;
    F t1 = F(1, F::ulp()/2);         // First translation
    F a = t1*t1 - t1*t1;
    F b = t1*t1 + t1*t1;
    F det = CGAL::determinant(a, b, a, b);
    double err = det.error();
    err += err * 3 * F::ulp(); // Correction due to "eps * maxx * maxy...".

    std::cerr << "*** epsilon for Side_of_oriented_circle_2 = " << err << std::endl;
    return err;
  }
};

} } } // namespace CGAL::internal::Static_filters_predicates

#endif // CGAL_INTERNAL_STATIC_FILTERS_SIDE_OF_ORIENTED_CIRCLE_2_H
